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Question: In addition to spiral cleavage, protostomes also undergo which other form of cleavage?
Choices:
A. straight
B. diagonal
C. dispersive
D. determinate
Let's think step by step. | There is a second distinction between the types of cleavage in protostomes and deuterostomes. In addition to spiral cleavage, protostomes also undergo determinate cleavage. This means that even at this early stage, the developmental fate of each embryonic cell is already determined. A cell does not have the ability to ... | https://huggingface.co/datasets/allenai/sciq |
Question: If the sum of six numbers is between 135 and 164, then the average (arithmetic mean) of the six numbers could be which of the following?
Choices:
A. 15.4.
B. 20.5
C. 25.5
D. 31.25
E. 32.5.
Let's think step by step | The problem is actually testing the concept of average and Maxima/Minima....
Let all the values be 135 , so the average will be 135/6 => 22.5 ( Minima )
Let all the values be 164, so the average will be 164/6 => 27.3 ( Minima )
Hence answer will be (C) { any number between the maximum and minimum value.... } | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: Baker Ram is storing cake boxes in cartons that measure 25 inches by 42 inches by 60 inches. If the measurement of each cake box is 8 inches by 7 inches by 5 inches, then what is the maximum number of cake boxes that can be placed in each carton?
Choices:
A. 330
B. 300
C. 252
D. 225
E. 210
Let's think step by... | Baker Ram is storing cake boxes in cartons The dimensions of the carton are 25x 42x 60and those of each cake box are 8x 7x 5.
To maximize number of boxes try and fit maximum into the base of the box. If you take the base as 25x 42and fit 5 x 6 boxes of 5x 7, then the total number of boxes is 5 x 6 x integer(60/8) = 5 x... | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: Working alone, machine X can manufacture 1,000 nails in 20 hours. Working together, machines X and Y can manufacture 1,000 nails in 5 hours. How many hours does it take machine Y to manufacture 1,000 nails working alone?
Choices:
A. 3 9/17
B. 5 1/3
C. 7
D. 7 1/5
E. 6 2/3
Let's think step by step | rate of machine x = 1000/20
(1000/20 + y)5=1000
y=150
150 * t = 1000
t=6 2/3
E. 6 2/3 | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: At an election 2 candidates are participated and a candidate got 45% of votes and defeated by 9000. and 83 votes are invalid. Find the total polled votes?
Choices:
A. 84512
B. 78452
C. 65893
D. 90083
E. 74502
Let's think step by step | Winner votes = 100-45 = 55
polled votes = [(100*9000)/2*55-100]+83 = 90083
Answer is D | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: At a certain food stand, the price of each apple is 40¢ and the price of each orange is 60¢. Mary selects a total of 10 apples and oranges from the food stand, and the average (arithmetic mean) price of the 10 pieces of fruit is 54¢. How many oranges must Mary put back so that the average price of the pieces ... | If the average price is 54, then Mary has 7 oranges and 3 apples (a ratio of 7:3).
For the average price to be 50, the ratio should be 1:1.
Mary must put back 4 oranges.
The answer is D. | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: When a number is divided by 6 &then multiply by 12 the answer is 9 what is the no.?
Choices:
A. 4.5
B. 5
C. 5.6
D. 5.7
E. 6.5
Let's think step by step | if $x$ is the number, x/6 * 12 = 9
=> 2x = 9
=> x = 4.5
A | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: In mammals, four specialized types of what serve to cut, tear, and grind food?
Choices:
A. teeth
B. scales
C. spines
D. plates
Let's think step by step. | Mammalian teeth are also important for digestion. The four types of teeth are specialized for different feeding functions, as shown in Figure below . Together, the four types of teeth can cut, tear, and grind food. This makes food easier and quicker to digest. Therefore the final answer is A | https://huggingface.co/datasets/allenai/sciq |
Question: The modern model of the atom, which scientists call the quantum mechanical model, is based on what scientist's work on orbitals?
Choices:
A. Newton
B. schrödinger
C. Sagan
D. Bohr
Let's think step by step. | Schrödinger’s work on orbitals is the basis of the modern model of the atom, which scientists call the quantum mechanical model. The modern model is also commonly called the electron cloud model. That’s because each orbital around the nucleus of the atom resembles a fuzzy cloud around the nucleus, like the ones shown i... | https://huggingface.co/datasets/allenai/sciq |
Question: A polling company found that, of 300 households surveyed, 120 spent at least $100 per month on both gasoline and electricity, 60 spent at least $100 per month on gasoline but not on electricity, and for every household that did not spend at least $100 per month on gasoline or electricity, 4 spent at least $10... | For every household that did not spend at least $100 per month on gasoline or electricity = P ,
4 spent at least $100 per month on electricity but not on gasoline = 4P
Spent = 300 - P
again spent = 60+120+4P
Now,
300 - P = 60+120+4P
or, 5P = 120
or, P = 24 (Answer) | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: How many numbers between 1 and 100 are divisible by 7 ?
Choices:
A. 9
B. 11
C. 17
D. 14
E. 12
Let's think step by step | No. of divisible by 7 7, 14 --------- 98, n = a + (N - 1)d
98 = 7 + (N - 1) 7, 98 = 7 + 7N - 7
98/7= N = 14
Answer:D | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: A shipment of 230 smartphones contains 84 that are defective. If a customer buys two smartphones at random from the shipment, what is the approximate probability that both phones are defective?
