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NLP Centre, Faculty of Informatics, Masaryk University 14

math_qa__pLDveC6o4gKncrq1

A bag marked at $80 is sold for $68. The rate of discount is? Choose the correct choice from the following answers: A) 10 % B) 15 % C) 20 % D) 25 % E) 30 %

<gadget id="calculator">80 - 68</gadget> <output>12</output> <gadget id="calculator">12 / 80</gadget> <output>3/20 = around 0.15</output> <gadget id="calculator">(3/20) * 100</gadget> <output>15</output> <result>B</result>

B

A bag marked at $80 is sold for $68. The rate of discount is?

multiply(divide(subtract(80, 68), 80), const_100)

subtract(n0,n1)|divide(#0,n0)|multiply(#1,const_100)|

"rate of discount = 12 / 80 * 100 = 15 % answer is b"

gain

math_qa__oL0JE8Mjnju81X2T

{5, 6, 3, 8, 4} If we want to get the median value of the set to be 10 which value should be inserted in the set of 5 values? Select the correct option: A) 5 B) 7 C) 15 D) 12 E) 13

<gadget id="calculator">5 + 6</gadget> <output>11</output> <gadget id="calculator">11 - 10</gadget> <output>1</output> <gadget id="calculator">1 + 1</gadget> <output>2</output> <gadget id="calculator">2 + 1</gadget> <output>3</output> <gadget id="calculator">3 + 1</gadget> <output>4</output> <gadget id="calculator">4 + 1</gadget> <output>5</output> <gadget id="calculator">5 + 1</gadget> <output>6</output> <gadget id="calculator">6 + 1</gadget> <output>7</output> <result>B</result>

B

{5, 6, 3, 8, 4} If we want to get the median value of the set to be 10 which value should be inserted in the set of 5 values?

add(add(add(add(add(add(subtract(add(5, 6), 10), const_1), subtract(add(5, 6), 10)), subtract(add(5, 6), 10)), subtract(add(5, 6), 10)), subtract(add(5, 6), 10)), subtract(add(5, 6), 10))

add(n0,n1)|subtract(#0,n5)|add(#1,const_1)|add(#2,#1)|add(#3,#1)|add(#4,#1)|add(#5,#1)|add(#6,#1)

median is the middle number of a sorted distribution . in case of even number of items , median will be the average of middle two values . the question asks fora new number that will cause the median of new set at 10 . mentionable that given set is already sorted and number of items of new set will be 5 + 1 = 6 . to get median 10 , the sum of 3 th 4 th term should be 20 i . e . 3 + 7 . so to keep the median 10 , the new item should be > = 7 answer is b

general

math_qa__tIrVCyEFZeWLa3Io

The area of a rhombus is equal to the area of a square whose side length is 8cm. If one of the diagonals is 16cm what is the length of other diagonal? Choose one A) 4 B) 8 C) 12 D) 16 E) 20

<gadget id="calculator">8 ** 2</gadget> <output>64</output> <gadget id="calculator">64 * 2</gadget> <output>128</output> <gadget id="calculator">128 / 16</gadget> <output>8</output> <result>B</result>

B

The area of a rhombus is equal to the area of a square whose side length is 8cm. If one of the diagonals is 16cm what is the length of other diagonal?

divide(multiply(square_area(8), const_2), 16)

square_area(n0)|multiply(#0,const_2)|divide(#1,n1)

area of the square = 8 x 8 = 64 let ' l ' be the unknown diagonal 0.5 x 16 x ' l ' = 64 which gives ' l ' = 8 cm answer : b

geometry

math_qa__BOOWsKrV4opVk3BL

In a kilometer race, A beats B by 20 meters or 10 seconds. What time does A take to complete the race? Choose the correct choice from the following choices. A) 290 sec B) 190 sec C) 199 sec D) 192 sec E) 490 sec

<gadget id="calculator">1 * 1_000</gadget> <output>1_000</output> <gadget id="calculator">20 / 10</gadget> <output>2</output> <gadget id="calculator">1_000 / 2</gadget> <output>500</output> <gadget id="calculator">500 - 10</gadget> <output>490</output> <result>E</result>

E

In a kilometer race, A beats B by 20 meters or 10 seconds. What time does A take to complete the race?

subtract(divide(multiply(const_1, const_1000), divide(20, 10)), 10)

divide(n0,n1)|multiply(const_1,const_1000)|divide(#1,#0)|subtract(#2,n1)|

"time taken by b run 1000 meters = ( 1000 * 10 ) / 20 = 500 sec . time taken by a = 500 - 10 = 490 sec . answer : e"

physics

math_qa__1Fuzwx4MSAautASt

A positive number when decreased by 4 is equal to 21 times the reciprocal of the number. The number is Choose the correct option: A) 3 B) 5 C) 7 D) 9 E) 12

<gadget id="calculator">4 * 21</gadget> <output>84</output> <gadget id="calculator">4 ** 2</gadget> <output>16</output> <gadget id="calculator">84 + 16</gadget> <output>100</output> <gadget id="calculator">100 ** (1/2)</gadget> <output>10</output> <gadget id="calculator">10 + 4</gadget> <output>14</output> <gadget id="calculator">14 / 2</gadget> <output>7</output> <result>C</result>

C

A positive number when decreased by 4 is equal to 21 times the reciprocal of the number. The number is

divide(add(sqrt(add(multiply(4, 21), power(4, const_2))), 4), const_2)

multiply(n0,n1)|power(n0,const_2)|add(#0,#1)|sqrt(#2)|add(n0,#3)|divide(#4,const_2)|

"sol . let the numbers be x . then , x - 4 = 21 / x ⇔ x 2 - 4 x - 21 = 0 ⇔ ( x - 7 ) ( x + 3 ) = 0 ⇔ x = 7 . answer c"

general

math_qa__z88IIwn326dU3qY3

At what price must an Book costing $47.50 be marked in order that after deducting 5% from the list price. It may be sold at a profit of 25% on the cost price? Choose the correct choice from the following answers: A) 72.5 B) 55.5 C) 62.5 D) 82.5 E) 60.5

<gadget id="calculator">100 + 25</gadget> <output>125</output> <gadget id="calculator">47.5 * 125</gadget> <output>5_937.5</output> <gadget id="calculator">5_937.5 / 100</gadget> <output>59.375</output> <gadget id="calculator">100 - 5</gadget> <output>95</output> <gadget id="calculator">59.375 / 95</gadget> <output>0.625</output> <gadget id="calculator">0.625 * 100</gadget> <output>62.5</output> <result>C</result>

C

At what price must an Book costing $47.50 be marked in order that after deducting 5% from the list price. It may be sold at a profit of 25% on the cost price?

multiply(divide(divide(multiply(47.50, add(const_100, 25)), const_100), subtract(const_100, 5)), const_100)

add(n2,const_100)|subtract(const_100,n1)|multiply(n0,#0)|divide(#2,const_100)|divide(#3,#1)|multiply(#4,const_100)|

"c $ 62.50 cp = 47.50 sp = 47.50 * ( 125 / 100 ) = 59.375 mp * ( 95 / 100 ) = 59.375 mp = 62.5"

gain

math_qa__UA04D26oZ3N5CVig

A car consumes 210 liters of petrol weekly. For how many days will 1470 liters of petrol be sufficient? Choose the correct choice from the following answers: A) 38 B) 20 C) 28 D) 49 E) 10

<gadget id="calculator">1_470 / 210</gadget> <output>7</output> <gadget id="calculator">4 + 3</gadget> <output>7</output> <gadget id="calculator">7 * 7</gadget> <output>49</output> <result>D</result>

D

A car consumes 210 liters of petrol weekly. For how many days will 1470 liters of petrol be sufficient?

multiply(divide(1470, 210), add(const_4, const_3))

add(const_3,const_4)|divide(n1,n0)|multiply(#0,#1)

explanation : no explanation is available for this question ! answer : d

physics

math_qa__m86Hm9QZEtAiQnqz

One type of liquid contains 20% of water and the second type of liquid contains 35% of water. A glass is filled with 10 parts of 1st liquid and 4 parts of 2nd liquid. The percentage of water in the new mixture in the glass is? Choose the correct choice from the following A) 22.15 % B) 23.5 % C) 24.3 % D) 25 % E) 29.6 %

<gadget id="calculator">10 + 4</gadget> <output>14</output> <gadget id="calculator">100 / 14</gadget> <output>50/7 = around 7.142857</output> <gadget id="calculator">20 * 10</gadget> <output>200</output> <gadget id="calculator">200 / 100</gadget> <output>2</output> <gadget id="calculator">35 * 4</gadget> <output>140</output> <gadget id="calculator">140 / 100</gadget> <output>7/5 = around 1.4</output> <gadget id="calculator">2 + (7/5)</gadget> <output>17/5 = around 3.4</output> <gadget id="calculator">(50/7) * (17/5)</gadget> <output>170/7 = around 24.285714</output> <result>C</result>

C

One type of liquid contains 20% of water and the second type of liquid contains 35% of water. A glass is filled with 10 parts of 1st liquid and 4 parts of 2nd liquid. The percentage of water in the new mixture in the glass is?

multiply(divide(const_100, add(10, 4)), add(divide(multiply(20, 10), const_100), divide(multiply(35, 4), const_100)))

add(n2,n4)|multiply(n0,n2)|multiply(n1,n4)|divide(#1,const_100)|divide(#2,const_100)|divide(const_100,#0)|add(#3,#4)|multiply(#6,#5)

required percentage = ( 20 % of 10 + 35 % of 4 ) / 10 + 4 * 100 = 3.4 / 14 * 100 = 24.3 % answer is c

gain

math_qa__zuQwzHONQV9JGjxC

Cuboid volume and Base area are 144 m^3 and 18m^3 respectively.Find the height of a cuboid? Choose the correct answer A) 5 m B) 12 m C) 6 m D) 8 m E) 10 m

<gadget id="calculator">144 / 18</gadget> <output>8</output> <result>D</result>

D

Cuboid volume and Base area are 144 m^3 and 18m^3 respectively.Find the height of a cuboid?

divide(144, 18)

divide(n0,n2)

height of the cuboid = volume * base area = 144 / 18 = 8 metre answer is option d

geometry

math_qa__Czs8NVumT8jHojlh

In a group of 650 readers who read science fiction or literacy works or both, 250 read science fiction and 550 read literacy works. How many read both science fiction and literacy works? Select the correct option. A) 650 B) 250 C) 150 D) 100 E) 400

<gadget id="calculator">250 + 550</gadget> <output>800</output> <gadget id="calculator">800 - 650</gadget> <output>150</output> <result>C</result>

C

In a group of 650 readers who read science fiction or literacy works or both, 250 read science fiction and 550 read literacy works. How many read both science fiction and literacy works?

subtract(add(250, 550), 650)

add(n1,n2)|subtract(#0,n0)|

"consider total number of reader n ( s u l ) = 650 people who read science fiction n ( s ) = 250 people who read literacy works n ( l ) = 550 both science fiction and literacy n ( s â ˆ © l ) = ? n ( s u l ) = n ( s ) + n ( l ) - n ( s â ˆ © l ) 650 = 250 + 550 - n ( s â ˆ © l ) n ( s â ˆ © l ) = 800 - 650 n ( s â ˆ © l ) = 150 so people read both science fiction and literacy works are 150 answer : c"

other

math_qa__999BVHh7hJzRCFip

The speed of a car is 80 km in the first hour and 40 km in the second hour. What is the average speed of the car? Choose the correct choice from the following choices. A) 72 kmph B) 60 kmph C) 30 kmph D) 80 kmph E) 82 kmph

<gadget id="calculator">80 + 40</gadget> <output>120</output> <gadget id="calculator">120 / 2</gadget> <output>60</output> <result>B</result>

B

The speed of a car is 80 km in the first hour and 40 km in the second hour. What is the average speed of the car?

divide(add(80, 40), const_2)

add(n0,n1)|divide(#0,const_2)|

"s = ( 80 + 40 ) / 2 = 60 kmph answer : b"

physics

math_qa__5Fxh6k3HCAaxOohe

Two trains 200m and 250m long run at the speed of 72kmph and 18kmph in opposite directions in parallel tracks. The time which they take to cross each other is? Pick one. A) 5.6 sec B) 8.9 sec C) 10.8 sec D) 12.6 sec E) 18 sec

<gadget id="calculator">200 + 250</gadget> <output>450</output> <gadget id="calculator">72 + 18</gadget> <output>90</output> <gadget id="calculator">10 / 36</gadget> <output>5/18 = around 0.277778</output> <gadget id="calculator">90 * (5/18)</gadget> <output>25</output> <gadget id="calculator">450 / 25</gadget> <output>18</output> <result>E</result>

E

Two trains 200m and 250m long run at the speed of 72kmph and 18kmph in opposite directions in parallel tracks. The time which they take to cross each other is?

divide(add(200, 250), multiply(add(72, 18), const_0_2778))

add(n0,n1)|add(n2,n3)|multiply(#1,const_0_2778)|divide(#0,#2)|

"relative speed = 72 + 18 = 90 kmph * 5 / 18 = 25 m / s distance covered in crossing each other = 200 + 250 = 450 m required time = 450 * 1 / 25 = 18 sec answer is e"

physics

math_qa__TfsE89ygTfRH3FjW

What is (19^7+19) / 19? Choose the correct choice from the following options. A) 45225766 B) 46855821 C) 47045882 D) 48925947 E) 49325989

<gadget id="calculator">19 ** 7</gadget> <output>893_871_739</output> <gadget id="calculator">893_871_739 + 19</gadget> <output>893_871_758</output> <gadget id="calculator">893_871_758 / 19</gadget> <output>47_045_882</output> <result>C</result>

C

What is (19^7+19) / 19?

divide(add(power(19, 7), 19), 19)

power(n0,n1)|add(n0,#0)|divide(#1,n0)|

"( 19 ^ 7 + 19 ) / 19 = 19 * ( 19 ^ 6 + 1 ) / 19 = 19 ^ 6 + 1 clearly this is a number which ends with a 2 in the units place . the answer is c ."

general

math_qa__BtBuscnGSCw94fJd

A = {0, 1, -3, 6, -8} B = {-1, 2, -4, 7} If a is a number that is randomly selected from Set A, and b is a number that is randomly selected from Set B, what is the probability that ab > 0? Choose the most appropriate option A) 1 / 4 B) 1 / 3 C) 2 / 5 D) 4 / 9 E) 1 / 2

<gadget id="calculator">1 + 4</gadget> <output>5</output> <gadget id="calculator">2 / 5</gadget> <output>2/5 = around 0.4</output> <gadget id="calculator">2 / 4</gadget> <output>1/2 = around 0.5</output> <gadget id="calculator">(2/5) * (1/2)</gadget> <output>1/5 = around 0.2</output> <gadget id="calculator">(1/5) + (1/5)</gadget> <output>2/5 = around 0.4</output> <result>C</result>

C

A = {0, 1, -3, 6, -8} B = {-1, 2, -4, 7} If a is a number that is randomly selected from Set A, and b is a number that is randomly selected from Set B, what is the probability that ab > 0?

add(multiply(divide(2, add(1, 4)), divide(2, 4)), multiply(divide(2, add(1, 4)), divide(2, 4)))

add(n1,n7)|divide(n6,n7)|divide(n6,#0)|multiply(#2,#1)|add(#3,#3)

for the product of 2 numbers to be positive either both of them must be positive or both of them must be negative : p ( positive , positive ) = 2 / 5 * 2 / 4 = 4 / 20 ; p ( negative , negative ) = 2 / 5 * 2 / 4 = 4 / 20 . p = 4 / 20 + 4 / 20 = 8 / 20 = 2 / 5 . answer : c .

