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Question: A sum of money becomes double itself in 4 years at simple interest. How many times will it become 10 years at the same rate?
Choices:
A. 1
B. 2
C. 3
D. 4
E. 5
Let's think step by step. | P ---- 2P ---- 4 years
5P ---- 10 years Answer: E | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: Tom opened a shop investing Rs.30000. Jose joined him 2 months later, investing Rs.45000. They earned a profit of Rs.54000 after completion of one year. What will be Jose's share of profit?
Choices:
A. 20000
B. 24000
C. 34000
D. 35000
E. 30000
Let's think step by step. | SoL = ~s- So Anju’s share = [5/9] x 54000 = 30000
E | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: If the third day of the month is Monday, Which of the following will be the fifth day from 21st of that month?
Choices:
A. Tuesday
B. Monday
C. Wednesday
D. Thursday
E. None of these
Let's think step by step. | 3rd dy is monday----so----1st day must be saturdy
1-8-15-22 are all saturdy..ok
so 21 will be friday so,
from firdy 5th day will be wednesday
ANSWER:C | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: X starts a business with Rs.54000. Y joins in the business after 9 months with Rs.27000. What will be the ratio in which they should share the profit at the end of the year?
Choices:
A. 1 : 2
B. 2 : 1
C. 8 : 3
D. 3 : 5
E. 8 : 1
Let's think step by step. | Explanation :
Ratio in which they should share the profit
= Ratio of the investments multiplied by the time period
= 54000 * 12: 27000 * 3
= 54 * 12: 27 * 3
= 2*4: 1
= 8:1. Answer : Option E | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: Excluding stoppages, the speed of a bus is 65 kmph and including stoppages, it is 48 kmph. For how many minutes does the bus stop per hour?
Choices:
A. 70 min
B. 15 min
C. 20.4 min
D. 15.6 min
E. 40 min
Let's think step by step. | D
15.6 min
Due to stoppages, it covers 17 km less.
Time taken to cover 17 km = (17/65 x 60) min = 15.6 min | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: A money lender lent a total of $1600 to two of his customers. He charged at the rate of 5%p.a. to one of them and 6% p.a. to the other. If he earned an average of 5.67% on $1600, how much did he lend to each of the two customers?
Choices:
A. 700; 1100
B. 1072; 528
C. 1000; 800
D. 1200; 800
E. None of the above
Let's think step by step. | The method given above is the one given in the book.
However the method I used was
(1*x*5)/100 + (1600-x)*6/100 = 1600*5.67/100
Simplifying we get x= 528
B | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: Mutations cannot be passed on to offspring if they occur in what type of cells?
Choices:
A. body cells
B. blood cells
C. put cells
D. kept cells
Let's think step by step. | Mutations that occur in body cells cannot be passed on to offspring. They are confined to just one cell and its daughter cells. These mutations may have little effect on an organism. Therefore the final answer is A | https://huggingface.co/datasets/allenai/sciq |
Question: At what rate percent on simple interest will Rs.750 amount to Rs.900 in 5 years?
Choices:
A. 4
B. 5
C. 2
D. 1
E. 3
Let's think step by step. | 150 = (750*5*R)/100
R = 4%
ANSWER A | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: The difference between the simple interest received from two different sources on Rs.1700 for 3 years is Rs.13.50. The difference between their rates of interest is
Choices:
A. 0.16%
B. 0.26%
C. 0.36%
D. 0.46%
E. 0.56%
Let's think step by step. | (1700xR1x3)/100-(100xR2x3)/100 =13.50
5100(R1-R2)=1350
R1-R2 = 1350/5100=0.26%
answer : B | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: In how many different number of ways 2 boys and 2 girls can sit on a bench?
Choices:
A. 70
B. 10
C. 24
D. 26
E. 82
Let's think step by step. | npn = n!
4p4 = 4 × 3 × 2 × 1 = 24
C) | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: The average age of 8 men increases by 2 years when two women are included in place of two men of ages 20 and 24 years. Find the average age of the women?
Choices:
A. 5
B. 10
C. 50
D. 40
E. 30
Let's think step by step. | 20 + 24 + 8 * 2 = 60/2 = 30
Answer: E | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: Two pipes A and B can fill a tank in 10hour and 15 hours respectively. If both the pipes are opened simultaneously, how much time will be taken to fill the tank?
Choices:
A. 2hrs
B. 6hrs
C. 5hrs
D. 4hrs
E. 1hr
Let's think step by step. | Part filled by A in 1 hour = 1/10
part filled by B in 1 hour = 1/15
Part filled by A+B in 1 hour = 1/10 + 1/15 = 1/6
Both the pipes will together will fill the tank in 6 hours.
Answer is B | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: The parameter of a square is double the perimeter of a rectangle. The area of the rectangle is 480 sq cm. Find the area of the square?
Choices:
A. 288
B. 270
C. 289
D. 480
E. 211
Let's think step by step. | Let the side of the square be a cm. Let the length and the breadth of the rectangle be l cm and b cm respectively.
4a = 2(l + b)
2a = l + b
l . b = 480
We cannot find ( l + b) only with the help of l . b. Therefore a cannot be found .
Area of the square cannot be found.
Answer: D | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: 165 liters of a mixture of milk and water contains in the ratio 3:2. How much water should now be added so that the ratio of milk and water becomes 3:4?
Choices:
A. 66 liters
B. 32 liters
C. 41 liters
D. 50 liters
E. 34 liters
Let's think step by step. | Milk = 3/5 * 165 = 99 liters
Water = 66 liters
99 : (66+P) = 3:4
198 + 3P = 396 => P = 66
66 liters of water are to be added for the ratio become 3:4.