Choices:
A. 1/250
B. 1/84
C. 1/11
D. 9/68
E. 1/3
Let's think step by step | Probability of chosing one defective phone from a lot of 230 which ontains 84 defective phones is = (84/230)
Probability of chosing one defective phone from a lot of 229(we already picked one) which ontains 83(we already picked one) defective phones is = (83/229)
Combined probability of series of events = product of th... | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: The value of C+5C(7C)(5CC)when C= 7 is:
Choices:
A. 420754
B. 420777
C. 420170
D. 420175
E. 420715
Let's think step by step | Solution:
C+5C(7C)(5CC)
Put the value of C= 7 in the above expression we get,
7+ 35(7 x 7)(5x7 x 7)
= 7+ 35(49)(5 × 49)
= 7 + 420175
=420175
Answer : D | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: The average of first five multiples of 2 is?
Choices:
A. 6
B. 8
C. 9
D. 5
E. 7
Let's think step by step | Average = 2(1 + 2 + 3 + 4 + 5)/5
= 30/5
= 6.
Answer:A | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: If 1/8 of a pencil is black ½ of the remaining is white and the remaining 3 ½ is blue find the total length of the pencil?
Choices:
A. 9
B. 5
C. 7
D. 8
E. 4
Let's think step by step | Let the total length be xm
Then black part =x/8cm
The remaining part=(x-x/8)cm=7x/8cm
White part=(1/2 *7x/8)=7x/16 cm
Remaining part=(7x/8-7x/16)=7x/16cm
7x/16=7/2
x=8cm
Answer is D. | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: A company that ships boxes to a total of 13 distribution centers uses color coding to identify each center. If either a single color or a pair of two different colors is chosen to represent each center and if each center is uniquely represented by that choice of one or two colors, what is the minimum number o... | Back-solving is the best way to solve this problem.
You basically need 13 combinations (including single colors)
If we start from option 1->
1=> 4C2 + 4 = 10 (Not enough)
2=> 5C2 + 5 = 15 (Enough)
Since the minimum number is asked. It should be 5.
Answer - B | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: A, B and C enter into partnership. A invests some money at the beginning, B invests double the amount after 6 months, and C invests thrice the amount after 8 months. If the annual gain be Rs.24000. A's share is?
Choices:
A. 2999
B. 8000
C. 6000
D. 2889
E. 6612
Let's think step by step | x* 12 : 2x* 6: 3x* 4
1:1:1
1/3 * 24000 = 8000
Answer:B | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: Find the percentage gain if a shop owner sells 39 mtr of fabric and gains Cost Price of 12 meters?
Choices:
A. 20.5%
B. 23.5%
C. 21.5%
D. 13.5%
E. 32.5%
Let's think step by step | Let cost of each metre be Rs. 100.
Therefore, cost price of 12m cloth = 12*100 =1200
cost price of 39m cloth = 39*100 = 3900
Since the trader made the CP of 12m from the sale of 39m therefore
Profit on sale of 39m = cost price of 12 m cloth = 1200
Selling price of 39m = 3900+1200 = 5100
Profit % = 23.5%
B | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: For which of the following values of n is (500+n)/n NOT an integer?
Choices:
A. 1
B. 2
C. 3
D. 4
E. 5
Let's think step by step | Solution:
This problem is easiest solved by plugging in each answer choice.
A) (500 + 1)/1 = 501/1 = 501
Answer choice A yields an integer.
B) (500 + 2)/2 = 502/2 = 251
Answer choice B yields an integer.
C) (500 + 3)/3 = 503/3 = 167, remainder 2
Answer choice C DOES NOT yield an integer.
Although we believe answer choi... | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: The monthly rent of a shop of dimension 20feet × 18feet is Rs.1440. What is the annual rent per square foot of the shop?
Choices:
A. 48
B. 56
C. 68
D. 87
E. 92
Let's think step by step | Sol. Monthly rent per square feet = 1440/(20*18) = 4
& Annual rent per square feet
=12*4=48
Answer : A | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: The total age of A and B is 13 years more than the total age of B and C. C is how many years younger than A.?
Choices:
A. 16
B. 12
C. 15
D. 20
E. 13
Let's think step by step | (A+B)-(B-C)=13
A-C=13
Answer is E | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: An Olympic diver received the following scores: 5, 3, 7, 6, and 4. The standard deviation of her scores is
Choices:
A. 1.41
B. 2.41
C. 3.41
D. 4.41
E. 5.41
Let's think step by step | 5+3+7+6+4/5 = 5
|5-5| = 0 0^2 = 0
|3-5| = 2 2^2 = 4
|7-5| = 2 2^2 = 4
|6-5| = 1 1^2 = 1
|4-5| = 1 1^2 = 1
SD = sqrt 10/5 =1.41
Answer : A | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: In a division sum, the divisor is ten times the quotient and five times the remainder. If the remainder is 52, the dividend is:
Choices:
A. 5336
B. 5340
C. 5342
D. 6345
E. 6812
Let's think step by step | Divisor = (5 * 52) = 260
= 10 * Quotient = Divisor
=> Quotient = 260/10 = 26
Dividend = (Divisor * Quotient) + Remainder
Dividend = (260 * 26) + 52 = 6812.
E | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: Three hundred students at College Q study a foreign language. Of these, 160 of those students study French, and 190 study Spanish. If at least 90 students who study a foreign language at College Q study neither French nor Spanish, then the number of students who study Spanish but not French could be any numbe... | 160 students study French
140 students do not study French
190 students study Spanish
110 students do not study Spanish
90 students study neither French nor Spanish
140-110=30
140-90=50
A. 30 to 50 | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: When a metal is oxidized and a nonmetal is reduced in a redox reaction, what is the resulting compound called?
Choices:
A. ionic compound
B. soluble compound
C. magnetic compound
D. alloy
Let's think step by step. | There are many other examples of redox reactions in which two neutral elements combine to make a compound. These often take the form of a metal being oxidized and a nonmetal being reduced, resulting in an ionic compound. Two nonmetallic elements can also undergo a redox reaction of this type, in which the less electron... | https://huggingface.co/datasets/allenai/sciq |
Question: In the coordinate plane, points (x, 1) and (7, y) are on line k. If line k passes through the origin and has slope 1/7, then x - y =
Choices:
A. 6
B. 7
C. 5
D. 8
E. 3
Let's think step by step | Line k passes through the origin and has slope 1/7 means that its equation is y=1/7*x.
