kurtos-ai/gsm-gpt2-rff
Text Generation • Updated
Datasets:
idx int64 0 730k | prompt stringlengths 19 4.43k | text stringlengths 47 5.74k | dataset_name stringclasses 5 values |
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0 | Question: 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?
Options: ['A)21', 'B)21.5', 'C)22', 'D)22.5', 'E)23']
Answer: | Question: 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?
Options: ['A)21', 'B)21.5', 'C)22', 'D)22.5', 'E)23']
Answer: If Q complete x kilometers, then P completes 1.15x kilometers.
x + 1.15x = 43
2.15x=43
x = 43/2.15 = 20
Then P will have have walked 1.15*20=23 km.
The answer is E.<|endoftext|> | aqua_rat |
1 | Question: 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?
Options: ['A)4 and 1', 'B)1 and 5', 'C)5 and 1', 'D)3 and 5', 'E)5 and 3']
Answer: | Question: 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?
Options: ['A)4 and 1', 'B)1 and 5', 'C)5 and 1', 'D)3 and 5', 'E)5 and 3']
Answer: 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: C<|endoftext|> | aqua_rat |
2 | Question: 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)
Options: ['A)II', 'B)I and II', 'C)I and III', 'D)II and III', 'E)All of the above']
Answer: | Question: 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)
Options: ['A)II', 'B)I and II', 'C)I and III', 'D)II and III', 'E)All of the above']
Answer: 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 B....<|endoftext|> | aqua_rat |
3 | Question: 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?
Options: ['A)$1600', 'B)$2000', 'C)$2150', 'D)$2500', 'E)$12000']
Answer: | Question: 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?
Options: ['A)$1600', 'B)$2000', 'C)$2150', 'D)$2500', 'E)$12000']
Answer: 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)% = 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 (A) looks correct.<|endoftext|> | aqua_rat |
4 | Question: 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?
Options: ['A)18 seconds', 'B)27 seconds', 'C)26 seconds', 'D)12 seconds', 'E)8 seconds']
Answer: | Question: 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?
Options: ['A)18 seconds', 'B)27 seconds', 'C)26 seconds', 'D)12 seconds', 'E)8 seconds']
Answer: Speed of the boat downstream = 25 +11
= 36 kmph
= 36 * 5/18 = 10 m/s
Hence time taken to cover 80 m = 80/10
= 8 seconds.
Answer:E<|endoftext|> | aqua_rat |
5 | Question: 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']
Answer: | Question: 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']
Answer: 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 A.<|endoftext|> | aqua_rat |
6 | Question: If (x^2 + 4x - 11)/5 ≤ x + 1, then x could be represented by which of the following?
Options: ['A)− 3 ≤ x ≤ 4', 'B)− 4 ≤ x ≤ 3', 'C)− 3 ≤ x ≤ 3', 'D)− 4 ≤ x ≤ − 3', 'E)3 ≤ x ≤ 4']
Answer: | Question: If (x^2 + 4x - 11)/5 ≤ x + 1, then x could be represented by which of the following?
Options: ['A)− 3 ≤ x ≤ 4', 'B)− 4 ≤ x ≤ 3', 'C)− 3 ≤ x ≤ 3', 'D)− 4 ≤ x ≤ − 3', 'E)3 ≤ x ≤ 4']
Answer: IMO A is correct answer
solving through eqautions
x^2 +4x-11<= 5x+5
(x+3)(x-4)<=0<|endoftext|> | aqua_rat |
7 | Question: Find the smallest number of five digits exactly divisible by 22,33,66 and 44.
Options: ['A)10101', 'B)11000', 'C)10110', 'D)10111', 'E)10100']
Answer: | Question: Find the smallest number of five digits exactly divisible by 22,33,66 and 44.
Options: ['A)10101', 'B)11000', 'C)10110', 'D)10111', 'E)10100']
Answer: 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 E.<|endoftext|> | aqua_rat |
8 | Question: 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?
Options: ['A)16', 'B)20.5', 'C)17.5', 'D)20', 'E)4.5']
Answer: | Question: 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?
Options: ['A)16', 'B)20.5', 'C)17.5', 'D)20', 'E)4.5']
Answer: Total entrance fee is (2*$5) + (1.20*5)= $16
Total rides fee is (0.50*3)*3= $4.50
Total money spent is $20.50
Answer is B<|endoftext|> | aqua_rat |
9 | Question: 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?
Options: ['A)15', 'B)31', 'C)12', 'D)27', 'E)91']
Answer: | Question: 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?
Options: ['A)15', 'B)31', 'C)12', 'D)27', 'E)91']
Answer: 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 C.<|endoftext|> | aqua_rat |
10 | Question: If Tim had lunch at $50 and he gave 20% tip, how much did he spend?
Options: ['A)A)$60.00', 'B)B)$35.42', 'C)C)$60.60', 'D)D)$21.56', 'E)E)$78.45']
Answer: | Question: If Tim had lunch at $50 and he gave 20% tip, how much did he spend?
Options: ['A)A)$60.00', 'B)B)$35.42', 'C)C)$60.60', 'D)D)$21.56', 'E)E)$78.45']
Answer: 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 = $60.00
correct answer is A)$60.00<|endoftext|> | aqua_rat |
11 | Question: 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 ?
Options: ['A)Rs. 1020.80', 'B)Rs. 1025', 'C)Rs. 1055', 'D)Data inadequate', 'E)None of these']
Answer: | Question: 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 ?
Options: ['A)Rs. 1020.80', 'B)Rs. 1025', 'C)Rs. 1055', 'D)Data inadequate', 'E)None of these']
Answer: 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 C<|endoftext|> | aqua_rat |
12 | Question: q is a positive integer and multiple of 2; p = 4^q, what is the remainder when p is divided by 10?
Options: ['A)10', 'B)6', 'C)4', 'D)0', 'E)It Cannot Be Determined']
Answer: | Question: q is a positive integer and multiple of 2; p = 4^q, what is the remainder when p is divided by 10?
Options: ['A)10', 'B)6', 'C)4', 'D)0', 'E)It Cannot Be Determined']
Answer: 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: B.<|endoftext|> | aqua_rat |
13 | Question: If q is the square of a positive integer, which of the following must be equal to the square of the next positive integer?