Answer:A | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: In an increasing sequence of 10 consecutive integers, the sum of the first 5 integers is 540. What is the sum of the last 5 integers in the sequence?
Choices:
A. 585
B. 580
C. 575
D. 570
E. 565
Let's think step by step. | All 5 integers are 5 numbers larger than in the first sum (eg. 1 becomes 6, 2 7...). 5*5=25+540=565
E | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: What percent is 120 of 60?
Choices:
A. 133 1/3 %
B. 134 1/3 %
C. 200 %
D. 140 1/3 %
E. 143 1/3 %
Let's think step by step. | 120/60 = 2/1
2 × 100 = 200 %
C | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: Joan and Karl each bought a TV and the sum of their purchases was $500. If twice of what Joan paid was $40 more than what Karl paid, what did Joan pay for her TV?
Choices:
A. $165
B. $170
C. $175
D. $180
E. $185
Let's think step by step. | J+K=500 so K=500-J
2J=K+40
2J=(500-J)+40
3J=540
J=180
The answer is D. | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: The number of new words that can be formed by rearranging the letters of the word 'REDUCTION' is ?
Choices:
A. 362879
B. 362889
C. 120
D. 5040
E. 5039
Let's think step by step. | Number of words which can be formed
= 9! - 1 = 362880 - 1
= 362879
Answer:A | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: Buses leave town B at 3 pm and every 10 hours after that. Buses leave town C at 4pm and every 15 hours after that. If the buses follow this schedule beginning on a Monday, what is the earliest day D on which the buses leave at the same time.
Choices:
A. D=Tuesday
B. D=Wednesday
C. Thursday
D. Sunday
E. D=The busses will never leave at the same time
Let's think step by step. | The answer is E.
I think the best way to do it is to look at the times on a 24 hour clock. Town B busses start at 15:00, and Town C start at 16:00. If you think about it that way, then for Town B you'd add 10 hours each time, and the number will always end in a 5. Town C you'd add 15 hours each time, and the numbers would always end in a 1 or 6. So you can see they'd never coincide.
Alternatively, you could see that if they left at the same time, they'd coincide every 30 hours, but since C is one hour ahead of B, every 30 hours C will still be one hour ahead of B.E | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: A can do a piece of work in 6days of 9 hours each and B alone can do it in 12 days of 9 hours each.how long will they take it to do working together
4 1/2 hours a day?
Choices:
A. 8 days
B. 9 days
C. 7 days
D. 6 days
E. 10 days
Let's think step by step. | A's work per hour=1/54
B's work per hour=1/108
A & B's work per hour together=(1/54)+(1/108)=3/108=1/36
so A & B together complete the work in 36 hours...
if they work 4 1/2=9/2 hours a day,
it will take (36)/(9/2) days=8 days...
ANSWER: A | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: Four different objects 1, 2, 3, 4 are distributed at random in four places marked 1, 2, 3, 4. What is the probability that none of the objects occupy the place corresponding to its number?
Choices:
A. 6/3
B. 3/8
C. 1/2
D. 5/8
E. 1/8
Let's think step by step. | There are 4! i.e. 24 ways in which four objects can be arranged in four places. There are a total of 9 instances where the objects are not occupying the place corresponding to the given number. They are as follows:
(2, 1, 4, 3) (2, 3, 4, 1) (2, 4, 1, 3) (3, 1, 4, 2) (3, 4, 1, 2) (3, 4, 2, 1) (4, 1, 2, 3) (4, 3, 1, 2) (4, 3, 2, 1)
Hence, the required probability = 9/24 = 3/8.
ANSWER:B | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: Simple interest on a certain sum is 16/25 of the sum. Find the rate percent and time, If both are numerically equal.
Choices:
A. Rate = 7% and Time = 7 years.
B. Rate = 8% and Time = 8 years.
C. Rate = 6% and Time = 6 years.
D. Rate = 5% and Time = 5 years.
E. None of these
Let's think step by step. | Explanation:
Sol: Let sum = X. Then S.I = 16x/25
Let rate = R% and Time = R years.
Therefore, (x * R * R)/100 = 16x/25 or R^2 = 1600/25, R = 40/5 = 8
Therefore, Rate = 8% and Time = 8 years.
Answer: B | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: There were two candidates in an election. Winner candidate received 62% of votes and won the election by 288 votes. Find the number of votes casted to the winning candidate?
Choices:
A. 456
B. 744
C. 912
D. 1200
E. 1400
Let's think step by step. | W = 62% L = 38%
62% - 38% = 24%
24% -------- 288
62% -------- ? => 744
ANSWER:B | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: One out of every 500 light bulbs are defected. If 2 out of every 10 defected light bulbs have a broken glass and there are 12 broken glass light bulbs in the shipment, how many light bulbs total are there in the shipment?
Choices:
A. 2,000
B. 5,000
C. 10,000
D. 30,000
E. 52,000
Let's think step by step. | out of 500 only 1 bulb is defective.So for 10 defective bulbs, we must have 5000 bulbs
Now out of these 10 bulbs, 2 bulbs, have broken glass
i.e 2 broken glass out of 5000 bulbs
12 broken glass will be from 30000 bulbs
Answer is D | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: What does the driving of turbines by the heating of water to steam accomplish?
Choices:
A. depletion of electricity
B. diffusion of electricity
C. generation of electricity
D. absorption of electricity
Let's think step by step. | Nuclear reactors heat water to steam to drive a turbine for generation of electricity. Therefore the final answer is C | https://huggingface.co/datasets/allenai/sciq |
Question: A ranch has both horses and ponies. Exactly 5/6 of the ponies have horseshoes, and exactly 2/3 of the ponies with horseshoes are from Iceland. If there are 4 more horses than ponies, what is the minimum possible combined number of horses and ponies on the ranch?