general

math_qa__qMXQTfXqTTwNmvcS

Two trains 140 m and 210 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is? Choose the correct answer: A) 12.6 sec B) 10.1 sec C) 10.6 sec D) 10.8 sec E) 10.2 sec

<gadget id="calculator">140 + 210</gadget> <output>350</output> <gadget id="calculator">60 + 40</gadget> <output>100</output> <gadget id="calculator">10 / 36</gadget> <output>5/18 = around 0.277778</output> <gadget id="calculator">100 * (5/18)</gadget> <output>250/9 = around 27.777778</output> <gadget id="calculator">350 / (250/9)</gadget> <output>63/5 = around 12.6</output> <result>A</result>

A

Two trains 140 m and 210 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is?

divide(add(140, 210), multiply(add(60, 40), const_0_2778))

add(n0,n1)|add(n2,n3)|multiply(#1,const_0_2778)|divide(#0,#2)|

"relative speed = 60 + 40 = 100 km / hr . = 100 * 5 / 18 = 250 / 9 m / sec . distance covered in crossing each other = 140 + 210 = 350 m . required time = 350 * 9 / 250 = 12.6 sec . answer : a"

physics

math_qa__GuYKBA0o3YZC3dyY

John and David can finish a job together in 1 hours. If John can do the job by himself in 2 hours, what percent of the job does David do? Choices: A) 40 % B) 45 % C) 50 % D) 55 % E) 60 %

<gadget id="calculator">1 / 2</gadget> <output>1/2 = around 0.5</output> <gadget id="calculator">1 - (1/2)</gadget> <output>1/2 = around 0.5</output> <gadget id="calculator">(1/2) * 100</gadget> <output>50</output> <result>C</result>

C

John and David can finish a job together in 1 hours. If John can do the job by himself in 2 hours, what percent of the job does David do?

multiply(subtract(1, inverse(2)), const_100)

inverse(n1)|subtract(n0,#0)|multiply(#1,const_100)

you can also plug in numbers . for example , bob and alice work at a donut factory and make 10 donuts which is the job ( i picked this as a smart number ) . john on his own works 10 / 2 = 5 donuts per hour . john and david work 10 / 1 = 10 donuts per hour so david works 5 donuts / hour to find out the percentage , david works 5 donuts / hr x 1 hours = 5 donuts per hour . therefore 5 donuts / 10 donuts = 1 / 2 = 50 % answer : c

gain

math_qa__gtNPmwUJRsI4qLbV

For the positive integers x, x + 2, x + 4, x + 7, and x + 17, the mean is how much greater than the median? Answers A) 0 B) 1 C) 2 D) 4 E) 7

<gadget id="calculator">2 + 4</gadget> <output>6</output> <gadget id="calculator">6 + 7</gadget> <output>13</output> <gadget id="calculator">13 + 17</gadget> <output>30</output> <gadget id="calculator">4 + 1</gadget> <output>5</output> <gadget id="calculator">30 / 5</gadget> <output>6</output> <gadget id="calculator">6 - 4</gadget> <output>2</output> <result>C</result>

C

For the positive integers x, x + 2, x + 4, x + 7, and x + 17, the mean is how much greater than the median?

subtract(divide(add(add(add(2, 4), 7), 17), add(4, const_1)), 4)

add(n0,n1)|add(const_1,n1)|add(n2,#0)|add(n3,#2)|divide(#3,#1)|subtract(#4,n1)|

"mean = ( x + x + 2 + x + 4 + x + 7 + x + 17 ) / 5 = ( 5 x + 30 ) / 5 = x + 6 median = x + 4 thus mean - median = x + 6 - ( x + 4 ) = 2 answer = c"

general

math_qa__1y6ZpQytYVepRouo

A man rows his boat 84 km downstream and 60 km upstream, taking 4 hours each time. Find the speed of the stream? Pick one: A) 76 kmph B) 6 kmph C) 14 kmph D) 8 kmph E) 3 kmph

<gadget id="calculator">84 / 4</gadget> <output>21</output> <gadget id="calculator">60 / 4</gadget> <output>15</output> <gadget id="calculator">21 - 15</gadget> <output>6</output> <gadget id="calculator">6 / 2</gadget> <output>3</output> <result>E</result>

E

A man rows his boat 84 km downstream and 60 km upstream, taking 4 hours each time. Find the speed of the stream?

divide(subtract(divide(84, 4), divide(60, 4)), const_2)

divide(n0,n2)|divide(n1,n2)|subtract(#0,#1)|divide(#2,const_2)|

"speed downstream = d / t = 84 / ( 4 ) = 21 kmph speed upstream = d / t = 60 / ( 4 ) = 15 kmph the speed of the stream = ( 21 - 15 ) / 2 = 3 kmph answer : e"

physics

math_qa__D9eaS9cy1gP0cCnG

A train is moving at a speed of 132 km/hour. If the length of the train is 110 meters, how long will it take to cross a railway platform 165 meters long. Options: A) 7 second B) 7.5 second C) 8 second D) 8.5 second E) none of these

<gadget id="calculator">110 + 165</gadget> <output>275</output> <gadget id="calculator">10 / 36</gadget> <output>5/18 = around 0.277778</output> <gadget id="calculator">132 * (5/18)</gadget> <output>110/3 = around 36.666667</output> <gadget id="calculator">275 / (110/3)</gadget> <output>15/2 = around 7.5</output> <result>B</result>

B

A train is moving at a speed of 132 km/hour. If the length of the train is 110 meters, how long will it take to cross a railway platform 165 meters long.

divide(add(110, 165), multiply(132, const_0_2778))

add(n1,n2)|multiply(n0,const_0_2778)|divide(#0,#1)

explanation : as we need to calculate answer in seconds , so first convert speed into meter / sec . we know 1 km / hr = 1 * ( 5 / 18 ) m / sec so , speed = 132 * ( 5 / 18 ) = 110 / 3 m / sec distance need to be covered in passing the platform = length of train + length of platform = 110 + 165 = 275 meters time = distance / speed = > time = 275 ∗ 3 / 110 = 15 / 2 = 7.5 seconds option b

physics

math_qa__lLdegbdiFYl1cpTm

Given a bag with 2 red balls and 3 yellow balls, you randomly select one of them, in order. If the second ball you take is yellow, what is the probability that the first one was also yellow? Choose the correct option: A) 1 / 2 B) 1 / 5 C) 3 / 4 D) 1 / 3 E) 3 / 5

<gadget id="calculator">2 + 3</gadget> <output>5</output> <gadget id="calculator">5 - 1</gadget> <output>4</output> <gadget id="calculator">2 / 4</gadget> <output>1/2 = around 0.5</output> <result>A</result>

A

Given a bag with 2 red balls and 3 yellow balls, you randomly select one of them, in order. If the second ball you take is yellow, what is the probability that the first one was also yellow?

divide(2, subtract(add(2, 3), const_1))

add(n0,n1)|subtract(#0,const_1)|divide(n0,#1)

this is a conditional probability question . basically we are told that out of 2 balls picked one is yellow and are asked to find the probability of the other one also to be yellow . so , possible options for this other ball would be : w , w , b , b ( as one yellow is already picked ) so the probability for that ball to be yellow too is 2 / 4 = 1 / 2 . option a

probability

math_qa__QqEl871TmvkpIwur

A water tank is one-fifth full. Pipe A can fill a tank in 10 minutes and pipe B can empty it in 6 minutes. If both the pipes are open, how many minutes will it take to empty or fill the tank completely? Select the correct option A) 3 B) 6 C) 9 D) 12 E) 15

<gadget id="calculator">1 + 4</gadget> <output>5</output> <gadget id="calculator">1 / 5</gadget> <output>1/5 = around 0.2</output> <gadget id="calculator">1 / 6</gadget> <output>1/6 = around 0.166667</output> <gadget id="calculator">1 / 10</gadget> <output>1/10 = around 0.1</output> <gadget id="calculator">(1/6) - (1/10)</gadget> <output>1/15 = around 0.066667</output> <gadget id="calculator">1 / (1/15)</gadget> <output>15</output> <gadget id="calculator">(1/5) * 15</gadget> <output>3</output> <result>A</result>

A

A water tank is one-fifth full. Pipe A can fill a tank in 10 minutes and pipe B can empty it in 6 minutes. If both the pipes are open, how many minutes will it take to empty or fill the tank completely?

multiply(divide(const_1, add(const_1, const_4)), divide(const_1, subtract(divide(const_1, 6), divide(const_1, 10))))

add(const_1,const_4)|divide(const_1,n1)|divide(const_1,n0)|divide(const_1,#0)|subtract(#1,#2)|divide(const_1,#4)|multiply(#3,#5)

the combined rate of filling / emptying the tank = 1 / 10 - 1 / 6 = - 1 / 15 since the rate is negative , the tank will be emptied . a full tank would take 15 minutes to empty . since the tank is only one - fifth full , the time is ( 1 / 5 ) * 15 = 3 minutes the answer is a .

physics

math_qa__aDJnwzoO8Hmyn8Mr

Jar Y has 10% more marbles than Jar X . What percent of marbles from Jar Y need to be moved into X so that both jars have equal marbles Select. A) 4.54 % B) 9.09 % C) 10 % D) 11 % E) 12.25 %

<gadget id="calculator">100 + 10</gadget> <output>110</output> <gadget id="calculator">100 + 110</gadget> <output>210</output> <gadget id="calculator">210 / 2</gadget> <output>105</output> <gadget id="calculator">110 - 105</gadget> <output>5</output> <gadget id="calculator">5 / 110</gadget> <output>1/22 = around 0.045455</output> <gadget id="calculator">(1/22) * 100</gadget> <output>50/11 = around 4.545455</output> <result>A</result>

A

Jar Y has 10% more marbles than Jar X . What percent of marbles from Jar Y need to be moved into X so that both jars have equal marbles

multiply(divide(subtract(add(const_100, 10), divide(add(const_100, add(const_100, 10)), const_2)), add(const_100, 10)), const_100)

add(n0,const_100)|add(#0,const_100)|divide(#1,const_2)|subtract(#0,#2)|divide(#3,#0)|multiply(#4,const_100)

no ; the choices will be approximated only when gmat question explicitly mentions that ; here the answer is very close 4.54 , not 5 . jar y has 10 % more marbles than x y = 1.1 x if k marbles are taken out of y . the remaining marbles in jar y = 1.1 x - k if k marbles are added to x . the new marbles ' count in jar x = x + k and we know they are equal ; x + k = 1.1 x - k 2 k = 0.1 x k = 0.05 x the marbles taken out of y = 0.05 x question is : 0.05 x is what percent of marbles that was originally there in y i . e . 1.1 x 0.05 x 1.1 x ∗ 1000.05 x 1.1 x ∗ 100 0.05 x 1.1 x ∗ 1000.05 x 1.1 x ∗ 100 5011 = 4.54 ¯ ≈ 4.545011 = 4.54 ¯ ≈ 4.54 answer : a

general

math_qa__hplBfgU0awZLEO50

A bag contains 3 blue and 5 white marbles. One by one, marbles are drawn out randomly until only two are left in the bag. What is the probability that out of the two, one is white and one is blue? Answers: A) 15 / 56 B) 41 / 56 C) 13 / 28 D) 15 / 28 E) 5 / 14

<gadget id="calculator">3 * 5</gadget> <output>15</output> <gadget id="calculator">3 + 5</gadget> <output>8</output> <gadget id="calculator">5 + 2</gadget> <output>7</output> <gadget id="calculator">8 * 7</gadget> <output>56</output> <gadget id="calculator">56 / 2</gadget> <output>28</output> <gadget id="calculator">15 / 28</gadget> <output>15/28 = around 0.535714</output> <result>D</result>

D

A bag contains 3 blue and 5 white marbles. One by one, marbles are drawn out randomly until only two are left in the bag. What is the probability that out of the two, one is white and one is blue?

divide(multiply(3, 5), divide(multiply(add(3, 5), add(5, const_2)), const_2))

add(n0,n1)|add(n1,const_2)|multiply(n0,n1)|multiply(#0,#1)|divide(#3,const_2)|divide(#2,#4)|

"the required probability = probability of choosing 6 balls out of the total 8 in such a way that we remove 4 out of 5 white and 2 out of 3 blue balls . ways to select 6 out of total 8 = 8 c 6 ways to select 4 out of 5 white balls = 5 c 4 ways to select 2 out of 3 blue balls = 3 c 2 thus the required probability = ( 5 c 4 * 3 c 2 ) / 8 c 6 = 15 / 28 . d is thus the correct answer ."

probability

math_qa__Xn5c63RqIhtDrFuX

A woman complete a journey in 10 hours. She travels first half of the journey at the rate of 21 km/hr and second half at the rate of 24 km/hr. Find the total journey in km. Choose the correct choice from the following answers A) 334 km . B) 216 km . C) 314 km . D) 224 km . E) 544 km .

<gadget id="calculator">10 * 24</gadget> <output>240</output> <gadget id="calculator">24 + 21</gadget> <output>45</output> <gadget id="calculator">240 / 45</gadget> <output>16/3 = around 5.333333</output> <gadget id="calculator">(16/3) * 21</gadget> <output>112</output> <gadget id="calculator">112 * 2</gadget> <output>224</output> <result>D</result>

D

A woman complete a journey in 10 hours. She travels first half of the journey at the rate of 21 km/hr and second half at the rate of 24 km/hr. Find the total journey in km.

multiply(multiply(divide(multiply(10, 24), add(24, 21)), 21), const_2)

add(n1,n2)|multiply(n0,n2)|divide(#1,#0)|multiply(n1,#2)|multiply(#3,const_2)|

"d 224 km . 0.5 x / 21 + 0.5 x / 24 = 10 - - > x / 21 + x / 24 = 20 - - > 15 x = 168 x 20 - - > x = ( 168 x 20 ) / 15 = 224 km ."

physics

math_qa__AfHrdquJrbCviKaZ

The speed of a train is 80 kmph. What is the distance covered by it in 6 minutes? Options: A) 15 kmph B) 11 kmph C) 18 kmph D) 8 kmph E) 12 kmph

<gadget id="calculator">6 / 60</gadget> <output>1/10 = around 0.1</output> <gadget id="calculator">(1/10) * 80</gadget> <output>8</output> <result>D</result>

D

The speed of a train is 80 kmph. What is the distance covered by it in 6 minutes?

multiply(divide(6, const_60), 80)

divide(n1,const_60)|multiply(n0,#0)|

"80 * 6 / 60 = 8 kmph answer : d"

physics

math_qa__uV9XO98j6bH3n9au

If 50% of the 880 students at a certain college are enrolled in biology classes, how many students at the college are NOT enrolled in a biology class? Choose one: A) 560 B) 540 C) 520 D) 440 E) 500

<gadget id="calculator">880 / 100</gadget> <output>44/5 = around 8.8</output> <gadget id="calculator">100 - 50</gadget> <output>50</output> <gadget id="calculator">(44/5) * 50</gadget> <output>440</output> <result>D</result>

D

If 50% of the 880 students at a certain college are enrolled in biology classes, how many students at the college are NOT enrolled in a biology class?