Options: ['A)√n + 1', 'B)n + 1', 'C)n^2 + 1', 'D)q + 2√q + 1', 'E)n^2 + 2n + 1']
Answer: | Question: If q is the square of a positive integer, which of the following must be equal to the square of the next positive integer?
Options: ['A)√n + 1', 'B)n + 1', 'C)n^2 + 1', 'D)q + 2√q + 1', 'E)n^2 + 2n + 1']
Answer: 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 D<|endoftext|> | aqua_rat |
14 | Question: 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?
Options: ['A)300', 'B)992', 'C)1120', 'D)552', 'E)312']
Answer: | Question: 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?
Options: ['A)300', 'B)992', 'C)1120', 'D)552', 'E)312']
Answer: 1/7:1/7:1/14 = 2:2:1
1/5*5600 = 1120
2240-1120 = 1120
Answer: C<|endoftext|> | aqua_rat |
15 | Question: If a/b=3/4 and 8a+5b=22,then find the value of a.
Options: ['A)1/2', 'B)3/2', 'C)5/2', 'D)4/2', 'E)7/2']
Answer: | Question: If a/b=3/4 and 8a+5b=22,then find the value of a.
Options: ['A)1/2', 'B)3/2', 'C)5/2', 'D)4/2', 'E)7/2']
Answer: (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 B.<|endoftext|> | aqua_rat |
16 | Question: Given that k/l < 1, and both k and l are positive integers, which one of the following must be greater than 1?
Options: ['A)k/l^2', 'B)k^2/l', 'C)k^2/l^2', 'D)l/k', 'E)√(k/l)']
Answer: | Question: Given that k/l < 1, and both k and l are positive integers, which one of the following must be greater than 1?
Options: ['A)k/l^2', 'B)k^2/l', 'C)k^2/l^2', 'D)l/k', 'E)√(k/l)']
Answer: 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 (D)<|endoftext|> | aqua_rat |
17 | Question: 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?
Options: ['A)20', 'B)32', 'C)40', 'D)50', 'E)60']
Answer: | Question: 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?
Options: ['A)20', 'B)32', 'C)40', 'D)50', 'E)60']
Answer: 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=32
B<|endoftext|> | aqua_rat |
18 | Question: John found that the average of 15 numbers is 40. If 10 is added to each number then the mean of number is?
Options: ['A)50', 'B)45', 'C)65', 'D)78', 'E)64']
Answer: | Question: John found that the average of 15 numbers is 40. If 10 is added to each number then the mean of number is?
Options: ['A)50', 'B)45', 'C)65', 'D)78', 'E)64']
Answer: (x+x1+...x14)/15 = 40
50
Option A<|endoftext|> | aqua_rat |
19 | Question: A person is traveling at 20 km/hr and reached his destiny in 2.5 hr then find the distance?
Options: ['A)53 km', 'B)55 km', 'C)52 km', 'D)60 km', 'E)50 km']
Answer: | Question: A person is traveling at 20 km/hr and reached his destiny in 2.5 hr then find the distance?
Options: ['A)53 km', 'B)55 km', 'C)52 km', 'D)60 km', 'E)50 km']
Answer: T = 2.5 hrs = 5/2 hrs
D= T*S = 20*5/2 = 50 km
Answer is E<|endoftext|> | aqua_rat |
20 | Question: The first five numbers in a regular sequence are 4, 10, X, 46, and 94. What is x ?
Options: ['A)28', 'B)26', 'C)30', 'D)22', 'E)24']
Answer: | Question: The first five numbers in a regular sequence are 4, 10, X, 46, and 94. What is x ?
Options: ['A)28', 'B)26', 'C)30', 'D)22', 'E)24']
Answer: 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
D<|endoftext|> | aqua_rat |
21 | Question: 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?
Options: ['A)2', 'B)4', 'C)6', 'D)8', 'E)10']
Answer: | Question: 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?
Options: ['A)2', 'B)4', 'C)6', 'D)8', 'E)10']
Answer: 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: C<|endoftext|> | aqua_rat |
22 | Question: What is the least value of x, So that 2x5475 is divisible by 9
Options: ['A)7', 'B)8', 'C)4', 'D)3', 'E)2']
Answer: | Question: What is the least value of x, So that 2x5475 is divisible by 9
Options: ['A)7', 'B)8', 'C)4', 'D)3', 'E)2']
Answer: 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 = 27
is divisible by 9.
Answer: Option C<|endoftext|> | aqua_rat |
23 | Question: Square P is inscribed in circle Q. If the perimeter of P is 40, what is the circumference of Q?
Options: ['A)11√ 2π', 'B)10√ 2π', 'C)9√ 2π', 'D)8√ 2π', 'E)7√ 2π']
Answer: | Question: Square P is inscribed in circle Q. If the perimeter of P is 40, what is the circumference of Q?
Options: ['A)11√ 2π', 'B)10√ 2π', 'C)9√ 2π', 'D)8√ 2π', 'E)7√ 2π']
Answer: 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 B.<|endoftext|> | aqua_rat |
24 | Question: 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?
Options: ['A)9', 'B)10', 'C)9', 'D)12', 'E)10']
Answer: | Question: 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?
Options: ['A)9', 'B)10', 'C)9', 'D)12', 'E)10']
Answer: 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
Answer is A<|endoftext|> | aqua_rat |
25 | Question: 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
Options: ['A)I,II only', 'B)I only', 'C)II,III only', 'D)II only', 'E)III only']
Answer: | Question: 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
Options: ['A)I,II only', 'B)I only', 'C)II,III only', 'D)II only', 'E)III only']
Answer: 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=$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: C<|endoftext|> | aqua_rat |
26 | Question: 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?
Options: ['A)Q=3', 'B)Q=4', 'C)6', 'D)8', 'E)12']
Answer: | Question: 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?
Options: ['A)Q=3', 'B)Q=4', 'C)6', 'D)8', 'E)12']
Answer: 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
A<|endoftext|> | aqua_rat |
27 | Question: 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?
Options: ['A) $32,500', 'B) $35,000', 'C) $37,500', 'D) $42,500', 'E) $50,000']
Answer: | Question: 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?
Options: ['A) $32,500', 'B) $35,000', 'C) $37,500', 'D) $42,500', 'E) $50,000']
Answer: let x be the average of 40 customers
40*x + 10* 95000 = 50*45000
solving this we have x= 32500
Answer is A.<|endoftext|> | aqua_rat |
28 | Question: 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']
Answer: | Question: 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']
Answer: π * 14 * 35= 1540
Answer:C<|endoftext|> | aqua_rat |
29 | Question: 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?