Thus: (x, 1)=(7, 1) and (7, y) = (7,1) --> x-y=7-1=6.
Answer: A | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: 70% of the employees in a multinational corporation have VCD players, 75 percent have microwave ovens, 80 percent have ACs and 85 percent have washing machines. At least what percentage of employees has all four gadgets?
Choices:
A. 15%
B. 5%
C. 10%
D. 20%
E. 25%
Let's think step by step | Given a population where A% has a certain characteristic X and B% has another characteristic Y (assuming both aren't exclusive), then you get the minimum overlap by assuming that the entire population that doesn't have X has characteristic Y, therefore the minimum portion of the population that has both characteristics... | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: If the following is true, can you find the value of (4 + 9)?
7 + 7 = 2
8 + 8 = 4
8 + 5 = 1
6 + 9 = 3
10 + 11 = 9
Choices:
A. 3
B. 2
C. 1
D. 4
E. 5
Let's think step by step | Solution:
1
Explanation:
4 + 9 = 1
The trick to solve is to assume the first number as the time in AM and the second number is the number of hours you have to add to it. You'll find the time in PM when you do that.
For example
7 AM + 7 hours = 14:00 or 2 PM
4 AM + 9 hours = 13:00 or 1 PM.
Answer C | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: if (p/q)-(q/p)=21/10
then what ia the value of(4p/q)+(4q/p)
Choices:
A. 58/5
B. 59/5
C. 121/105
D. 101/105
E. 1/2
Let's think step by step | p/q =a then q/p = 1/a
a+1/a=21/10
by solving this we get a=5/2
then 4*5/2+4*2/5 = 58/5
ANSWER:A | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: The cubic f(x) = x3 +bx2 +cx+d satisfies f(1) = 3, f(2) = 6, and f(4) = 12. Compute f(3).
Choices:
A. 6
B. 7
C. 8
D. 9
E. 10
Let's think step by step | Note that f(x) - 3x = (x - 1)(x- 2)(x - 4), so f(x) = (x - 1)(x - 2)(x- 4) + 3x
and therefore f(3) = 2 *1 *(-1) + 9 = 7 .
correct answer B | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: Catalysts can greatly increase the rates of chemical what?
Choices:
A. photosynthesis
B. effects
C. reactions
D. decay
Let's think step by step. | and procaine. Not only do catalysts greatly increase the rates of reactions, but in some cases such as in petroleum refining, they also control which products are formed. The acceleration of a reaction by a catalyst is called catalysis. Therefore the final answer is C | https://huggingface.co/datasets/allenai/sciq |
Question: Shekhar started a business investing Rs.25,000 in 1999.In 2000,he invested an additional amount of Rs.10,000 and Rajeev joined him with an amount of Rs.35,000.In 2001,Shekhar invested another additional amount of Rs.10,000 and Jatin joined them with an amount of Rs.35,000.What will be Rajeev’s share in the pr... | Solution
Shekhar : Rajeev : Jatin
= (25000x12+35000x12+45000x12) :(35000x24) : (35000x12)
= 1260000 : 840000 : 420000 = 3 : 2 : 1.
∴ Rajeev’s share = Rs.(21000x2/6) = Rs. 70,000. Answer C | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: A Table is bought for Rs.1600/- and sold at a loss of 20% find its selling price?
Choices:
A. s.1280/-
B. s.1560/-
C. s.1580/-
D. s.1250/-
E. s.1300/-
Let's think step by step | 100 % ------> 1600 (100 * 16 = 1600)
80 % ------> 1280 (80 * 16 = 1280)
Selling price = Rs.1280/-
Option 'A' | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: There are two sets A and B. The range of set A is 7, and the range of set B is 13. If the two sets are combined and get a new set W, which cannot be the range of the set W?
Choices:
A. 8
B. B.11
C. C.14
D. D.17
E. E.21
Let's think step by step | Let Set A has 1,8 as elements
B has 1,14 as elements.. So Range for Combined set W becomes 14-1=13
For range to be 14,
A = 1,8
B= 2,15 (Range=14)
For range to be 17
A=1,8
B= 5,18
For range to be 21:
A=1,8
B= 9 ,22
So we are left with A and B.
Now consider A has elements A= -1,-8 and Thus Range =-1-(-8) =7
So for Range ... | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: Running at the same constant rate, 5 identical machines can produce a total of 270 bottles per minute. At this rate, how many bottles could 10 such machines produce in 4 minutes?
Choices:
A. 648
B. 1,800
C. 2,160
D. 10,800
E. 64,800
Let's think step by step | 5 machines produce 270 bottles per minute;
1 machine produces 270/5=54 bottles per minute;
10 machines produce 54*10=540 bottles per minute;
In 4 minutes 10 machines produce 540*4=2,160 bottles.
Answer: C. | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: Why does metal conduct heat and electricity so well?
Choices:
A. electromagnetism
B. free flowing photons
C. insulation
D. free flowing electrons
Let's think step by step. | The metallic bonding model explains the physical properties of metals. Metals conduct electricity and heat very well because of their free-flowing electrons. As electrons enter one end of a piece of metal, an equal number of electrons flow outward from the other end. When light is shone on to the surface of a metal, it... | https://huggingface.co/datasets/allenai/sciq |
Question: A rectangular surface have length 15m and breadth 8m.calculate its area and diagonal.
Choices:
A. 120,18
B. 120,17
C. 115,17
D. 115,18
E. 120,18
Let's think step by step | area=length*breadth=15*8=120 sq.m
Diagonal=√(15)^2+(8)^2=√289=17 m
Answer B | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: A cube of side one meter length is cut into small cubes of side 10 cm each. How many such small cubes can be obtained?