multiply(divide(880, const_100), subtract(const_100, 50))

divide(n1,const_100)|subtract(const_100,n0)|multiply(#0,#1)

we know 50 % people study biology , therefore the no of people not studying = 100 - 50 = 50 % > therefore the people not studying biology out of a total 880 people are = 50 % of 880 > ( 50 / 100 ) * 880 = 440 people d

other

math_qa__BIcvV326hvgEv6Da

Ram covers a part of the journey at 20 kmph and the balance at 70 kmph taking total of 8 hours to cover the distance of 400 km. How many hours has been driving at 20 kmph? Choose the correct choice from the following options A) 3.2 hr B) 3.4 hr C) 3.6 hr D) 3.8 hr E) 4.2 hr

<gadget id="calculator">8 * 70</gadget> <output>560</output> <gadget id="calculator">560 - 400</gadget> <output>160</output> <gadget id="calculator">70 - 20</gadget> <output>50</output> <gadget id="calculator">160 / 50</gadget> <output>16/5 = around 3.2</output> <result>A</result>

A

Ram covers a part of the journey at 20 kmph and the balance at 70 kmph taking total of 8 hours to cover the distance of 400 km. How many hours has been driving at 20 kmph?

divide(subtract(multiply(8, 70), 400), subtract(70, 20))

multiply(n1,n2)|subtract(n1,n0)|subtract(#0,n3)|divide(#2,#1)

let see d / t = v then x / 20 + ( 400 - x ) / 70 = 8 x = 64 kmh t = 64 / 20 = 3.2 hr answer : a

physics

math_qa__RFl8O0JJReQGfRTn

A shopkeeper sells 10% of his stock at 20% profit ans sells the remaining at a loss of 5%. He incurred an overall loss of Rs. 400. Find the total worth of the stock? Pick A) 20000 B) 16000 C) 18000 D) 17000 E) 15000

<gadget id="calculator">5 / 100</gadget> <output>1/20 = around 0.05</output> <gadget id="calculator">100 - 10</gadget> <output>90</output> <gadget id="calculator">90 / 100</gadget> <output>9/10 = around 0.9</output> <gadget id="calculator">(1/20) * (9/10)</gadget> <output>9/200 = around 0.045</output> <gadget id="calculator">20 / 100</gadget> <output>1/5 = around 0.2</output> <gadget id="calculator">10 / 100</gadget> <output>1/10 = around 0.1</output> <gadget id="calculator">(1/5) * (1/10)</gadget> <output>1/50 = around 0.02</output> <gadget id="calculator">(9/200) - (1/50)</gadget> <output>1/40 = around 0.025</output> <gadget id="calculator">400 / (1/40)</gadget> <output>16_000</output> <result>B</result>

B

A shopkeeper sells 10% of his stock at 20% profit ans sells the remaining at a loss of 5%. He incurred an overall loss of Rs. 400. Find the total worth of the stock?

divide(400, subtract(multiply(divide(5, const_100), divide(subtract(const_100, 10), const_100)), multiply(divide(20, const_100), divide(10, const_100))))

divide(n2,const_100)|divide(n1,const_100)|divide(n0,const_100)|subtract(const_100,n0)|divide(#3,const_100)|multiply(#1,#2)|multiply(#0,#4)|subtract(#6,#5)|divide(n3,#7)|

"let the total worth of the stock be rs . x . the sp of 20 % of the stock = 1 / 10 * x * 6 / 5 = 6 x / 50 the sp of 80 % of the stock = 9 / 10 * x * 0.95 = 171 x / 200 total sp = 24 x / 200 + 171 / 200 = 49 x / 50 overall loss = x - 195 / 20050 = 5 x / 200 5 x / 200 = 400 = > x = 16000 answer : b"

gain

math_qa__KvMihTPzjALhPOnz

In one hour,a boat goes 13 km along the stream and 9 km against the stream.The speed of the boat in still water (in km/hr) is : Answers: A) 3 B) 5 C) 11 D) 9 E) 10

<gadget id="calculator">13 + 9</gadget> <output>22</output> <gadget id="calculator">22 / 2</gadget> <output>11</output> <result>C</result>

C

In one hour,a boat goes 13 km along the stream and 9 km against the stream.The speed of the boat in still water (in km/hr) is :

divide(add(13, 9), const_2)

add(n0,n1)|divide(#0,const_2)|

"solution speed in still water = 1 / 2 ( 13 + 9 ) kmph . = 11 kmph . answer c"

physics

math_qa__x5g8KaNmcNbTOKPM

The price of a cycle is reduced by 25 per cent. The new price is reduced by a further 50 per cent. The two reductions together are equal to a single reduction of Choose the correct option A) 45 % B) 62.5 % C) 35 % D) 32.5 % E) 30 %

<gadget id="calculator">100 - 50</gadget> <output>50</output> <gadget id="calculator">50 / 100</gadget> <output>1/2 = around 0.5</output> <gadget id="calculator">100 - 25</gadget> <output>75</output> <gadget id="calculator">(1/2) * 75</gadget> <output>75/2 = around 37.5</output> <gadget id="calculator">100 - (75/2)</gadget> <output>125/2 = around 62.5</output> <result>B</result>

B

The price of a cycle is reduced by 25 per cent. The new price is reduced by a further 50 per cent. The two reductions together are equal to a single reduction of

subtract(const_100, multiply(divide(subtract(const_100, 50), const_100), subtract(const_100, 25)))

subtract(const_100,n1)|subtract(const_100,n0)|divide(#0,const_100)|multiply(#2,#1)|subtract(const_100,#3)|

"price = p initially price reduced by 25 % which means new price is 3 / 4 p now on this new price further 50 percent is reduced which means the new price is merely 50 percent of 3 / 4 p = = > ( 3 / 4 ) x ( 1 / 2 ) p = 3 / 8 p is the new price after both deduction which is 37.5 percent of the original value p . this implies this entire series of deduction is worth having discounted 62.5 % of p . so answer is b = 62.5 %"

general

math_qa__sqwEt6wjIdDb9iyJ

Audrey 4 hours to complete a certain job. Ferris can do the same job in 3hours. Audrey and Ferris decided to collaborate on the job, working at their respective rates. While Audrey worked continuously, Ferris took 6 breaks of equal length. If the two completed the job together in 2 hours, how many minutes long was each of Ferris’ breaks ? Options A) 2 B) 5 C) 15 D) 20 E) 25

<gadget id="calculator">6 * 10</gadget> <output>60</output> <gadget id="calculator">2 * 60</gadget> <output>120</output> <gadget id="calculator">3 / 2</gadget> <output>3/2 = around 1.5</output> <gadget id="calculator">(3/2) * 60</gadget> <output>90</output> <gadget id="calculator">120 - 90</gadget> <output>30</output> <gadget id="calculator">30 / 6</gadget> <output>5</output> <result>B</result>

B

Audrey 4 hours to complete a certain job. Ferris can do the same job in 3hours. Audrey and Ferris decided to collaborate on the job, working at their respective rates. While Audrey worked continuously, Ferris took 6 breaks of equal length. If the two completed the job together in 2 hours, how many minutes long was each of Ferris’ breaks ?

divide(subtract(multiply(2, multiply(6, const_10)), multiply(divide(3, 2), multiply(6, const_10))), 6)

divide(n1,n3)|multiply(n2,const_10)|multiply(n3,#1)|multiply(#0,#1)|subtract(#2,#3)|divide(#4,n2)

audery and ferris collective work rate : 1 / 4 + 1 / 3 = 7 / 12 collective work time = 12 / 7 = 1.7 hrs job was actually done in = 2 ( includes breaks ) breaks = actual time taken - collective work time = 2 - 1.7 = . 3 hrs = 1 / 2 so ferrais took 6 breaks = . 3 / 6 = . 06 hrs = 5 m so answer is b ) 10 mins

physics

math_qa__jlmsBygKAUkWWMTh

By selling an article at Rs.250, a profit of 25% is made. Find its cost price? Answers: A) s . 486 B) s . 455 C) s . 220 D) s . 480 E) s . 200

<gadget id="calculator">250 * 100</gadget> <output>25_000</output> <gadget id="calculator">100 + 25</gadget> <output>125</output> <gadget id="calculator">25_000 / 125</gadget> <output>200</output> <result>E</result>

E

By selling an article at Rs.250, a profit of 25% is made. Find its cost price?

divide(multiply(250, const_100), add(const_100, 25))

add(n1,const_100)|multiply(n0,const_100)|divide(#1,#0)|

"sp = 250 cp = ( sp ) * [ 100 / ( 100 + p ) ] = 250 * [ 100 / ( 100 + 25 ) ] = 250 * [ 100 / 125 ] = rs . 200 answer : e"

gain

math_qa__zJTjFvh8AlWJfpc8

4 guys buy same cellphones cost them 250 each. Two guy have 25% of for his first cellphone. What is the total cost all of them pay to seller. Choose the most appropriate option. A) 1000 B) 850 C) 875 D) 775 E) 750

<gadget id="calculator">250 * 4</gadget> <output>1_000</output> <gadget id="calculator">1_000 - 100</gadget> <output>900</output> <result>C</result>

C

4 guys buy same cellphones cost them 250 each. Two guy have 25% of for his first cellphone. What is the total cost all of them pay to seller.

subtract(multiply(250, 4), const_100)

multiply(n0,n1)|subtract(#0,const_100)

solution : c . 250 * 2 = 500 for 2 guy without discount , for other 2 ( 250 * 2 ) with 25 % is 375 . total cost 500 + 375 = 875

gain

math_qa__TMpoftpWDUckyRvt

If x and y are integers and |x - y| = 11, what is the minimum possible value of xy? Choose the correct option. A) - 10 B) - 18 C) - 28 D) - 30 E) - 32

<gadget id="calculator">2 + 3</gadget> <output>5</output> <gadget id="calculator">-5</gadget> <output>-5</output> <gadget id="calculator">11 - 5</gadget> <output>6</output> <gadget id="calculator">(-5) * 6</gadget> <output>-30</output> <result>D</result>

D

If x and y are integers and |x - y| = 11, what is the minimum possible value of xy?

multiply(negate(add(const_2, const_3)), subtract(11, add(const_2, const_3)))

add(const_2,const_3)|negate(#0)|subtract(n0,#0)|multiply(#1,#2)

sometimes the answer choices to a given question provide a big ' hint ' as to how you can go about solving it . this prompt can also be solved without any complex math ideas - you just need to do a bit of ' brute force ' math and you ' ll have the answer relatively quickly . we ' re told that x and y are integers and | x - y | = 11 . we ' re asked for the minimum possible value of ( x ) ( y ) . since all of the answer choices are negative , this tells us that one of the two variables must be negative ( and the other must be positive ) , so we should restrict our work to those options . if . . . x = 10 , y = - 1 , then xy = - 10 x = 9 , y = - 2 , then xy = - 18 x = 8 , y = - 3 , then xy = - 24 x = 7 , y = - 4 , then xy = - 28 x = 6 , y = - 5 , then xy = - 30 x = 5 , y = - 6 , then xy = - 30 x = 4 , y = - 7 , then xy = - 28 from this , we can conclude the xy will start to get bigger as x continues to decrease down to 1 , so there ' s no need to do any additional work . final answer : d

general

math_qa__iM0lgrcOlYMRLYOS

15 : 5 seconds :: ? : 10 minutes Select the correct option: A) 10 B) 15 C) 30 D) 25 E) 30

<gadget id="calculator">15 / 5</gadget> <output>3</output> <gadget id="calculator">10 * 3</gadget> <output>30</output> <result>C</result>

C

15 : 5 seconds :: ? : 10 minutes

multiply(10, divide(15, 5))

divide(n0,n1)|multiply(n2,#0)|

"15 * 10 = 5 * x x = 30 answer : c"

physics

math_qa__s7LeN4k1MjMRUQ69

A train 75m long takes 6 sec to cross a man walking at 5kmph in a direction opposite to that of the train. Find the speed of the train? Choose the correct choice from the following options: A) 35 kmph B) 40 kmph C) 45 kmph D) 50 kmph E) 55 kmph

<gadget id="calculator">75 / 6</gadget> <output>25/2 = around 12.5</output> <gadget id="calculator">10 / 36</gadget> <output>5/18 = around 0.277778</output> <gadget id="calculator">(25/2) / (5/18)</gadget> <output>45</output> <gadget id="calculator">45 - 5</gadget> <output>40</output> <result>B</result>

B

A train 75m long takes 6 sec to cross a man walking at 5kmph in a direction opposite to that of the train. Find the speed of the train?

subtract(divide(divide(75, 6), const_0_2778), 5)

divide(n0,n1)|divide(#0,const_0_2778)|subtract(#1,n2)|

"let the speed of the train be x kmph speed of the train relative to man = x + 5 = ( x + 5 ) * 5 / 18 m / sec 75 / [ ( x + 5 ) * 5 / 18 ] = 6 30 ( x + 5 ) = 1350 x = 40 kmph answer is b"

physics

math_qa__hFoySiNnzEjhSNUd

Shreehari has 125 pencils. There are 25 students are studying in his class. He would like to give each student the same amount of pencils, how much should he give to each student? Choose the correct choice: A) 12 B) 7 C) 5 D) 15 E) 6

<gadget id="calculator">125 / 25</gadget> <output>5</output> <result>C</result>

C

Shreehari has 125 pencils. There are 25 students are studying in his class. He would like to give each student the same amount of pencils, how much should he give to each student?

divide(125, 25)

divide(n0,n1)

125 / 25 = 5 the answer is c .

general

math_qa__FjqwoQXzwXMngMtc

The consumption of diesel per hour of a bus varies directly as square of its speed. When the bus is travelling at 60 kmph its consumption is 1 litre per hour. if each litre costs $60 and other expenses per hous is $ 60, then what would be the minimum expenditure required to cover a distance of 600 Km? Choose the correct choice from the following answers: A) 120 B) 1250 C) 1200 D) 1100 E) 1150

<gadget id="calculator">600 / 60</gadget> <output>10</output> <gadget id="calculator">10 * 60</gadget> <output>600</output> <gadget id="calculator">600 + 600</gadget> <output>1_200</output> <result>C</result>

C

The consumption of diesel per hour of a bus varies directly as square of its speed. When the bus is travelling at 60 kmph its consumption is 1 litre per hour. if each litre costs $60 and other expenses per hous is $ 60, then what would be the minimum expenditure required to cover a distance of 600 Km?

add(multiply(divide(600, 60), 60), multiply(divide(600, 60), 60))

divide(n4,n0)|multiply(n2,#0)|multiply(n3,#0)|add(#1,#2)|

"60 kmph consumption is 1 lt / hr so 600 km will take 10 hrs and the consumption is 10 lt for entire distance . 1 lt costs $ 60 so 10 lt costs $ 600 extra expenses for 1 hr - $ 60 10 hrs - $ 600 total expense - $ 600 + $ 600 = $ 1200 answer : c"

physics

math_qa__I5ErUnnXnvHaBFM4

There were two candidates in an election. Winner candidate received 62% of votes and won the election by 288 votes. Find the number of votes casted to the winning candidate? Choose the correct choice from the following answers: A) 456 B) 744 C) 912 D) 1200 E) 1400

<gadget id="calculator">100 - 62</gadget> <output>38</output> <gadget id="calculator">62 - 38</gadget> <output>24</output> <gadget id="calculator">24 / 100</gadget> <output>6/25 = around 0.24</output> <gadget id="calculator">288 / (6/25)</gadget> <output>1_200</output> <gadget id="calculator">1_200 * 62</gadget> <output>74_400</output> <gadget id="calculator">74_400 / 100</gadget> <output>744</output> <result>B</result>

