MU-NLPC/calcformer-t5-large
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aqua_rat__TeUuCx2QFEzwmZzg | Two friends plan to walk along a 43-km trail, starting at opposite ends of the trail at the same time. If Friend P's rate is 15% faster than Friend Q's, how many kilometers will Friend P have walked when they pass each other? Pick one:
A) 21 B) 21.5 C) 22 D) 22.5 E) 23 | If Q complete x kilometers, then P completes 1.15x kilometers. x + 1.15x = 43 2.15x=43 x = 43/2.15=
<gadget id="calculator">43/2.15</gadget>
<output>20</output>
20 Then P will have have walked 1.15*20=
<gadget id="calculator"> 1.15*20</gadget>
<output>23</output>
23 km. The answer is 23.
<result>E</result> | E | {
"A": "21",
"B": "21.5",
"C": "22",
"D": "22.5",
"E": "23"
} | Two friends plan to walk along a 43-km trail, starting at opposite ends of the trail at the same time. If Friend P's rate is 15% faster than Friend Q's, how many kilometers will Friend P have walked when they pass each other? |
aqua_rat__d1N8uAzKGBWh9sVZ | In the coordinate plane, points (x, 1) and (5, y) are on line k. If line k passes through the origin and has slope 1/5, then what are the values of x and y respectively? Answers.
A) 4 and 1 B) 1 and 5 C) 5 and 1 D) 3 and 5 E) 5 and 3 | Line k passes through the origin and has slope 1/5 means that its equation is y=1/5*x. Thus: (x, 1)=(5, 1) and (5, y) = (5,1) -->x=5 and y=1 Answer: 5 and 1
<result>C</result> | C | {
"A": "4 and 1",
"B": "1 and 5",
"C": "5 and 1",
"D": "3 and 5",
"E": "5 and 3"
} | In the coordinate plane, points (x, 1) and (5, y) are on line k. If line k passes through the origin and has slope 1/5, then what are the values of x and y respectively? |
aqua_rat__Ku26s7LMkFHGZjga | For all numbers p and q, the operation @ is defined by p@q = p^2 - pq. If xy ≠ 0, then which of the following can be equal to zero?
I. x@y
II. (xy)@y
III. x@(x + y) Choose the correct choice from the following options.
A) II B) I and II C) I and III D) II and III E) All of the above | p@q = p^2 - pq=p(p-q).... so p@q will be zero if p=q or p=0.. but a cannot be equal to 0.. as per Q, x and y can take any int value except 0... now lets look at the choices.. when x=y, it will be 0... so ok... when we put xy=y, it is possible when x=1 and y any integer... so ok again when we put x=x+y.... only possibility when y=0 and it is given x and y cannot be 0....so not possible only l and ll possible ans I and II....
<result>B</result> | B | {
"A": "II",
"B": "I and II",
"C": "I and III",
"D": "II and III",
"E": "All of the above"
} | For all numbers p and q, the operation @ is defined by p@q = p^2 - pq. If xy ≠ 0, then which of the following can be equal to zero?
I. x@y
II. (xy)@y
III. x@(x + y) |
aqua_rat__mMVjT0dId80oSABw | Carl is facing very difficult financial times and can only pay the interest on a $10,000 loan he has taken. The bank charges him a quarterly compound rate of 4%. What is the approximate interest he pays annually? Pick.
A) $1600 B) $2000 C) $2150 D) $2500 E) $12000 | Usually, you are given the annual rate of interest and it is mentioned that it is annual rate. The bank charges him a quarterly compounded ANNUAL rate of 16%. Here you find per quarter rate as (16/4)=
<gadget id="calculator"> (16/4)</gadget>
<output>4</output>
4% I have actually never seen a question with quarter rate given but since this question did not mentionannual rate of interestand since the options did not make sense with 4% annual rate of interest, it is apparent that the intent was a 4% quarterly rate. So the bank charges 4% every quarter and compounds it in the next quarter. Had it been a simple quarterly rate, we would have just found 4 * 4% of 10,000= $1600 as our answer. But since, the interest is compounded, it will be a bit more than $1600. Option ($1600) looks correct.
<result>A</result> | A | {
"A": "$1600",
"B": "$2000",
"C": "$2150",
"D": "$2500",
"E": "$12000"
} | Carl is facing very difficult financial times and can only pay the interest on a $10,000 loan he has taken. The bank charges him a quarterly compound rate of 4%. What is the approximate interest he pays annually? |
aqua_rat__zJXUL7KMKxsygmfH | The speed at which a man can row a boat in still water is 25 kmph. If he rows downstream, where the speed of current is 11 kmph, what time will he take to cover 80 metres? Choose the correct choice from the following options
A) 18 seconds
B) 27 seconds
C) 26 seconds
D) 12 seconds
E) 8 seconds | Speed of the boat downstream = 25 +11=
<gadget id="calculator">25 +11</gadget>
<output>36</output>
36 kmph= 36 * 5/18=
<gadget id="calculator">36 * 5/18</gadget>
<output>10</output>
10 m/s Hence time taken to cover 80 m= 80/10=
<gadget id="calculator">80/10</gadget>
<output>8</output>
8 seconds. Answer:8 seconds
<result>E</result> | E | {
"A": "18 seconds",
"B": "27 seconds",
"C": "26 seconds",
"D": "12 seconds",
"E": "8 seconds"
} | The speed at which a man can row a boat in still water is 25 kmph. If he rows downstream, where the speed of current is 11 kmph, what time will he take to cover 80 metres? |
aqua_rat__RXYewtShMyFutPvN | There are k-2 members in a certain band, including Jim and Ellen. Two members are to be selected to attend the Grammy awards ceremony. If there are 6 possible combinations in which Jim and Ellen are not selected, what is the value of k? Options
A) 8
B) 9
C) 10
D) 11
E) 12 | There are k-2 members in the band, and k-4 members without Jim and Ellen. (k-4)C2 = 6 (k-4)(k-5)/2 = 6 (k-4)(k-5) = 12 = 4*3 k = 8 The answer is 8.
<result>A</result> | A | {
"A": "8",
"B": "9",
"C": "10",
"D": "11",
"E": "12"
} | There are k-2 members in a certain band, including Jim and Ellen. Two members are to be selected to attend the Grammy awards ceremony. If there are 6 possible combinations in which Jim and Ellen are not selected, what is the value of k? |
aqua_rat__nOz1TNhsGLvSkda3 | If (x^2 + 4x - 11)/5 ≤ x + 1, then x could be represented by which of the following? Choose the most appropriate option:
A) − 3 ≤ x ≤ 4
B) − 4 ≤ x ≤ 3
C) − 3 ≤ x ≤ 3
D) − 4 ≤ x ≤ − 3
E) 3 ≤ x ≤ 4 | IMO − 3 ≤ x ≤ 4 is correct answer solving through eqautions x^2 +4x-11<= 5x+5 (x+3)(x-4)<=0
<result>A</result> | A | {
"A": "− 3 ≤ x ≤ 4",
"B": "− 4 ≤ x ≤ 3",
"C": "− 3 ≤ x ≤ 3",
"D": "− 4 ≤ x ≤ − 3",
"E": "3 ≤ x ≤ 4"
} | If (x^2 + 4x - 11)/5 ≤ x + 1, then x could be represented by which of the following? |
aqua_rat__b5D8hplUgG9PfYCV | Find the smallest number of five digits exactly divisible by 22,33,66 and 44. Pick one
A) 10101 B) 11000 C) 10110 D) 10111 E) 10100 | Smallest number of five digits is 10000. Required number must be divisible by L.C.M. of 22,33,66,44 i.e 132, On dividing 10000 by 132,we get 32 as remainder. Therefore, Required number = 10000 +( 132 – 32 ) = 10100. Answer is 10100.
<result>E</result> | E | {
"A": "10101",
"B": "11000",
"C": "10110",
"D": "10111",
"E": "10100"
} | Find the smallest number of five digits exactly divisible by 22,33,66 and 44. |
aqua_rat__EMBH4aTeKLdjZHsH | The entrance fee for a fair is $5 for persons under the age of 18, and 20% more for persons older. Each ride at the fair costs $0.50. If Joe goes with her 6 years old twin brothers, and they each took 3 rides in total. How much money does Joe end up spending at the fair?
Choose the correct choice:
A) 16 B) 20.5 C) 17.5 D) 20 E) 4.5 | Total entrance fee is (2*$5) + (1.20*5)= $16 Total rides fee is (0.50*3)*3(2* 5) + (1.20*5)=
<gadget id="calculator">(2* 5) + (1.20*5)</gadget>
<output>16</output>
$16 Total rides fee is (0.50*3)*3=
<gadget id="calculator"> (0.50*3)*3</gadget>
<output>4.5</output>
$4.50 Total money spent is $20.50 Answer is 20.5
<result>B</result> | B | {
"A": "16",
"B": "20.5",
"C": "17.5",
"D": "20",
"E": "4.5"
} | The entrance fee for a fair is $5 for persons under the age of 18, and 20% more for persons older. Each ride at the fair costs $0.50. If Joe goes with her 6 years old twin brothers, and they each took 3 rides in total. How much money does Joe end up spending at the fair? |
aqua_rat__s1dS8YePCNjS8nhc | If X and Y are digits and 8XY is a 3-digit number that is divisible by 2, which of the following is a possible product of X and Y? Choose the correct choice from the following answers
A) 15 B) 31 C) 12 D) 27 E) 91 | Key to this question is to remember the fact that a number divisible by 2 must end with even OR 0 (i.e Y). If Y had to be 0, product should also be 0 regardless of X. Otherwise, product is a multiple of 2. Only one answer choice meets the requirement. Ans 12.
<result>C</result> | C | {
"A": "15",
"B": "31",
"C": "12",
"D": "27",
"E": "91"
} | If X and Y are digits and 8XY is a 3-digit number that is divisible by 2, which of the following is a possible product of X and Y? |
aqua_rat__Tj3IgP3myYtguBSU | If Tim had lunch at $50 and he gave 20% tip, how much did he spend?