Choices:
A. 2997
B. 2799
C. 1000
D. 2272
E. 2702
Let's think step by step | Along one edge, the number of small cubes that can be cut
= 100/10 = 10
Along each edge 10 cubes can be cut. (Along length, breadth and height). Total number of small cubes that can be cut = 10 * 10 * 10
=1000
Answer:C | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: The average mark of the students of a class in a particular exam is 80. If 5 students whose average mark in that exam is 40 are excluded, the average mark of the remaining will be 90. Find the number of students who wrote the exam.
Choices:
A. 22
B. 27
C. 25
D. 99
E. 21
Let's think step by step | Let the number of students who wrote the exam be x.
Total marks of students = 80 x.
Total marks of (x - 5) students = 90(x - 5)
80x - (5 * 40) = 90(x - 5)
250 = 10x => x = 25.Answer: C | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: Helen went to the stationers and bought things worth Euro 35, out of which 30 paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?
Choices:
A. Euro 15
B. Euro 15.7
C. Euro 19.7
D. Euro 29.7
E. None
Let's think step by step | Explanation: Let the amount taxable purchases be Euro x.
Then, 6% of x = 30/100
x = (30/100 x 100/6) = 5.
Cost of tax free items = Euro [35 - (5 + 0.30)] = Euro 29.70
Answer: Option D | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: what is next number in sequence
212 427 303 336 394 ?
Choices:
A. 123
B. 345
C. 560
D. 567
E. 245
Let's think step by step | E
245
space them properly as 21 24 27 30 33 36 39 42 45 ? | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: What decimal fraction is 90 ml of a litre ?
Choices:
A. .9
B. .009
C. .09
D. 0.09
E. None of these
Let's think step by step | Answer
Required fraction = 90/1000
= 9/100
= .09
Correct Option: C | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: A group of 10 representatives is to be selected out of 12 seniors and 10 juniors. In how many different ways can the group be selected, if it should have 5 seniors and 5 juniors?
Choices:
A. ¹²C₅ * 10
B. ¹²C₇ * 10
C. ¹²C₇ * ¹â°Câ‚…
D. 12 * ¹â°Câ‚…
E. None of these
Let's think step by step | Explanation:
Here, five seniors out of 12 seniors can be selected in ¹²Câ‚… ways. Also, five juniors out of ten juniors can be selected ¹â°Câ‚… ways. Hence the total number of different ways of selection = ¹²Câ‚… * ¹â°Câ‚… = ¹²C₇ * ¹â°Câ‚…
= ¹²C₅ = ¹²C₇
ANSWER IS C | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: A committee is to be formed by randomly choosing 5 people from 7 candidates. If Alice and Bob are candidates, what is the probability that Alice will be selected but Bob will not?
Choices:
A. 3/7
B. 4/7
C. 5/21
D. 6/21
E. 9/42
Let's think step by step | The total number of ways to form a committee is 7C5=21.
The number of committees which include Alice but not Bob is 5C4=5.
The probability that Alice is selected but Bob is not selected is 5/21.
The answer is C. | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: A fair 2 sided coin is flipped 7 times. What is the probability that tails will be the result at least twice, but not more than 7 times?
Choices:
A. 119/128
B. 120/113
C. 114/210
D. 121/141
E. 104/117
Let's think step by step | at least twice, but not more than 7 timesmeans exactly 2 times, 3 times, 4 times, 5 times, 6 times, 7 times
The probability of getting exactly k results out of n flips is nCk/2^n
7C2/2^7+7C3/2^7+7C4/2^7+7C5/2^7+7C6/2^7=119/128
Option: A | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: If x is positive and y is negative, which of the following must be true?
Choices:
A. The product of x and y is positive
B. The sum of x and y is positive
C. The sum of x and y is negative
D. The difference of x and y is positive
E. The sum of x^2 and y^2 is positive
Let's think step by step | To solve this question, we need to remember the following things:
-ve * -ve = +ve
+ve *+ve = +ve
-ve * +ve = -ve
Given that x = +ve and y = -ve
Checking the options:
A. The product of x and y is positive. FALSE
B. The sum of x and y is positive.
Cannot be said. This will depend on the values of x and y
C. The sum of x ... | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: In how many different number of ways 4 boys and 3 girls can sit on a bench such that girls always sit together?
Choices:
A. 720
B. 740
C. 760
D. 790
E. 800
Let's think step by step | Option 'A' | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: A and B starts a business with Rs.8000 each, and after 4 months, B withdraws half of his capital . How should they share the profits at the end of the 18 months?
Choices:
A. 18:11
B. 18:15
C. 18:10
D. 18:12
E. 18:13
Let's think step by step | A invests Rs.8000 for 18 months, but B invests Rs.8000 for the first 4 months and then withdraws Rs.4000. So, the investment of B for remaining 14 months is Rs.4000 only.
A : B
8000*18 : (8000*4) + (4000*14)
14400 : 88000
A:B = 18:11 .Answer: A | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: A started a business with Rs.25000 and is joined afterwards by B with Rs.30,000. After how many months did B join, if profit per annum is divieded equally?
Choices:
A. 2 months
B. 4 months
C. 5 months
D. 7 months
E. 9 months
Let's think step by step | Given their profits are equal per annum so
25000*12=30000*x
x=10 months
12-10=2 months
ANSWER:A | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: If the average (arithmetic mean) of five consecutive negative integers is 2k – 1, what is the difference Q between the greatest and least of the five integers?