Options: ['A)1', 'B)5', 'C)4', 'D)6', 'E)2']
Answer: | Question: 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?
Options: ['A)1', 'B)5', 'C)4', 'D)6', 'E)2']
Answer: 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
=.125*8
=1
Answer: A<|endoftext|> | aqua_rat |
30 | Question: 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?
Options: ['A)8', 'B)9', 'C)10', 'D)11', 'E)16']
Answer: | Question: 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?
Options: ['A)8', 'B)9', 'C)10', 'D)11', 'E)16']
Answer: 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
Answer:-A<|endoftext|> | aqua_rat |
31 | Question: 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']
Answer: | Question: 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']
Answer: For 3 years:
Diff.=Sum×(rate)2(300+rate)/(100)3
= 2000×10×10×310/100×100×100 = 62
Answer C<|endoftext|> | aqua_rat |
32 | Question: 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?
Options: ['A)9%', 'B)10%', 'C)23%', 'D)21%', 'E)22%']
Answer: | Question: 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?
Options: ['A)9%', 'B)10%', 'C)23%', 'D)21%', 'E)22%']
Answer: 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 C ) ANSWER:C<|endoftext|> | aqua_rat |
33 | Question: Find the constant k so that : -x2 - (k + 11)x - 8 = -(x - 2)(x - 4)
Options: ['A)11', 'B)12', 'C)17', 'D)14', 'E)15']
Answer: | Question: Find the constant k so that : -x2 - (k + 11)x - 8 = -(x - 2)(x - 4)
Options: ['A)11', 'B)12', 'C)17', 'D)14', 'E)15']
Answer: -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 C<|endoftext|> | aqua_rat |
34 | Question: A positive whole number has factors of 3 and 5. The number MUST be divisible by: I. 15 II. 30 III. 60
Options: ['A)I & II', 'B)III', 'C)I & III', 'D)II & III', 'E)II']
Answer: | Question: A positive whole number has factors of 3 and 5. The number MUST be divisible by: I. 15 II. 30 III. 60
Options: ['A)I & II', 'B)III', 'C)I & III', 'D)II & III', 'E)II']
Answer: 15 , 30 is not divisible by 60.But 60 is divisible by 3,5,15,30
So answer is III
Answer : B<|endoftext|> | aqua_rat |
35 | Question: 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?
Options: ['A)Rs.78000', 'B)Rs.48000', 'C)Rs.6000', 'D)Rs.82000', 'E)Rs.32000']
Answer: | Question: 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?
Options: ['A)Rs.78000', 'B)Rs.48000', 'C)Rs.6000', 'D)Rs.82000', 'E)Rs.32000']
Answer: 6:1
2:1
------
12:1
1 ----- 6000
13 ----- ? => Rs.78,000
Answer: A<|endoftext|> | aqua_rat |
36 | Question: 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?
Options: ['A)10', 'B)30', 'C)28', 'D)60', 'E)90']
Answer: | Question: 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?
Options: ['A)10', 'B)30', 'C)28', 'D)60', 'E)90']
Answer: 10 players are there.
two players play one game with one another.
so 8C2=8*7/2
=28
SO OPTION C is correct<|endoftext|> | aqua_rat |
37 | Question: 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
Options: ['A)50 min', 'B)60 min', 'C)90 min', 'D)80 min', 'E)120 min']
Answer: | Question: 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
Options: ['A)50 min', 'B)60 min', 'C)90 min', 'D)80 min', 'E)120 min']
Answer: pipe a can do a work 60 min.
lets leakage time is x;
then
1/60 -1/x=1/120
x=120 min
ANSWER:E<|endoftext|> | aqua_rat |
38 | Question: Today is 22 days before Mariah's graduation. If she graduates on a Friday, what day of the week is it today?
Options: ['A)Monday', 'B)Friday', 'C)Tuesday', 'D)Thursday', 'E)Sunday']
Answer: | Question: Today is 22 days before Mariah's graduation. If she graduates on a Friday, what day of the week is it today?
Options: ['A)Monday', 'B)Friday', 'C)Tuesday', 'D)Thursday', 'E)Sunday']
Answer: 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: D<|endoftext|> | aqua_rat |
39 | Question: 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?
Options: ['A)1', 'B)4', 'C)9', 'D)11', 'E)no such integers exist']
Answer: | Question: 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?
Options: ['A)1', 'B)4', 'C)9', 'D)11', 'E)no such integers exist']
Answer: 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 = 11.
correct answer D<|endoftext|> | aqua_rat |
40 | Question: 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 :
Options: ['A)36 years', 'B)45 years', 'C)50 years', 'D)55 years', 'E)75 years']
Answer: | Question: 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 :
Options: ['A)36 years', 'B)45 years', 'C)50 years', 'D)55 years', 'E)75 years']
Answer: 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. Answer A<|endoftext|> | aqua_rat |
41 | Question: A bottle of coke contains 200gm in place of 1kg of fluid. Find the actual % difference, given a 10% gain on initial fluid?
Options: ['A)32.5%', 'B)112.5%', 'C)35%', 'D)40%', 'E)50%']
Answer: | Question: A bottle of coke contains 200gm in place of 1kg of fluid. Find the actual % difference, given a 10% gain on initial fluid?
Options: ['A)32.5%', 'B)112.5%', 'C)35%', 'D)40%', 'E)50%']
Answer: fluid price of 200gm = 100+10 = 110
Difference = 110-20 = 90
% of difference = 90*100/80 =112.5 %
Answer is B<|endoftext|> | aqua_rat |
42 | Question: 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?
Options: ['A)20', 'B)30', 'C)48', 'D)64', 'E)72']
Answer: | Question: 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?
Options: ['A)20', 'B)30', 'C)48', 'D)64', 'E)72']
Answer: Total distance = 64
Distance = 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 = 8
Walking distance = s1*t1 = 8*8 = 64
Answer: D<|endoftext|> | aqua_rat |
43 | Question: 5358 x 51 = ?
Options: ['A)273258', 'B)273268', 'C)273348', 'D)273358', 'E)None of these']
Answer: | Question: 5358 x 51 = ?