Choose the correct option: A) A)$60.00 B) B)$35.42 C) C)$60.60 D) D)$21.56 E) E)$78.45 | The tip is 20% of what he paid for lunch. tip = 20% of 50.00 = (20/100)*50.00 = = $10.00 Total spent 50.00 + 10.00=
<gadget id="calculator"> 50.00 + 10.00</gadget>
<output>60</output>
$60.00 correct answer is $60.00)$60.00
<result>A</result> | A | {
"A": "A)$60.00",
"B": "B)$35.42",
"C": "C)$60.60",
"D": "D)$21.56",
"E": "E)$78.45"
} | If Tim had lunch at $50 and he gave 20% tip, how much did he spend? |
aqua_rat__kDNBILqRl9FheIjb | Rs. 825 becomes Rs. 956 in 3 years at a certain rate of simple interest.If the rate of interest is increased by 4% ,What amount will Rs. 825 become in 3 years ? Choices:
A) Rs. 1020.80 B) Rs. 1025 C) Rs. 1055 D) Data inadequate E) None of these | Solution S.I. = Rs.(956-825 )=Rs.131 Rate = (100x131/825x3) = 524/99% New rate = (524/99 +4)% = 920/99% New S.I. = Rs.(825 x 920/99 x 3/100) Rs. 230. ∴ New amount = Rs.(825+230)= Rs. 1055. Answer Rs. 1055
<result>C</result> | C | {
"A": "Rs. 1020.80",
"B": "Rs. 1025",
"C": "Rs. 1055",
"D": "Data inadequate",
"E": "None of these"
} | Rs. 825 becomes Rs. 956 in 3 years at a certain rate of simple interest.If the rate of interest is increased by 4% ,What amount will Rs. 825 become in 3 years ? |
aqua_rat__DgQuuFj2Bk6OYv4X | q is a positive integer and multiple of 2; p = 4^q, what is the remainder when p is divided by 10? Answers
A) 10
B) 6
C) 4
D) 0
E) It Cannot Be Determined | It is essential to recognize that the remainder when an integer is divided by 10 is simply the units digit of that integer. To help see this, consider the following examples: 4/10 is 0 with a remainder of 4 14/10 is 1 with a remainder of 4 5/10 is 0 with a remainder of 5 105/10 is 10 with a remainder of 5 It is also essential to remember that the q is a positive integer and multiple of 2. Any integer that is a multiple of 2 is an even number. So, q must be a positive even integer. With these two observations, the question can be simplified to:what is the units digit of 4 raised to an even positive integer? The units digit of 4 raised to an integer follows a specific repeating pattern: 4^1 = 4 4^2 = 16 4^3 = 64 4^4 = 256 4^(odd number) --> units digit of 4 4^(even number) --> units digit of 6 There is a clear pattern regarding the units digit. 4 raised to any odd integer has a units digit of 4 while 4 raised to any even integer has a units digit of 6. Since q must be an even integer, the units digit of p=4^q will always be 6. Consequently, the remainder when p=4^q is divided by 10 will always be 6. In case this is too theoretical, consider the following examples: q=2 --> p=4^q=16 --> p/10 = 1 with a remainder of 6 q=4 --> p=4^q=256 --> p/10 = 25 with a remainder of 6 q=6 --> p=4^q=4096 --> p/10 = 409 with a remainder of 6 q=8 --> p=4^q=65536 --> p/10 = 6553 with a remainder of 6 Answer: 6.
<result>B</result> | B | {
"A": "10",
"B": "6",
"C": "4",
"D": "0",
"E": "It Cannot Be Determined"
} | q is a positive integer and multiple of 2; p = 4^q, what is the remainder when p is divided by 10? |
aqua_rat__QoR7AAVHtUiIqufg | If q is the square of a positive integer, which of the following must be equal to the square of the next positive integer?
Choose the correct choice from the following answers:
A) √n + 1
B) n + 1
C) n^2 + 1
D) q + 2√q + 1
E) n^2 + 2n + 1 | If q is the square of a positive integer, which of the following must be equal to the square of the next positive integer? q = (x)^2 where x is a positive integer To calculate - (x+1)^2 = x^2 + 2x + 1 root(q) = x Ans - q + 2 root(q) + 1 This should be q + 2√q + 1
<result>D</result> | D | {
"A": "√n + 1",
"B": "n + 1",
"C": "n^2 + 1",
"D": "q + 2√q + 1",
"E": "n^2 + 2n + 1"
} | If q is the square of a positive integer, which of the following must be equal to the square of the next positive integer? |
aqua_rat__Das8qgSicXo34jBU | Rs. 5600 is divided into three parts A, B and C. How much A is more than C if their ratio is 1/7:1/7:1/14? Choose the correct choice:
A) 300 B) 992 C) 1120 D) 552 E) 312 | 1/7:1/7:1/14 = 2:2:1 1/5*5600=
<gadget id="calculator">1/5*5600</gadget>
<output>1_120</output>
1120 2240-1120=
<gadget id="calculator">2240-1120</gadget>
<output>1_120</output>
1120 Answer: 1120
<result>C</result> | C | {
"A": "300",
"B": "992",
"C": "1120",
"D": "552",
"E": "312"
} | Rs. 5600 is divided into three parts A, B and C. How much A is more than C if their ratio is 1/7:1/7:1/14? |
aqua_rat__FoYU5HMC6nL50Rfi | If a/b=3/4 and 8a+5b=22,then find the value of a. Select: A) 1/2 B) 3/2 C) 5/2 D) 4/2 E) 7/2 | (a/b)=3/4 b=(4/3) a. Therefore, 8a+5b=22 = 8a+5*(4/3) a=22 8a+(20/3) a=22 =44a = 66 = a=(66/44)=3/2 Answer is 3/2.
<result>B</result> | B | {
"A": "1/2",
"B": "3/2",
"C": "5/2",
"D": "4/2",
"E": "7/2"
} | If a/b=3/4 and 8a+5b=22,then find the value of a. |
aqua_rat__M0dbyrMEZitBL40m | Given that k/l < 1, and both k and l are positive integers, which one of the following must be greater than 1?
Choose the correct choice from the following:
A) k/l^2
B) k^2/l
C) k^2/l^2
D) l/k
E) √(k/l) | Since k/l is a fraction l must always be > 1 Given - Which one of the following must be greater than 1 We can get the result one only when the denominator in k/l ( Which is less than 1 ) becomes numerator.. Among the given options only (D) has the required characteristic we are looking for... Hence answer will be (l/k)
<result>D</result> | D | {
"A": "k/l^2",
"B": "k^2/l",
"C": "k^2/l^2",
"D": "l/k",
"E": "√(k/l)"
} | Given that k/l < 1, and both k and l are positive integers, which one of the following must be greater than 1? |
aqua_rat__B93wo8aZsDiGVU96 | Mike took 5 mock tests before appearing for the GMAT. In each mock test he scored 10 points more than the previous mock test. If he scored 760 on the GMAT and his average score for the mocks and the GMAT was 716.67, what was the difference in the score of his last mock and his GMAT score? Choices.
A) 20
B) 32
C) 40
D) 50
E) 60 | One way to do this would be weighted average method.. 1) let the average of 5 mocks be x... so take it as a mix of5 quantitites of xand1 quantity of 760resulting in an average of 716.67... By alligation/weighted average.. the difference in 760 and 716.67 is 5/6 of difference of 760 and x.. 760-716.67 = 5/6 * (760-x) 760-x= 43.33*6/5=52... so x = 708.. the last of mock test will be 708+10+10=728... so ans = 760-728=
<gadget id="calculator">760-728</gadget>
<output>32</output>
32 32
<result>B</result> | B | {
"A": "20",
"B": "32",
"C": "40",
"D": "50",
"E": "60"
} | Mike took 5 mock tests before appearing for the GMAT. In each mock test he scored 10 points more than the previous mock test. If he scored 760 on the GMAT and his average score for the mocks and the GMAT was 716.67, what was the difference in the score of his last mock and his GMAT score? |
aqua_rat__JeU9gdDQDMnciKFi | John found that the average of 15 numbers is 40. If 10 is added to each number then the mean of number is?
Choose the correct choice from the following.
A) 50 B) 45 C) 65 D) 78 E) 64 | (x+x1+...x14)/15 = 40 50 Option 50
<result>A</result> | A | {
"A": "50",
"B": "45",
"C": "65",
"D": "78",
"E": "64"
} | John found that the average of 15 numbers is 40. If 10 is added to each number then the mean of number is? |
aqua_rat__6kG2wFRZjD9SkRT8 | A person is traveling at 20 km/hr and reached his destiny in 2.5 hr then find the distance? Choose the correct answer
A) 53 km B) 55 km C) 52 km D) 60 km E) 50 km | T = 2.5 hrs = 5/2 hrs D= T*S = 20*5/2=
<gadget id="calculator">20*5/2</gadget>
<output>50</output>
50 km Answer is 50 km
<result>E</result> | E | {
"A": "53 km",
"B": "55 km",
"C": "52 km",
"D": "60 km",
"E": "50 km"
} | A person is traveling at 20 km/hr and reached his destiny in 2.5 hr then find the distance? |
aqua_rat__Hv4pMgWv4Si8VoWm | The first five numbers in a regular sequence are 4, 10, X, 46, and 94. What is x ? Choose the correct choice from the following answers:
A) 28 B) 26 C) 30 D) 22 E) 24 | it is a good Q to learn to pick up number properties in the given set, even if we do not get a Q on these line in actuals.. when we see the sequence 4, 10, x, 46, and 94, we see that each succeeding number is some value more than twice the previous number.. 10=2*4+2.. x=2*10+2 = 22.. and so on.. so next number= 22 22
<result>D</result> | D | {
"A": "28",
"B": "26",
"C": "30",
"D": "22",
"E": "24"
} | The first five numbers in a regular sequence are 4, 10, X, 46, and 94. What is x ? |
aqua_rat__tW3MoiW9G7TcgBQx | Tim has 350 pounds of cement in 100, 50, and 25 pound bags. He has an equal number of each size bag. How many bags of cement does Tim have?
Answers
A) 2 B) 4 C) 6 D) 8 E) 10 | Let the number of each sized bag = c
100c + 50c + 25c = 350
175c = 350
c = 2
Therefore, Tim has 3c = 6 bags of cement
Answer: 6
<result>C</result> | C | {
"A": "2",
"B": "4",
"C": "6",
"D": "8",
"E": "10"
} | Tim has 350 pounds of cement in 100, 50, and 25 pound bags. He has an equal number of each size bag. How many bags of cement does Tim have? |
aqua_rat__WkbE8VGmDbT9n8w0 | What is the least value of x, So that 2x5475 is divisible by 9 Choose the correct choice: A) 7 B) 8 C) 4 D) 3 E) 2 | Explanation: The sum of the digits of the number is divisible by 9. Then the number is divisible by 9. 2 + x + 5 + 4 + 7 + 5 = 23 + x Least value of x may be '4', So that the total 23 + 4=
<gadget id="calculator">23 + 4</gadget>
<output>27</output>
27 is divisible by 9. Answer: Option 4
<result>C</result> | C | {
"A": "7",
"B": "8",
"C": "4",
"D": "3",
"E": "2"
} | What is the least value of x, So that 2x5475 is divisible by 9 |
aqua_rat__YeC6ZOev3KbxsaeG | Square P is inscribed in circle Q. If the perimeter of P is 40, what is the circumference of Q? Choose one.
A) 11√ 2π B) 10√ 2π C) 9√ 2π D) 8√ 2π E) 7√ 2π | square forms two right angled triangles. Any time we have a right angle triangle inside a circle, the hypotenuse is the diameter. hypotenuse here = diagonal of the square = 10 sqrt(2) = diameter => radius = 5 sqrt(2) Circumference of the circle = 2pi r = 10 pi sqrt(2) Answer is 10√ 2π.
<result>B</result> | B | {
"A": "11√ 2π",
"B": "10√ 2π",
"C": "9√ 2π",
"D": "8√ 2π",
"E": "7√ 2π"
} | Square P is inscribed in circle Q. If the perimeter of P is 40, what is the circumference of Q? |
aqua_rat__vYSkOK0SIEtEv6y4 | A debtor reached an agreement with his creditor to repay a loan by making a monthly payment which is double of the amount she paid the previous month. If the debtors first payment was $200, and he is expected to pay back 51200, how many months will it take to fully repay the loan? Select.
A) 9 B) 10 C) 9 D) 12 E) 10 | First payment--$200 Total amount to be repaid--$25600 First month payment--$200 Second month payment( double the previous month payment)--$200*2=$400 Third month payment( double the previous month payment)--$400*2=$800 Fourth month payment( double the previous month payment)--$800*2=$1600 Fifth month payment( double the previous month payment)--$1600*2=$3200 Sixth month payment( double the previous month payment)--$3200*2=$6400 Seventh month payment( double the previous month payment)--$6400*2=$12800 Eight month payment( double the previous month payment)--$12800*2=$25600 Ninth month payment( double the previous month payment)--$25600*2=$51200 9nswer is 9
<result>A</result> | A | {
"A": "9",
"B": "10",
"C": "9",
"D": "12",
"E": "10"
} | A debtor reached an agreement with his creditor to repay a loan by making a monthly payment which is double of the amount she paid the previous month. If the debtors first payment was $200, and he is expected to pay back 51200, how many months will it take to fully repay the loan? |
aqua_rat__G2WPaEVZ6fcaiUp6 | As a bicycle salesperson, James earns a fixed salary of $30 per week plus $6 per bicycle for the first 6 bicycles he sells, $12 per bicycle for the next 6 bicycles he sells, and $18 per bicycle for every bicycle sold after first 12. This week, he earned more than twice as much as he did last week. If he sold x bicycles last week and y bicycles this week, which of the following statements must be true?