Choices:
A. 4K
B. 4k^2 -4k
C. 4-4k
D. 4
E. 4k+4
Let's think step by step | (n-2 + n - 1 + n + n + 1 + n + 2)/5 = 2k - 1
=> n = 10k - 5
Greatest = n + 2 = 10k - 5 + 2 = 10k - 3
Least = n - 2 = 10k - 5 - 2
=> Difference Q= 10k - 3 - (10k - 7)
= 4
Answer - D | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: Excluding stoppages, the speed of a train is 45 kmph and including stoppages it is 37 kmph. Of how many minutes does the train stop per hour?
Choices:
A. 73
B. 83
C. 12
D. 83
E. 11
Let's think step by step | Explanation:
T = 8/45 * 60 = 11
Answer: Option E | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: there are 5 envelope and 5 letters placed at random. what is the probability that no single letter is placed in the right envelope
Choices:
A. 117/120
B. 118/120
C. 119/120
D. 116/120
E. 115/120
Let's think step by step | probability that no single letter is placed in the right envelop is = 1- (placing all the letters in the right envelop)
i.e 5 letters will go in their right envelops in only 1 way, and total cases is 5!
so, 1-(1/5!) = 119/120
ANSWER:C | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: If y = 2 + 2K and y≠0y≠0, then 2/y + 1/y + 1/y + 1/y = ?
Choices:
A. 1/(8+8k.
B. 5/2(1+k.
C. 1/(8+k.
D. 4/(8+k.
E. 4/(1+k.
Let's think step by step | 2/Y + 1/Y + 1/Y + 1/Y
= 5/Y
= 5/(2 + 2K)
= 5/2(1 + K)
ANSWER:B | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: The mean of (54,821)^2 and (54,823)^2 =
Choices:
A. (54,821. ^2
B. (54,821.5. ^2
C. (54,820.5. ^2
D. (54,821. ^2 + 1
E. (54,822. ^2 + 1
Let's think step by step | 54821^2 = (54822-1)^2 = 54822^2 + 1^2 - 2*54822*1
54823^2 = (54822+1)^2 = 54822^2 +1^2 + 2*54821*1
Taking the average of above 2 , we get (54822)^2 +1
hence the answer is E | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: Find the simple interest on Rs.350 for 10 months at 5 paisa per month?
Choices:
A. 277
B. 175
C. 288
D. 266
E. 121
Let's think step by step | I = (350*10*5)/100 = 175
Answer: B | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: A cistern has a leak which would empty the cistern in 20 minutes. A tap is turned on which admits 4 liters a minute into the cistern, and it is emptied in 24 minutes. How many liters does the cistern hold?
Choices:
A. 480
B. 487
C. 481
D. 729
E. 268
Let's think step by step | 1/x - 1/20 = -1/24
x = 120
120 * 4 = 480
Answer:A | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: Henry sold an item for Rs.7200/- and incurred a loss of 20%. At what price should he have sold the item to have gained a profit of 20%?
Choices:
A. 10600
B. 10800
C. 11000
D. 11200
E. 11400
Let's think step by step | Explanation:
20% loss means SP = 80% of CP
:. CP = Rs.7200x100/80 = Rs.9000.
The SP for a gain of 20% = 9000+20% of 9000 = 9000+1800 =Rs10800.
Answer: Option B | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: A tour group of 25 people paid a total of $1155 for entrance to a museum. If this price included a 5% sales tax, and all the tickets cost the same amount, what was the face value of each ticket price without the sales tax?
Choices
Choices:
A. $22
B. $23.94
C. $44
D. $25.20
E. $30
Let's think step by step | Soln:-
1155/25=x+0.05x
1155/25=1.05x
x=44
ANSWER:C | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: The sum an integer N and its reciprocal is equal to 78/15. What is the value of N?
Choices:
A. 3
B. 4
C. 5
D. 6
E. 7
Let's think step by step | Write equation in N as follows
N + 1/N = 78/15
Multiply all terms by N, obtain a quadratic equation and solve to obtain N = 5.
correct answer C | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: The total weight of six nougat nuggets is 7 oz. What is the average (arithmetic mean) weight of one such nougat nugget?
Choices:
A. 0.18 oz.
B. 0.5 oz.
C. 1.8 oz.
D. 5 oz.
E. 1.2 oz
Let's think step by step | Average = Total/Number of items
= 7/6 = 1.2.
Hence, E | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: In a flower shop there were 8 flowers in each bouquet. If the seller has doubled the number of flowers in each bouquet then the new average of flowers in each bouque is
Choices:
A. 12
B. 16
C. 8
D. 9
E. None of these
Let's think step by step | Answer
Now required average
= old average x Multiplicand
= 8 x 2 = 16
Correct Option: B | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: Jaya invests in a new mutual fund. The fund averages 10% growth annually for the first three years, but it loses 30% of its value in the fourth year. At the end of four years, the value of the mutual fund is approximately what percent of the amount Jaya originally paid?
Choices:
A. 93%
B. 90%
C. 88%
D. 85%
E.... | Let the initial amount be 100.
Since it grew on constant basis as 10% for three years = 100*1.1^3 = 11*11*1.1 = 132 [Taking 1.1 as 1]
It eroded by 30% = 132 * .7 = 92.something approximated to 93%
So, The correct answer will be (A) 93% | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: Which of the following is the lowest positive integer that is divisible by 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12?
Choices:
A. 15,450
B. 18,760
C. 21,520
D. 24,360
E. 27,720
Let's think step by step | The number needs to be divisible by 2, 3, 2^2, 5, 2*3, 7, 2^3, 3^2, 2*5, 11, and 2^2*3.
The lowest positive integer is 7 * 2^3 * 3^2 * 5 * 11 = 27,720
The answer is E. | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: In a particular year, the month of january had exactly 4 thursdays, and 4 sundays. On which day of the week did january 1st occur in the year.