Options: ['A)273258', 'B)273268', 'C)273348', 'D)273358', 'E)None of these']
Answer: Explanation:
5358 x 51 = 5358 x (50 + 1)
= 5358 x 50 + 5358 x 1
= 267900 + 5358
= 273258.
ANSWER IS A<|endoftext|> | aqua_rat |
44 | Question: 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?
Options: ['A)5/7', 'B)4/5', 'C)2/5', 'D)3/5', 'E)11/8']
Answer: | Question: 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?
Options: ['A)5/7', 'B)4/5', 'C)2/5', 'D)3/5', 'E)11/8']
Answer: 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: D.<|endoftext|> | aqua_rat |
45 | Question: 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?
Options: ['A)27/343', 'B)3/7', 'C)27/125', 'D)199/245', 'E)9/125']
Answer: | Question: 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?
Options: ['A)27/343', 'B)3/7', 'C)27/125', 'D)199/245', 'E)9/125']
Answer: Let us take 7*5=35 as the total number of customers. So 7*3=21 customers bought a bagel and 5*5=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 D.<|endoftext|> | aqua_rat |
46 | Question: |x+3| – |4-x| = |8+x| How many S solutions will this equation have?
Options: ['A)0', 'B)1', 'C)2', 'D)3', 'E)4']
Answer: | Question: |x+3| – |4-x| = |8+x| How many S solutions will this equation have?
Options: ['A)0', 'B)1', 'C)2', 'D)3', 'E)4']
Answer: |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.A<|endoftext|> | aqua_rat |
47 | Question: 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?
Options: ['A)20%', 'B)24%', 'C)30%', 'D)32%', 'E)79%']
Answer: | Question: 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?
Options: ['A)20%', 'B)24%', 'C)30%', 'D)32%', 'E)79%']
Answer: 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) = O
=> x = 24.24%
So, answer will be B<|endoftext|> | aqua_rat |
48 | Question: 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?
Options: ['A)2/7', 'B)1/3', 'C)1/2', 'D)2/3', 'E)5/7']
Answer: | Question: 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?
Options: ['A)2/7', 'B)1/3', 'C)1/2', 'D)2/3', 'E)5/7']
Answer: 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 = 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 [E]<|endoftext|> | aqua_rat |
49 | Question: 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
Options: ['A)8500 cm3', 'B)9000 cm3', 'C)9250 cm3', 'D)9261 cm3', 'E)None']
Answer: | Question: 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
Options: ['A)8500 cm3', 'B)9000 cm3', 'C)9250 cm3', 'D)9261 cm3', 'E)None']
Answer: Solution
Surface area = (34398 / 13)
‹=›2646cm3
‹=›6a2= 2646
‹=›a2= 441
‹=›a = 21.
So,volume =(21x21x21)cm3= 9261cm3.
Answer D<|endoftext|> | aqua_rat |
50 | Question: A man sold 20 articles for $60 and gained 20%. How many articles should he sell for $50 to incur a loss 20%?
Options: ['A)25', 'B)36', 'C)40', 'D)50', 'E)48']
Answer: | Question: A man sold 20 articles for $60 and gained 20%. How many articles should he sell for $50 to incur a loss 20%?
Options: ['A)25', 'B)36', 'C)40', 'D)50', 'E)48']
Answer: 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 A is correct.<|endoftext|> | aqua_rat |
51 | Question: 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:
Options: ['A)3:5', 'B)2:1', 'C)16:15', 'D)4:5', 'E)None of these']
Answer: | Question: 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:
Options: ['A)3:5', 'B)2:1', 'C)16:15', 'D)4:5', 'E)None of these']
Answer: 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: C<|endoftext|> | aqua_rat |
52 | Question: 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?
Options: ['A)Rs. 45', 'B)Rs. 50', 'C)Rs. 55', 'D)Rs. 60', 'E)Rs. 65']
Answer: | Question: 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?
Options: ['A)Rs. 45', 'B)Rs. 50', 'C)Rs. 55', 'D)Rs. 60', 'E)Rs. 65']
Answer: 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.
ANSWER IS A<|endoftext|> | aqua_rat |
53 | Question: A train 500 m long can cross an electric pole in 20 sec and then find the speed of the train?
Options: ['A)95 Kmph', 'B)90 Kmph', 'C)92 Kmph', 'D)95 Kmph', 'E)98 Kmph']
Answer: | Question: A train 500 m long can cross an electric pole in 20 sec and then find the speed of the train?
Options: ['A)95 Kmph', 'B)90 Kmph', 'C)92 Kmph', 'D)95 Kmph', 'E)98 Kmph']
Answer: Length = Speed * time
Speed = L/T
S = 500/20
S = 25 M/Sec
Speed= 25*18/5 (To convert M/Sec in to Kmph multiply by 18/5)
Speed = 90 Kmph
ANSWER:B<|endoftext|> | aqua_rat |
54 | Question: The smallest number when increased by " 1 " is exactly divisible by 6,9,15,35,45 is:
Options: ['A)631', 'B)630', 'C)359', 'D)629', 'E)600']
Answer: | Question: The smallest number when increased by " 1 " is exactly divisible by 6,9,15,35,45 is:
Options: ['A)631', 'B)630', 'C)359', 'D)629', 'E)600']
Answer: LCM = 630
630 - 1 = 629
ANSWER:D<|endoftext|> | aqua_rat |
55 | Question: How many keystrokes are needed to type the numbers from 1 to 500?
Options: ['A)1156', 'B)1392', 'C)1480', 'D)1562', 'E)1788']
Answer: | Question: How many keystrokes are needed to type the numbers from 1 to 500?
Options: ['A)1156', 'B)1392', 'C)1480', 'D)1562', 'E)1788']
Answer: 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 B.<|endoftext|> | aqua_rat |
56 | Question: 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?
Options: ['A)82', 'B)41', 'C)14', 'D)56', 'E)28']
Answer: | Question: 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?
Options: ['A)82', 'B)41', 'C)14', 'D)56', 'E)28']
Answer: 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 E) 28<|endoftext|> | aqua_rat |
57 | Question: The edge of a cube is 7a cm. Find its surface?
Options: ['A)24a8', 'B)24a4', 'C)24a1', 'D)24a2', 'E)294a2']
Answer: | Question: The edge of a cube is 7a cm. Find its surface?
Options: ['A)24a8', 'B)24a4', 'C)24a1', 'D)24a2', 'E)294a2']
Answer: 6a2 = 6 * 7a * 7a = 294a2
Answer:E<|endoftext|> | aqua_rat |
58 | Question: 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?