I. y<2x
II. y>x
III. y>3 Choose the correct choice from the following:
A) I,II only B) I only C) II,III only D) II only E) III only | II. y>x --> since this week, James earned more than he did last week and the total salary is in direct relationship with the # of bicycle sold, then y (# of bicycle sold this week) must be more than x (# of bicycle sold last week); III. y>3 --> if James sold 3 bicycles this week then this week he earned 30+3*6=
<gadget id="calculator">30+3*6</gadget>
<output>48</output>
$48, which cannot be more than twice as much as he earned the last week, since the minimum salary is fixed to $30. So y must be more than 3; I. y<2x --> is not always true. Answer: II,III only
<result>C</result> | C | {
"A": "I,II only",
"B": "I only",
"C": "II,III only",
"D": "II only",
"E": "III only"
} | As a bicycle salesperson, James earns a fixed salary of $30 per week plus $6 per bicycle for the first 6 bicycles he sells, $12 per bicycle for the next 6 bicycles he sells, and $18 per bicycle for every bicycle sold after first 12. This week, he earned more than twice as much as he did last week. If he sold x bicycles last week and y bicycles this week, which of the following statements must be true?
I. y<2x
II. y>x
III. y>3 |
aqua_rat__r6fYYPL8sgCbhikH | A school currently maintains a fixed number of students per class. If the ratio of students per class were to be increased by 1, 10 fewer classes would be run for a total of 120 students. What is the current ratio Q of students per class?
Pick one:
A) Q=3 B) Q=4 C) 6 D) 8 E) 12 | Another way to look at the problem... Since the total is 120, RATIO * CLASSES = R*C = 120.....(i) we are looking where ratio increases by 1 and # of classes decreases by 10 = (R+1)(C-10) = RC+C-10R-10=120....(ii) (ii)-(i).... C=10R+10 = 10(R+1)....... so # of classes has to be multiple of 10 AS RC=120.... 10(R+1)*R = 120...................R(R+1) = 12.. so 12 is a multiple of consecutive numbers ONLY 3 *4 fits in..... and R=3 Q=3
<result>A</result> | A | {
"A": "Q=3",
"B": "Q=4",
"C": "6",
"D": "8",
"E": "12"
} | A school currently maintains a fixed number of students per class. If the ratio of students per class were to be increased by 1, 10 fewer classes would be run for a total of 120 students. What is the current ratio Q of students per class? |
aqua_rat__vrbZeqyt9rVQU7r6 | A survey reveals that the average income of a company’s customers is $45,000 per year. If 50 customers respond to the survey and the average income of the wealthiest 10 of those customers is $95,000, what is the average income of the other 40 customers?
Is there a way to solve this using weighted average concept instead of doing tedious calculations? Choose the correct option: A) $32,500 B) $35,000 C) $37,500 D) $42,500 E) $50,000 | let x be the average of 40 customers 40*x + 10* 95000 = 50*45000 solving this we have x= 32500 $32,500nswer is $32,500.
<result>A</result> | A | {
"A": "$32,500",
"B": "$35,000",
"C": "$37,500",
"D": "$42,500",
"E": "$50,000"
} | A survey reveals that the average income of a company’s customers is $45,000 per year. If 50 customers respond to the survey and the average income of the wealthiest 10 of those customers is $95,000, what is the average income of the other 40 customers?
Is there a way to solve this using weighted average concept instead of doing tedious calculations? |
aqua_rat__OaPx4m3ewzNRBy9A | The slant height of a cone is 35 cm and radius of the base is 14cm, find the curved surface of the cone.
Options: A) 4150 B) 1780 C) 1540 D) 1500 E) 6100 | π * 14 * 35= 1540 Answer:1540
<result>C</result> | C | {
"A": "4150",
"B": "1780",
"C": "1540",
"D": "1500",
"E": "6100"
} | The slant height of a cone is 35 cm and radius of the base is 14cm, find the curved surface of the cone. |
aqua_rat__CELFumwUHkjO4RHs | A cheese factory sells its cheese in rectangular blocks. A normal block has a volume of 8 cubic feet. If a small block has half the width, half the depth, and half the length of a normal block, what is the volume of cheese in a small block in cubic feet? Choose the correct option:
A) 1
B) 5
C) 4
D) 6
E) 2 | Volume of cube=lbh=8 New cube l ,b, h are decreases of .5l, .5b,.5h New volume of cube =.5l*.5b*.5h=.125*lbh .5 *.5 *.5=
<gadget id="calculator">.5 *.5 *.5</gadget>
<output>0.125</output>
.125*lbh=.125*8=
<gadget id="calculator">.125*8</gadget>
<output>1</output>
1 1nswer: 1
<result>A</result> | A | {
"A": "1",
"B": "5",
"C": "4",
"D": "6",
"E": "2"
} | A cheese factory sells its cheese in rectangular blocks. A normal block has a volume of 8 cubic feet. If a small block has half the width, half the depth, and half the length of a normal block, what is the volume of cheese in a small block in cubic feet? |
aqua_rat__DsBMsugX5tICVv9O | In a new housing development, trees are to be planted along the sidewalk of a certain street. Each tree takes up one square foot of sidewalk space, and there are to be 20 feet between each tree. How many trees can be planted if the road is 148 feet long? Select:
A) 8 B) 9 C) 10 D) 11 E) 16 | Let T be the number of trees. Then the length required for trees on the sidewalk will be 1*T= T To maximize the number of trees, the number of 20 feet spaces between trees should be 1 less than total number of trees. For example, If there are 3 trees, then there should be 2 spaces between them. So the number of 20 feet spaces will be T-1. Then, the length of sidewalk required for 20 feet spaces will be 20*(T-1) It is given that total length of sidewalk is 148 feet. or 20(T-1)+T = 148 or 20T-20+T = 148 or 21T = 168 or T=8 8nswer:-8
<result>A</result> | A | {
"A": "8",
"B": "9",
"C": "10",
"D": "11",
"E": "16"
} | In a new housing development, trees are to be planted along the sidewalk of a certain street. Each tree takes up one square foot of sidewalk space, and there are to be 20 feet between each tree. How many trees can be planted if the road is 148 feet long? |
aqua_rat__iVZ8NVidH1v7edaJ | What will be the difference in simple and compound interest on 2000 after three years at the rate of 10 percent per annum? Options:
A) 160
B) 42
C) 62
D) 20
E) None of these | For 3 years: Diff.=Sum×(rate)2(300+rate)/(100)3 = 2000×10×10×310/100×100×100 = 62 Answer 62
<result>C</result> | C | {
"A": "160",
"B": "42",
"C": "62",
"D": "20",
"E": "None of these"
} | What will be the difference in simple and compound interest on 2000 after three years at the rate of 10 percent per annum? |
aqua_rat__GviW51OdQQR6G6nX | A $500 investment and a $1,500 investment have a combined yearly return of 19 percent of the total of the two investments. If the $500 investment has a yearly return of 7 percent, what percent yearly return does the $1,500 investment have? Answers: A) 9% B) 10% C) 23% D) 21% E) 22% | The equation we can form the question : Return on Total Investment = Sum of individual Investments (500+1500)(19)=(500∗7)+(1500x), where x is the return on investment of 1500. Solving the equation, we get x = 23% ( Option 23% ) ANSWER:23%
<result>C</result> | C | {
"A": "9%",
"B": "10%",
"C": "23%",
"D": "21%",
"E": "22%"
} | A $500 investment and a $1,500 investment have a combined yearly return of 19 percent of the total of the two investments. If the $500 investment has a yearly return of 7 percent, what percent yearly return does the $1,500 investment have? |
aqua_rat__2xJ0gxHhnAuYfjkd | Find the constant k so that : -x2 - (k + 11)x - 8 = -(x - 2)(x - 4) Choose one.
A) 11 B) 12 C) 17 D) 14 E) 15 | -x2 - (k + 11)x - 8 = -(x - 2)(x - 4) : given -x2 - (k + 11)x - 8 = -x2 + 6x - 8 -(k + 11) = 6 : two polynomials are equal if their corresponding coefficients are equal. k = -17 : solve the above for k correct answer 17
<result>C</result> | C | {
"A": "11",
"B": "12",
"C": "17",
"D": "14",
"E": "15"
} | Find the constant k so that : -x2 - (k + 11)x - 8 = -(x - 2)(x - 4) |
aqua_rat__eY6Xtt9jIxDkmodX | A positive whole number has factors of 3 and 5. The number MUST be divisible by: I. 15 II. 30 III. 60 Select the correct option:
A) I & II
B) III
C) I & III
D) II & III
E) II | 15 , 30 is not divisible by 60.IIIut 60 is divisible by 3,5,15,30 So answer is III Answer : III
<result>B</result> | B | {
"A": "I & II",
"B": "III",
"C": "I & III",
"D": "II & III",
"E": "II"
} | A positive whole number has factors of 3 and 5. The number MUST be divisible by: I. 15 II. 30 III. 60 |
aqua_rat__253nMNk6XpiQMHWg | Krishan and Nandan jointly started a business. Krishan invested six times as Nandan did and invested his money for double time as compared to Nandan. Nandan earned Rs. 6000. If the gain is proportional to the money invested and the time for which the money is invested then the total gain was? Choose the correct choice from the following choices: A) Rs.78000 B) Rs.48000 C) Rs.6000 D) Rs.82000 E) Rs.32000 | 6:1 2:1 ------ 12:1 1 ----- 6000 13 ----- ? => Rs.78,000 Rs.78000nswer: Rs.78000
<result>A</result> | A | {
"A": "Rs.78000",
"B": "Rs.48000",
"C": "Rs.6000",
"D": "Rs.82000",
"E": "Rs.32000"
} | Krishan and Nandan jointly started a business. Krishan invested six times as Nandan did and invested his money for double time as compared to Nandan. Nandan earned Rs. 6000. If the gain is proportional to the money invested and the time for which the money is invested then the total gain was? |
aqua_rat__Uz4Rb9XtntdXa4t2 | There are 8 players in a chess group, and each player plays each of the others once. Given that each game is played by two players, how many total games will be played? Choose the correct option:
A) 10 B) 30 C) 28 D) 60 E) 90 | 10 players are there. two players play one game with one another. so 8282=8*7/2=
<gadget id="calculator">8*7/2</gadget>
<output>28</output>
28 SO OPTION 28 is correct
<result>C</result> | C | {
"A": "10",
"B": "30",
"C": "28",
"D": "60",
"E": "90"
} | There are 8 players in a chess group, and each player plays each of the others once. Given that each game is played by two players, how many total games will be played? |
aqua_rat__UIyOGAlU6D74Z2re | A pipe takes a hours to fill the tank. But because of a leakage it took 2 times of its original time. Find the time taken by the leakage to empty the tank Choose the correct choice from the following choices.