Choices:
A. sunday
B. monday
C. tuesday
D. wednesday
E. friday
Let's think step by step | series of days may be either one of two:
(i)sun-4,mon-4,tue-4,wed-4,thu-4,fri-3 or 5,sat-3 or 5
(ii)thu-4,fri-4,sat-4,sun-4,mon-3or5,tue-3or5,wed-3or5
Lets check through option,
sun=1,8,15,22,29 jan ... which is not satisfies // wrong
Mon=1,8,15,22,29 jan,,,This satisfy option(ii) with thu-4,fri-4,sat-4,sun-4,mon-5,tue... | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: If s, t, and u are distinct positive prime numbers, then (s^3)(t)(u) has how many different positive factors greater than 1?
Choices:
A. a. 8
B. b. 9
C. c. 12
D. d. 7
E. e. 27
Let's think step by step | Let Number is (s^3)(t)(u) = (1^3)(5)(6) = 30
We can write 30 as product of two numbers in following ways
1*30
2*15
3*10
5*6
4 cases = 4*2 i.e. 8 factors (including 1)
Factors greater than 1 = 7
Answer: Option D | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: If the ratio of a to b is 4 to 3 and the ratio of b to c is 1 to 5, what is the ratio of a to c?
Choices:
A. 4/15
B. 1/3
C. 2/5
D. 4/5
E. 7/6
Let's think step by step | a:b = 4:3 -- 1
b:c = 1:5
=>b:c = 3 :15 --2
From 1 and 2 , we get
a:c = 4:15
Answer A | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: Seven people went to a restaurant for dinner. Six of them spent $9 each on their meals and the seventh person spent $12 more than the average expenditure of all seven people. What was the total amount of money that the seven people spent?
Choices:
A. $71
B. $73
C. $75
D. $77
E. $79
Let's think step by step | Let T be the total amount of money spent.
6*9 + (T/7 + 12) = T
66 = 6T/7
T = (7*66)/6 = 77
The answer is D. | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: The price of rice falls by 25%. How much rice can be bought now with the money that was sufficient to buy 20 kg of rice previously?
Choices:
A. 5 kg
B. 15 kg
C. 26.67 kg
D. 30 kg
E. None
Let's think step by step | Solution: Let Rs. 100 be spend on rice initially for 20 kg.
As the price falls by 20%, new price for 20 kg rice,
= (100 -25% of 100) = 75
New price of rice = 75/20 = Rs. 3.75 per kg.
Rice can bought now at = 100/3.75 = 26.67 kg.
Answer: Option C | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: What is the measure of the radius of the circle inscribed in a triangle whose sides measure 8, 15 and 27 units?
Choices:
A. 8.5 units
B. 6 units
C. 3 units
D. 5 units
E. 2 units
Let's think step by step | Sides are 8, 15 and 27...thus it is right angle triangle Since 27^2 = 8^2 + 15^2
therefore, area = 1/2 * 15 * 8 = 60
We have to find in-radius
Therefore, area of triangle = S*r ....where S=semi-perimeter and r= in-radius
Now S=semi-perimeter = 27+15+8 /2 = 30
Thus , 60 =30*r
and hence r=in-radius= 2
Option E | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: You have been given a physical balance and 5 weights of 45, 42, 37, 36 and 67 kgs. Keeping weights on one pan and object on the other, what is the maximum you can weigh less than 157 kgs.
Choices:
A. 160
B. 151
C. 154
D. 153
E. 152
Let's think step by step | 45+42+67 = 154
Answer: C | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: A merchant marks his goods up in such a way that the profit made on selling 30 articles is equal to the cost price of 20 articles. What is the E % profit made by the merchant?
Choices:
A. 66.67 %
B. 50 %
C. 200 %
D. 100 %
E. 33.33 %
Let's think step by step | C.P of 1 article= $30(say)
C.P of 20 articles=30*20=$600
Now, C.P of 20 articles=Profit on 30 articles
Therefore, profit on 1 article=$600/30=$20
Profit E%=(20/30)*100=66.67%
Answer A | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: Four of the five parts numbered (a),(b),(c),(d) and (e) in the following equation are exactly equal. Which of the parts is not equal to the other four? The number of that part is the answer.
Choices:
A. 45 × 120 + 5(2. × 10
B. 113 × 25 × 2
C. 27 × 25 × 8 + 15 × 6 + 4 × 40
D. 226 × 5 + 113 × 45 =
E. 50(2. × ... | Others equal 5650.
Answer D | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: Which of the following CANNOT be weighed using a balance scale and these unit weights: 1, 4, 7, and 10
Choices:
A. 13
B. 15
C. 17
D. 19
E. 21
Let's think step by step | A. 13 (cannot be weighed)
B. 15 (can be weighed by keeping weights of 10,4 and 1 kg)
C. 17 (can be weighed by keeping weights of 10 and 7 kg)
D. 11(can be weighed by keeping weights of 10 and 1 kg)
E. 21 (can be weighed by keeping weights of 10, 7 and 4 kg)
A | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: In a renowned city, the average birth rate is 6 people every two seconds and the death rate is 2 people every two seconds. Estimate the size of the population net increase that occurs in one day.
Choices:
A. 32,300
B. 172,800
C. 468,830
D. 338,200
E. 259,200
Let's think step by step | Every 2 seconds, 4 persons are added (6-2). Every second 2 persons are added.
In a day 24hrs = 24 * 60 Minutes = 24 * 60 * 60 = 86400 seconds.
86400 * 2 = 172800
Option B is the answer. | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: Two persons start running simultaneously around a circular track of length 700 m from the same point at speeds of 15 km/hr and 25 km/hr. When will they meet for the first time any where on the track if they are moving in opposite directions?
Choices:
A. 63
B. 10
C. 28
D. 27
E. 12
Let's think step by step | Time taken to meet for the first time anywhere on the track
= length of the track / relative speed
= 700 / (15 + 25)5/18 = 700* 18 / 40 * 5 = 63 seconds.