B

There were two candidates in an election. Winner candidate received 62% of votes and won the election by 288 votes. Find the number of votes casted to the winning candidate?

divide(multiply(divide(288, divide(subtract(62, subtract(const_100, 62)), const_100)), 62), const_100)

subtract(const_100,n0)|subtract(n0,#0)|divide(#1,const_100)|divide(n1,#2)|multiply(n0,#3)|divide(#4,const_100)

w = 62 % l = 38 % 62 % - 38 % = 24 % 24 % - - - - - - - - 288 62 % - - - - - - - - ? = > 744 answer : b

gain

math_qa__PaSl4ItRicdvRDWG

There are 17 teams in the hockey league, and each team faces all the other teams 10 times each. How many games are played in the season? Choose the correct choice from the following. A) 980 B) 1150 C) 1360 D) 1540 E) 1720

<gadget id="calculator">17 - 1</gadget> <output>16</output> <gadget id="calculator">17 * 16</gadget> <output>272</output> <gadget id="calculator">272 * 10</gadget> <output>2_720</output> <gadget id="calculator">2_720 / 2</gadget> <output>1_360</output> <result>C</result>

C

There are 17 teams in the hockey league, and each team faces all the other teams 10 times each. How many games are played in the season?

divide(multiply(multiply(17, subtract(17, const_1)), 10), const_2)

subtract(n0,const_1)|multiply(n0,#0)|multiply(n1,#1)|divide(#2,const_2)|

"the number of ways to choose two teams is 17 c 2 = 17 * 16 / 2 = 136 the total number of games in the season is 10 * 136 = 1360 . the answer is c ."

general

math_qa__wtTrZL07WGahFcuQ

30 carrots on a scale weigh 5.94 kg. When 3 carrots are removed from the scale, the average weight of the 27 carrots is 200 grams. What is the average weight (in grams) of the 3 carrots which were removed? Options. A) 165 B) 170 C) 175 D) 180 E) 185

<gadget id="calculator">27 * 200</gadget> <output>5_400</output> <gadget id="calculator">5_400 / 1_000</gadget> <output>27/5 = around 5.4</output> <gadget id="calculator">5.94 - (27/5)</gadget> <output>0.54</output> <gadget id="calculator">0.54 / 3</gadget> <output>0.18</output> <gadget id="calculator">0.18 * 1_000</gadget> <output>180</output> <result>D</result>

D

30 carrots on a scale weigh 5.94 kg. When 3 carrots are removed from the scale, the average weight of the 27 carrots is 200 grams. What is the average weight (in grams) of the 3 carrots which were removed?

multiply(divide(subtract(5.94, divide(multiply(27, 200), const_1000)), 3), const_1000)

multiply(n3,n4)|divide(#0,const_1000)|subtract(n1,#1)|divide(#2,n2)|multiply(#3,const_1000)

27 * 200 = 5400 . the other 3 carrots weigh a total of 540 grams . the average weight is 540 / 3 = 180 grams . the answer is d .

general

math_qa__PCRGUfNMK4pGlvoZ

Two trains start at same time from two stations and proceed towards each other at the rate of 20 km/hr and 25 km/hr respectively. When they meet, it is found that one train has traveled 75 km more than the other. What is the distance between the two stations? Choose the correct choice A) 540 km B) 675 km C) 276 km D) 178 km E) 176 km

<gadget id="calculator">20 + 25</gadget> <output>45</output> <gadget id="calculator">25 - 20</gadget> <output>5</output> <gadget id="calculator">75 / 5</gadget> <output>15</output> <gadget id="calculator">45 * 15</gadget> <output>675</output> <result>B</result>

B

Two trains start at same time from two stations and proceed towards each other at the rate of 20 km/hr and 25 km/hr respectively. When they meet, it is found that one train has traveled 75 km more than the other. What is the distance between the two stations?

multiply(add(20, 25), divide(75, subtract(25, 20)))

add(n0,n1)|subtract(n1,n0)|divide(n2,#1)|multiply(#0,#2)|

"explanation : let us assume that trains meet after ' x ' hours distance = speed * time distance traveled by two trains = 20 x km and 25 x km resp . as one train travels 75 km more than the other , 25 x â € “ 20 x = 75 5 x = 75 x = 15 hours as the two trains are moving towards each other , relative speed = 20 + 25 = 45 km / hr therefore , total distance = 45 * 15 = 675 km . answer : b"

general

math_qa__mFAtXP6nJ6cFZtVK

Two ants, Arthur and Amy, have discovered a picnic and are bringing crumbs back to the anthill. Amy makes twice as many trips and carries one and a half times as many crumbs per trip as Arthur. If Arthur carries a total of c crumbs to the anthill, how many crumbs will Amy bring to the anthill, in terms of c? Pick one A) x / 2 B) x C) 3 x / 2 D) 2 x E) 3 x

<gadget id="calculator">1 / 2</gadget> <output>1/2 = around 0.5</output> <gadget id="calculator">1 + (1/2)</gadget> <output>3/2 = around 1.5</output> <gadget id="calculator">2 * (3/2)</gadget> <output>3</output> <result>E</result>

E

Two ants, Arthur and Amy, have discovered a picnic and are bringing crumbs back to the anthill. Amy makes twice as many trips and carries one and a half times as many crumbs per trip as Arthur. If Arthur carries a total of c crumbs to the anthill, how many crumbs will Amy bring to the anthill, in terms of c?

multiply(const_2, add(const_1, divide(const_1, const_2)))

divide(const_1,const_2)|add(#0,const_1)|multiply(#1,const_2)|

"lets do it by picking up numbers . let arthur carry 2 crumbs per trip , this means amy carries 3 crumbs per trip . also let arthur make 2 trips and so amy makes 4 trips . thus total crumbs carried by arthur ( c ) = 2 x 2 = 4 , total crumbs carried by amy = 3 x 4 = 12 . 12 is 3 times 4 , so e"

general

math_qa__7s6ZLGk2sswikQL0

A cubical block of metal weighs 4 pounds. How much will another cube of the same metal weigh if its sides are twice as long? Choose the correct answer. A) 48 B) 32 C) 24 D) 18 E) 12

<gadget id="calculator">2 * 4</gadget> <output>8</output> <gadget id="calculator">4 * 8</gadget> <output>32</output> <result>B</result>

B

A cubical block of metal weighs 4 pounds. How much will another cube of the same metal weigh if its sides are twice as long?

multiply(4, multiply(const_2, const_4))

multiply(const_2,const_4)|multiply(n0,#0)|

"for example our cube have a side 1 meter , so we have 1 cubical meter in this cube and this cubical meter weigth 4 pounds if we take cube with side 2 meters we will have 8 cubical meters in this cube 8 meters * 4 pounds = 32 pounds so answer is b and similar but more theoretical approach : if we have sides a and b than they have equal ration with their areas : a / b = a ^ 2 / b ^ 2 and they have equal ration with their volumes : a / b = a ^ 3 / b ^ 3 we have two sides 1 / 2 so their volume will be in ratio 1 / 8 weight of one cube * volume of another cube 4 * 8 = 32 so answer is b"

geometry

math_qa__GRPM85Z2xQ89VRq8

The price of a coat in a certain store is $500. If the price of the coat is to be reduced by $200, by what percent is the price to be reduced? Choose the correct option. A) 10 % B) 15 % C) 20 % D) 25 % E) 40 %

<gadget id="calculator">200 / 500</gadget> <output>2/5 = around 0.4</output> <gadget id="calculator">(2/5) * 100</gadget> <output>40</output> <result>E</result>

E

The price of a coat in a certain store is $500. If the price of the coat is to be reduced by $200, by what percent is the price to be reduced?

multiply(divide(200, 500), const_100)

divide(n1,n0)|multiply(#0,const_100)|

"price of a coat in a certain store = $ 500 the price of the coat is to be reduced by $ 200 % change = ( final value - initial value ) * 100 / initial value % reduction = ( reduction in price ) * 100 / initial value i . e . % reduction = ( 200 ) * 100 / 500 = 40 % answer : option e"

gain

math_qa__wid8mG2HPtC6OVcp

Bob wants to run a mile in the same time as his sister. If Bob’s time for a mile is currently 10 minutes 40 seconds and his sister’s time is currently 10 minutes 8 seconds, by what percent does Bob need to improve his time in order run a mile in the same time as his sister? Choices: A) 3 % B) 5 % C) 8 % D) 10 % E) 12 %

<gadget id="calculator">10 * 10</gadget> <output>100</output> <gadget id="calculator">10 * 60</gadget> <output>600</output> <gadget id="calculator">600 + 8</gadget> <output>608</output> <gadget id="calculator">600 + 40</gadget> <output>640</output> <gadget id="calculator">608 / 640</gadget> <output>19/20 = around 0.95</output> <gadget id="calculator">1 - (19/20)</gadget> <output>1/20 = around 0.05</output> <gadget id="calculator">100 * (1/20)</gadget> <output>5</output> <result>B</result>

B

Bob wants to run a mile in the same time as his sister. If Bob’s time for a mile is currently 10 minutes 40 seconds and his sister’s time is currently 10 minutes 8 seconds, by what percent does Bob need to improve his time in order run a mile in the same time as his sister?

multiply(multiply(10, 10), subtract(const_1, divide(add(multiply(10, const_60), 8), add(multiply(10, const_60), 40))))

multiply(n0,n0)|multiply(n2,const_60)|multiply(n0,const_60)|add(n3,#1)|add(n1,#2)|divide(#3,#4)|subtract(const_1,#5)|multiply(#0,#6)|

"bob ' s time = 640 secs . his sis ' time = 608 secs . percent increase needed = ( 640 - 608 / 640 ) * 100 = 32 / 640 * 100 = 5 % . ans ( b ) ."

physics

math_qa__IQU2TPV6WG0XreIr

Bella is taking a trip in her car from New York (point A) Chicago, Illinois (point B). She is traveling at an average speed of 50 miles per hour, If the total distance from point A to point B is 790 miles, in approximately how long will Bella reach her destination? Pick one: A) 10 hours B) 12.50 hours C) 15.80 hours D) 25 hours E) 1 day

<gadget id="calculator">790 / 50</gadget> <output>79/5 = around 15.8</output> <result>C</result>

C

Bella is taking a trip in her car from New York (point A) Chicago, Illinois (point B). She is traveling at an average speed of 50 miles per hour, If the total distance from point A to point B is 790 miles, in approximately how long will Bella reach her destination?

divide(790, 50)

divide(n1,n0)

answer is ( c ) . if she is traveling at a speed of 50 miles per hour and her trip is a total of 790 miles , 790 miles divided by 50 miles per hours would equal 15.80 hours , just shy of 16 hours .

physics

math_qa__KTwJfCS1FpLg44Jr

Because he’s taxed by his home planet, Mork pays a tax rate of 10% on his income, while Mindy pays a rate of 20% on hers. If Mindy earned 3 times as much as Mork did, what was their combined tax rate? Choose the correct choice from the following: A) 32.5 % B) 17.5 % C) 20 % D) 36 % E) 37.5 %

<gadget id="calculator">10 / 100</gadget> <output>1/10 = around 0.1</output> <gadget id="calculator">20 / 100</gadget> <output>1/5 = around 0.2</output> <gadget id="calculator">3 * (1/5)</gadget> <output>3/5 = around 0.6</output> <gadget id="calculator">(1/10) + (3/5)</gadget> <output>7/10 = around 0.7</output> <gadget id="calculator">1 + 3</gadget> <output>4</output> <gadget id="calculator">(7/10) / 4</gadget> <output>7/40 = around 0.175</output> <gadget id="calculator">100 * (7/40)</gadget> <output>35/2 = around 17.5</output> <result>B</result>

B

Because he’s taxed by his home planet, Mork pays a tax rate of 10% on his income, while Mindy pays a rate of 20% on hers. If Mindy earned 3 times as much as Mork did, what was their combined tax rate?

multiply(const_100, divide(add(divide(10, const_100), multiply(3, divide(20, const_100))), add(const_1, 3)))

add(n2,const_1)|divide(n0,const_100)|divide(n1,const_100)|multiply(n2,#2)|add(#1,#3)|divide(#4,#0)|multiply(#5,const_100)|

"say morks income is - 100 so tax paid will be 10 say mindys income is 3 * 100 = 300 so tax paid is 20 % * 300 = 60 total tax paid = 10 + 60 = 70 . combined tax % will be 70 / 100 + 300 = 15.5 %"

gain

math_qa__PTSLCC7bX2OJZw3z

The probability that event A occurs is 0.4, and the probability that events A and B both occur is 0.25. If the probability that either event A or event B occurs is 0.6, what is the probability that event B will occur? Select the correct option. A) 0.05 B) 0.15 C) 0.45 D) 0.5 E) 0.55

<gadget id="calculator">0.6 + 0.25</gadget> <output>0.85</output> <gadget id="calculator">0.85 - 0.4</gadget> <output>0.45</output> <result>C</result>

C

The probability that event A occurs is 0.4, and the probability that events A and B both occur is 0.25. If the probability that either event A or event B occurs is 0.6, what is the probability that event B will occur?

subtract(add(0.6, 0.25), 0.4)

add(n1,n2)|subtract(#0,n0)

p ( a or b ) = p ( a ) + p ( b ) - p ( a n b ) 0.6 = 0.4 + p ( b ) - 0.25 p ( b ) = 0.45 answer : c

other

math_qa__eDWs4CebpAdif9m8

There are 437 doctors and nurses in a hospital. If the ratio of the doctors to the nurses is 8 : 11, then how many nurses are there in the hospital? Choose the correct choice from the following options. A) 152 B) 253 C) 57 D) 171 E) 181

<gadget id="calculator">11 - 8</gadget> <output>3</output> <gadget id="calculator">8 * 3</gadget> <output>24</output> <gadget id="calculator">24 * 11</gadget> <output>264</output> <result>B</result>

B

There are 437 doctors and nurses in a hospital. If the ratio of the doctors to the nurses is 8 : 11, then how many nurses are there in the hospital?

multiply(multiply(8, subtract(11, 8)), 11)

subtract(n2,n1)|multiply(n1,#0)|multiply(n2,#1)|

"given , the ratio of the doctors to the nurses is 8 : 11 number of nurses = 11 / 19 x 437 = 253 answer : b"

other

math_qa__Ori8FOtbXaVUYW8U

If the length of the sides of two cubes are in the ratio 4:1, what is the ratio of their total surface area? Pick A) 4 : 1 B) 6 : 1 C) 8 : 1 D) 16 : 1 E) 64 : 1

<gadget id="calculator">4 * 4</gadget> <output>16</output> <result>D</result>

D

If the length of the sides of two cubes are in the ratio 4:1, what is the ratio of their total surface area?

multiply(4, 4)

multiply(n0,n0)

let x be the length of the small cube ' s side . the total surface area of the small cube is 6 x ^ 2 . the total surface area of the large cube is 6 ( 4 x ) ^ 2 = 96 x ^ 2 . the ratio of surface areas is 16 : 1 . the answer is d .

geometry

math_qa__icWcIkhEKjpHEols

The average weight of 20 persons sitting in a boat had some value. A new person added to them whose weight was 47 kg only. Due to his arrival, the average weight of all the persons decreased by 5 kg. Find the average weight of first 20 persons? Choose the correct choice: A) 55 B) 56 C) 57 D) 58 E) 59