A) 50 min B) 60 min C) 90 min D) 80 min E) 120 min | pipe a can do a work 60 min. lets leakage time is x; then 1/60 -1/x=1/120 x=120 min ANSW120 minR:120 min
<result>E</result> | E | {
"A": "50 min",
"B": "60 min",
"C": "90 min",
"D": "80 min",
"E": "120 min"
} | A pipe takes a hours to fill the tank. But because of a leakage it took 2 times of its original time. Find the time taken by the leakage to empty the tank |
aqua_rat__DZ8JlbJKzVdCu6PK | Today is 22 days before Mariah's graduation. If she graduates on a Friday, what day of the week is it today? Answers:
A) Monday B) Friday C) Tuesday D) Thursday E) Sunday | Each weekday is repeated every 7 days. 22 divided by 7 is 3, with a remainder of 1. Therefore, 22 days before the graduation occurs 1 day before the weekday of the graduation. Answer: Thursday
<result>D</result> | D | {
"A": "Monday",
"B": "Friday",
"C": "Tuesday",
"D": "Thursday",
"E": "Sunday"
} | Today is 22 days before Mariah's graduation. If she graduates on a Friday, what day of the week is it today? |
aqua_rat__95AwJPpiJsNFXDg3 | Suppose a, b, and c are positive integers with a < b < c such that
1/a
+
1/b
+
1/c
= 1. What is
a + b + c? Answers.
A) 1 B) 4 C) 9 D) 11 E) no such integers exist | First note that we must have 1/a < 1, so a > 1. Since 1/a > 1/b > 1/c, we must also have 1/a > 1/3; so a < 3. Thus, a/ 2. Now 1/b + 1/c = 1/2 where 2 < b < c. Similar to before, 1/b > 1/4, so b < 4. Thus, b = 3. With a = 2 and b = 3 we have 1/2+1/3+1/c = 1, which is satisfied when c = 6. To conclude, a+b+c = 2+3+6=
<gadget id="calculator">2+3+6</gadget>
<output>11</output>
11. correct answer 11
<result>D</result> | D | {
"A": "1",
"B": "4",
"C": "9",
"D": "11",
"E": "no such integers exist"
} | Suppose a, b, and c are positive integers with a < b < c such that
1/a
+
1/b
+
1/c
= 1. What is
a + b + c? |
aqua_rat__6YCdHI3SNqKeQ9zi | The age of man is three times the sum of the ages of his two sons.Four years hence,his age will be double of the sum of the ages of his sons.The father’s present age is : Choices.
A) 36 years B) 45 years C) 50 years D) 55 years E) 75 years | Solution Let the sum of present ages of the two sons be x years. Then,father's present age = 3x years. ∴ (3x + 4)=2 (x +8) ⇔ 3x + 4 = 2x + 16 ⇔ x =12. Hence,father's present age = 36 years. 36 yearsnswer 36 years
<result>A</result> | A | {
"A": "36 years",
"B": "45 years",
"C": "50 years",
"D": "55 years",
"E": "75 years"
} | The age of man is three times the sum of the ages of his two sons.Four years hence,his age will be double of the sum of the ages of his sons.The father’s present age is : |
aqua_rat__yVAkLURr4l3npxg8 | A bottle of coke contains 200gm in place of 1kg of fluid. Find the actual % difference, given a 10% gain on initial fluid? Choose the correct answer:
A) 32.5%
B) 112.5%
C) 35%
D) 40%
E) 50% | fluid price of 200gm = 100+10=
<gadget id="calculator">100+10</gadget>
<output>110</output>
110 Difference= 110-20=
<gadget id="calculator">110-20</gadget>
<output>90</output>
90 % of difference= 90*100/80=
<gadget id="calculator">90*100/80</gadget>
<output>225/2 = around 112.5</output>
112.5 % Answer is 112.5%
<result>B</result> | B | {
"A": "32.5%",
"B": "112.5%",
"C": "35%",
"D": "40%",
"E": "50%"
} | A bottle of coke contains 200gm in place of 1kg of fluid. Find the actual % difference, given a 10% gain on initial fluid? |
aqua_rat__m08AjRE9R56et1WP | A person can walk at a constant rate of 8mph and can bike at a rate of 16mph. If he wants to travel 64 miles in 8 hours using bike and walking at their constant rates, how much distance would he require to walk? Choose the correct choice from the following answers: A) 20 B) 30 C) 48 D) 64 E) 72 | Total distance = 64 64istance = Speed * Time Walking speed = s1 = 8 Walking time = t1 Bike speed = s2 = 16 Time traveled in bike = t2 d1 + d2 = 64 s1t1 + s2t2 = 64 8*t1 + 16*t2 = 64 t1 + 2*t2 = 8 ----- (1) Given: t1 + t2 = 8 ----- (2) (1) - (2) --> t2 = 0 and t1 = 8 - 0=
<gadget id="calculator">8 - 0</gadget>
<output>8</output>
8 Walking distance= s1*t1 = 8*8=
<gadget id="calculator">8*8</gadget>
<output>64</output>
64 Answer: 64
<result>D</result> | D | {
"A": "20",
"B": "30",
"C": "48",
"D": "64",
"E": "72"
} | A person can walk at a constant rate of 8mph and can bike at a rate of 16mph. If he wants to travel 64 miles in 8 hours using bike and walking at their constant rates, how much distance would he require to walk? |
aqua_rat__8Ybkbbh4iO4hORPE | 5358 x 51 = ? Answers
A) 273258 B) 273268 C) 273348 D) 273358 E) None of these | Explanation: 5358 x 51 = 5358 x (50 + 1) = 5358 x 50 + 5358 x 1 = 267900 + 5358=
<gadget id="calculator">267900 + 5358</gadget>
<output>273_258</output>
273258. 273258NSWER IS 273258
<result>A</result> | A | {
"A": "273258",
"B": "273268",
"C": "273348",
"D": "273358",
"E": "None of these"
} | 5358 x 51 = ? |
aqua_rat__M32PiMTlZUY5hHhI | 3 persons (1 couple and 1 single) are seated at random in a row of 5 chairs. What is the probability that the couple does not sit together? Pick one
A) 5/7
B) 4/5
C) 2/5
D) 3/5
E) 11/8 | Let's find the probability that a couple sits together (right next to each other) and subtract that value from 1. Total # of ways 3 persons C1C1, C2C2 and SS to be seated in a row of 5 seats is 5!2!=605!2!=60. Consider this, we are interested in arrangement of C1, C2, S, E, EC1, C2, S, E, E, so in arrangement of 5 letters out of which 2 E's are identical (E denotes an empty seat); # of ways for a couple to sit together is 4!2!∗2=244!2!∗2=24. Consider a couple as a single unit: {C1,C2}, S, E, E{C1,C2}, S, E, E, so we have total of 4 units out of which 2 E's are identical, # of arrangement of these units is 4!2!4!2!, but C1C1, C2C2 within their unit can be arranged in 2 ways ({C1,C2}{C1,C2} or {C2,C1}{C2,C1}), so total # of arrangement for this case is 4!2!∗2=244!2!∗2=24; P=1−2460=35P=1−2460=35. Answer: 3/5.
<result>D</result> | D | {
"A": "5/7",
"B": "4/5",
"C": "2/5",
"D": "3/5",
"E": "11/8"
} | 3 persons (1 couple and 1 single) are seated at random in a row of 5 chairs. What is the probability that the couple does not sit together? |
aqua_rat__54LK63t7cuBPPpYx | In a recent survey at a local deli, it was observed that 3 out of 5 customers bought a bagel and 5 out of 7 customers bought a coffee. Some customers bought both. If 8 customers are selected, what are the chances that at least 1 customer bought a coffee and a bagel? Choose the correct choice from the following options
A) 27/343 B) 3/7 C) 27/125 D) 199/245 E) 9/125 | Let us take 7*5=
<gadget id="calculator">7*5</gadget>
<output>35</output>
35 as the total number of customers. So 7*3=
<gadget id="calculator"> 7*3</gadget>
<output>21</output>
21 customers bought a bagel and 5*5=
<gadget id="calculator">5*5</gadget>
<output>25</output>
25 customers bought a coffee. chances that at least 1 customer bought a coffee and a bagel= 1 - chances that no customer bought a coffee and a bagel chances that no customer bought a coffee and a bagel=24/35*23/34*22/33*21/32*20/31*19/30*18/29*17/28=46/245 chances that at least 1 customer bought a coffee and a bagel= 1 - 46/245 = 199/245 Answer 199/245.
<result>D</result> | D | {
"A": "27/343",
"B": "3/7",
"C": "27/125",
"D": "199/245",
"E": "9/125"
} | In a recent survey at a local deli, it was observed that 3 out of 5 customers bought a bagel and 5 out of 7 customers bought a coffee. Some customers bought both. If 8 customers are selected, what are the chances that at least 1 customer bought a coffee and a bagel? |
aqua_rat__3ZE1yXKIYRZl3clb | |x+3| – |4-x| = |8+x| How many S solutions will this equation have? Pick one
A) 0
B) 1
C) 2
D) 3
E) 4 | |x| = x when x >= 0 (x is either positive or 0) |x| = -x when x < 0 (note here that you can put the equal to sign here as well x <= 0 because if x = 0, |0| = 0 = -0 (all are the same) So the '=' sign can be put with x > 0 or with x < 0. We usually put it with 'x > 0' for consistency.0
<result>A</result> | A | {
"A": "0",
"B": "1",
"C": "2",
"D": "3",
"E": "4"
} | |x+3| – |4-x| = |8+x| How many S solutions will this equation have? |
aqua_rat__XwvRjbPT3MhEJuKe | The output of a factory was increased by 10% to keep up with rising demand. To handle the holiday rush, this new output was increased by 20%. By approximately what percent would the output now have to be decreased in order to restore the original output? Pick one: A) 20% B) 24% C) 30% D) 32% E) 79% | Let initial output is O then after 10% increase it will be 1.1O and after 20% increase on this new output the latest output will be 1.1O * 1.20 = 1.32O Now we have to decrease the output by some percentage so that the new output is same as the starting output (O) so, 1.32O * (1-x/100) 1.1 * 1.20=
<gadget id="calculator"> 1.1 * 1.20</gadget>
<output>1.32</output>
1.32O Now we have to decrease the output by some percentage so that the new output is same as the starting output (O) so, 1.32O * (1-x/100)= O => x = 24.24% So, answer will be 24%
<result>B</result> | B | {
"A": "20%",
"B": "24%",
"C": "30%",
"D": "32%",
"E": "79%"
} | The output of a factory was increased by 10% to keep up with rising demand. To handle the holiday rush, this new output was increased by 20%. By approximately what percent would the output now have to be decreased in order to restore the original output? |
aqua_rat__jJ9oJ4hpOvj5OmiY | In a graduate physics course, 70 percent of the students are male and 30 percent of the students are married. If two-sevenths of the male students are married, what fraction of the male students is single? Choose the correct choice from the following answers
A) 2/7 B) 1/3 C) 1/2 D) 2/3 E) 5/7 | let assume there are 100 students of which 70 are male and 30 are females if 30 are married then 70 will be single. now its given that two-sevenths of the male students are married that means 2/7 of 70 = 20 males are married if 30 is the total number of students who are married and out of that 20 are males then the remaining 10 will be females who are married. total females = 70 married males = 20 then single males = 70-20=
<gadget id="calculator">70-20</gadget>
<output>50</output>
50 we need to find the fraction of male students who are single i.e single male students / total male student= 50/70 = 5/7 [5/7]
<result>E</result> | E | {
"A": "2/7",
"B": "1/3",
"C": "1/2",
"D": "2/3",
"E": "5/7"
} | In a graduate physics course, 70 percent of the students are male and 30 percent of the students are married. If two-sevenths of the male students are married, what fraction of the male students is single? |
aqua_rat__GpdL2Ftcr6AJW96h | The cost of painting the whole surface area of a cube at the rate of 13 paise per Sq.cm is Rs. 343.98. Then the volume of the cube is Choose the most appropriate option: A) 8500 cm3 B) 9000 cm3 C) 9250 cm3 D) 9261 cm3 E) None | Solution Surface area = (34398 / 13)=
<gadget id="calculator">(34398 / 13)</gadget>
<output>2_646</output>
›2646cm3 ‹=›6a2= 2646 ‹=›a2= 441 ‹=›a = 21. So,volume =(21x21x21)cm3= 9261cm3. Answer 9261 cm3
<result>D</result> | D | {
"A": "8500 cm3",
"B": "9000 cm3",
"C": "9250 cm3",
"D": "9261 cm3",
"E": "None"
} | The cost of painting the whole surface area of a cube at the rate of 13 paise per Sq.cm is Rs. 343.98. Then the volume of the cube is |
aqua_rat__vLZDTzIU7T6QL3BS | A man sold 20 articles for $60 and gained 20%. How many articles should he sell for $50 to incur a loss 20%? Choose the correct choice from the following answers.