Answer: A | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: 200,190,180,....,160,150,140
Insert the missing number
Choices:
A. 155
B. 156
C. 157
D. 170
E. 158
Let's think step by step | Missing number : 170
Answer : D | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: A, B and C can do a work in 7 , 14 and 21 days respectively. They completed the work and got $242. What is the share of C?
Choices:
A. $25
B. $48
C. $44
D. $49
E. $40
Let's think step by step | C
$44
The ratio of their working rates = 1/7 : 1/14 : 1/21 = 6 : 3 : 2.
Since, they work together, the share of C
= 2/11 * 242 = $44 | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: A train covers a distance in 50 min, if it runs at a speed of 48kmph on an average. The speed at which the train must run to reduce the time of journey to 50min will be.
Choices:
A. 60 km/h
B. 55 km/h
C. 48 km/h
D. 70 km/h
E. 65 km/h
Let's think step by step | Time=50/60 hr=5/6hr
Speed=48mph
distance=S*T=48*5/6=40km
time=50/60hr=5/6hr
New speed = 40* 6/5 kmph= 48kmph
Answer : C | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: Company M produces two kinds of stereos: basic and deluxe. Of the stereos produced by Company M last month, 2/3 were basic and the rest were deluxe. If it takes 7/5 as many hours to produce a deluxe stereo as it does to produce a basic stereo, then the number of hours it took to produce the deluxe stereos las... | # of basic stereos was 3/4 of total and # of deluxe stereos was 1/4 of total, let's assume total=16, then Basic=12 and Deluxe=4.
Now, if time needed to produce one Deluxe stereo is 1 unit than time needed to produce one Basic stereo would be 7/5 units. Total time for Basic would be 12*1=12 and total time for Deluxe wou... | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: Most carcinogens produce mutations in genes that control what?
Choices:
A. proteins cycle
B. ubiquitous cycle
C. digestive cycle
D. cell cycle
Let's think step by step. | Most carcinogens produce mutations in genes that control the cell cycle. Therefore the final answer is D | https://huggingface.co/datasets/allenai/sciq |
Question: What develop inside chambers called ovaries, which originate within flowers and mature into fruits?
Choices:
A. trematode seeds
B. tomoxia seeds
C. pollen seeds
D. angiosperm seeds
Let's think step by step. | Therefore the final answer is D | https://huggingface.co/datasets/allenai/sciq |
Question: Jean drew a gumball at random from a jar of pink and blue gumballs. Since the gumball she selected was blue and she wanted a pink one, she replaced it and drew another. The second gumball also happened to be blue and she replaced it as well. If the probability of her drawing the two blue gumballs was 16/49 wh... | The probability of drawing a pink gumball both times is the same. The probability that she drew two blue gumballs = 16/49 = (4/7) * (4/7)
Therefore probability that the next one she draws is pink = 3/7
Option (C) | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: What is 12.5 % of 4/12 of 600?
Choices:
A. 25
B. 24
C. 30
D. 27
E. 28
Let's think step by step | 12.5 % = 12.5 / 100 = 1/8 of 4/12 = 1/8 * 4/12 = 1 / 24 of 600 = 1/24 * 600 = 25
Ans -A | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: What is the sum of all the composite numbers up to 22?
Choices:
A. 228
B. 277
C. 153
D. 132
E. 281
Let's think step by step | Explanation:
4 + 6 + 8 + 9 + 10 + 12 + 14 + 15 + 16 + 18 +21= 153
Answer: C | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: Sony and Johnny caught 75 fishes. Sony caught four times as many as Johnny. How many fishes did Johnny catch?
Choices:
A. 12
B. 16
C. 34
D. 38
E. 15
Let's think step by step | s+j=75
s=4*j
j=15
ANSWER:E | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: A fruit vendor purchased 20 dozens of bananas at Rs. 15 per dozen. But one-fourth of the bananas were rotten and had to be thrown away. He sold two-third of the remaining bananas at Rs. 22.50 per dozen. At what price per dozen should he sell the remaining bananas to make neither a profit nor a loss?
Choices:
... | CP of 20 dozen of bananas = 15 * 20 = Rs. 300
Number of bananas which are rotten = 1/4 * 20 = 5 dozen.
SP of two-third of remaining bananas = (2/3 * 15) * 22.5 = Rs. 225
SP of remaining 5 dozens of bananas to make no profit and no loss =(300 - 225) = Rs. 75.
SP of 1 dozen bananas = 75/5 = Rs. 15.Answer:B | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: Coxal glands collect liquid waste from what?
Choices:
A. plasma
B. heart
C. blood
D. lungs
Let's think step by step. | Some arthropods have special excretory structures. They are called coxal glands and Malpighian tubules . Coxal glands collect and concentrate liquid waste from blood. They excrete the waste from the body through a pore. Malphigian tubules carry waste from the digestive tract to the anus. The waste is excreted through t... | https://huggingface.co/datasets/allenai/sciq |
Question: 20. A certain church bell rings the bell twice at half past the hour and four
times at the hour plus an additional number of rings equal to what ever
time it is. How many rings will the clock make from 6:20 in the morning
to 09:50 in the morning?
Choices:
A. 44.
B. 36.
C. 42.
D. 46.
E. 50.
Let's think step by... | unless i understood the problem correctly, i get 58
@ 6:30 - 2
@ 7 - 4+7 =11
@ 7:30 - 2
@ 8 - 12
@ 8:30 - 2
@ 9 - 13
@ 9:30 - 2
totals to A=44 | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: If the arithmetic mean of p and q is 10 and the arithmetic mean of q and r is 24, what is the value of r-p?