Options: ['A)1.9', 'B)1.7', 'C)1.2', 'D)1.5', 'E)1.6']
Answer: | Question: 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?
Options: ['A)1.9', 'B)1.7', 'C)1.2', 'D)1.5', 'E)1.6']
Answer: 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: B<|endoftext|> | aqua_rat |
59 | Question: A board 7ft. 9 inches long is divided into 3 equal parts . What is the length of each part?
Options: ['A)31 inches', 'B)32 inches', 'C)33 inches', 'D)34 inches', 'E)35 inches']
Answer: | Question: A board 7ft. 9 inches long is divided into 3 equal parts . What is the length of each part?
Options: ['A)31 inches', 'B)32 inches', 'C)33 inches', 'D)34 inches', 'E)35 inches']
Answer: 7 ft 9 in is 84 + 9 = 93 inches. so 93/3 = 31 inches or 2 ft. 7 inch.
ANSWER:A<|endoftext|> | aqua_rat |
60 | Question: Find the number of zeroes in the expression 15*32*25*22*40*75*98*112*125
Options: ['A)12', 'B)9', 'C)14', 'D)7', 'E)6']
Answer: | Question: Find the number of zeroes in the expression 15*32*25*22*40*75*98*112*125
Options: ['A)12', 'B)9', 'C)14', 'D)7', 'E)6']
Answer: (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:B<|endoftext|> | aqua_rat |
61 | Question: The diagonals of a rhombus are 18 cm and 22 cm. Find its area?
Options: ['A)277', 'B)266', 'C)198', 'D)288', 'E)212']
Answer: | Question: The diagonals of a rhombus are 18 cm and 22 cm. Find its area?
Options: ['A)277', 'B)266', 'C)198', 'D)288', 'E)212']
Answer: 1/2 * 18 * 22 = 198
Answer: C<|endoftext|> | aqua_rat |
62 | Question: If rupee one produces rupees nine over a period of 40 years, find the rate of simple interest?
Options: ['A)22 1/8 %', 'B)22 3/2 %', 'C)28 1/2 %', 'D)22 1/2 %', 'E)32 1/2 %']
Answer: | Question: If rupee one produces rupees nine over a period of 40 years, find the rate of simple interest?
Options: ['A)22 1/8 %', 'B)22 3/2 %', 'C)28 1/2 %', 'D)22 1/2 %', 'E)32 1/2 %']
Answer: 9 = (1*40*R)/100
R = 22 1/2 %
Answer:D<|endoftext|> | aqua_rat |
63 | Question: 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?
Options: ['A)32:99', 'B)8:21', 'C)32:45', 'D)34:89', 'E)35:21']
Answer: | Question: 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?
Options: ['A)32:99', 'B)8:21', 'C)32:45', 'D)34:89', 'E)35:21']
Answer: A : B
(6000*4)+(3000*8) : (12000*6)+(9000*6)
48000 : 126000
8 : 21
Answer:B<|endoftext|> | aqua_rat |
64 | Question: 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?
Options: ['A)m', 'B)m', 'C)m', 'D)m', 'E)m']
Answer: | Question: 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?
Options: ['A)m', 'B)m', 'C)m', 'D)m', 'E)m']
Answer: Speed = (10/10 * 60) km/hr
= (60 * 5/18) m/sec = 50/3 m/sec.
Length of the train = 50/3 * 6
= 100 m.
Answer:C<|endoftext|> | aqua_rat |
65 | Question: 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?
Options: ['A)2.5', 'B)3.0', 'C)3.25', 'D)3.75', 'E)4.0']
Answer: | Question: 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?
Options: ['A)2.5', 'B)3.0', 'C)3.25', 'D)3.75', 'E)4.0']
Answer: 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 = $3.25 C<|endoftext|> | aqua_rat |
66 | Question: 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?
Options: ['A)209', 'B)(4!-1)*(5!-1)*(6!-1)', 'C)119', 'D)29295', 'E)None']
Answer: | Question: 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?
Options: ['A)209', 'B)(4!-1)*(5!-1)*(6!-1)', 'C)119', 'D)29295', 'E)None']
Answer: 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 D<|endoftext|> | aqua_rat |
67 | Question: 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?
Options: ['A)4', 'B)5', 'C)7', 'D)8', 'E)2']
Answer: | Question: 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?
Options: ['A)4', 'B)5', 'C)7', 'D)8', 'E)2']
Answer: 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.
D<|endoftext|> | aqua_rat |
68 | Question: 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?
Options: ['A)A)37', 'B)B)85', 'C)C)48', 'D)D)43', 'E)E)54']
Answer: | Question: 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?
Options: ['A)A)37', 'B)B)85', 'C)C)48', 'D)D)43', 'E)E)54']
Answer: 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 E<|endoftext|> | aqua_rat |
69 | Question: 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 ?
Options: ['A)20', 'B)45', 'C)36', 'D)90', 'E)95']
Answer: | Question: 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 ?
Options: ['A)20', 'B)45', 'C)36', 'D)90', 'E)95']
Answer: number of handshakes = 9C2= 9*8/2 = 36
ANSWER:C<|endoftext|> | aqua_rat |
70 | Question: 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?
Options: ['A)20', 'B)22', 'C)25', 'D)26', 'E)29']
Answer: | Question: 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?
Options: ['A)20', 'B)22', 'C)25', 'D)26', 'E)29']
Answer: (a + b + c)2 = a2 + b2 + c2 + 2(ab +bc + ca) = 351 + 2* 245
a + b + c = √841 = 29
E<|endoftext|> | aqua_rat |
71 | Question: What is the are of an equilateral triangle of side 16 cm?
Options: ['A)64√6 cm2', 'B)64√3 cm2', 'C)64√9 cm2', 'D)34√3 cm2', 'E)24√3 cm2']
Answer: | Question: What is the are of an equilateral triangle of side 16 cm?
Options: ['A)64√6 cm2', 'B)64√3 cm2', 'C)64√9 cm2', 'D)34√3 cm2', 'E)24√3 cm2']
Answer: Area of an equilateral triangle = √3/4 S2
If S = 16, Area of triangle = √3/4 * 16 * 16
= 64√3 cm2;
Answer: D<|endoftext|> | aqua_rat |
72 | Question: Each of the following equations W has at least one solution EXCEPT
Options: ['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']
Answer: | Question: Each of the following equations W has at least one solution EXCEPT
Options: ['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']
Answer: 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.<|endoftext|> | aqua_rat |
73 | Question: 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?