Choices:
A. 18
B. 21
C. 38
D. 40
E. 57
Let's think step by step. | 5/6*P have horseshoes, so P is a multiple of 6.
2/3*5/6*P = 5/9*P are Icelandic ponies with horseshoes, so P is a multiple of 9.
The minimum value of P is 18. Then H = P+4 = 22.
The minimum number of horses and ponies is 40.
The answer is D. | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: Rs.200 contained in a box consists of one rupee, 50 paisa and 25 paisa coins in the ratio 4:5:6. What is the number of 25 paisa coins?
Choices:
A. 388
B. 266
C. 120
D. 150
E. 267
Let's think step by step. | 4x 5x 6x
100 50 25
400x + 250x + 150x = 20000
x = 25
6x = 150
Answer: D | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: 1⁄5 + 1⁄7 + 2⁄3 = ?
Choices:
A. 1 1⁄105
B. 104⁄105
C. 1 1⁄7
D. 1 2⁄105
E. None of these
Let's think step by step. | 1⁄5 + 1⁄7 + 2⁄3 = ?
or, ? = 21+15+70/105=106/105=1 1/105
Answer A | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: If a coin is tossed twice, what is the probability that the coin lands on heads on both tosses?
Choices:
A. 1/6
B. 1/3
C. 1/4
D. 1/2
E. 1
Let's think step by step. | P(2 heads) = 1/2*1/2=1/4
The answer is C. | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: What is the least number which when divided by 5, 6, 9 and 12 leaves remainder 4 in each care?
Choices:
A. 130
B. 140
C. 156
D. 184
E. 196
Let's think step by step. | Explanation:
LCM of 5, 6, 9 and 12 is 180
Required number = 180 + 4 = 184
Answer: Option D | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: Isotopes have different number of these in their nuclei?
Choices:
A. atoms
B. neutrons
C. electrons
D. protons
Let's think step by step. | Isotopes have different numbers of neutrons in their nuclei. Therefore the final answer is B | https://huggingface.co/datasets/allenai/sciq |
Question: If Teena is driving at 55 miles per hour and is currently 7.5 miles behind Joe, who is driving at 40 miles per hour in the same direction then in how many minutes will Teena be 37.5 miles ahead of Joe?
Choices:
A. 15
B. 60
C. 180
D. 90
E. 105
Let's think step by step. | This type of questions should be solved without any complex calculations as these questions become imperative in gaining that extra 30-40 seconds for a difficult one.
Teena covers 55 miles in 60 mins.
Joe covers 40 miles in 60 mins
So teena gains 15 miles every 60 mins
Teena need to cover 7.5 +37.5 miles.
Teena can cover 7.5 miles in 30 mins
Teena will cover 37.5 miles in 150 mins
So answer 30+150= 180 mins. (ANSWER C) | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: A train is 360 meter long is running at a speed of 45 km/hour. In what time will it pass a bridge of 140 meter length?
Choices:
A. 22
B. 28
C. 40
D. 27
E. 12
Let's think step by step. | Speed = 45 Km/hr = 45*(5/18) m/sec = 25/2 m/sec
Total distance = 360+140 = 500 meter
Time = Distance/speed
= 500 * (2/25) = 40 seconds.
Answer: C: | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: In May, Xiang sold 15 used cars. For these 15 cars, the range of the selling price was $15,000 and the lowest selling price was $4,500. In June, Xiang sold 10 used cars. For these 10 cars, the range of the selling prices was $16,500 and the lowest selling price was $6,300. What was the range of the selling prices of the 25 used cars sold by Xiang in May and June?
Choices:
A. 1. $15,600
B. 2. $15,750
C. 3. $16,820
D. 4. $18,300
E. 5. $19,200
Let's think step by step. | Edited the question as there was a typo.
Range = Highest Value - Lowest Value.
Range in May was 15,000 and the lowest price in May was 4,500, thus the highest price in May was 15,000+4,500=19,500.
Range in June was 16,500 and the lowest price in June was 6,300, thus the highest price in June was 16,500+6,300=22,800.
Lowest price of a car in May-June was 4,500 (May) and the highest price of a car in May-June was 22,800, thus the range for May-June is 22,800-4,500=18,300.
Answer: D. | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: What does the urea cycle process?
Choices:
A. nitrogen
B. calcium
C. oxygen
D. urine
Let's think step by step. | Freely available amino acids are used to create proteins. If amino acids exist in excess, the body has no capacity or mechanism for their storage; thus, they are converted into glucose or ketones, or they are decomposed. Amino acid decomposition results in hydrocarbons and nitrogenous waste. However, high concentrations of nitrogen are toxic. The urea cycle processes nitrogen and facilitates its excretion from the body. Therefore the final answer is A | https://huggingface.co/datasets/allenai/sciq |
Question: Pipes A and B can fill a tank in 5 and 6 hours respectively. Pipe C can empty it in 12 hours. If all the three pipes are opened together, then the tank will be filled in?
Choices:
A. 3 9/97 hrs
B. 3 9/77 hrs
C. 3 9/17 hrs
D. 3 9/27 hrs
E. 3 9/19 hrs
Let's think step by step. | Net part filled in 1 hour = 1/5 + 1/6 - 1/12
= 17/60
The tank will be full in 60/17 hrs, i.e., 3 9/17 hrs.