A) 25 B) 36 C) 40 D) 50 E) 48 | Production cost per article: $60*(100%-20%) / 20 = $2.40 Required production costs for a loss of 20%: $50*(100% + 20%) = $60 Number of articles to be sold for $60 to incur a 20% loss: $60 / $2.40 = 25 Thus, solution 25 is correct.60 / 2.40=
<gadget id="calculator">60 / 2.40</gadget>
<output>25</output>
25 Thus, solution 25 is correct.
<result>A</result> | A | {
"A": "25",
"B": "36",
"C": "40",
"D": "50",
"E": "48"
} | A man sold 20 articles for $60 and gained 20%. How many articles should he sell for $50 to incur a loss 20%? |
aqua_rat__kFcvnaZNHuBr5qMX | A man invests some money partly in 9% stock at 96 and partly in 12% stock at 120. To obtain equal dividends from both, he must invest the money in the ratio: Choose one: A) 3:5 B) 2:1 C) 16:15 D) 4:5 E) None of these | Explanation: For an income of Re. 1 in 9% stock at 96, investment = Rs. 96/9 = Rs.32/3 For an income Re. 1 in 12% stock at 120, investment = Rs. 120/12 = Rs. 10. Ratio of investments =(32/3) : 10 = 32 : 30 = 16 : 15. Answer: 16:15
<result>C</result> | C | {
"A": "3:5",
"B": "2:1",
"C": "16:15",
"D": "4:5",
"E": "None of these"
} | A man invests some money partly in 9% stock at 96 and partly in 12% stock at 120. To obtain equal dividends from both, he must invest the money in the ratio: |
aqua_rat__npULvp5yKx9lVNbe | A, B, C rent a pasture. A puts 10 oxen for 7 months, B puts 12 oxen for 5 months and C puts 15 oxen for 3 months for grazing. If the rent of the pasture is Rs. 175, how much must C pay as his share of rent? Choose the correct choice from the following answers: A) Rs. 45 B) Rs. 50 C) Rs. 55 D) Rs. 60 E) Rs. 65 | Explanation: A : B : C = (10 x 7) : (12 x 5) : (15 x 3) = 70 : 60 : 45 = 14 : 12 : 9. C's rent = Rs.(175 x 9/35)= Rs. 45. Rs. 45NSWER IS Rs. 45
<result>A</result> | A | {
"A": "Rs. 45",
"B": "Rs. 50",
"C": "Rs. 55",
"D": "Rs. 60",
"E": "Rs. 65"
} | A, B, C rent a pasture. A puts 10 oxen for 7 months, B puts 12 oxen for 5 months and C puts 15 oxen for 3 months for grazing. If the rent of the pasture is Rs. 175, how much must C pay as his share of rent? |
aqua_rat__IBnEMLFawvSlCric | A train 500 m long can cross an electric pole in 20 sec and then find the speed of the train? Choices
A) 95 Kmph B) 90 Kmph C) 92 Kmph D) 95 Kmph E) 98 Kmph | Length = Speed * time Speed = L/T S = 500/20=
<gadget id="calculator">500/20</gadget>
<output>25</output>
25 M/Sec Speed= 25*18/5 (To convert M/Sec in to Kmph multiply by 18/5) Speed = 90 Kmph ANSWER:90 Kmph
<result>B</result> | B | {
"A": "95 Kmph",
"B": "90 Kmph",
"C": "92 Kmph",
"D": "95 Kmph",
"E": "98 Kmph"
} | A train 500 m long can cross an electric pole in 20 sec and then find the speed of the train? |
aqua_rat__2mfh8gSoqrK3sjB4 | The smallest number when increased by " 1 " is exactly divisible by 6,9,15,35,45 is:
Choose the correct choice from the following
A) 631
B) 630
C) 359
D) 629
E) 600 | LCM = 630 630 - 1=
<gadget id="calculator">630 - 1</gadget>
<output>629</output>
629 ANSWER:629
<result>D</result> | D | {
"A": "631",
"B": "630",
"C": "359",
"D": "629",
"E": "600"
} | The smallest number when increased by " 1 " is exactly divisible by 6,9,15,35,45 is: |
aqua_rat__7pSPKRGWBNS6J3VA | How many keystrokes are needed to type the numbers from 1 to 500? Choose the correct choice from the following options: A) 1156 B) 1392 C) 1480 D) 1562 E) 1788 | There are 9 one-digit numbers from 1 to 9. There are 90 two-digit numbers from 10 to 99. There are 401 three-digit numbers from 100 to 500. 9 + 90(2) + 401(3) = 1392 The answer is 1392.
<result>B</result> | B | {
"A": "1156",
"B": "1392",
"C": "1480",
"D": "1562",
"E": "1788"
} | How many keystrokes are needed to type the numbers from 1 to 500? |
aqua_rat__Yv6o6Q351qjtVIal | In a two-digit number, the digit in the unit's place is four times the digit in ten's place and the sum of the digits is equal to 10. What is the number? Choose the correct option.
A) 82 B) 41 C) 14 D) 56 E) 28 | Let the ten's digit be x. then, unit's digit = 4x therefore x + 4x = 10 ==> 5x = 10 ==> x = 2 so ten's digit is 2 and unit's digit is 8, so the number is 28 so the correct answer is option 28) 28
<result>E</result> | E | {
"A": "82",
"B": "41",
"C": "14",
"D": "56",
"E": "28"
} | In a two-digit number, the digit in the unit's place is four times the digit in ten's place and the sum of the digits is equal to 10. What is the number? |
aqua_rat__eGEcGFIxsCs6uJJE | The edge of a cube is 7a cm. Find its surface? Choose the correct answer.
A) 24a8 B) 24a4 C) 24a1 D) 24a2 E) 294a2 | 6a2 = 6 * 7a * 7a = 294a2 Answer:294a26 * 7 * 7=
<gadget id="calculator">6 * 7 * 7</gadget>
<output>294</output>
294a2 Answer:294a2
<result>E</result> | E | {
"A": "24a8",
"B": "24a4",
"C": "24a1",
"D": "24a2",
"E": "294a2"
} | The edge of a cube is 7a cm. Find its surface? |
aqua_rat__8SiV4NcRmaXoMjVL | A shop sells chocolates It is used to sell chocolates for Rs.2 each but there were no sales at that price.When it reduced the price all the chocolates sold out enabling the shopkeeper to realize Rs 164.90 from the chocolates alone If the new price was not less than half the original price quoted How many chocolates were sold? Choose the correct choice from the following choices.
A) 1.9 B) 1.7 C) 1.2 D) 1.5 E) 1.6 | 16490 = 2 × 5 × 17 × 97 Now now chocolate price should be greater than 1 and less than 2. So 2 x 5 x 17 = 170 So Total chocolates sold = 97 and New chocolate price = Rs.1.7 Answer: 1.7
<result>B</result> | B | {
"A": "1.9",
"B": "1.7",
"C": "1.2",
"D": "1.5",
"E": "1.6"
} | A shop sells chocolates It is used to sell chocolates for Rs.2 each but there were no sales at that price.When it reduced the price all the chocolates sold out enabling the shopkeeper to realize Rs 164.90 from the chocolates alone If the new price was not less than half the original price quoted How many chocolates were sold? |
aqua_rat__0dyKd7hFQqHBuZN1 | A board 7ft. 9 inches long is divided into 3 equal parts . What is the length of each part? Select.
A) 31 inches B) 32 inches C) 33 inches D) 34 inches E) 35 inches | 7 ft 9 in is 84 + 9=
<gadget id="calculator"> 84 + 9</gadget>
<output>93</output>
93 inches. so 93/3=
<gadget id="calculator"> 93/3</gadget>
<output>31</output>
31 inches or 2 ft. 7 inch. 31 inchesNSWER:31 inches
<result>A</result> | A | {
"A": "31 inches",
"B": "32 inches",
"C": "33 inches",
"D": "34 inches",
"E": "35 inches"
} | A board 7ft. 9 inches long is divided into 3 equal parts . What is the length of each part? |
aqua_rat__It8u63JM06vtdd6Z | Find the number of zeroes in the expression 15*32*25*22*40*75*98*112*125 Choose the correct choice from the following: A) 12 B) 9 C) 14 D) 7 E) 6 | (3*5)*(2*2*2*2*2)*(5*5)*(2*11)*(2*2*2*2*5)*(5*5*3)*(2*7*7)*(2*2*2*2*7)*(5*5*5) there are 9 (5*2) pairs which gives zero so.no of zeros 9 ANSWER:9
<result>B</result> | B | {
"A": "12",
"B": "9",
"C": "14",
"D": "7",
"E": "6"
} | Find the number of zeroes in the expression 15*32*25*22*40*75*98*112*125 |
aqua_rat__48MvRLAWV688Zkbs | The diagonals of a rhombus are 18 cm and 22 cm. Find its area? Choose one:
A) 277
B) 266
C) 198
D) 288
E) 212 | 1/2 * 18 * 22=
<gadget id="calculator">1/2 * 18 * 22</gadget>
<output>198</output>
198 Answer: 198
<result>C</result> | C | {
"A": "277",
"B": "266",
"C": "198",
"D": "288",
"E": "212"
} | The diagonals of a rhombus are 18 cm and 22 cm. Find its area? |
aqua_rat__bwG1xAZjNzR3d9Xv | If rupee one produces rupees nine over a period of 40 years, find the rate of simple interest?
Pick:
A) 22 1/8 %
B) 22 3/2 %
C) 28 1/2 %
D) 22 1/2 %
E) 32 1/2 % | 9 = (1*40*R)/100 R = 22 1/2 % Answer:22 1/2 %
<result>D</result> | D | {
"A": "22 1/8 %",
"B": "22 3/2 %",
"C": "28 1/2 %",
"D": "22 1/2 %",
"E": "32 1/2 %"
} | If rupee one produces rupees nine over a period of 40 years, find the rate of simple interest? |
aqua_rat__aIukfMNhQAWng8qC | A and B invests Rs.6000 and Rs.12000 in a business. After 4 months, A withdraws half of his capital and 2 months later, B withdraws one-third of his capital. In what ratio should they share the profits at the end of the year? Choose the correct choice from the following:
A) 32:99 B) 8:21 C) 32:45 D) 34:89 E) 35:21 | A : 8:21 (6000*4)+(3000*8) : (12000*6)+(9000*6) 48000 : 126000 8 : 21 Answer:8:21
<result>B</result> | B | {
"A": "32:99",
"B": "8:21",
"C": "32:45",
"D": "34:89",
"E": "35:21"
} | A and B invests Rs.6000 and Rs.12000 in a business. After 4 months, A withdraws half of his capital and 2 months later, B withdraws one-third of his capital. In what ratio should they share the profits at the end of the year? |
aqua_rat__OlujTlyf6zXw0kAe | A train covers a distance of 10km in 10 min. If it takes 6 sec to pass a telegraph post, then the length of the train is? Choose the correct answer.