Options: ['A)90', 'B)120', 'C)150', 'D)180', 'E)160']
Answer: | Question: 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?
Options: ['A)90', 'B)120', 'C)150', 'D)180', 'E)160']
Answer: Answer = 1.5 * 60 = 90
Answer is A<|endoftext|> | aqua_rat |
74 | Question: 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?
Options: ['A)288', 'B)180', 'C)288', 'D)277', 'E)265']
Answer: | Question: 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?
Options: ['A)288', 'B)180', 'C)288', 'D)277', 'E)265']
Answer: Length of the train be ‘X’
X + 120/15 = X + 180/18
6X + 720 = 5X + 900
X = 180m .Answer: B<|endoftext|> | aqua_rat |
75 | Question: Find the area of a rhombus whose side is 25 cm and one of the diagonals is 30 cm?
Options: ['A)272 sq.cm', 'B)267 sq.cm', 'C)286 sq.cm', 'D)251 sq.cm', 'E)600 sq.cm']
Answer: | Question: Find the area of a rhombus whose side is 25 cm and one of the diagonals is 30 cm?
Options: ['A)272 sq.cm', 'B)267 sq.cm', 'C)286 sq.cm', 'D)251 sq.cm', 'E)600 sq.cm']
Answer: 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)
= √400 = 20,
AC = 20 + 20 = 40 cm.
Area of a rhombus
= 1/2 * d1d2
= 1/2 * 40 * 30
= 600 sq.cm.
Answer:E<|endoftext|> | aqua_rat |
76 | Question: How long does a train 110 m long running at the speed of 72 km/hr takes to cross a bridge 132 m length?
Options: ['A)12.8 sec', 'B)12.1 sec', 'C)12.2 sec', 'D)12.6 sec', 'E)11.1 sec']
Answer: | Question: How long does a train 110 m long running at the speed of 72 km/hr takes to cross a bridge 132 m length?
Options: ['A)12.8 sec', 'B)12.1 sec', 'C)12.2 sec', 'D)12.6 sec', 'E)11.1 sec']
Answer: Speed = 72 * 5/18 = 20 m/sec
Total distance covered = 110 + 132 = 242 m.
Required time = 242/20 = 12.1 sec.
Answer: B<|endoftext|> | aqua_rat |
77 | Question: 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?
Options: ['A)120', 'B)1250', 'C)1200', 'D)1100', 'E)1150']
Answer: | Question: 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?
Options: ['A)120', 'B)1250', 'C)1200', 'D)1100', 'E)1150']
Answer: 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<|endoftext|> | aqua_rat |
78 | Question: 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 ?
Options: ['A)7/36', 'B)9/144', 'C)1/36', 'D)1/18', 'E)5/18']
Answer: | Question: 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 ?
Options: ['A)7/36', 'B)9/144', 'C)1/36', 'D)1/18', 'E)5/18']
Answer: We may have (3 men and 2 women) = (7C3 x 6C2) = 525
or (4 men and 1 woman) = (7C4 x 6C1) = 210
or (5 men only) = (7C5) = 21
Required ways = 756
Probability of having 0 woman in committee = 21 / 756 =1/36
ans - C<|endoftext|> | aqua_rat |
79 | Question: 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.?
Options: ['A)20/69', 'B)20/63', 'C)20/65', 'D)20/61', 'E)20/62']
Answer: | Question: 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.?
Options: ['A)20/69', 'B)20/63', 'C)20/65', 'D)20/61', 'E)20/62']
Answer: Required probability = (10 * 4)/126 = 20/63.Answer: B<|endoftext|> | aqua_rat |
80 | Question: 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?
Options: ['A)228', 'B)240', 'C)887', 'D)166', 'E)180']
Answer: | Question: 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?
Options: ['A)228', 'B)240', 'C)887', 'D)166', 'E)180']
Answer: Speed = 54 * 5/18 = 15 m/sec.
Length of the train = 15 * 20 = 300 m.
Let the length of the platform be x m . Then,
(x + 300)/32 = 15 => x = 180 m.
Answer: E<|endoftext|> | aqua_rat |
81 | Question: If |w|=−w, which of the following must be true?
Options: ['A)x≥0', 'B)w≤0', 'C)x2>x', 'D)x3<0', 'E)2x<x']
Answer: | Question: If |w|=−w, which of the following must be true?
Options: ['A)x≥0', 'B)w≤0', 'C)x2>x', 'D)x3<0', 'E)2x<x']
Answer: |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 B<|endoftext|> | aqua_rat |
82 | Question: Two numbers are less than third number by 30% and 37% respectively. How much percent is the second number less than by the first
Options: ['A)8%', 'B)9%', 'C)10%', 'D)11%', 'E)12%']
Answer: | Question: Two numbers are less than third number by 30% and 37% respectively. How much percent is the second number less than by the first
Options: ['A)8%', 'B)9%', 'C)10%', 'D)11%', 'E)12%']
Answer: Explanation:
Let the third number is x.
then first number = (100-30)% of x
= 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 = (100-30)% of x
= 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 C<|endoftext|> | aqua_rat |
83 | Question: How many numbers from 39 to 79 are exactly divisible by 11?
Options: ['A)5', 'B)7', 'C)4', 'D)11', 'E)12']
Answer: | Question: How many numbers from 39 to 79 are exactly divisible by 11?
Options: ['A)5', 'B)7', 'C)4', 'D)11', 'E)12']
Answer: 39/11 = 1 and 79/11 = 7 ==> 7 - 3 = 4 Numbers
Answer : C<|endoftext|> | aqua_rat |
84 | Question: 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:
Options: ['A)4', 'B)6', 'C)8', 'D)9', 'E)cannot be determined']
Answer: | Question: 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:
Options: ['A)4', 'B)6', 'C)8', 'D)9', 'E)cannot be determined']
Answer: if edge of cube = a
volume of cube = a^3
surface area = 6(a^2)
then
a^3 = 6(a^2)
a = 6
ANSWER:B<|endoftext|> | aqua_rat |
85 | Question: 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?
Options: ['A)3', 'B)2', 'C)6', 'D)1', 'E)7']
Answer: | Question: 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?