Answer:C | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: A rectangular block 12cm by 36cm by 60cm is cut into an exact number of equal cubes. Find the least possible number of cubes?
Choices:
A. 6
B. 10
C. 15
D. 40
E. 22
Let's think step by step. | Volume of the block = 12*36*60 = 25920 cm^3
Side of the largest cube = H.C.F of 12,36,60 = 12cm
Volume of the cube = 12*12*12= 1728 cm^3
Number of cubes = 25920/1728 = 15
Answer is C | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: A train 1600 m long can cross a pole in 40 sec and then find the speed of the train?
Choices:
A. 140
B. 142
C. 144
D. 146
E. 148
Let's think step by step. | Length = Speed * time
Speed = L/T
S = 1600/40
S = 40 M/Sec
Speed= 40*18/5 (To convert M/Sec in to Kmph multiply by 18/5)
Speed = 144 Kmph
Answer:C | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: If the function Q is defined by the formula Q = 5w/(4d(z^2)), by what factor will Q be multiplied if w is quadrupled, d is doubled, and z is tripled?
Choices:
A. 1/9
B. 2/9
C. 4/9
D. 3/9
E. 2/27
Let's think step by step. | We just need to find the factor thats all,
w -> quadrupled -> 4w
d-> doubled -> 2d
z-> tripled -> 3Z
Hence, Z^2 = 9Z^2
W is in numerator, and d*z in denominator.
Hence,
Additional factor being introduced = 4/2*9
=4/18 = 2/9 = B | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: Tough and Tricky questions: Word Problems.
If Bill's salary increased by 16 percent, he would earn $812 per month. If instead, his salary were to increase by only 10 percent, how much money T would he earn per month?
Choices:
A. $700
B. $754
C. $770
D. $782
E. $893
Let's think step by step. | OFFICIAL SOLUTION:
(C) If Bill’s salary increased by 16% he would earn $812. Algebraically, this can be written as:
$812 = 1.16S, where S is his current salary.
Then S = $812/1.16 = $700.
Now that we know his current salary is $700, we can calculate what his salary would be if it were increased by 10%. We know that 10% of $700 is $70, so his salary would be:
T=$700 + $70 = $770.
The correct answer is choice (C). | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: Mr. Jones sold two pipes at $2.50 each. Based on the cost, his profit one was 30% and his loss on the other was 20%. On the sale of the pipes. Find the amount of his profit or loss?
Choices:
A. gain 0.25 cents
B. lost 4 cents
C. broke even
D. gained 4 cents
E. gained 10 cents
Let's think step by step. | 30 % profit on $ 2.50
= $ 30/100 × 2.50
= $ 0.30× 2.50
= $ 0.75
Similarly, 25 % loss on $ 2.50
= $ 20/100 × 2.50
= $ 0.20× 2.50
= $ 0.50
Therefore, in one pipe his profit is $ 0.75 and in the other pipe his loss is $ 0.50
So profit by amount 0.25 cents
Answer is A. | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: What is a key factor in the growth of populations?
Choices:
A. immigration
B. gentrification
C. legislation
D. assimilation
Let's think step by step. | Moving into an area, or immigration, is a key factor in the growth of populations. Shown above is actual vintage luggage left by some of the millions of immigrants who came through Ellis Island and into the United States. Therefore the final answer is A | https://huggingface.co/datasets/allenai/sciq |
Question: There is 60% increase in an amount in 6 years at S.I. What will be the C.I. of Rs. 12,000 after 3 years at the same rate?
Choices:
A. 2387
B. 2978
C. 3972
D. 2671
E. 1871
Let's think step by step. | Explanation:
Let P = Rs. 100. Then, S.I. Rs. 60 and T = 6 years.
R = (100 * 60)/(100 * 6) = 10% p.a.
Now, P = Rs. 12000, T = 3 years and R = 10% p.a.
C.I. = [12000 * {(1 + 10/100)3 - 1}]
= 12000 * 331/1000 = Rs. 3972
Answer: C | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: Out of 7 fruits in a basket, 2 are rotten. If two fruits are drawn at random from the basket, the probability of both being rotten is
Choices:
A. 1/21
B. 10/21
C. 20/21
D. 11/21
E. 2/21
Let's think step by step. | The number of exhaustive events = 7C2 = 21.
Let E be event of the 2 fruits being rotten. The number of favourable cases are
2C2 = 1 way.
Required probability = 1/21.
ANSWER:A | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: A person borrows 7000 for 3 years at 6% p.a. simple interest. He immediately lends it to another person at 31 % p.a. for 3 years. Find his gain in the transaction per year.
Choices:
A. 1600
B. 1700
C. 1550
D. 1650
E. 1750
Let's think step by step. | Gain in 3 years
= [(7000×31×3/100)−(7000×6×3/100)]
= (6510 – 1260) = 5250.
∴ Gain in 1 year = (5250â„3) = 1750
Answer E | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: A trained covered x km at 40 kmph and another 2x km at 20 kmph. Find the average speed of the train in covering the entire 7x km.
Choices:
A. 56
B. 18
C. 24
D. 19
E. 12
Let's think step by step. | Total time taken = x/40 + 2x/20 hours
= 5x/40 = x/8 hours
Average speed = 7x/(x/8) = 56 kmph
Answer: A | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: A man buys two articles for Rs.1980 each and he gains 10% on the first and loses 10% on the next. Find his total gain or loss percent?
Choices:
A. 9
B. 8
C. 7
D. 6
E. 5
Let's think step by step. | (30*30)/100 = 9%loss
Answer: A | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: What is the remainder when 3^33 is divided by 5?