A) m B) m C) m D) m E) m | Speed = (10/10 * 60) km/hr = (60 * 5/18) m/sec = 50/3 m/sec. Length of the train = 50/3 * 6=
<gadget id="calculator">50/3 * 6</gadget>
<output>100</output>
100 m. Answer:m
<result>C</result> | C | {
"A": "m",
"B": "m",
"C": "m",
"D": "m",
"E": "m"
} | A train covers a distance of 10km in 10 min. If it takes 6 sec to pass a telegraph post, then the length of the train is? |
aqua_rat__6oaoZUka4tSNvHB2 | The rental charge for a car is 34 cents for the first 1/4 mile driven and 6 cents for every 1/5 mile driven over the initial 1/4 mile. If a man paid $1.24 in rental charges, how many miles did he drive? Pick one:
A) 2.5
B) 3.0
C) 3.25
D) 3.75
E) 4.0 | Total Rent = Rent for the first 0.25 mile + Rent After 0.25 mile Rent for the first 0.25 mile = 34 cents Rent After 0.25 mile = [6 cent/(1/5 mile)]*(x - 0.25) = 30(x-0.25) Therefore, Total Rent = 35 + 30(x - 0.25) 124 = 34 + 30(x - 0.25) 90 = 30(x - 0.25) 3 = x - 0.25 x = 3 + 0.25=
<gadget id="calculator">3 + 0.25</gadget>
<output>3.25</output>
$3.25 3.25
<result>C</result> | C | {
"A": "2.5",
"B": "3.0",
"C": "3.25",
"D": "3.75",
"E": "4.0"
} | The rental charge for a car is 34 cents for the first 1/4 mile driven and 6 cents for every 1/5 mile driven over the initial 1/4 mile. If a man paid $1.24 in rental charges, how many miles did he drive? |
aqua_rat__pyLg6hGNm0EtKCJY | A question paper consists of three sections 4,5 and 6 questions respectively. Attempting one question from each section is compulsory but a candidate need not attempt all the questions. In how many ways can a candidate attempt the questions?
Select the correct option.
A) 209 B) (4!-1)*(5!-1)*(6!-1) C) 119 D) 29295 E) None | Solution: At least 1 question from each section is compulsory, so from the 1st section the candidate can attempt 1 or 2 or 3 or 4 questions. In each section each question can be dealt with in 2 ways, i.e. either he attempts it or leaves it. So far 4 question there are 2 *2 *2 *2 ways to attempt. As he has to attempt at least 1 question, the total number of ways in which he can attempt questions from 1st section is 24−1. Similarly for the 2nd section there are 25−1 ways in which he can attempt and for the 3rd section there are 26−1 ways. The ways in which the attempts one or more questions in any section is independent of the number of ways in which he attempts one or more questions from the other sections. Thus, total number of ways Answer: Option 29295
<result>D</result> | D | {
"A": "209",
"B": "(4!-1)*(5!-1)*(6!-1)",
"C": "119",
"D": "29295",
"E": "None"
} | A question paper consists of three sections 4,5 and 6 questions respectively. Attempting one question from each section is compulsory but a candidate need not attempt all the questions. In how many ways can a candidate attempt the questions? |
aqua_rat__JUwcXhwNeia3pyCA | 10 women can complete a work in 9 days and 10 children take 12 days to complete the work. How many days will 6 women and 7 children take to complete the work?
Choose the correct choice: A) 4 B) 5 C) 7 D) 8 E) 2 | 1 women's 1 day work = 1/90 1 child's 1 day work = 1/120 (6 women + 7 children)'s 1 day work = (6/90 + 7/120) = 1/8 6 women and 7 children will complete the work in 8 days. 8
<result>D</result> | D | {
"A": "4",
"B": "5",
"C": "7",
"D": "8",
"E": "2"
} | 10 women can complete a work in 9 days and 10 children take 12 days to complete the work. How many days will 6 women and 7 children take to complete the work? |
aqua_rat__8qOsiLHiakQDWy5z | Three numbers are in the ratio 5 : 6 : 7. The sum of its longest and smallest numbers equals the sum of the third number and 54. Find the third number? Choose the correct option:
A) A)37 B) B)85 C) C)48 D) D)43 E) E)54 | Let the numbers be 5x, 6x, 7x. Largest number = 7x. Smallest number = 5x. Third number = 6x. 7x + 5x = 6x + 54 6x = 54 => third number is 54. Answer: Option 54
<result>E</result> | E | {
"A": "A)37",
"B": "B)85",
"C": "C)48",
"D": "D)43",
"E": "E)54"
} | Three numbers are in the ratio 5 : 6 : 7. The sum of its longest and smallest numbers equals the sum of the third number and 54. Find the third number? |
aqua_rat__ye85VguY59DzZfh4 | At the end of a business conference the nine people present all shake hands with each other once. How many handshakes will there be altogether ?
Select the correct option.
A) 20 B) 45 C) 36 D) 90 E) 95 | number of handshakes = 9362= 9*8/2=
<gadget id="calculator">9*8/2</gadget>
<output>36</output>
36 ANSWER:36
<result>C</result> | C | {
"A": "20",
"B": "45",
"C": "36",
"D": "90",
"E": "95"
} | At the end of a business conference the nine people present all shake hands with each other once. How many handshakes will there be altogether ? |
aqua_rat__C4mmpuRStiyiptOd | Sum of the squares of three numbers is 351 and the sum of their products taken two at a time is 245. Find the sum?
Select the correct option:
A) 20 B) 22 C) 25 D) 26 E) 29 | (a + b + c)2 = a2 + b2 + c2 + 2(ab +bc + ca) = 351 + 2* 245 a + b + c = √841 = 29 29
<result>E</result> | E | {
"A": "20",
"B": "22",
"C": "25",
"D": "26",
"E": "29"
} | Sum of the squares of three numbers is 351 and the sum of their products taken two at a time is 245. Find the sum? |
aqua_rat__hbq15cpW36og7bNJ | What is the are of an equilateral triangle of side 16 cm? Choose the correct answer:
A) 64√6 cm2 B) 64√3 cm2 C) 64√9 cm2 D) 34√3 cm2 E) 24√3 cm2 | Area of an equilateral triangle = √3/4 S2 If S = 16, Area of triangle = √3/4 * 16 * 16 = 64√3 cm2; Answer: 34√3 cm2
<result>D</result> | D | {
"A": "64√6 cm2",
"B": "64√3 cm2",
"C": "64√9 cm2",
"D": "34√3 cm2",
"E": "24√3 cm2"
} | What is the are of an equilateral triangle of side 16 cm? |
aqua_rat__CWpxJoL9BNyX53tB | Each of the following equations W has at least one solution EXCEPT Choose the most appropriate option.
A) W=–2^n = (–2)^-n B) 2^-n = (–2)^n C) 2^n = (–2)^-n D) (–2)^n = –2^n E) (–2)^-n = –2^-n | While it is possible to reason out which of these choices must not work, we may not have time or the confidence to do so. However, this problem has variable in its answer choice, and relatively simple math. Therefore, an easy alternative is picking numbers. Since we're dealing with exponents, we want to keep things as easy as possible. Hence, we'll start with the easiest exponent possible: n = 1. A, B, and C are not solved (x^-n = 1/(x^n), so we're comparing integers to fractions), but choices D and E both end up valid, eliminating them from contention. In the process of doing this, however, we've uncovered a major clue to our next step: A, B, and C, all compared integers to fractions, and the only integer equal to it's reciprocal is 1, which is equal to 1/1. This, in turn, tells us the we need to pick n = 0. Remember, for all non-zero x, x^0 = 1. If we plug n = 0 into choices B and C, we end up with 1 = 1 both times. Choice A, however, results in the false 1 = -1. Thus, we conclude that the first choice has no valid solutions, and is therefore the correct answer.
<result>A</result> | A | {
"A": "W=–2^n = (–2)^-n",
"B": "2^-n = (–2)^n",
"C": "2^n = (–2)^-n",
"D": "(–2)^n = –2^n",
"E": "(–2)^-n = –2^-n"
} | Each of the following equations W has at least one solution EXCEPT |
aqua_rat__Vqz8rLftB4rqWHSn | If the population of a certain country increases at the rate of one person every 40 seconds, by how many persons does the population increase in 1 hour? Choose the most appropriate option.
A) 90
B) 120
C) 150
D) 180
E) 160 | 90nswer = 1.5 * 60=
<gadget id="calculator">1.5 * 60</gadget>
<output>90</output>
90 90nswer is 90
<result>A</result> | A | {
"A": "90",
"B": "120",
"C": "150",
"D": "180",
"E": "160"
} | If the population of a certain country increases at the rate of one person every 40 seconds, by how many persons does the population increase in 1 hour? |
aqua_rat__CRTyco4lS8AsAUzB | A train crosses a platform of 120 m in 15 sec, same train crosses another platform of length 180 m in 18 sec. then find the length of the train?
Select the correct option: A) 288 B) 180 C) 288 D) 277 E) 265 | Length of the train be ‘X’ X + 120/15 = X + 180/18 6X + 720 = 5X + 900 X = 180m .Answer: 180
<result>B</result> | B | {
"A": "288",
"B": "180",
"C": "288",
"D": "277",
"E": "265"
} | A train crosses a platform of 120 m in 15 sec, same train crosses another platform of length 180 m in 18 sec. then find the length of the train? |
aqua_rat__e3c5TiD9f3yM432N | Find the area of a rhombus whose side is 25 cm and one of the diagonals is 30 cm? Choose the correct choice from the following options.
A) 272 sq.cm B) 267 sq.cm C) 286 sq.cm D) 251 sq.cm E) 600 sq.cm | Consider the rhombus ABCD. Let the diagonals intersect at E. Since diagonals bisect at right angles in a rhombus. BE2 + AE2 = AB2 252 = 152 + AE2 AE = √(625 - 225)=
<gadget id="calculator">(625 - 225)</gadget>
<output>400</output>
√400= 20, AC = 20 + 20=
<gadget id="calculator">20 + 20</gadget>
<output>40</output>
40 cm. Area of a rhombus= 1/2 * d1d2 = 1/2 * 40 * 30=
<gadget id="calculator">1/2 * 40 * 30</gadget>
<output>600</output>
600 sq.cm. Answer:600 sq.cm
<result>E</result> | E | {
"A": "272 sq.cm",
"B": "267 sq.cm",
"C": "286 sq.cm",
"D": "251 sq.cm",
"E": "600 sq.cm"
} | Find the area of a rhombus whose side is 25 cm and one of the diagonals is 30 cm? |
aqua_rat__TeJvntbCwrclv5ve | How long does a train 110 m long running at the speed of 72 km/hr takes to cross a bridge 132 m length? Select the correct option:
A) 12.8 sec B) 12.1 sec C) 12.2 sec D) 12.6 sec E) 11.1 sec | Speed = 72 * 5/18=
<gadget id="calculator">72 * 5/18</gadget>
<output>20</output>
20 m/sec Total distance covered= 110 + 132=
<gadget id="calculator">110 + 132</gadget>
<output>242</output>
242 m. Required time= 242/20=
<gadget id="calculator">242/20</gadget>
<output>121/10 = around 12.1</output>
12.1 sec. Answer: 12.1 sec
<result>B</result> | B | {
"A": "12.8 sec",
"B": "12.1 sec",
"C": "12.2 sec",
"D": "12.6 sec",
"E": "11.1 sec"
} | How long does a train 110 m long running at the speed of 72 km/hr takes to cross a bridge 132 m length? |
aqua_rat__SoA9sW24OlrH7rhx | 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 options.