Options: ['A)3', 'B)2', 'C)6', 'D)1', 'E)7']
Answer: 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:D<|endoftext|> | aqua_rat |
86 | Question: How long does a train 165 meters long running at the rate of 72 kmph take to cross a bridge 660 meters in length?
Options: ['A)28', 'B)41.25', 'C)55', 'D)18', 'E)12']
Answer: | Question: How long does a train 165 meters long running at the rate of 72 kmph take to cross a bridge 660 meters in length?
Options: ['A)28', 'B)41.25', 'C)55', 'D)18', 'E)12']
Answer: T = (660 + 165)/72 * 18/5
T = 41.25
Answer: B<|endoftext|> | aqua_rat |
87 | Question: 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?
Options: ['A)27.5%', 'B)30%', 'C)35%', 'D)37.5%', 'E)40%']
Answer: | Question: 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?
Options: ['A)27.5%', 'B)30%', 'C)35%', 'D)37.5%', 'E)40%']
Answer: Assume the total price = 100x
Price after 20% markup = 120x
Price after 25%further markup = 1.25*120x = 150x
Price after the discount = 0.85*150x = 127.5x
Hence total profit = 27.5%
Option A<|endoftext|> | aqua_rat |
88 | Question: Half of 2 percent written as decimal is
Options: ['A)0.01', 'B)0.5', 'C)0.05', 'D)0.005', 'E)None of these']
Answer: | Question: Half of 2 percent written as decimal is
Options: ['A)0.01', 'B)0.5', 'C)0.05', 'D)0.005', 'E)None of these']
Answer: Explanation:
It will be 1/2(2%) = 1/2(2/100) = 2/200 = 0.01
Option A<|endoftext|> | aqua_rat |
89 | Question: 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 ?
Options: ['A)Rs. 1650', 'B)Rs. 3000', 'C)Rs. 1521', 'D)Rs. 1400', 'E)Rs. 1560']
Answer: | Question: 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 ?
Options: ['A)Rs. 1650', 'B)Rs. 3000', 'C)Rs. 1521', 'D)Rs. 1400', 'E)Rs. 1560']
Answer: 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 C<|endoftext|> | aqua_rat |
90 | Question: 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.
Options: ['A)40', 'B)90', 'C)120', 'D)80', 'E)100']
Answer: | Question: 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.
Options: ['A)40', 'B)90', 'C)120', 'D)80', 'E)100']
Answer: 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 B must be 60*(3/2) = 90 kmph
Answer B<|endoftext|> | aqua_rat |
91 | Question: 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?
Options: ['A)1/3', 'B)2/3', 'C)3/3', 'D)4/3', 'E)5/3']
Answer: | Question: 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?
Options: ['A)1/3', 'B)2/3', 'C)3/3', 'D)4/3', 'E)5/3']
Answer: 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
Answer A<|endoftext|> | aqua_rat |
92 | Question: 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?
Options: ['A)10', 'B)41', 'C)31', 'D)21', 'E)22']
Answer: | Question: 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?
Options: ['A)10', 'B)41', 'C)31', 'D)21', 'E)22']
Answer: 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 B<|endoftext|> | aqua_rat |
93 | Question: 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?
Options: ['A)16', 'B)77', 'C)566', 'D)197', 'E)161']
Answer: | Question: 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?
Options: ['A)16', 'B)77', 'C)566', 'D)197', 'E)161']
Answer: 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
ANSWER: A<|endoftext|> | aqua_rat |
94 | Question: 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?
Options: ['A)9:6', 'B)9:8', 'C)9:1', 'D)9:9', 'E)9:5']
Answer: | Question: 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?
Options: ['A)9:6', 'B)9:8', 'C)9:1', 'D)9:9', 'E)9:5']
Answer: (3*6 + 6*6): (4*12)
54:48 => 9:8.Answer:B<|endoftext|> | aqua_rat |
95 | Question: 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
Options: ['A)I only', 'B)II only', 'C)III only', 'D)I and II', 'E)II and III']
Answer: | Question: 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
Options: ['A)I only', 'B)II only', 'C)III only', 'D)I and II', 'E)II and III']
Answer: 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: 'B'<|endoftext|> | aqua_rat |
96 | Question: If each side of a square is increased by 25%, find the percentage change in its area?
Options: ['A)65.25', 'B)56.25', 'C)65', 'D)56', 'E)25']
Answer: | Question: If each side of a square is increased by 25%, find the percentage change in its area?
Options: ['A)65.25', 'B)56.25', 'C)65', 'D)56', 'E)25']
Answer: 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: B<|endoftext|> | aqua_rat |
97 | Question: If the sum and difference of two numbers are 20 and 8 respectively, then the difference of their square is:
Options: ['A)12', 'B)28', 'C)160', 'D)180', 'E)18']
Answer: | Question: If the sum and difference of two numbers are 20 and 8 respectively, then the difference of their square is:
Options: ['A)12', 'B)28', 'C)160', 'D)180', 'E)18']
Answer: Let the numbers be x and y.
Then, x + y = 20 and x - y = 8
x2 - y2 = (x + y)(x - y) = 20 * 8 = 160.
ANSWER:C<|endoftext|> | aqua_rat |
98 | Question: 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?
Options: ['A)$750.00', 'B)$823.50', 'C)$973.25', 'D)$1000.25', 'E)$1100.00']
Answer: | Question: 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?
Options: ['A)$750.00', 'B)$823.50', 'C)$973.25', 'D)$1000.25', 'E)$1100.00']
Answer: 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 = $800
i.e. B option seems the closest possible answer
Answer: option B<|endoftext|> | aqua_rat |
99 | Question: 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 ?
Options: ['A)7.5 l', 'B)15 l', 'C)22.5 l', 'D)It is impossible', 'E)none of these']
Answer: | Question: 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 ?
Options: ['A)7.5 l', 'B)15 l', 'C)22.5 l', 'D)It is impossible', 'E)none of these']
Answer: 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:D<|endoftext|> | aqua_rat |
End of preview. Expand
in Data Studio
gsm-gpt2-rff
A reproducible, standardized mathematical reasoning dataset constructed from five public sources, with controllable data selection fractions (γ) using a Generalized Linear Model with Random Fourier Feature for selection.