Choices:
A. 0
B. 1
C. 2
D. 3
E. 4
Let's think step by step. | The units digit of powers of 3 follow a repeating cycle of four: {3, 9, 7, 1}
33 has the form 4k+1, so the units digit of 3^33 is 3.
The remainder when dividing by 5 is 3.
The answer is D. | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: In an examination, there were 2,000 candidates, out of which 900 candidates were girls and rest were Boys. If 32% of the boys and 32% of the girls passed, then the total percentage of failed candidates is?
Choices:
A. 35.67%
B. 64.75%
C. 68.00%
D. 69.57%
E. none of these
Let's think step by step. | Girls = 900, Boys = 1100
Passed = ( 32% of 1100 ) + ( 32% of 900)
= 352 + 288 = 640
Failed = 2000 - 640 = 1360
Failed % = [(1360/2000) x 100]%
= 68%.
ANSWER:C | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: The average of 6 no.'s is 3.95. The average of 2of them is 3.4, while the average of theother 2 is 3.85. What is the average of the remaining 2 no's?
Choices:
A. 2.3
B. 2.5
C. 3.5
D. 3.6
E. 4.6
Let's think step by step. | Sum of the remaining two numbers = (3.95 * 6) - [(3.4 * 2) + (3.85 * 2)]
= 23.70 - (6.8 + 7.7) = 23.70 - 14.5 = 9.20.
Required average = (9.2 / 2) = 4.6.
E | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: Which of the following reaches the largest value over the range -1 <= R <= 1?
Choices:
A. R+1
B. R+2
C. (R. ^2
D. (R-1. ^2
E. (R. ^3
Let's think step by step. | Evaluate all of the expressions:
R+1 has a maximum value of 2, at R=1
R+2 has a maximum value of 3, at R=1
R^2 has a maximum value of 1, at R=+/-1
(R-1)^2 has a maximum value of 4, at R= -1
R^3 has a maximum value of 1, at R=1
Therefore, the answer is D | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: What moves nitrogen back and forth between the atmosphere and organisms?
Choices:
A. the nitrogen cycle
B. the calcium cycle
C. the leakage cycle
D. the Krebs cycle
Let's think step by step. | The nitrogen cycle moves nitrogen back and forth between the atmosphere and organisms. Therefore the final answer is A | https://huggingface.co/datasets/allenai/sciq |
Question: Three pipes of same capacity can fill a tank in 12 hours. If there are only two pipes of same capacity, the tank can be filled in?
Choices:
A. 18
B. 8
C. 12
D. 6
E. 4
Let's think step by step. | The part of the tank filled by three pipes in one hour
= 1/12
=> The part of the tank filled by two pipes in 1 hour
= 2/3 * 1/12 = 1/18.
The tank can be filled in 18 hours.
Answer:A | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: If 20 liters of chemical X are added to 80 liters of a mixture that is 5% chemical X and 95% chemical Y, then what percentage of the resulting mixture is chemical X?
Choices:
A. 24%
B. 26%
C. 28%
D. 30%
E. 32%
Let's think step by step. | The amount of chemical X in the solution is 20 +0.05(80) = 24 liters.
24 liters / 100 liters = 24%
The answer is A. | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: Elena’s bread recipe calls for 8 ounces of butter for each 14 cups of flour used. She needs to make 4 times the original recipe. If 12 ounces of butter is used, then how many cups of flour are needed?
Choices:
A. 1
B. 4
C. 9
D. 13
E. 56
Let's think step by step. | Solving through algebra route:
8B + 14F = x amount
If we multiply this equation with 4 we get:
32B + 56F =4X
Therefore, we got 32 ounces of butter and 4X amount of quantity when we use 56 ounces of floor.
Ans:E | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: For a group of n people, k of whom are of the same sex, the (n-k)/n expression yields an index for a certain phenomenon in group dynamics for members of that sex. For a group that consists of 20 people, 6 of whom are females, by how much does the index for the females exceed the index for the males in the group?
Choices:
A. 0.4
B. 0.0625
C. 0.2
D. 0.25
E. 0.6
Let's think step by step. | Index for females = (20-6)/20 = 7/10 = 0.7
Index for males = (20-14/20 = 3/10 = 0.3
Index for females exceeds males by 0.7 - 0.3 = 0.4
Answer: A | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: If 0 < x < 1 < y, which of the following must be true?
Choices:
A. 1 < 1/x < 1/y
B. 1/x < 1 < 1/y
C. 1/x < 1/y < 1
D. 1/y < 1 < 1/x
E. 1/y < 1/x < 1
Let's think step by step. | Soln:
0<x<1<y. Let x=1/2 and y =2
Substituting values:
A. 1<2<1/2 --- Wrong
B. 2<1< 1/2 --- Wrong
C. 2<1/2<1 --- Wrong
D. 1/2<1<2 --- Correct
E. 1/2<2<1 --- Wrong
Hence answer is D | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 sec. The speed of the train is?
Choices:
A. 27
B. 50
C. 22
D. 26
E. 28
Let's think step by step. | Speed of the train relative to man
= 125/10
= 25/2 m/sec.
= 25/2 * 18/5 = 45 km/hr
Let the speed of the train be x km/hr. Then, relative speed
= (x - 5) km/hr.
x - 5 = 45 => x
= 50 km/hr.
Answer:B | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: The duplicate ratio of 3:4 is?