A) 120
B) 1250
C) 1200
D) 1100
E) 1150 | 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 : 1200
<result>C</result> | C | {
"A": "120",
"B": "1250",
"C": "1200",
"D": "1100",
"E": "1150"
} | 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? |
aqua_rat__oWOBGAgeSSwvObdW | From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there on the committee. What is the probability of having 0 woman in committee ? Choose the correct choice:
A) 7/36 B) 9/144 C) 1/36 D) 1/18 E) 5/18 | We may have (3 men and 2 women) = (71/363 x 61/362) = 525 or (4 men and 1 woman) = (71/364 x 61/361) = 210 or (5 men only) = (71/365) = 21 Required ways = 756 Probability of having 0 woman in committee = 21 / 756 =1/36 ans - 1/36
<result>C</result> | C | {
"A": "7/36",
"B": "9/144",
"C": "1/36",
"D": "1/18",
"E": "5/18"
} | From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there on the committee. What is the probability of having 0 woman in committee ? |
aqua_rat__gyyb5y0DYZaYlqe3 | A box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that exactly three bulbs are good.? Answers:
A) 20/69 B) 20/63 C) 20/65 D) 20/61 E) 20/62 | Required probability = (10 * 4)/126 = 20/63.Answer: 20/63
<result>B</result> | B | {
"A": "20/69",
"B": "20/63",
"C": "20/65",
"D": "20/61",
"E": "20/62"
} | A box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that exactly three bulbs are good.? |
aqua_rat__7XQxUDd2Lc4u0Yz8 | A train passes a station platform in 32 sec and a man standing on the platform in 20 sec. If the speed of the train is 54 km/hr. What is the length of the platform? Select the correct option: A) 228 B) 240 C) 887 D) 166 E) 180 | Speed = 54 * 5/18=
<gadget id="calculator">54 * 5/18</gadget>
<output>15</output>
15 m/sec. Length of the train= 15 * 20=
<gadget id="calculator">15 * 20</gadget>
<output>300</output>
300 m. Let the length of the platform be x m . Then, (x + 300)/32= 15 => x = 180 m. Answer: 180
<result>E</result> | E | {
"A": "228",
"B": "240",
"C": "887",
"D": "166",
"E": "180"
} | A train passes a station platform in 32 sec and a man standing on the platform in 20 sec. If the speed of the train is 54 km/hr. What is the length of the platform? |
aqua_rat__IbdsUawWBYvCDvaj | If |w|=−w, which of the following must be true? Choose the correct choice from the following options:
A) x≥0
B) w≤0
C) x2>x
D) x3<0
E) 2x<x | |w| =-w means absolute value of w is equal to negative of w. Since absolute value cannot be negative hence negative of w should result in a non negative number. It means w is a non positive number i.e. w<0. Answer is w≤0
<result>B</result> | B | {
"A": "x≥0",
"B": "w≤0",
"C": "x2>x",
"D": "x3<0",
"E": "2x<x"
} | If |w|=−w, which of the following must be true? |
aqua_rat__ImfrU48lTv9nBJMG | Two numbers are less than third number by 30% and 37% respectively. How much percent is the second number less than by the first Choose the correct choice from the following options:
A) 8% B) 9% C) 10% D) 11% E) 12% | Explanation: Let the third number is x. then first number = (100-30)=
<gadget id="calculator">(100-30)</gadget>
<output>70</output>
70% of x= 7x/10 Second number is (63x/100) Difference = 7x/10 - 63x/100 = 7x/10 So required percentage is, difference is what percent of first number => (7x/100 * 10/7x * 100 )% = 10%Explanation: Let the third number is x. then first number (7 /100 * 10/7 * 100 )=
<gadget id="calculator">(7 /100 * 10/7 * 100 )</gadget>
<output>10</output>
10%Explanation: Let the third number is x. then first number= (100-30)=
<gadget id="calculator">(100-30)</gadget>
<output>70</output>
70% of x= 7x/10 Second number is (63x/100) Difference = 7x/10 - 63x/100 = 7x/10 So required percentage is, difference is what percent of first number => (7x/100 * 10/7x * 100 )% = 10% Option 10%(7 /100 * 10/7 * 100 )=
<gadget id="calculator">(7 /100 * 10/7 * 100 )</gadget>
<output>10</output>
10% Option 10%
<result>C</result> | C | {
"A": "8%",
"B": "9%",
"C": "10%",
"D": "11%",
"E": "12%"
} | Two numbers are less than third number by 30% and 37% respectively. How much percent is the second number less than by the first |
aqua_rat__wj7yMURCryAtDVIN | How many numbers from 39 to 79 are exactly divisible by 11? Pick one.
A) 5 B) 7 C) 4 D) 11 E) 12 | 39/11 = 1 and 79/11 = 7 ==> 7 - 3=
<gadget id="calculator">7 - 3</gadget>
<output>4</output>
4 Numbers Answer : 4
<result>C</result> | C | {
"A": "5",
"B": "7",
"C": "4",
"D": "11",
"E": "12"
} | How many numbers from 39 to 79 are exactly divisible by 11? |
aqua_rat__woGZMI6OJ90iSUHl | It is found that the volume of a cube is numerically equal to its surface area. Then the measure of its edge in meters is: Answers
A) 4
B) 6
C) 8
D) 9
E) cannot be determined | if edge of cube = a volume of cube = a^3 surface area = 6(a^2) then a^3 = 6(a^2) a = 6 ANSWER:6
<result>B</result> | B | {
"A": "4",
"B": "6",
"C": "8",
"D": "9",
"E": "cannot be determined"
} | It is found that the volume of a cube is numerically equal to its surface area. Then the measure of its edge in meters is: |
aqua_rat__P4n9t6H1Q6eRxDz3 | if there are 30 cans out of them one is poisned if a person tastes very little he will die within 14 hours so if there are mice to test and 24 hours to test, how many mices are required to find the poisned can? Choose the correct option: A) 3 B) 2 C) 6 D) 1 E) 7 | as we know only one can is poisoned so try mice every can n notice the time for ex suppose for ist can time was 12:05 then after 5 min test for can 2 means 12:10..n if 1st can contain poision then according to time it can be cleared.. ANSWER:1
<result>D</result> | D | {
"A": "3",
"B": "2",
"C": "6",
"D": "1",
"E": "7"
} | if there are 30 cans out of them one is poisned if a person tastes very little he will die within 14 hours so if there are mice to test and 24 hours to test, how many mices are required to find the poisned can? |
aqua_rat__kVpmoOSTWfQl4Joq | How long does a train 165 meters long running at the rate of 72 kmph take to cross a bridge 660 meters in length? Pick:
A) 28
B) 41.25
C) 55
D) 18
E) 12 | T = (660 + 165)/72 * 18/5=
<gadget id="calculator">(660 + 165)/72 * 18/5</gadget>
<output>165/4 = around 41.25</output>
41.25 Answer: 41.25
<result>B</result> | B | {
"A": "28",
"B": "41.25",
"C": "55",
"D": "18",
"E": "12"
} | How long does a train 165 meters long running at the rate of 72 kmph take to cross a bridge 660 meters in length? |
aqua_rat__f1oYTQAR4DyFiHbP | A particular store purchased a stock of turtleneck sweaters and marked up its cost by 20%. During the New Year season, it further marked up its prices by 25% of the original retail price. In February, the store then offered a discount of 15%. What was its profit on the items sold in February?
Choose one:
A) 27.5% B) 30% C) 35% D) 37.5% E) 40% | 27.5%ssume the total price = 100x Price after 20% markup = 120x Price after 25%further markup = 1.25*120=
<gadget id="calculator">1.25*120</gadget>
<output>150</output>
150x Price after the discount= 0.85*150=
<gadget id="calculator">0.85*150</gadget>
<output>127.5</output>
127.5x Hence total profit= 27.5% Option 27.5%
<result>A</result> | A | {
"A": "27.5%",
"B": "30%",
"C": "35%",
"D": "37.5%",
"E": "40%"
} | A particular store purchased a stock of turtleneck sweaters and marked up its cost by 20%. During the New Year season, it further marked up its prices by 25% of the original retail price. In February, the store then offered a discount of 15%. What was its profit on the items sold in February? |
aqua_rat__WQpgTRbZgUx6awFA | If books bought at prices ranging from Rs. 98 to Rs. 195 are sold at prices ranging from Rs. 120 to Rs 215, what is the greatest possible profit that might be made in selling 13 books ?
Select.
A) Rs. 1650 B) Rs. 3000 C) Rs. 1521 D) Rs. 1400 E) Rs. 1560 | The greatest profit is possible only if the cost price of the books are minimum and selling prices are maximum. Let lowest cost price of the 13 books = 98*13 = Rs. 1,274 Maximum selling price of 13 books = 215 *13 = Rs. 2,795 So, maximum profit = 2795 - 1274 = Rs. 1,521 ANSWER : OPTION Rs. 1521
<result>C</result> | C | {
"A": "Rs. 1650",
"B": "Rs. 3000",
"C": "Rs. 1521",
"D": "Rs. 1400",
"E": "Rs. 1560"
} | If books bought at prices ranging from Rs. 98 to Rs. 195 are sold at prices ranging from Rs. 120 to Rs 215, what is the greatest possible profit that might be made in selling 13 books ? |
aqua_rat__1di3BpVh52EFdL2Z | Two trains A and B starting from two points and travelling in opposite directions, reach their destinations 9 hours and 4 hours respectively after meeting each other. If the train A travels at 60kmph, find the rate at which the train B runs.