<gadget id="calculator">20 + 1</gadget> <output>21</output> <gadget id="calculator">21 * 5</gadget> <output>105</output> <gadget id="calculator">105 - 47</gadget> <output>58</output> <result>D</result>

D

The average weight of 20 persons sitting in a boat had some value. A new person added to them whose weight was 47 kg only. Due to his arrival, the average weight of all the persons decreased by 5 kg. Find the average weight of first 20 persons?

subtract(multiply(add(20, const_1), 5), 47)

add(n0,const_1)|multiply(n2,#0)|subtract(#1,n1)|

"20 x + 47 = 21 ( x – 5 ) x = 58 answer : d"

general

math_qa__KTttj8zySLwLb2cB

P can do a work in 24 days. Q can do the samework in 9 days & R can do the same work in 12 days. Q & R start the work and leave after 3 days. P finishes the remaining work in how many days. Choices: A) 8 B) 10 C) 14 D) 16 E) 19

<gadget id="calculator">1 / 12</gadget> <output>1/12 = around 0.083333</output> <gadget id="calculator">1 / 9</gadget> <output>1/9 = around 0.111111</output> <gadget id="calculator">(1/12) + (1/9)</gadget> <output>7/36 = around 0.194444</output> <gadget id="calculator">(7/36) * 3</gadget> <output>7/12 = around 0.583333</output> <gadget id="calculator">1 - (7/12)</gadget> <output>5/12 = around 0.416667</output> <gadget id="calculator">1 / 24</gadget> <output>1/24 = around 0.041667</output> <gadget id="calculator">(5/12) / (1/24)</gadget> <output>10</output> <result>B</result>

B

P can do a work in 24 days. Q can do the samework in 9 days & R can do the same work in 12 days. Q & R start the work and leave after 3 days. P finishes the remaining work in how many days.

divide(subtract(const_1, multiply(add(divide(const_1, 12), divide(const_1, 9)), 3)), divide(const_1, 24))

divide(const_1,n2)|divide(const_1,n1)|divide(const_1,n0)|add(#0,#1)|multiply(n3,#3)|subtract(const_1,#4)|divide(#5,#2)

work done by p in 1 day = 1 / 24 work done by q in 1 day = 1 / 9 work done by r in 1 day = 1 / 12 work done by q and r in 1 day = 1 / 9 + 1 / 12 = 7 / 36 work done by q and r in 3 days = 3 × 7 / 36 = 7 / 12 remaining work = 1 – 7 / 12 = 5 / 12 number of days in which p can finish the remaining work = ( 5 / 12 ) / ( 1 / 24 ) = 10 b

physics

math_qa__dmrY53nWu0CQpHuN

What is the difference between the C.I. on Rs. 8000 for 1 1/2 years at 4% per annum compounded yearly and half-yearly? Pick one. A) s . 3.26 B) s . 2.08 C) s . 2.02 D) s . 2.83 E) s . 2.42

<gadget id="calculator">2 / 100</gadget> <output>1/50 = around 0.02</output> <gadget id="calculator">1 + (1/50)</gadget> <output>51/50 = around 1.02</output> <gadget id="calculator">(51/50) * (51/50)</gadget> <output>2_601/2_500 = around 1.0404</output> <gadget id="calculator">(2_601/2_500) * (51/50)</gadget> <output>132_651/125_000 = around 1.061208</output> <gadget id="calculator">8_000 * (132_651/125_000)</gadget> <output>1_061_208/125 = around 8_489.664</output> <gadget id="calculator">4 / 100</gadget> <output>1/25 = around 0.04</output> <gadget id="calculator">1 + (1/25)</gadget> <output>26/25 = around 1.04</output> <gadget id="calculator">(51/50) * (26/25)</gadget> <output>663/625 = around 1.0608</output> <gadget id="calculator">8_000 * (663/625)</gadget> <output>42_432/5 = around 8_486.4</output> <gadget id="calculator">(1_061_208/125) - (42_432/5)</gadget> <output>408/125 = around 3.264</output> <result>A</result>

A

What is the difference between the C.I. on Rs. 8000 for 1 1/2 years at 4% per annum compounded yearly and half-yearly?

subtract(multiply(8000, multiply(multiply(add(1, divide(2, const_100)), add(1, divide(2, const_100))), add(1, divide(2, const_100)))), multiply(8000, multiply(add(1, divide(2, const_100)), add(1, divide(4, const_100)))))

divide(n3,const_100)|divide(n4,const_100)|add(#0,n1)|add(#1,n1)|multiply(#2,#2)|multiply(#2,#3)|multiply(#2,#4)|multiply(n0,#5)|multiply(n0,#6)|subtract(#8,#7)|

"c . i . when interest is compounded yearly = [ 8000 * ( 1 + 4 / 100 ) * ( 1 + ( 1 / 2 * 4 ) / 100 ] = 8000 * 26 / 25 * 51 / 50 = rs . 8486.4 c . i . when interest is compounded half - yearly = [ 8000 * ( 1 + 2 / 100 ) 2 ] = ( 8000 * 51 / 50 * 51 / 50 * 51 / 50 ) = rs . 8489.66 difference = ( 8489.66 - 8486.4 = rs . 3.26 . answer : a"

general

math_qa__YW7RAduulS2Tya3K

The number of timeshare condos available at Sunset Beach is 2/5 the number of timeshare condos available at Playa del Mar. If the total number of timeshare condos available at the two beaches combined is 210, what is the difference between the number of condos available at Sunset Beach and the number of condos available at Playa del Mar? Options: A) 60 B) 90 C) 120 D) 150 E) 240

<gadget id="calculator">210 * 2</gadget> <output>420</output> <gadget id="calculator">420 / 5</gadget> <output>84</output> <gadget id="calculator">2 * 5</gadget> <output>10</output> <gadget id="calculator">84 + 10</gadget> <output>94</output> <result>B</result>

B

The number of timeshare condos available at Sunset Beach is 2/5 the number of timeshare condos available at Playa del Mar. If the total number of timeshare condos available at the two beaches combined is 210, what is the difference between the number of condos available at Sunset Beach and the number of condos available at Playa del Mar?

add(divide(multiply(210, 2), 5), multiply(2, 5))

multiply(n0,n2)|multiply(n0,n1)|divide(#0,n1)|add(#2,#1)|

"let x be the number of timeshare condos available at playa del mar . then number of timeshare condos available at sunset beach = 3 / 5 x we know , x + 2 / 5 x = 210 hence , x = 150 . so , number of timeshare condos available at playa del mar = 150 the difference between the number of condos available at sunset beach and the number of condos available at playa del mar = x - 2 / 5 x = 2 / 5 x = 3 / 5 ( 150 ) = 90 the correct answer is b"

general

math_qa__ewRNtfjQRUkxXozq

A can do a particular work in 6 days . B can do the same work in 8 days. A and B signed to do it for Rs. 3840. They completed the work in 3 days with the help of C. How much is to be paid to C? Select the correct option. A) s . 380 B) s . 600 C) s . 420 D) s . 400 E) s . 480

<gadget id="calculator">1 / 3</gadget> <output>1/3 = around 0.333333</output> <gadget id="calculator">1 / 6</gadget> <output>1/6 = around 0.166667</output> <gadget id="calculator">1 / 8</gadget> <output>1/8 = around 0.125</output> <gadget id="calculator">(1/6) + (1/8)</gadget> <output>7/24 = around 0.291667</output> <gadget id="calculator">(1/3) - (7/24)</gadget> <output>1/24 = around 0.041667</output> <gadget id="calculator">3 * (1/24)</gadget> <output>1/8 = around 0.125</output> <gadget id="calculator">(1/8) * 3_840</gadget> <output>480</output> <result>E</result>

E

A can do a particular work in 6 days . B can do the same work in 8 days. A and B signed to do it for Rs. 3840. They completed the work in 3 days with the help of C. How much is to be paid to C?

multiply(multiply(3, subtract(divide(const_1, 3), add(divide(const_1, 6), divide(const_1, 8)))), 3840)

divide(const_1,n3)|divide(const_1,n0)|divide(const_1,n1)|add(#1,#2)|subtract(#0,#3)|multiply(n3,#4)|multiply(n2,#5)|

"explanation : amount of work a can do in 1 day = 1 / 6 amount of work b can do in 1 day = 1 / 8 amount of work a + b can do in 1 day = 1 / 6 + 1 / 8 = 7 / 24 amount of work a + b + c can do = 1 / 3 amount of work c can do in 1 day = 1 / 3 - 7 / 24 = 1 / 24 work a can do in 1 day : work b can do in 1 day : work c can do in 1 day = 1 / 6 : 1 / 8 : 1 / 24 = 4 : 3 : 1 amount to be paid to c = 3840 × ( 1 / 8 ) = 480 answer : option e"

physics

math_qa__4lIxQPEwqT05QPO8

On dividing 13698 by a certain number, we get 89 as quotient and 14 as remainder. What is the divisor? Pick: A) 743 B) 154 C) 852 D) 741 E) 785

<gadget id="calculator">13_698 - 14</gadget> <output>13_684</output> <gadget id="calculator">13_684 / 89</gadget> <output>13_684/89 = around 153.752809</output> <result>B</result>

B

On dividing 13698 by a certain number, we get 89 as quotient and 14 as remainder. What is the divisor?

divide(subtract(13698, 14), 89)

subtract(n0,n2)|divide(#0,n1)

divisor * quotient + remainder = dividend divisor = ( dividend ) - ( remainder ) / quotient ( 13698 - 14 ) / 89 = 154 answer ( b )

general

math_qa__FY4S2gGNQIBhOoXk

A father said his son , " I was as old as you are at present at the time of your birth. " If the father age is 38 now, the son age 5 years back was Options: A) 14 B) 17 C) 11 D) 19 E) 99

<gadget id="calculator">38 / 2</gadget> <output>19</output> <gadget id="calculator">19 - 5</gadget> <output>14</output> <result>A</result>

A

A father said his son , " I was as old as you are at present at the time of your birth. " If the father age is 38 now, the son age 5 years back was

subtract(divide(38, const_2), 5)

divide(n0,const_2)|subtract(#0,n1)|

"let the son ' s present age be x years . then , ( 38 - x ) = x x = 19 . son ' s age 5 years back = ( 19 - 5 ) = 14 years answer : a"

general

math_qa__cv4qhoZg5qpHLnxT

The number of people who purchased book A is twice the number of people who purchased book B. The number of people who purchased both books A and B is 500, which is twice the number of people who purchased only book B. What is the number of people X who purchased only book A? Choose the most appropriate option. A) 250 B) 500 C) 750 D) 1000 E) 1500

<gadget id="calculator">500 / 2</gadget> <output>250</output> <gadget id="calculator">500 + 250</gadget> <output>750</output> <gadget id="calculator">750 * 2</gadget> <output>1_500</output> <gadget id="calculator">1_500 - 500</gadget> <output>1_000</output> <result>D</result>

D

The number of people who purchased book A is twice the number of people who purchased book B. The number of people who purchased both books A and B is 500, which is twice the number of people who purchased only book B. What is the number of people X who purchased only book A?

subtract(multiply(add(500, divide(500, const_2)), const_2), 500)

divide(n0,const_2)|add(n0,#0)|multiply(#1,const_2)|subtract(#2,n0)|

"this is best solved using overlapping sets or a venn diagram . we know that a = 2 b , and that 500 people purchased both a and b . further , those purchasing both was double those purchasing b only . this gives us 250 people purchasing b only . with the 500 that pruchased both , we have a total of 750 that purchased b and this is 1 / 2 of those that purchased a . so , 1500 purchased a . less the 500 that purchased both , x = 1000 purchased a only . ( this is much simpler to solve using the venn diagram ) . correct answer is d . 1000"

general

math_qa__pQ8fWfqpQzRECrfl

In how many seconds will a train 150 meters long pass an oak tree, if the speed of the train is 54 km/hr? Select the correct option: A) 6 B) 8 C) 10 D) 12 E) 14

<gadget id="calculator">10 / 36</gadget> <output>5/18 = around 0.277778</output> <gadget id="calculator">(5/18) * 54</gadget> <output>15</output> <gadget id="calculator">150 / 15</gadget> <output>10</output> <result>C</result>

C

In how many seconds will a train 150 meters long pass an oak tree, if the speed of the train is 54 km/hr?

divide(150, multiply(const_0_2778, 54))

multiply(n1,const_0_2778)|divide(n0,#0)|

"speed = 54 * 5 / 18 = 15 m / s time = 150 / 15 = 10 seconds the answer is c ."

physics

math_qa__HrgzH9PyF8r8VXRA

Cereal A is 10% sugar by weight, whereas healthier but less delicious Cereal B is 3% sugar by weight. To make a delicious and healthy mixture that is 4% sugar, what should be the ratio of Cereal A to Cereal B, by weight? Choose the correct answer: A) 2 : 9 B) 2 : 7 C) 1 : 6 D) 1 : 4 E) 1 : 3

<gadget id="calculator">4 - 3</gadget> <output>1</output> <gadget id="calculator">10 - 4</gadget> <output>6</output> <gadget id="calculator">1 / 6</gadget> <output>1/6 = around 0.166667</output> <result>C</result>

C

Cereal A is 10% sugar by weight, whereas healthier but less delicious Cereal B is 3% sugar by weight. To make a delicious and healthy mixture that is 4% sugar, what should be the ratio of Cereal A to Cereal B, by weight?

divide(subtract(4, 3), subtract(10, 4))

subtract(n2,n1)|subtract(n0,n2)|divide(#0,#1)|

"ratio of a / ratio of b = ( average wt of mixture - wt of b ) / ( wt of a - average wt of mixture ) = > ratio of a / ratio of b = ( 4 - 3 ) / ( 10 - 4 ) = 1 / 6 so they should be mixed in the ratio 1 : 6 answer - c"

general

math_qa__YVMcmzL04Z8kWjTp

In a certain game, each player scores either 2 points or 5 points. If n players score 2 points and m players score 5 points, and the total number of points scored is 50, what is the least possible positive E difference between n and m? Choices A) 1 B) 3 C) 5 D) 7 E) 9

<gadget id="calculator">5 - 2</gadget> <output>3</output> <result>B</result>

B

In a certain game, each player scores either 2 points or 5 points. If n players score 2 points and m players score 5 points, and the total number of points scored is 50, what is the least possible positive E difference between n and m?

subtract(5, 2)

subtract(n1,n0)

we have equation 2 n + 5 m = 50 we have factor 2 in first number and we have factor 5 in second number . lcm ( 2 , 5 ) = 10 so we can try some numbers and we should start from 5 because it will be less list than for 2 2 * 5 = 10 and n should be equal 20 4 * 5 = 20 and n should be equal 15 6 * 5 = 30 and n should be equal 10 8 * 5 = 40 and n should be equal 5 10 * 5 = 50 and n should be equal 0 third variant give us the mininal difference n - m = 10 - 6 = 4 and there is some mistake in my way of thinking because we do n ' t have such answer ) if we change the task and will seek for difference between m and n than minimal result e will be 8 - 5 = 3 and answer b

general

math_qa__yWgFuJyr3mGgieeX

A palindrome is a word or a number that reads the same forward and backward. For example, 2442 and 111 are palindromes. If 5-digit palindromes are formed using one or more of the digits 1, 2, 3, 4, and 5, how many palindromes are possible? Choose one A) 25 B) 75 C) 125 D) 225 E) 625