Choices:
A. 9:19
B. 9:13
C. 9:16
D. 9:12
E. 9:11
Let's think step by step. | 32: 42 = 9:16
Answer: C | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: A man rows 750 m in 675 seconds against the stream and returns in 7 and half minutes. His rowing speed in still water is
Choices:
A. 4 kmph
B. 5 kmph
C. 6 kmph
D. 7 kmph
E. None of these
Let's think step by step. | Explanation:
Rate upstream = (750/675) = 10/9 m/sec
Rate downstream (750/450) m/sec = 5/3 m/sec
Rate in still water = (1/2)*[(10/9) + (5/3)] m/sec.
= 25/18 m/sec
= (25/18)*(18/5) kmph
= 5 kmph
Option B | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: On a certain road 10% of the motorists exceed the posted speed limit and receive speeding tickets, but 40% of the motorists who exceed the posted speed limit do not receive speeding tickets. What percent of the motorists on the road exceed the posted speed limit?
Choices:
A. 10.5%
B. 12.5%
C. 15%
D. 22%
E. 16%
Let's think step by step. | 0.1 M = 0.60 E
=> E/M = 1/6 * 100 = 16%
So answer is E.
M - # of Motorists
E - # of Motorists exceeding speed | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: For which of the following does y(a)−y(b)=y(a−b) for all values of a and b?
Choices:
A. y(x. =x^2
B. y(x. =x/2
C. y(x. =x+5
D. y(x. =2x−1
E. y(x. =|x|
Let's think step by step. | To solve this easiest way is just put the value and see that if it equals or not.
with option 1. y(a) = a^2 and y(b) = b^2
so L.H.S = a^2 - b^2
and R.H.S = (a-b)^2 ==> a^2 + b^2 -2ab.
so L.H.S not equal to R.H.S
with option 2. y(a) = a/2 and y(b) = b/2
L.H.S = a/2 - b/2 ==> 1/2(a-b)
R.H.S = (a-b)/2
so L.H.S = R.H.S which is the correct answer.
answer:B | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: a man have 800kg mango.he found 8% of its mango are rotten.then how much mango is rotten?
Choices:
A. 64
B. 72
C. 68
D. 65
E. 82
Let's think step by step. | 8% of 800kg =(800*8)/100.
=64 mangoes
answer A | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: Which of the following functions does not intersect with Q = 3x^2 + 2x + 1
Choices:
A. Q= 3x^2 + 3x + 1
B. Q = 2x^2 + 3x + 1
C. Q = 3x^2 + 2x + 3
D. Q = 4x^2 + 2x - 3
E. Q = x^2 + 2x + 3
Let's think step by step. | Let’s find the actual intersecting point of given function and each choice Q
A. 3x^2 + 2x + 1 = 3x^2 + 3x + 1 --> x=0
B. 3x^2 + 2x + 1 = 2x^2 + 3x + 1 --> x^2 – x =0 --> x=0 or 1
C. 3x^2 + 2x + 1 = 3x^2 + 2x + 3 --> 1=3(X) --> they don’t have any intersect.
D. 3x^2 + 2x + 1 = 4x^2 + 2x - 3 --> x^2 –4=0 --> x= 2 or -2
E. 3x^2 + 2x + 1 = x^2 + 2x + 3 --> 2x^2 –2 =0 --> x= 1 or –1.
So only choice (C) has no intersecting point. The answer is (C). | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: In which kind of animals does parthenogenesis occur?
Choices:
A. mammals
B. invertebrates
C. species
D. tissues
Let's think step by step. | Note that in fragmentation, there is generally a noticeable difference in the size of the individuals, whereas in fission, two individuals of approximate size are formed. Parthenogenesis Parthenogenesis is a form of asexual reproduction where an egg develops into a complete individual without being fertilized. The resulting offspring can be either haploid or diploid, depending on the process and the species. Parthenogenesis occurs in invertebrates such as water flees, rotifers, aphids, stick insects, some ants, wasps, and bees. Bees use parthenogenesis to produce haploid males (drones) and diploid females (workers). If an egg is fertilized, a queen is produced. The queen bee controls the reproduction of the hive bees to regulate the type of bee produced. Some vertebrate animals—such as certain reptiles, amphibians, and fish—also reproduce through parthenogenesis. Although more common in plants, parthenogenesis has been observed in animal species that were segregated by sex in terrestrial or marine zoos. Two female Komodo dragons, a hammerhead shark, and a blacktop shark have produced parthenogenic young when the females have been isolated from males. Therefore the final answer is B | https://huggingface.co/datasets/allenai/sciq |
Question: x% of y is increased by x%. What is the result in terms of x and y?
Choices:
A. 100xy + x
B. xy + x/100
C. 100xy + x/100
D. 100xy + xy/100
E. xy(x + 100. /10000
Let's think step by step. | x% of y=xy/100
Increment is x% =xyx/100∗100
Total=xy/100+xyx/100∗100=xy(x+100)/10000
Answer = E | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: John is three times as old as Sam. If John will be twice as old as Sam in six years, how old was Sam three years ago?
Choices:
A. 2
B. 3
C. 6
D. 8
E. 16
Let's think step by step. | j= 3s
after 6 years
j +6 = 2(s+6)
j= 2s+6
2s +6 = 3s
s= 6
three years ago
s= 6-3= 3
B is the answer | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: Bag A contains red, white and blue marbles such that the red to white marble ratio is 1:3 and the white to blue marble ratio is 2:3. Bag B contains red and white marbles in the ratio of 1:4. Together, the two bags contain 20 white marbles. How many red marbles could be in bag A?
Choices:
A. 1
B. 3
C. 4
D. 6
E. 8
Let's think step by step. | 6 is the answer.