Choose the correct choice from the following options:
A) 40 B) 90 C) 120 D) 80 E) 100 | If two objects A and B start simultaneously from opposite points and, after meeting, reach their destinations in ‘a’ and ‘b’ hours respectively (i.e. A takes ‘a hrs’ to travel from the meeting point to his destination and B takes ‘b hrs’ to travel from the meeting point to his destination), then the ratio of their speeds is given by: Sa/Sb = √(b/a) i.e. Ratio of speeds is given by the square root of the inverse ratio of time taken. Sa/Sb = √(4/9) = 2/3 This gives us that the ratio of the speed of A : speed of B as 2:3. Since speed of A is 60 kmph, speed of 90 must be 60*(3/2)=
<gadget id="calculator">60*(3/2)</gadget>
<output>90</output>
90 kmph Answer 90
<result>B</result> | B | {
"A": "40",
"B": "90",
"C": "120",
"D": "80",
"E": "100"
} | Two trains A and B starting from two points and travelling in opposite directions, reach their destinations 9 hours and 4 hours respectively after meeting each other. If the train A travels at 60kmph, find the rate at which the train B runs. |
aqua_rat__t0KGNvv6MLgBFEzR | I bought three toys for my triplet boys (one for each). I placed the toys in the dark store. One by one each boy went to the store and pick the toy. What is the probability that no boy will choose his own toy? Choose the correct choice from the following choices
A) 1/3 B) 2/3 C) 3/3 D) 4/3 E) 5/3 | Solution: 1/3 Assuming T1 is the Toy for brother1, T2 is the toy for brother2 and T3 is the toy for brother3. Following are the possible cases for toys distribution: Boy1 Boy2 Boy3 T1 T2 T3 T1 T3 T2 T2 T1 T3 T2 T3 T1 .... (A) T3 T1 T2 .... (B) T3 T2 T1 In both steps (A) & (B), no one gets the correct toy. Therefore probability that none brother can get the own toy is 2/6 = 1/3 1/3nswer 1/3
<result>A</result> | A | {
"A": "1/3",
"B": "2/3",
"C": "3/3",
"D": "4/3",
"E": "5/3"
} | I bought three toys for my triplet boys (one for each). I placed the toys in the dark store. One by one each boy went to the store and pick the toy. What is the probability that no boy will choose his own toy? |
aqua_rat__0FL2xyx2UyEk9Cxw | A man, a woman and a boy can complete a job in 3 days, 4 days and 12 days respectively. How many boys must assist 1 man and 1 woman to complete the job in 1/4th of a day? Choose the most appropriate option
A) 10 B) 41 C) 31 D) 21 E) 22 | Explanation: 1 man’s 1 day’s work = 1/3, ¼ day’s work = 1/3 × ¼ = 1/12 1 woman’s 1 day’s work = ¼, ¼ day’s work = ¼ × ¼ = 1/16 1 boy’s 1 day’s work = 1/12, ¼ day’s work = 1/12 × ¼ = 1/48 Let ‘x’ be the No. of boys required. Then, (1 man + 1 woman + x boy)’s ¼ day’s work 1/12 + 1/16 + x/48 = 1 = (4 + 3 + x)/48 = 1 i.e. 7 + x= 48 and x = 41. Answer: Option 41
<result>B</result> | B | {
"A": "10",
"B": "41",
"C": "31",
"D": "21",
"E": "22"
} | A man, a woman and a boy can complete a job in 3 days, 4 days and 12 days respectively. How many boys must assist 1 man and 1 woman to complete the job in 1/4th of a day? |
aqua_rat__GCwQLKvZwuwDNaoQ | At present, the ratio between the ages of Amit and Dhiraj is 5 : 4. After 6 years, Amit’s age will be 26 years. What is the age of Dhiraj at present? Choose the correct choice from the following choices:
A) 16 B) 77 C) 566 D) 197 E) 161 | Explanation: Let the present ages of Amit and Dhiraj be 5x years and 4x years respectively. Then, 5x + 6 = 26 5x = 20 x = 4 Dhiraj’s age = 4x = 16 years 16NSWER: 16
<result>A</result> | A | {
"A": "16",
"B": "77",
"C": "566",
"D": "197",
"E": "161"
} | At present, the ratio between the ages of Amit and Dhiraj is 5 : 4. After 6 years, Amit’s age will be 26 years. What is the age of Dhiraj at present? |
aqua_rat__B9yBqOch37uBulvs | A and B invests Rs.3000 and Rs.4000 respectively in a business. If A doubles his capital after 6 months. In what ratio should A and B divide that year's profit?
Choose one:
A) 9:6 B) 9:8 C) 9:1 D) 9:9 E) 9:5 | (3*6 + 6*6): (4*12) 54:48 => 9:8.Answer:9:8
<result>B</result> | B | {
"A": "9:6",
"B": "9:8",
"C": "9:1",
"D": "9:9",
"E": "9:5"
} | A and B invests Rs.3000 and Rs.4000 respectively in a business. If A doubles his capital after 6 months. In what ratio should A and B divide that year's profit? |
aqua_rat__z8La6MmH9WAPIMLc | If x-y=10, which of the following must be true?
I. Both x and y are positive
II. If x is negative, y must be negative
III.If x is positive, y must be positive
Choose the correct option
A) I only
B) II only
C) III only
D) I and II
E) II and III | The best way to approach such questions is to plug in values for x and y Given: x-y=10 I. Both x and y are positive: Let x=12 and y=2 x-y=10 But, Let x=6 and y=-4 x-y=8 Therefore, NOT TRUE III. If x is positive, y must be positive Let x=12 and y=2 x-y=10 But, Let x = 6 and y=-4 x-y=10 Therefore, NOT TRUE II. If x is negative, y must be negative If x is negative, for the expression x-y=8 to be true, y must be a -ve number. Otherwise, the sum of two negative numbers will yield another negative number! Therefore, TRUE Ans: 'II only'
<result>B</result> | B | {
"A": "I only",
"B": "II only",
"C": "III only",
"D": "I and II",
"E": "II and III"
} | If x-y=10, which of the following must be true?
I. Both x and y are positive
II. If x is negative, y must be negative
III.If x is positive, y must be positive |
aqua_rat__KE0rNIjDizoQlKi1 | If each side of a square is increased by 25%, find the percentage change in its area?
Choose the correct choice from the following: A) 65.25 B) 56.25 C) 65 D) 56 E) 25 | let each side of the square be a , then area = a x a New side = 125a / 100 = 5a / 4 New area =(5a x 5a) / (4 x 4) = (25a²/16) increased area== (25a²/16) - a² Increase %= [(9a²/16 ) x (1/a² ) x 100]% = 56.25% Answer: 56.25
<result>B</result> | B | {
"A": "65.25",
"B": "56.25",
"C": "65",
"D": "56",
"E": "25"
} | If each side of a square is increased by 25%, find the percentage change in its area? |
aqua_rat__rbKvO6JoRynFVe0L | If the sum and difference of two numbers are 20 and 8 respectively, then the difference of their square is: Choose the correct choice from the following options:
A) 12
B) 28
C) 160
D) 180
E) 18 | Let the numbers be x and y. Then, x + y = 20 and x - y = 8 x2 - y2 = (x + y)(x - y) = 20 * 8=
<gadget id="calculator">20 * 8</gadget>
<output>160</output>
160. ANSWER:160
<result>C</result> | C | {
"A": "12",
"B": "28",
"C": "160",
"D": "180",
"E": "18"
} | If the sum and difference of two numbers are 20 and 8 respectively, then the difference of their square is: |
aqua_rat__TG78Yjd68EjP0Wc6 | If $500 is deposited into a savings account at an annual interest rate of 5% that compounds monthly, what is the value of the investment after 10 years? Choose the correct choice from the following:
A) $750.00
B) $823.50
C) $973.25
D) $1000.25
E) $1100.00 | ROI = 5% per annum compounded Monthly Tenure, n = 10 years = 120 month Principal = $500 5% per annum compounded monthly will be a little more than 5% at end of an year compounded anually = 6% per annum (approx) in 10 years the among simple rate will increase by 60% but at coumpound rate the amount wil increase more by 60% This question can only be solved by approximation 60% of $500 = $300 i.e. amount after 10 years will be a little more than 500+300=
<gadget id="calculator"> 500+300</gadget>
<output>800</output>
$800 i.e. $823.50 option seems the closest possible answer Answer: option $823.50
<result>B</result> | B | {
"A": "$750.00",
"B": "$823.50",
"C": "$973.25",
"D": "$1000.25",
"E": "$1100.00"
} | If $500 is deposited into a savings account at an annual interest rate of 5% that compounds monthly, what is the value of the investment after 10 years? |
aqua_rat__gHwbrsT5326kXUDH | Two jars contain milk and water in the ratio 5: 4 and 2: 1 regpectively. What volume should be taken out from the first jar if volumes have to be taken out from both jars so as to fill up a third 30 l jar with milk to water in the ratio 1: 1 ? Pick:
A) 7.5 l B) 15 l C) 22.5 l D) It is impossible E) none of these | In both jars concentration of milk is more than 50%. Therefore, in jar three concentration of milk cannot be 50%. Hence, we cannot decide the volumes ANSWER:It is impossible
<result>D</result> | D | {
"A": "7.5 l",
"B": "15 l",
"C": "22.5 l",
"D": "It is impossible",
"E": "none of these"
} | Two jars contain milk and water in the ratio 5: 4 and 2: 1 regpectively. What volume should be taken out from the first jar if volumes have to be taken out from both jars so as to fill up a third 30 l jar with milk to water in the ratio 1: 1 ? |
aqua_rat__fdOsAaEb3pAqzIIh | A clock shows the time as 9 a.m. If the minute hand gains 5 minutes every hour, how many minutes will the clock gain by 5 p.m.? Choose the correct choice from the following answers: A) 30 min B) 35 min C) 45 min D) 40 min E) 55 min | there are 8 hours in between 9 a.m. to 5 p.m. 8*5=
<gadget id="calculator">8*5</gadget>
<output>40</output>
40 minutes. ANSWER:40 min
<result>D</result> | D | {
"A": "30 min",
"B": "35 min",
"C": "45 min",
"D": "40 min",
"E": "55 min"
} | A clock shows the time as 9 a.m. If the minute hand gains 5 minutes every hour, how many minutes will the clock gain by 5 p.m.? |
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Dataset Card for Calc-aqua_rat
Summary
This dataset is an instance of AQuA-RAT dataset extended with in-context calls of a sympy calculator.
Supported Tasks
The dataset is intended for training Chain-of-Thought reasoning models able to use external tools to enhance the factuality of their responses. This dataset presents in-context scenarios where models can outsource the computations in the reasoning chain to a calculator.
Construction Process
The dataset was constructed automatically by evaluating all candidate calls to a sympy library that were extracted from the originally annotated
rationales. The selection of candidates is pivoted by the matching of equals ('=') symbols in the chain, where the left-hand side of the equation is evaluated,
and accepted as a correct gadget call, if the result occurs closely on the right-hand side.
Therefore, the extraction of calculator calls may inhibit false negatives (where the calculator could have been used but was not), but not any known
false positives.
We also perform in-dataset and cross-dataset data-leak detection within the Calc-X collection. Specifically for AQuA-RAT, we removed a few percent of the train split that were near-duplicates with some of the test or validation examples.
A full description of the extraction process can be found in the corresponding parse script,
If you find an issue in the dataset or in the fresh version of the parsing script, we'd be happy if you report it, or create a PR.
Data splits
The dataset with the near-duplicates removed can be loaded in the default config using:
datasets.load_dataset("MU-NLPC/calc-aqua_rat")
If you want the unfiltered version, you can use:
datasets.load_dataset("MU-NLPC/calc-aqua_rat", "original-splits")
Attributes
- id: an id of the example
- question: A natural language definition of the problem to solve, including the options to choose from
- chain: A natural language step-by-step solution with automatically inserted calculator calls and outputs of the sympy calculator
- result: The correct option (one of A...E)
- options: a dictionary with 5 possible options (A, B, C, D and E), among which one is correct
- question_without_options: same as question but without the options inserted
Attributes id, question, chain, and result are present in all datasets in Calc-X collection.
Related work
This dataset was created as a part of a larger effort in training models capable of using a calculator during inference, which we call Calcformers.
- Calc-X collection - datasets for training Calcformers
- Calcformers collection - calculator-using models we trained and published on HF
- Calc-X and Calcformers paper
- Calc-X and Calcformers repo
Here are links to the original dataset:
License
Apache-2.0, consistently with the original aqua-rat dataset.
Cite
If you use this dataset in research, please cite the original AQuA-RAT paper, and Calc-X paper as follows:
@inproceedings{kadlcik-etal-2023-soft,
title = "Calc-X and Calcformers: Empowering Arithmetical Chain-of-Thought through Interaction with Symbolic Systems",
author = "Marek Kadlčík and Michal Štefánik and Ondřej Sotolář and Vlastimil Martinek",
booktitle = "Proceedings of the The 2023 Conference on Empirical Methods in Natural Language Processing: Main track",
month = dec,
year = "2023",
address = "Singapore, Singapore",
publisher = "Association for Computational Linguistics",
url = "https://arxiv.org/abs/2305.15017",
}
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