<gadget id="calculator">5 ** 3</gadget> <output>125</output> <result>C</result>

C

A palindrome is a word or a number that reads the same forward and backward. For example, 2442 and 111 are palindromes. If 5-digit palindromes are formed using one or more of the digits 1, 2, 3, 4, and 5, how many palindromes are possible?

power(5, const_3)

power(n2,const_3)

there are 5 choices for each of the first three digits . the number of possible palindromes is 5 ^ 3 = 125 . the answer is c .

general

math_qa__uTVDe2bukkZMBHHn

If the personal income tax rate is lowered from 40% to 33%, what is the differential savings for a tax payer having an annual income before tax to the tune of $45000? Choose the correct choice from the following choices A) $ 3500 B) $ 5000 C) $ 3150 D) $ 7000 E) $ 10000

<gadget id="calculator">45_000 / 100</gadget> <output>450</output> <gadget id="calculator">40 - 33</gadget> <output>7</output> <gadget id="calculator">450 * 7</gadget> <output>3_150</output> <result>C</result>

C

If the personal income tax rate is lowered from 40% to 33%, what is the differential savings for a tax payer having an annual income before tax to the tune of $45000?

multiply(divide(45000, const_100), subtract(40, 33))

divide(n2,const_100)|subtract(n0,n1)|multiply(#0,#1)|

"saving = ( 40 - 33 ) % of 45000 = 3150 . answer : c"

gain

math_qa__MrTdW6A2DzotiUjD

Jonathan can type a 50 page document in 40 minutes, Susan can type it in 30 minutes, and Jack can type it in 24 minutes. Working together, how much time will it take them to type the same document? Choices A) 5 minutes B) 10 minutes C) 15 minutes D) 18 minutes E) 20 minutes

<gadget id="calculator">50 / 24</gadget> <output>25/12 = around 2.083333</output> <gadget id="calculator">50 / 40</gadget> <output>5/4 = around 1.25</output> <gadget id="calculator">50 / 30</gadget> <output>5/3 = around 1.666667</output> <gadget id="calculator">(5/4) + (5/3)</gadget> <output>35/12 = around 2.916667</output> <gadget id="calculator">(25/12) + (35/12)</gadget> <output>5</output> <gadget id="calculator">50 / 5</gadget> <output>10</output> <result>B</result>

B

Jonathan can type a 50 page document in 40 minutes, Susan can type it in 30 minutes, and Jack can type it in 24 minutes. Working together, how much time will it take them to type the same document?

divide(50, add(divide(50, 24), add(divide(50, 40), divide(50, 30))))

divide(n0,n1)|divide(n0,n2)|divide(n0,n3)|add(#0,#1)|add(#3,#2)|divide(n0,#4)|

"you may set up common equation like this : job / a + job / b + job / c = job / x memorize this universal formula , you will need it definitely for gmat . and find x from this equation in this specific case , the equation will look like this : 50 / 40 + 50 / 30 + 50 / 24 = 50 / x if you solve this equation , you get the same answer b ( 10 )"

physics

math_qa__nR4dlcgwMBDJBEO0

Find the annual income derived by investing $ 6800 in 30% stock at 136. Choices A) 550 B) 1500 C) 250 D) 1300 E) 400

<gadget id="calculator">6_800 * 30</gadget> <output>204_000</output> <gadget id="calculator">204_000 / 136</gadget> <output>1_500</output> <result>B</result>

B

Find the annual income derived by investing $ 6800 in 30% stock at 136.

divide(multiply(6800, 30), 136)

multiply(n0,n1)|divide(#0,n2)

by investing $ 136 , income obtained = $ 30 . by investing $ 6800 , income obtained = $ [ ( 30 / 136 ) * 6800 ] = $ 1500 . answer b .

gain

math_qa__UpKrP0JRze23yRGV

The average age of 6 men increases by 2 years when two women are included in place of two men of ages 10 and 12 years. Find the average age of the women? Pick one A) 87 B) 12 C) 30 D) 28 E) 17

<gadget id="calculator">10 + 12</gadget> <output>22</output> <gadget id="calculator">6 * 2</gadget> <output>12</output> <gadget id="calculator">22 + 12</gadget> <output>34</output> <gadget id="calculator">34 / 2</gadget> <output>17</output> <result>E</result>

E

The average age of 6 men increases by 2 years when two women are included in place of two men of ages 10 and 12 years. Find the average age of the women?

divide(add(add(10, 12), multiply(6, 2)), const_2)

add(n2,n3)|multiply(n0,n1)|add(#0,#1)|divide(#2,const_2)|

"10 + 12 + 6 * 2 = 34 / 2 = 17 answer : e"

general

math_qa__LKJusnWBacD1zFVx

It takes 35 identical printing presses 15 hours to print 500,000 papers. How many hours would it take 25 of these printing presses to print 500,000 papers? Choose one: A) 18 B) 20 C) 21 D) 24 E) 25

<gadget id="calculator">1_000 / 2</gadget> <output>500</output> <gadget id="calculator">500 * 1_000</gadget> <output>500_000</output> <gadget id="calculator">500_000 / 35</gadget> <output>100_000/7 = around 14_285.714286</output> <gadget id="calculator">(100_000/7) / 15</gadget> <output>20_000/21 = around 952.380952</output> <gadget id="calculator">(20_000/21) * 25</gadget> <output>500_000/21 = around 23_809.52381</output> <gadget id="calculator">500_000 / (500_000/21)</gadget> <output>21</output> <result>C</result>

C

It takes 35 identical printing presses 15 hours to print 500,000 papers. How many hours would it take 25 of these printing presses to print 500,000 papers?

divide(multiply(divide(const_1000, const_2), const_1000), multiply(divide(divide(multiply(divide(const_1000, const_2), const_1000), 35), 15), 25))

divide(const_1000,const_2)|multiply(#0,const_1000)|divide(#1,n0)|divide(#2,n1)|multiply(n3,#3)|divide(#1,#4)|

"35 printing presses can do 1 / 15 of the job each hour . 25 printing presses can do 5 / 7 * 1 / 15 = 1 / 21 of the job each hour . the answer is c ."

physics

math_qa__CeFh7NGjybIVGNDz

3639 + 11.95 - x = 3054. Find the value of x. Select the correct option: A) 407.09 B) 479.75 C) 523.93 D) 596.95 E) none of these

<gadget id="calculator">3_639 + 11.95</gadget> <output>3_650.95</output> <gadget id="calculator">3_650.95 - 3_054</gadget> <output>596.95</output> <result>D</result>

D

3639 + 11.95 - x = 3054. Find the value of x.

subtract(add(3639, 11.95), 3054)

add(n0,n1)|subtract(#0,n2)|

"explanation : let 3639 + 11.95 – x = 3054 then , x = ( 3639 + 11.95 ) – 3054 = 3650.95 – 3054 = 596.95 answer : d"

general

math_qa__EVe6qAfC2ZT2cg0G

The cost per pound of milk powder and coffee were the same in June. In July, the price of coffee shot up by 300% and that of milk powder dropped by 80%. If in July, a mixture containing equal quantities of milk powder and coffee costs $6.30 for 3lbs, how much did a pound of milk powder cost in July? Choose the correct choice from the following choices A) $ 4 B) $ 0.2 C) $ 1 D) $ 3 E) $ 1.65

<gadget id="calculator">80 / 100</gadget> <output>4/5 = around 0.8</output> <gadget id="calculator">1 - (4/5)</gadget> <output>1/5 = around 0.2</output> <result>B</result>

B

The cost per pound of milk powder and coffee were the same in June. In July, the price of coffee shot up by 300% and that of milk powder dropped by 80%. If in July, a mixture containing equal quantities of milk powder and coffee costs $6.30 for 3lbs, how much did a pound of milk powder cost in July?

subtract(const_1, divide(80, const_100))

divide(n1,const_100)|subtract(const_1,#0)

lets assume price of coffee in june = 100 x price of milk powder in june = 100 x price of coffee in july = 400 x ( because of 300 % increase in price ) price of milk powder in july = 20 x ( because of 80 % decrease in price ) price of 1.5 pound of coffee 1.5 pound of milk powder in july will be = 600 x + 30 x = 630 x as per question 630 x = 6.30 $ x = 0.01 s so the price of milk powder in july = 20 x = 20 x 0.01 = 0.2 $ / pound answer b

general

math_qa__ZMl4gJfp9sWDiVXh

A certain class of students is being divided into teams. The class can either be divided into 18 teams with an equal number of players on each team or 24 teams with an equal number of players on each team. What is the lowest possible number of students in the class? Pick one: A) 6 B) 36 C) 48 D) 60 E) 72

<gadget id="calculator">lcm(18, 24)</gadget> <output>72</output> <result>E</result>

E

A certain class of students is being divided into teams. The class can either be divided into 18 teams with an equal number of players on each team or 24 teams with an equal number of players on each team. What is the lowest possible number of students in the class?

lcm(18, 24)

lcm(n0,n1)

prime factorization of 18 = 2 * 3 ^ 2 prime factorization of 24 = 2 ^ 3 * 3 lcm of the given numbers = 2 ^ 3 * 3 ^ 2 = 72 answer e

general

math_qa__s0OilXFUbuuNDysa

Daniel went to a shop and bought things worth Rs. 25, out of which 30 Paise went on sales tax on taxable purchases. If the tax rate was 10%, then what was the cost of the tax free items? Choose the correct choice from the following answers A) 19.7 B) 20 C) 21.3 D) 21.7 E) 22

<gadget id="calculator">30 / 100</gadget> <output>3/10 = around 0.3</output> <gadget id="calculator">25 - (3/10)</gadget> <output>247/10 = around 24.7</output> <gadget id="calculator">30 / 10</gadget> <output>3</output> <gadget id="calculator">(247/10) - 3</gadget> <output>217/10 = around 21.7</output> <result>D</result>

D

Daniel went to a shop and bought things worth Rs. 25, out of which 30 Paise went on sales tax on taxable purchases. If the tax rate was 10%, then what was the cost of the tax free items?

subtract(subtract(25, divide(30, const_100)), divide(30, 10))

divide(n1,const_100)|divide(n1,n2)|subtract(n0,#0)|subtract(#2,#1)|

"total cost of the items he purchased = rs . 25 given that out of this rs . 25 , 30 paise is given as tax = > total tax incurred = 30 paise = rs . 30 / 100 let the cost of the tax free items = x given that tax rate = 10 % ∴ ( 25 − 30 / 100 − x ) 10 / 100 = 30 / 100 ⇒ 10 ( 25 − 0.3 − x ) = 30 ⇒ ( 25 − 0.3 − x ) = 3 ⇒ x = 25 − 0.3 − 3 = 21.7 d"

gain

math_qa__Tmrzg0geXpHfVKtQ

If a person buy radio worth Rs 2468 and pay 7% sales .how much price of radio should reduce to pay only Rs 2468. Choose the correct choice from the following answers A) 162 B) 158 C) 159 D) 130 E) 160

<gadget id="calculator">7 / 100</gadget> <output>7/100 = around 0.07</output> <gadget id="calculator">1 + (7/100)</gadget> <output>107/100 = around 1.07</output> <gadget id="calculator">2_468 / (107/100)</gadget> <output>246_800/107 = around 2_306.542056</output> <gadget id="calculator">2_468 - (246_800/107)</gadget> <output>17_276/107 = around 161.457944</output> <result>A</result>

A

If a person buy radio worth Rs 2468 and pay 7% sales .how much price of radio should reduce to pay only Rs 2468.

subtract(2468, divide(2468, add(const_1, divide(7, const_100))))

divide(n1,const_100)|add(#0,const_1)|divide(n0,#1)|subtract(n0,#2)

( x + . 07 x ) = 2468 1.07 x = 2468 x = 2306 reduce = 2468 - 2306 = 162 answer : a

gain

math_qa__WRDS7HMt39PhgSqS

3 buffaloes eat as much as 4 cows or 2 oxen. At a farm, there are 15 buffaloes, 8 oxen, and 24 cows. The fodder for these cattle is available for 48 days. If 60 more cows and 30 more buffaloes are brought in, how many days will the fodder last? Choose the correct answer: A) 15 days B) 18 days C) 21 days D) 24 days E) 27 days

<gadget id="calculator">24 / 4</gadget> <output>6</output> <gadget id="calculator">6 * 3</gadget> <output>18</output> <gadget id="calculator">15 + 18</gadget> <output>33</output> <gadget id="calculator">8 / 2</gadget> <output>4</output> <gadget id="calculator">4 * 3</gadget> <output>12</output> <gadget id="calculator">33 + 12</gadget> <output>45</output> <gadget id="calculator">48 * 45</gadget> <output>2_160</output> <gadget id="calculator">15 + 30</gadget> <output>45</output> <gadget id="calculator">24 + 60</gadget> <output>84</output> <gadget id="calculator">84 / 4</gadget> <output>21</output> <gadget id="calculator">21 * 3</gadget> <output>63</output> <gadget id="calculator">45 + 63</gadget> <output>108</output> <gadget id="calculator">108 + 12</gadget> <output>120</output> <gadget id="calculator">2_160 / 120</gadget> <output>18</output> <result>B</result>

B

3 buffaloes eat as much as 4 cows or 2 oxen. At a farm, there are 15 buffaloes, 8 oxen, and 24 cows. The fodder for these cattle is available for 48 days. If 60 more cows and 30 more buffaloes are brought in, how many days will the fodder last?

divide(multiply(48, add(add(15, multiply(divide(24, 4), 3)), multiply(divide(8, 2), 3))), add(add(add(15, 30), multiply(divide(add(24, 60), 4), 3)), multiply(divide(8, 2), 3)))

add(n3,n8)|add(n5,n7)|divide(n5,n1)|divide(n4,n2)|divide(#1,n1)|multiply(n0,#2)|multiply(n0,#3)|add(n3,#5)|multiply(n0,#4)|add(#7,#6)|add(#0,#8)|add(#10,#6)|multiply(n6,#9)|divide(#12,#11)

2 oxen = 3 buffaloes = 4 cows also : 15 buffaloes + 8 oxen + 24 cows = 10 oxen + 8 oxen + 12 oxen = 30 oxen there is enough fodder for 1 oxen for 30 * 48 days . 60 cows + 30 buffaloes = 30 oxen + 20 oxen = 50 oxen the new total is equal to 80 oxen instead of 30 oxen . 30 * 48 / 80 oxen = 18 days the answer is b .

general

math_qa__VNOsw14lTgTyAmO3

Two thirds of the roads from A to B are at least 5 miles long, and 3/4 of the roads from B to C are at least 5 miles long. If you randomly pick a road from A to B and then randomly pick a road from B to C, what is the probability that at least one of the roads you pick is at least 5 miles long? Choose the correct choice A) 1 / 6 B) 1 / 4 C) 2 / 3 D) 3 / 4 E) 11 / 12

<gadget id="calculator">2 / 3</gadget> <output>2/3 = around 0.666667</output> <gadget id="calculator">1 - (2/3)</gadget> <output>1/3 = around 0.333333</output> <gadget id="calculator">3 / 4</gadget> <output>3/4 = around 0.75</output> <gadget id="calculator">1 - (3/4)</gadget> <output>1/4 = around 0.25</output> <gadget id="calculator">(1/3) * (1/4)</gadget> <output>1/12 = around 0.083333</output> <gadget id="calculator">1 - (1/12)</gadget> <output>11/12 = around 0.916667</output> <result>E</result>