Overview
This dataset is an aggregate of five widely used mathematical reasoning datasets:
deepmind/aqua_rat(raw, train split)openai/gsm8k(main, train split)allenai/math_qa(train split)meta-math/MetaMathQA(train split)microsoft/orca-math-word-problems-200k(train split)
All datasets were reformatted and standardized into a common schema with the following fields:
idx(int64)prompt(string)text(string)dataset_name(string)
The repository is organized as multiple configurations, where each configuration corresponds to a different selection fraction (gamma) of the underlying candidate pool. All configurations expose a single train split.
Available Configurations
Each gamma value is a separate dataset configuration. gamma corresponds to the fraction of examples selected from the full candidate pool. Selection is based on model scores produced by the GLM + RFF, not random subsampling.
| Config | Selection Fraction | Train Examples | Dataset Size (bytes) |
|---|---|---|---|
gamma_0.01 |
0.01 | 7,298 | 5,136,288 |
gamma_0.02 |
0.02 | 14,596 | 10,638,320 |
gamma_0.05 |
0.05 | 36,490 | 27,335,104 |
gamma_0.1 |
0.10 | 72,981 | 56,654,864 |
full |
1.00 | 729,812 | 333,220,118 |
Example usage:
from datasets import load_dataset
ds = load_dataset("kurtos-ai/gsm-gpt2-rff", "gamma_0.1")
print(ds["train"][0])
{
"idx": 0,
"prompt": "Question: 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?\nOptions: ['A)21', 'B)21.5', 'C)22', 'D)22.5', 'E)23']\nAnswer: ",
"text": "Question: 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?\nOptions: ['A)21', 'B)21.5', 'C)22', 'D)22.5', 'E)23']\nAnswer: If Q complete x kilometers, then P completes 1.15x kilometers.\nx + 1.15x = 43\n2.15x=43\nx = 43/2.15 = 20\nThen P will have have walked 1.15*20=23 km.\nThe answer is E.<|endoftext|>",
"dataset_name": "aqua_rat"
}
Dataset Construction
Source aggregation
Each example originates from one of the five datasets listed above. The original train splits were used at fixed revisions for reproducibility. Namely,
- deepmind/aqua_rat @
33301c6 - openai/gsm8k @
cc7b047 - allenai/math_qa @
fafb9f7 - meta-math/MetaMathQA @
aa4f34d - microsoft/orca-math-word-problems-200k @
29255d1
Standardization
Each source dataset was transformed into the standardized schema (idx, prompt, text, dataset_name) using source-specific formatter configs:
aqua_ratinput_fields:["question", "options"]output_field:rationaleprompt_template:Question: {question}\nOptions: {options}\nAnswer:
gsm8kinput_fields:["question"]output_field:answerprompt_template:Question: {question}\nAnswer:
math_qainput_fields:["Problem", "options"]output_field:Rationaleprompt_template:Problem: {Problem}\nOptions: {options}\nAnswer:
metamathqainput_fields:["query"]output_field:responseprompt_template:Question: {query}\nAnswer:
orca_math_200kinput_fields:["question"]output_field:answerprompt_template:Question: {question}\nStep-by-step Solution:
For all sources:
promptis rendered from the source-specificprompt_templatetextis populated from the correspondingoutput_fielddataset_namerecords the source identifieridxis an integer row id assigned after combining all standardized sources
Selection
The selection procedure was run in 4xRTX-5090.
The selection procedure was done by a Generalized Linear Model, derived from GPT-2 embeddings with Random Fourier Features.
Number of parameters:
- GPT-2 hidden dimension: 768
- RFF dimension: 1024
- Vocabulary size: 50257
The GLM predicts vocabulary logits using a linear layer over concatenated GPT-2 embeddings and RFF features. The number of trainable parameters is
- Total: 50257 x (768 + 1024) = 90M parameters
Training of the GLM (10 epochs on the whole dataset) took:
2h, 24min, 24sor$8.57at runpod's price of$3.56/h. Each selection run took approximately:29 minor$1.72at runpod's price
Dataset Statistics
Source composition by gamma configuration (train split):
| Gamma | Total Examples | aqua_rat | gsm8k | math_qa | metamathqa | orca_math_200k |
|---|---|---|---|---|---|---|
gamma_0.01 |
7,298 | 4,205 (57.62%) | 1 (0.01%) | 2,457 (33.67%) | 342 (4.69%) | 293 (4.01%) |
gamma_0.02 |
14,596 | 8,324 (57.03%) | 9 (0.06%) | 4,553 (31.19%) | 833 (5.71%) | 877 (6.01%) |
gamma_0.05 |
36,490 | 20,581 (56.40%) | 65 (0.18%) | 10,522 (28.84%) | 3,399 (9.31%) | 1,923 (5.27%) |
gamma_0.1 |
72,981 | 39,109 (53.59%) | 257 (0.35%) | 17,033 (23.34%) | 11,474 (15.72%) | 5,108 (7.00%) |
full |
729,812 | 97,467 (13.36%) | 7,473 (1.02%) | 29,837 (4.09%) | 395,000 (54.12%) | 200,035 (27.41%) |
The source distribution shifts substantially as gamma decreases, reflecting the scoring model's preference over datasets.
Intended Use
This dataset is intended for:
- Training language models in mathematical reasoning tasks (grade school level).
- Data selection research.
- Curriculum learning experiments.
- Scaling law studies.
Users should validate performance on held-out and external benchmarks before drawing broad generalization claims.
Associated model
We ran a GPT-2 LoRA finetuning experiment on each gamma configuration with identical compute budgets. The resulting models and their performances (loss and accuracy across several evaluation datasets) can be seen here: kurtos-ai/gsm-gpt2-rff
Limitations
- Source datasets vary in annotation style and quality.
- Source datasets differ largely in number of examples.
- The selection procedure may amplify biases present in GPT-2 embeddings.
- No test splits are included; users must evaluate on external benchmarks.
Licensing
This dataset is distributed under the Apache License 2.0.
This dataset is a derivative compilation of datasets originally released under Apache 2.0 and MIT licenses. All original licenses remain applicable to their respective portions. Users are responsible for complying with the licenses of the original datasets:
deepmind/aqua_ratopenai/gsm8kallenai/math_qameta-math/MetaMathQAmicrosoft/orca-math-word-problems-200k
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Size of downloaded dataset files:
383 MB
Size of the auto-converted Parquet files:
383 MB
Number of rows:
861,177
Models trained or fine-tuned on kurtos-ai/gsm-gpt2-rff