Choices:
A. 28
B. 10
C. 30
D. 40
E. 5
Let's think step by step | Arithmetic mean expression for p and q:
(p+q)/2=10 ; p+q=20 ----eq1
Arithmetic mean expression for q and r:
(q+r)/2=20 ; q+r=48 ----eq2
Subtracting eq1 from eq2 we get: r-p=28
Hence, the correct answer is A | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: How many prime numbers Z exist such that 90 < Z < 106 and n is a factor of 99999919?
Choices:
A. 1. Zero
B. 2. One
C. 3. Two
D. 4. Three
E. 5. More than three
Let's think step by step | I found that considering the constraint..Z is a prime num in between 90 to 106 not inclusive , only 3 numbers (91,97 and 101) are present but those numbers are not the factors of the number mentioned....Therefore, i doubt the answer.C | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: On a certain farm the ratio of horses to cows is 6:1. If the farm were to sell 15 horses and buy 15 cows, the ratio of horses to cows would then be 3:1. After the transaction, how many more horses than cows would the farm own?
Choices:
A. 40
B. 50
C. 60
D. 70
E. 80
Let's think step by step | Originally, there were 6k horses and k cows.
(6k-15) = 3(k+15)
6k-3k = 45+15
3k = 60
k = 20
The difference between horses and cows is (6k-15)-(k+15) = 5k-30 = 70
The answer is D. | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: A certain stationary store arranges notebooks on display such that each of the seven different colors of notebooks white,yellow, orange, green, red, blue, and purple are consecutive in a repeating pattern. If eight consecutively displayed notebooks are purchased, what is the probability that two of the notebo... | After white,yellow, orange, green, red, blue, and purple, the next book can be of any given seven colours, therefore we have total seven possibilities, out of which we need purple i.e. 1 therefore prob is 1/7
Answer:C | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: If A:B = 1/3: 1/3 B:C = 1/2:1/3 then A:B:C?
Choices:
A. 9:9:6
B. 9:6:8
C. 9:6:2
D. 9:6:4
E. 9:6:1
Let's think step by step | A:B = 1/3:1/3 = 3:3
B:C = 1/2:1/3 = 3:2
--------------------
A:B:C = 9:9:6
Answer:A: | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: Find the simple interest on Rs.850 for 10 months at 7 paisa per month?
Choices:
A. s.768
B. s.329
C. s.595
D. s.600
E. s.725
Let's think step by step | Explanation:
I = (850*10*7)/100 = 595
Answer: Option C | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: Two trains are moving in opposite directions at 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.9 km respectively. The time taken by the slower train to cross the faster train in seconds is?
Choices:
A. 22
B. 37
C. 48
D. 266
E. 121
Let's think step by step | Relative speed = 60 + 90 = 150 km/hr.
= 150 * 5/18 = 125/3 m/sec.
Distance covered = 1.10 + 0.9 = 2 km = 2000 m.
Required time = 2000 * 3/125 = 48 sec.
Answer: C | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: A teacher grades students’ tests by subtracting twice the number of incorrect responses from the number of correct responses. If Student A answers each of the 100 questions on her test and receives a score of 73, how many questions did Student A answer correctly?
Choices:
A. 55
B. 60
C. 73
D. 82
E. 91
Let's t... | let the number of correct responses be x
then the number of incorrect responses =100-x
according to question
x-2(100-x)=73 (subtracting twice of incorrect from correct)
3x=273
x=91
ANSWER:E | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: Out of 16 students studying in a class, 7 are from Maharashtra, 5 are from Karnataka and 3 are from Goa. Four students are to be selected at random. What are the chances that at least one is from Karnataka?
Choices:
A. 12â„13
B. 11â„13
C. 9/11
D. 1â„15
E. None of these
Let's think step by step | Total possible ways of selecting 4 students out of 16 students = 16C4 =1820
The no. of ways of selecting 4 students in which no student belongs to Karnataka = 11C4=330
∴ Hence no. of ways of selecting at least one student from Karnataka = 16C4 – 11C4 = 1490
∴ Probability = 1490â„1820 = 9â„11
Answer C | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: At 1:20 PM, Train X departed from Station A on the road to Station B. At 1:30 PM, Train Y departed Station B on the same road for Station A. If Station A and Station B are p miles apart, Train X’s speed is r miles per hour, and Train Y’s speed is s miles per hour, how many hours after 1:00 PM, in terms of p, ... | The distance A is going to cover between 1:00 and 1:30
= .5r
now the distance between the two trains = (p-.5r)
the relative velocity = (r-(-s)) = r+s
From 1:30, time is going to take when they meet = (p-.5r)/(r+s)
so the ans is .5+((p-.5r)/(r+s)) [.5 is added for the time from 1:00 to 1:30]
ans is D | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: If X = the product of four distinct prime numbers, how many factors does X have besides 1 and itself?
Choices:
A. 10
B. 11
C. 12
D. 13
E. 14
Let's think step by step | Let's take the four primes: 2, 3, 5 and 7 --> each of the 4 primes will be a factor of the product
All the possible combinations of the four primes will be factors (10 possible combinations):
2x3
2x5
2x7
3x5
3x7
5x7
2x3x5
2x3x7
2x5x7
3x5x7
Thus, in total there are 10 + 4 = 14 factors.
ANSWER:E | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: Three consecutive odd integers are in increasing order such that the sum of the last two integers is 15 more than the first integer. Find the three integers?
Choices:
A. 7, 9, 29
B. 7, 2, 10
C. 7, 9, 10
D. 9, 11,13
E. 7, 9, 29
Let's think step by step | Explanation:
Let the three consecutive odd integers be x, x + 2 and x + 4 respectively.
x + 4 + x + 2 = x + 15 => x = 9
Hence three consecutive odd integers are 9, 11 and 13.
Answer:D | https://huggingface.co/datasets/deepmind/aqua_rat |
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