E

Two thirds of the roads from A to B are at least 5 miles long, and 3/4 of the roads from B to C are at least 5 miles long. If you randomly pick a road from A to B and then randomly pick a road from B to C, what is the probability that at least one of the roads you pick is at least 5 miles long?

subtract(const_1, multiply(subtract(const_1, divide(const_2, 3)), subtract(const_1, divide(3, 4))))

divide(const_2,n1)|divide(n1,n2)|subtract(const_1,#0)|subtract(const_1,#1)|multiply(#2,#3)|subtract(const_1,#4)

so please : find the probability of the event thatnoneof the roads you pick will be at least 5 miles long and subtract from 1 to get the probability thatat least oneof the roads you pick will be at least 5 miles long : p = 1 - 1 / 3 * 1 / 4 = 11 / 12 . answer : e .

physics

math_qa__bRdGPUBsSWMDZ4fU

A sum of money is to be divided among Ann, Bob and Chloe. First, Ann receives $4 plus one-half of what remains. Next, Bob receives $4 plus one-third of what remains. Finally, Chloe receives the remaining $32. How much money T did Bob receive? Choose one. A) 20 B) 22 C) 24 D) 26 E) 52

<gadget id="calculator">32 * 2</gadget> <output>64</output> <gadget id="calculator">64 / 3</gadget> <output>64/3 = around 21.333333</output> <result>B</result>

B

A sum of money is to be divided among Ann, Bob and Chloe. First, Ann receives $4 plus one-half of what remains. Next, Bob receives $4 plus one-third of what remains. Finally, Chloe receives the remaining $32. How much money T did Bob receive?

divide(multiply(32, const_2), const_3)

multiply(n2,const_2)|divide(#0,const_3)|

"notice that we need not consider ann ' s portion in the solution . we can just let k = the money remaining after ann has received her portion and go from there . our equation will use the fact that , once we remove bob ' s portion , we have $ 32 for chloe . so , we getk - bob ' s $ = 32 bob received 4 dollars plus one - third of what remained once bob receives $ 4 , the amount remaining is k - 4 dollars . so , bob gets a 1 / 3 of that as well . 1 / 3 of k - 4 is ( k - 4 ) / 3 so altogether , bob receives 4 + ( k - 4 ) / 3 so , our equation becomes : k - [ 4 + ( k - 4 ) / 3 ] = 32 simplify to get : k - 4 - ( k - 4 ) / 3 = 32 multiply both sides by 3 to get : 3 k - 12 - k + 4 = 96 simplify : 2 k - 8 = 96 solve : k = 52 plug this k - value intok - bob ' s $ = 32 to get : 52 - bob ' s $ = 32 so , bob ' s $ t = 20 answer : b"

general

math_qa__8dfcDRwJm1F4VJaZ

Maxwell leaves his home and walks toward Brad's house at the same time that Brad leaves his home and runs toward Maxwell's house. If the distance between their homes is 40 kilometers, Maxwell's walking speed is 3 km/h, and Brad's running speed is 5 km/h. What is the distance traveled by Maxwell when they meet in the middle? Pick one: A) 16 B) 17 C) 18 D) 15 E) 14

<gadget id="calculator">3 + 5</gadget> <output>8</output> <gadget id="calculator">40 / 8</gadget> <output>5</output> <gadget id="calculator">3 * 5</gadget> <output>15</output> <result>D</result>

D

Maxwell leaves his home and walks toward Brad's house at the same time that Brad leaves his home and runs toward Maxwell's house. If the distance between their homes is 40 kilometers, Maxwell's walking speed is 3 km/h, and Brad's running speed is 5 km/h. What is the distance traveled by Maxwell when they meet in the middle?

multiply(3, divide(40, add(3, 5)))

add(n1,n2)|divide(n0,#0)|multiply(n1,#1)|

"consider max starts from point a and brad starts from point b and move towards each other . assume they shall meet at point o after time ' t ' . the question asks us to find oa . from the question stem we can make out : - distance oa = 50 km - distance ob = > 3 xt = 40 - 5 xt ( i . e distance = speed x time ) = > 8 t = 40 hence t = 5 oa = 3 x 5 = 15 km answer : d"

physics

math_qa__FAA2Jv7Q94TNmW1L

In a urban village of india named "owlna" , 70% people have refrigerator , 75% people have television , 65% people got computers and 95% got Air-conditionor. how many people(minimum) got all these luxury. Choose the correct answer A) 5 % B) 7 % C) 3 % D) 9 % E) 15 %

<gadget id="calculator">100 - 70</gadget> <output>30</output> <gadget id="calculator">100 - 75</gadget> <output>25</output> <gadget id="calculator">30 + 25</gadget> <output>55</output> <gadget id="calculator">100 - 65</gadget> <output>35</output> <gadget id="calculator">55 + 35</gadget> <output>90</output> <gadget id="calculator">100 - 95</gadget> <output>5</output> <gadget id="calculator">90 + 5</gadget> <output>95</output> <result>A</result>

A

In a urban village of india named "owlna" , 70% people have refrigerator , 75% people have television , 65% people got computers and 95% got Air-conditionor. how many people(minimum) got all these luxury.

subtract(const_100, add(add(add(subtract(const_100, 70), subtract(const_100, 75)), subtract(const_100, 65)), subtract(const_100, 95)))

subtract(const_100,n0)|subtract(const_100,n1)|subtract(const_100,n2)|subtract(const_100,n3)|add(#0,#1)|add(#4,#2)|add(#5,#3)|subtract(const_100,#6)

a 10 % 100 - [ ( 100 - 65 ) + ( 100 - 95 ) + ( 100 - 75 ) + ( 100 - 70 ) ] = 100 - ( 30 + 25 + 35 + 5 ) = 100 - 95

general

math_qa__q3t3OrovFNVXfp59

what will be the ci on a sum of rs . 25000 after 3 years at the rate of 12 per year ? Choose the correct choice from the following options: A) rs . 10100 B) rs . 10110 C) rs . 10123.20 D) rs . 10135.50 E) rs . 10167.20

<gadget id="calculator">12 / 100</gadget> <output>3/25 = around 0.12</output> <gadget id="calculator">(3/25) + 1</gadget> <output>28/25 = around 1.12</output> <gadget id="calculator">(28/25) ** 3</gadget> <output>21_952/15_625 = around 1.404928</output> <gadget id="calculator">(21_952/15_625) * 25_000</gadget> <output>175_616/5 = around 35_123.2</output> <gadget id="calculator">(175_616/5) - 25_000</gadget> <output>50_616/5 = around 10_123.2</output> <result>C</result>

C

what will be the ci on a sum of rs . 25000 after 3 years at the rate of 12 per year ?

subtract(multiply(power(add(divide(12, const_100), const_1), 3), 25000), 25000)

divide(n2,const_100)|add(#0,const_1)|power(#1,n1)|multiply(n0,#2)|subtract(#3,n0)

amount = rs . 25000 x 1 + 12 3 100 = rs . 25000 x 28 x 28 x 28 25 25 25 = rs . 35123.20 c . i . = rs . ( 35123.20 - 25000 ) = rs . 10123.20 c

gain

math_qa__aZOFLjBBj9Uk9rIC

A rectangular grass field is 85 m * 55 m, it has a path of 2.5 m wide all round it on the outside. Find the area of the path and the cost of constructing it at Rs.2 per sq m? Choose the correct choice: A) 1450 B) 1971 C) 9676 D) 1679 E) 2691

<gadget id="calculator">2.5 * 2</gadget> <output>5</output> <gadget id="calculator">85 + 5</gadget> <output>90</output> <gadget id="calculator">55 + 5</gadget> <output>60</output> <gadget id="calculator">90 * 60</gadget> <output>5_400</output> <gadget id="calculator">85 * 55</gadget> <output>4_675</output> <gadget id="calculator">5_400 - 4_675</gadget> <output>725</output> <gadget id="calculator">725 * 2</gadget> <output>1_450</output> <result>A</result>

A

A rectangular grass field is 85 m * 55 m, it has a path of 2.5 m wide all round it on the outside. Find the area of the path and the cost of constructing it at Rs.2 per sq m?

multiply(subtract(rectangle_area(add(85, multiply(2.5, 2)), add(55, multiply(2.5, 2))), rectangle_area(85, 55)), 2)

multiply(n2,n3)|rectangle_area(n0,n1)|add(n0,#0)|add(n1,#0)|rectangle_area(#2,#3)|subtract(#4,#1)|multiply(n3,#5)|

"area = ( l + b + 2 d ) 2 d = ( 85 + 55 + 2.5 * 2 ) 2 * 2.5 = > 725 725 * 2 = rs . 1450 answer : a"

geometry

math_qa__7e2npmGBxEX6Wmsn

Two trains are moving at 50 kmph and 70 kmph in opposite directions. Their lengths are 170 m and 100 m respectively. The time they will take to pass each other completely is? Choose the correct choice from the following answers. A) 3 sec B) 8 sec C) 9 sec D) 5 sec E) 7 sec

<gadget id="calculator">170 + 100</gadget> <output>270</output> <gadget id="calculator">50 + 70</gadget> <output>120</output> <gadget id="calculator">10 / 36</gadget> <output>5/18 = around 0.277778</output> <gadget id="calculator">120 * (5/18)</gadget> <output>100/3 = around 33.333333</output> <gadget id="calculator">270 / (100/3)</gadget> <output>81/10 = around 8.1</output> <result>B</result>

B

Two trains are moving at 50 kmph and 70 kmph in opposite directions. Their lengths are 170 m and 100 m respectively. The time they will take to pass each other completely is?

divide(add(170, 100), multiply(add(50, 70), const_0_2778))

add(n2,n3)|add(n0,n1)|multiply(#1,const_0_2778)|divide(#0,#2)|

"70 + 50 = 120 * 5 / 18 = 100 / 3 mps d = 170 + 100 = 270 m t = 270 * 3 / 100 = 8 sec answer : b"

physics

math_qa__fYU121eEKY1tARJz

Having scored 96 runs in the 19th inning, a cricketer increases his average score by 4. What will be his average score after 19 innings? Choose the correct choice: A) 28 B) 27 C) 26 D) 22 E) 24

<gadget id="calculator">19 * 4</gadget> <output>76</output> <gadget id="calculator">96 - 76</gadget> <output>20</output> <gadget id="calculator">20 + 4</gadget> <output>24</output> <result>E</result>

E

Having scored 96 runs in the 19th inning, a cricketer increases his average score by 4. What will be his average score after 19 innings?

add(subtract(96, multiply(19, 4)), 4)

multiply(n1,n2)|subtract(n0,#0)|add(n2,#1)|

"explanation : let the average score of the first 18 innings be n 18 n + 96 = 19 ( n + 4 ) = > n = 20 so , average score after 19 th innings = x + 4 = 24 . answer : e"

general

math_qa__bVcGwySmZhMRYaQo

What least number should be added to 1019, so that the sum is completely divisible by 25? Choose the correct choice from the following options: A) 4 B) 3 C) 2 D) 0 E) 6

<gadget id="calculator">1_019 % 25</gadget> <output>19</output> <gadget id="calculator">25 - 19</gadget> <output>6</output> <result>E</result>

E

What least number should be added to 1019, so that the sum is completely divisible by 25?

subtract(25, reminder(1019, 25))

reminder(n0,n1)|subtract(n1,#0)

1019 ã · 25 = 40 with remainder = 19 19 + 6 = 25 . hence 6 should be added to 1019 so that the sum will be divisible by 25 answer : option e

general

math_qa__sojG8AfAGNEJfTNz

In a school having roll strength 286, the ratio of boys and girls is 8:5. If 22 more girls get admitted into the school, the ratio of boys and girls becomes Select: A) 12 : 7 B) 10 : 7 C) 8 : 7 D) 4 : 3 E) none

<gadget id="calculator">8 + 5</gadget> <output>13</output> <gadget id="calculator">286 / 13</gadget> <output>22</output> <gadget id="calculator">22 * 8</gadget> <output>176</output> <gadget id="calculator">22 * 5</gadget> <output>110</output> <gadget id="calculator">110 + 22</gadget> <output>132</output> <gadget id="calculator">176 / 132</gadget> <output>4/3 = around 1.333333</output> <result>D</result>

D

In a school having roll strength 286, the ratio of boys and girls is 8:5. If 22 more girls get admitted into the school, the ratio of boys and girls becomes

divide(multiply(divide(286, add(8, 5)), 8), add(multiply(divide(286, add(8, 5)), 5), 22))

add(n1,n2)|divide(n0,#0)|multiply(n1,#1)|multiply(n2,#1)|add(n3,#3)|divide(#2,#4)

solution : boys : girls = 8 : 5 ; ( let the boys = 8 x ; girl = 5 x ) total strength = 286 ; 8 x + 5 x = 286 ; 13 x = 286 ; or , x = 286 / 13 = 22 ; boys = 176 and girls = 110 ; 22 more girls get admitted then number of girls become , ( 5 x + 22 ) = 110 + 22 = 132 ; now , new ratio of boys and girls = 176 : 132 = 4 : 3 . answer : option d

other

math_qa__Fu98p3Xe1Ov5VNUo

The ratio of sum of squares of first n natural numbers to square of sum of first n natural numbers is 17:325. the value of n is Choose the correct choice: A) 15 B) 25 C) 35 D) 30 E) none of these

<gadget id="calculator">325 + 100</gadget> <output>425</output> <gadget id="calculator">425 / 17</gadget> <output>25</output> <result>B</result>

B

The ratio of sum of squares of first n natural numbers to square of sum of first n natural numbers is 17:325. the value of n is

divide(add(325, const_100), 17)

add(n1,const_100)|divide(#0,n0)

sum of 1 st n natural no . s is n ( n + 1 ) / 2 , sum of sqaures of 1 st n natural no . s is n ( n + 1 ) ( 2 n + 1 ) / 6 , the ratio of sum of squares of first n natural numbers to square of sum of first n natural numbers = n ( n + 1 ) ( 2 n + 1 ) * 2 * 2 / ( n * n * ( n + 1 ) * ( n + 1 ) ) = 2 ( 2 n + 1 ) / ( 3 n ( n + 1 ) ) now by hit and trial for the given options , if we put 25 then this will give 17 / 325 therefore the answer is 25 answer : b

other

math_qa__IUjL8lMB5Pg5knJr

A man is walking at a speed of 10 km per hour. After every kilometre, he takes rest for 5 minutes. How much time will be take to cover a distance of 5 kilometres? Choose the correct choice from the following: A) 48 min . B) 50 min . C) 45 min . D) 55 min . E) none of these

<gadget id="calculator">5 / 10</gadget> <output>1/2 = around 0.5</output> <gadget id="calculator">60 / 1</gadget> <output>60</output> <gadget id="calculator">(1/2) * 60</gadget> <output>30</output> <gadget id="calculator">4 * 5</gadget> <output>20</output> <gadget id="calculator">30 + 20</gadget> <output>50</output> <result>B</result>

B

A man is walking at a speed of 10 km per hour. After every kilometre, he takes rest for 5 minutes. How much time will be take to cover a distance of 5 kilometres?

add(multiply(divide(5, 10), speed(const_60, const_1)), multiply(const_4, 5))

divide(n1,n0)|multiply(n1,const_4)|speed(const_60,const_1)|multiply(#0,#2)|add(#3,#1)

rest time = number of rest × time for each rest = 4 × 5 = 20 minutes total time to cover 5 km = ( 5 ⁄ 10 × 60 ) minutes + 20 minutes = 50 minutes answer b

physics

math_qa__uWrgdRL9XUe17kYR

An error 4% in excess is made while measuring the side of a square. The percentage of error in the calculated area of the square is Choose one A) 8.04 % B) 8.14 % C) 8.23 % D) 8.16 % E) 8.5 %