Bag A-
R:W:B = 2:6:9
Let W in bag A be 6K
Bab B -
R:W = 1:4
Let W in bag B be 4k
W = 20 = 6K+4k
k=2
Total Red's in bag A will be 2K = 4
C | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: A certain country had a total annual expenditure of $4.8 x 10^11 last year. If the population of the country was 240 million last year, what was the per capita expenditure?
Choices:
A. $ 500
B. $1,000
C. $2,000
D. $3,000
E. $5,000
Let's think step by step. | Total expenditure / Population = per capita expenditure
Hence, (4,8 x 10^11) / 240 000 000 = (4,8 x 10^11) / (2,4 x 10^8) = 2 x 10^(11-8) =
2 x 10^3 = 2000.
Answer is 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 79, how many questions did Student A answer correctly?
Choices:
A. 55
B. 60
C. 93
D. 82
E. 91
Let's think step by step. | let the number of correct responses be x
then the number of incorrect responses =100-x
according to question
x-2(100-x)=79 (subtracting twice of incorrect from correct)
3x=279
x=93
ANSWER:C | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: The captain of a cricket team of 11 members is 26 years old and the wicket keeper is 3 years older. If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. What is the average age of the team ?
Choices:
A. 11 year
B. 12 year
C. 23 year
D. 25 year
E. 27 year
Let's think step by step. | Let the average age of the whole team be x years.
11x - (26 + 29) = 9 (x - 1)
=> 11x - 9x = 46
=> 2x = 46
=> x = 23.
So, average age of the team is 23 years.
Answer: C | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: 10 men, working 3 hours a day can complete a work in 18 days. How many hours a day must 15 men work to complete the work in 12 days ?
Choices:
A. 3 hours a day
B. 5 hours a day
C. 6 hours a day
D. 7 hours a day
E. 8 hours a day
Let's think step by step. | Explanation:
More Men, Less Hours {Indirect Proportion}
Less Days, More Hours {Indirect Proportion}
[men 15 10
days 12 18] ::3:x
=>x∗15∗12=10∗18∗3
=>x=10∗18∗3/ 15∗12
=>x=3
Option A | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: How many ways could four cars can be parked at a parking lot with seven parking empty parking spots in which three of the seven spots will remain empty?
Choices:
A. 840
B. 28
C. 7
D. 920
E. 838
Let's think step by step. | ways in which 4 spots out 7 can be selected = 7C4
ways in which 4 cars can be arranged in 4 seats = 4!
Total ways of arrangement =7C4*4!
=(7*6*5/3*2)*24
=35*24
=840
Ans = A | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: The number of sequences in which 5 players can throw a ball, so that the youngest player may not be the last is ?
Choices:
A. 100
B. 96
C. 8
D. 62
E. 10
Let's think step by step. | x Not younger
The last ball can be thrown by any of the remaining 5 players. The first 4 players can throw the ball in 4P4 ways.
The required number of ways = 4(4!)
= 96
Answer:B | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: Given 2 integers a and b, if a is negative and b is positive, which of the following options must be positive?
Choices:
A. ab
B. a/b
C. 4a/b
D. (a + b. ^4
E. 2ab
Let's think step by step. | A.ab
-ve*+ve= -ve
will be negative
B. a/b
-ve/+ve=-ve
will be negative
C. 4a/b
-ve/+ve=-ve
D. (a + b)^4
= (a + b)^4 will be positive irrespective of the absolute values of x and y
will be positive always
E. 2ab
-ve*+ve= -ve
will be negative
Answer D | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: Of the films Empty Set Studios released last year, 60% were comedies and the rest were horror films. 75% of the comedies were profitable, but 75% of the horror moves were unprofitable. If the studio made a total of 41 films, and broke even on none of them, how many of their films were profitable?
Choices:
A. 18
B. 19
C. 20
D. 21
E. 40
Let's think step by step. | After fiddling some more, this is how I got to answer choice E...but did I get here using voodoo math or is it sound?
(.60*.75) + (.40*.25) = .44 + .10 = .55
55/100 = 11/20
Then subtract from 41:
41 - 11/20 = 40 (answer E) | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: How much time will a train of length 200 m moving at a speed of 72 kmph take to cross another train of length 300 m, moving at 36 kmph in the same direction?
Choices:
A. sec
B. sec
C. sec
D. sec
E. sec
Let's think step by step. | The distance to be covered = Sum of their lengths = 200 + 300 = 500 m.
Relative speed = 72 -36 = 36 kmph = 36 * 5/18 = 10 mps.
Time required = d/s = 500/10 = 50 sec.
Answer: A | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: Lloyd normally works 7.5 hours per day and earns $4.50 per hour. For each hour he works in excess of 7.5 hours on a given day, he is paid 2.5 times his regular rate. If Lloyd works 10.5 hours on a given day, how much does he earn for that day?
Choices:
A. $33.75
B. $47.25
C. $51.75
D. $54.00
E. $67.50
Let's think step by step. | Daily working hour*Regular Rate + Overtime*Increased Rate
7.5*4.5+ 3*4.5*2.5=67.5
Answer E | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: If a farmer sells 5 of his chickens, his stock of feed will last for 4 more days than planned, but if he buys 20 more chickens, he will run out of feed 1 day earlier than planned. If no chickens are sold or bought, the farmer will be exactly on schedule. How many chickens does the farmer have?
Choices:
A. 15
B. 20
C. 20/3
D. 25
E. 10
Let's think step by step. | Let x = total feed required for the planned period
n= number of chicken
t = total time of the planned feed
x = nt
1) x = (n-5) * (t+4)
2) x = (n+20) * (t-1)
equating 1 &2
(n-5) * (t+4) = (n+20) * (t-1)
5n = 25t
n =5t
x= n * n/5
substituting this value in 1
n * n/5 = (n-5) * (n/5+4)
15n = 100
n =20/3
C | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: The profits of QRS company rose 40% from March to April, then dropped 20% from April to May, then rose 50% from May to June. What was the percent increase for the whole quarter, from March to June?