<gadget id="calculator">100 + 4</gadget> <output>104</output> <gadget id="calculator">104 ** 2</gadget> <output>10_816</output> <gadget id="calculator">100 ** 2</gadget> <output>10_000</output> <gadget id="calculator">10_816 - 10_000</gadget> <output>816</output> <gadget id="calculator">816 * 100</gadget> <output>81_600</output> <gadget id="calculator">81_600 / 10_000</gadget> <output>204/25 = around 8.16</output> <result>D</result>

D

An error 4% in excess is made while measuring the side of a square. The percentage of error in the calculated area of the square is

divide(multiply(subtract(square_area(add(const_100, 4)), square_area(const_100)), const_100), square_area(const_100))

add(n0,const_100)|square_area(const_100)|square_area(#0)|subtract(#2,#1)|multiply(#3,const_100)|divide(#4,#1)|

"100 cm is read as 102 cm . a 1 = ( 100 x 100 ) cm 2 and a 2 ( 102 x 102 ) cm 2 . ( a 2 - a 1 ) = [ ( 104 ) 2 - ( 100 ) 2 ] = ( 104 + 100 ) x ( 104 - 100 ) = 816 cm 2 . percentage error = 8.16 d"

gain

math_qa__tOoq7OXXzIvD2mVB

Harkamal purchased 8kg of grapes at the rate of 70 per kg and 9 kg of mangoes at the rate of 55 per kg. How much amount did he pay to the shopkeeper? Choose the correct choice from the following answers: A) 1000 B) 1055 C) 1065 D) 1075 E) 1080

<gadget id="calculator">8 * 70</gadget> <output>560</output> <gadget id="calculator">9 * 55</gadget> <output>495</output> <gadget id="calculator">560 + 495</gadget> <output>1_055</output> <result>B</result>

B

Harkamal purchased 8kg of grapes at the rate of 70 per kg and 9 kg of mangoes at the rate of 55 per kg. How much amount did he pay to the shopkeeper?

add(multiply(8, 70), multiply(9, 55))

multiply(n0,n1)|multiply(n2,n3)|add(#0,#1)|

"cost of 8 kg grapes = 70 × 8 = 560 . cost of 9 kg of mangoes = 55 × 9 = 490 . total cost he has to pay = 560 + 490 = 1055 . b )"

gain

math_qa__BXC1Yr92dBLoonzN

A man started driving at a constant speed, from the site of a blast, the moment he heard the blast. He heard a second blast after a time of 30 mins and 12 seconds. If the second blast occurred exactly 30 mins after the first, how many meters was he from the site when he heard the second blast? ( speed of sound = 330 m/s) Choose the correct option. A) 3120 B) 3330 C) 3540 D) 3750 E) 3960

<gadget id="calculator">330 * 12</gadget> <output>3_960</output> <result>E</result>

E

A man started driving at a constant speed, from the site of a blast, the moment he heard the blast. He heard a second blast after a time of 30 mins and 12 seconds. If the second blast occurred exactly 30 mins after the first, how many meters was he from the site when he heard the second blast? ( speed of sound = 330 m/s)

multiply(330, 12)

multiply(n1,n3)|

"the distance the sound traveled to the man is 12 * 330 = 3960 meters the answer is e ."

physics

math_qa__p7Ff28aHjbrc9b82

A train leaves Delhi at 9 a.m. at a speed of 30 kmph. Another train leaves at 2 p.m. at a speed of 40 kmph on the same day and in the same direction. How far from Delhi, will the two trains meet? Select the correct option. A) 900 km B) 800 km C) 600 km D) 690 km E) 609 km

<gadget id="calculator">3 + 2</gadget> <output>5</output> <gadget id="calculator">30 * 5</gadget> <output>150</output> <gadget id="calculator">40 - 30</gadget> <output>10</output> <gadget id="calculator">150 / 10</gadget> <output>15</output> <gadget id="calculator">15 * 40</gadget> <output>600</output> <result>C</result>

C

A train leaves Delhi at 9 a.m. at a speed of 30 kmph. Another train leaves at 2 p.m. at a speed of 40 kmph on the same day and in the same direction. How far from Delhi, will the two trains meet?

multiply(divide(multiply(30, add(const_3, const_2)), subtract(40, 30)), 40)

add(const_2,const_3)|subtract(n3,n1)|multiply(n1,#0)|divide(#2,#1)|multiply(n3,#3)

explanation : d = 30 * 5 = 150 rs = 40 – 30 = 10 t = 150 / 10 = 15 d = 40 * 15 = 600 km answer : option c

physics

math_qa__MS2xo5zHlGecgOJO

A 5% stock yields 10%. The market value of the stock is: Choose the most appropriate option A) rs . 56 B) rs . 55 C) rs . 50 D) rs . 90 E) rs . 75

<gadget id="calculator">100 / 10</gadget> <output>10</output> <gadget id="calculator">10 * 5</gadget> <output>50</output> <result>C</result>

C

A 5% stock yields 10%. The market value of the stock is:

multiply(divide(const_100, 10), 5)

divide(const_100,n1)|multiply(n0,#0)|

"explanation : for an income of rs . 10 , investment = rs . 100 . for an income of rs 5 , investment = rs . 100 / 10 x 5 = rs 50 market value of rs . 100 stock = rs . 50 answer is c"

gain

math_qa__7UoeINrKVBkfOKIR

A train 120 m long passes a man,running at 6 kmph in the direction opposite to that of the train,in 6 seconds.The speed of the train is Choose the correct choice from the following answers: A) 54 kmph B) 60 kmph C) 66 kmph D) 72 kmph E) 82 kmph

<gadget id="calculator">10 / 36</gadget> <output>5/18 = around 0.277778</output> <gadget id="calculator">6 * (5/18)</gadget> <output>5/3 = around 1.666667</output> <gadget id="calculator">(5/3) * 6</gadget> <output>10</output> <gadget id="calculator">120 - 10</gadget> <output>110</output> <gadget id="calculator">110 / 6</gadget> <output>55/3 = around 18.333333</output> <gadget id="calculator">(55/3) / (5/18)</gadget> <output>66</output> <result>C</result>

C

A train 120 m long passes a man,running at 6 kmph in the direction opposite to that of the train,in 6 seconds.The speed of the train is

divide(divide(subtract(120, multiply(multiply(6, const_0_2778), 6)), 6), const_0_2778)

multiply(n1,const_0_2778)|multiply(n1,#0)|subtract(n0,#1)|divide(#2,n1)|divide(#3,const_0_2778)|

"speed of train relative to man : 120 / 6 * 18 / 5 km / hr = 72 km / hr let speed of train = x therefore x + 6 = 72 x = 72 - 6 x = 66 km / hr answer : c"

physics

math_qa__Tm2ogpySDSm8TWPw

Every day Daniel drives 64 miles back from work. On Sunday, Daniel drove all the way back from work at a constant speed of x miles per hour. On Monday, Daniel drove the first 32 miles back from work at (2x) miles per hour, and the rest of the way at (x/2) miles per hour. The time it took Daniel to drive back from work on Monday is longer than the time it took him to drive back from work on Sunday by what percent? Choose the correct choice from the following choices: A) 15 % B) 25 % C) 35 % D) 45 % E) 55 %

<gadget id="calculator">32 / 2</gadget> <output>16</output> <gadget id="calculator">64 - 32</gadget> <output>32</output> <gadget id="calculator">32 * 2</gadget> <output>64</output> <gadget id="calculator">16 + 64</gadget> <output>80</output> <gadget id="calculator">80 - 64</gadget> <output>16</output> <gadget id="calculator">16 / 64</gadget> <output>1/4 = around 0.25</output> <gadget id="calculator">(1/4) * 100</gadget> <output>25</output> <result>B</result>

B

Every day Daniel drives 64 miles back from work. On Sunday, Daniel drove all the way back from work at a constant speed of x miles per hour. On Monday, Daniel drove the first 32 miles back from work at (2x) miles per hour, and the rest of the way at (x/2) miles per hour. The time it took Daniel to drive back from work on Monday is longer than the time it took him to drive back from work on Sunday by what percent?

multiply(divide(subtract(add(divide(32, 2), multiply(subtract(64, 32), 2)), 64), 64), const_100)

divide(n1,n2)|subtract(n0,n1)|multiply(#1,n2)|add(#0,#2)|subtract(#3,n0)|divide(#4,n0)|multiply(#5,const_100)|

"let ' s test x = 4 . . . . on sunday , daniel drove 64 miles at 4 miles / hour . d = ( r ) ( t ) 64 = ( 4 ) ( t ) 64 / 4 = 16 = t it takes 16 hours to drive home on monday , daniel drove the first 32 miles at ( 2 ) ( 4 ) = 8 miles / hour and the rest of the way ( 32 miles ) at 4 / 2 = 2 miles / hour d = ( r ) ( t ) 32 = ( 8 ) ( t ) 32 / 8 = 4 = t it takes 4 hours for the first part d = ( r ) ( t ) 32 = ( 2 ) ( t ) 32 / 2 = 16 = t it takes 16 hours for the second part total time to drive home on monday = 4 + 16 = 20 hours we ' re asked by what percent 20 hours is greater than 16 hours . 20 / 16 = 1.25 , so it is 25 % greater . b"

physics

math_qa__CoJURgyLfytiaLex

The diagonal of a rhombus are 25 m and 50 m. Its area is: Pick one A) 900 B) 800 C) 700 D) 625 E) 650

<gadget id="calculator">(25 * 50) / 2</gadget> <output>625</output> <result>D</result>

D

The diagonal of a rhombus are 25 m and 50 m. Its area is:

rhombus_area(25, 50)

rhombus_area(n0,n1)|

"area of the rhombus = 1 / 2 d 1 d 2 = ( 1 / 2 ã — 25 ã — 50 ) cm ( power ) 2 = 25 ã — 25 = 625 cm ( power ) 2 answer is d ."

geometry

math_qa__hmdITvxAeBTVIICS

The diameter of a cylindrical tin is 14cm and height is 5 cm. Find the volume of the cylinder? Choices A) 230 B) 141 C) 66 D) 245 E) 21

<gadget id="calculator">14 / 2</gadget> <output>7</output> <gadget id="calculator">pi * (7 ** 2) * 5</gadget> <output>245*pi = around 769.6902</output> <gadget id="calculator">(245*pi) / pi</gadget> <output>245</output> <result>D</result>

D

The diameter of a cylindrical tin is 14cm and height is 5 cm. Find the volume of the cylinder?

divide(volume_cylinder(divide(14, const_2), 5), const_pi)

divide(n0,const_2)|volume_cylinder(#0,n1)|divide(#1,const_pi)|

"r = 7 h = 5 π * 7 * 7 * 5 = 45 π cc answer : d"

geometry

math_qa__SVrYU7ITBnqOju6n

If 40 men take 15 days to to complete a job, in how many days can 25 men finish that work? Options: A) 24 B) 25 C) 26 D) 27 E) 28

<gadget id="calculator">40 * 15</gadget> <output>600</output> <gadget id="calculator">600 / 25</gadget> <output>24</output> <result>A</result>

A

If 40 men take 15 days to to complete a job, in how many days can 25 men finish that work?

divide(multiply(40, 15), 25)

multiply(n0,n1)|divide(#0,n2)|

ans . 24 days

physics

math_qa__FylexBzgQwoZM3pI

It takes printer A 4 more minutes more than printer B to print 40 pages. Working together, the two printers can print 50 pages in 6 minutes. How long will it take Printer A to print 160 pages? Select the correct option: A) 12 B) 18 C) 48 D) 20 E) 30

<gadget id="calculator">4 * 2</gadget> <output>8</output> <gadget id="calculator">8 + 4</gadget> <output>12</output> <gadget id="calculator">160 * 12</gadget> <output>1_920</output> <gadget id="calculator">1_920 / 40</gadget> <output>48</output> <result>C</result>

C

It takes printer A 4 more minutes more than printer B to print 40 pages. Working together, the two printers can print 50 pages in 6 minutes. How long will it take Printer A to print 160 pages?

divide(multiply(160, add(multiply(4, const_2), 4)), 40)

multiply(n0,const_2)|add(n0,#0)|multiply(n4,#1)|divide(#2,n1)

if it takes 4 more minutes for a to print 40 pages than it takes b , it takes 5 more minutes for a to print 50 pages than it takes b . thus if b is the number of minutes than b takes to print 50 pages , we can write : 1 / b + 1 / ( b + 5 ) = 1 / 6 ( since in 1 minute , they print 1 / 6 th of the 50 page job ) 6 ( 2 b + 5 ) = b ( b + 5 ) b ^ 2 - 7 b - 30 = 0 ( b - 10 ) ( b + 3 ) = 0 b = 10 thus it takes a 15 minutes to print 50 pages and 15 * 160 / 50 = 48 minutes to print 160 pages ( answer c )

physics

math_qa__ppvyBt7KFUpljyMn

Find the cost of fencing around a circular field of diameter 22 m at the rate of Rs.3 a meter? Pick one A) 288 B) 132 C) 772 D) 207.3 E) 261

<gadget id="calculator">22 / 2</gadget> <output>11</output> <gadget id="calculator">2 * pi * 11</gadget> <output>22*pi = around 69.115038</output> <gadget id="calculator">(22*pi) * 3</gadget> <output>66*pi = around 207.345115</output> <result>D</result>

D

Find the cost of fencing around a circular field of diameter 22 m at the rate of Rs.3 a meter?

multiply(circumface(divide(22, const_2)), 3)

divide(n0,const_2)|circumface(#0)|multiply(n1,#1)|

"2 * 22 / 7 * 11 = 69.1 69.1 * 3 = rs . 207.3 answer : d"

physics

math_qa__CQ4GoDVgDlzujk7z

There are 6 people in the elevator. Their average weight is 156 lbs. Another person enters the elevator, and increases the average weight to 151 lbs. What is the weight of the 7th person. Select A) 121 B) 168 C) 189 D) 190 E) 200

<gadget id="calculator">151 * 7</gadget> <output>1_057</output> <gadget id="calculator">6 * 156</gadget> <output>936</output> <gadget id="calculator">1_057 - 936</gadget> <output>121</output> <result>A</result>

A

There are 6 people in the elevator. Their average weight is 156 lbs. Another person enters the elevator, and increases the average weight to 151 lbs. What is the weight of the 7th person.

subtract(multiply(151, 7), multiply(6, 156))

multiply(n2,n3)|multiply(n0,n1)|subtract(#0,#1)

solution average of 7 people after the last one enters = 151 . â ˆ ´ required weight = ( 7 x 151 ) - ( 6 x 156 ) = 1057 - 936 = 121 . answer a

general

math_qa__5rxD2muohCwwTJtJ

Each child has 2 pencils and 13 Skittles. If there are 15 children, how many pencils are there in total? Choose the correct choice from the following choices. A) 30 B) 12 C) 18 D) 22 E) 08

<gadget id="calculator">2 * 15</gadget> <output>30</output> <result>A</result>

A

Each child has 2 pencils and 13 Skittles. If there are 15 children, how many pencils are there in total?

multiply(2, 15)

multiply(n0,n2)

2 * 15 = 30 . answer is a .

general