Choices:
A. 15%
B. 32%
C. 40%
D. 68%
E. 80%
Let's think step by step. | Assume 100 in march , then 140 in April as 40% increase , Then 112 in may as 20% decrease from April , and then 168 in june which is 150% of 112 .
So overall increase is from 100 to 168 is 68%
Answer D | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: X percents of the rooms are suits, Y percent of the rooms are painted light blue. Which of the following best represents the least percentage of the light blue painted suits?
Choices:
A. X-Y
B. Y-X +100
C. 100X-Y
D. X+Y-100
E. 100-XY
Let's think step by step. | Using the simple formula
100 = X + Y - BOTH - > Here X = % of Suits , Y = % of light blue painted rooms and BOTH = % of suits painted in light blue colour
So now, BOTH = X+Y -100 and now you can manipulate the value of X and Y to get the max and minimum values.
Hence Answer D | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: Analysis of the various vehicle prices in a car dealership shop revealed that :
I) trucks cost 12% less than SUVs
II) Minivans cost 20% less than trucks
III) sedans cost 8% less than minivans
what percent of SUV's cost is a sedan?
Choices:
A. 88.9%
B. 90%
C. 66.24%
D. 70.3%
E. 78.8%
Let's think step by step. | Let the cost of suv be $100
I) trucks cost 10% less than SUVs--100-10=90
II) Minivans cost 20% less than trucks--90-18=72
III) sedans cost 8% less than minivans--72-5.76=66.24
what percent of SUV's cost is a sedan=66.24*100/100
Answer is C | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: From 2005 to 2015 the world's population grew by 11.27%, and from 2005 to 2010 the world's population grew by 6.20%. What was the percentage growth in the world's population from 2010 to 2015?
Choices:
A. 5%
B. 6%
C. 2%
D. 2.5%
E. 5.5%
Let's think step by step. | Let the world's population in 2005 = x; then,
for 2005-2010, the population equation is x + 0.0620x = 1.0620x,
for 2005-2015, the population equation is x + 0.1127x = 1.1127x;
so, the growth from 2010 to 2015 = (1.1127x - 1.060x)/(1.062x) = 0.05 (rounded). Thus, the answer is 5%.
Answer is A | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: The area of a square garden is Q square feet and the perimeter is P feet. If Q=2P+33, what is the perimeter of the garden in feet?
Choices:
A. 28
B. 32
C. 36
D. 40
E. 44
Let's think step by step. | Let x be the length of one side of the square garden.
x^2 = 8x + 33
x^2 - 8x - 33 = 0
(x-11)(x+3) = 0
x = 11, -3
P = 4(11) = 44
The answer is E. | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: The speed of a car increases by 2 kms after every one hour. If the distance travelling in the first one hour was 35 kms. what was the total distance travelled in 12 hours?
Choices:
A. 456 kms
B. 482 kms
C. 552 kms
D. 556 kms
E. 500 kms
Let's think step by step. | Explanation:
Total distance travelled in 12 hours =(35+37+39+.....upto 12 terms)
This is an A.P with first term, a=35, number of terms,
n= 12,d=2.
Required distance = 12/2[2 x 35+{12-1) x 2]
=6(70+23)
= 552 kms.
ANSWER IS C | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: It takes Avery 2.5 hours to build a brick wall while Tom can do it in 4 hours. If the two start working together and after an hour Avery leaves, how much time will it take Tom to complete the wall on his own?
Choices:
A. 1 hour and 24 minutes.
B. 50 minutes.
C. 1 hour and 40 minutes.
D. 2 hours and 10 minutes
E. 1 hour and 20 minutes
Let's think step by step. | Avery's efficiency is 100/2.5 = 40%
Tom's = 100/4= 25%
they worked together for 1 hour and finished 65% of the job
remaining = 35 %
Tom will complete 25 % in 60 minutes , and
10% in 60*10/25 minutes = 24 minutes
Time taken by Tom to finish the remaining on his own = 60+24 = 84 minutes
ANSWER:A | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: What are the two types of vascular plants?
Choices:
A. seedless and seed
B. ants and seed
C. dahlias and seed
D. Water and spore
Let's think step by step. | Vascular plants are further divided into seedless and seed plants. Therefore the final answer is A | https://huggingface.co/datasets/allenai/sciq |
Question: In a certain random experiment, exactly one of the outcomes A, B, and C will occur. In each random experiment, the probability that outcome A will occur is 1/3 , and the probability that outcome B will occur is 1/3. What is the probability that when the random experiment is conducted 6 independent times, each of outcomes A, B, and C will occur twice?
Choices:
A. 5/243
B. 1/12
C. 10/81
D. 1/6
E. 16/81
Let's think step by step. | Given that P(A) = P(B) = P(C) = 1/3.
P(AABBCC) = (13)^6∗6!2!2!2!=1081 we multiply by 6!/(2!2!2!) because AABBCC scenario can occur in several ways: AABBCC, AABCBC, AACBBC, ... (the number of permutations of 6 letters AABBCC is 6!(2!2!2!)).
Answer: C. | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: The dimensions of a room are 25 feet * 15 feet * 12 feet. What is the cost of white washing the four walls of the room at Rs. 9 per square feet if there is one door of dimensions 6 feet * 3 feet and three WINDOWS of dimensions 4 feet * 3 feet each?
Choices:
A. 4000
B. 345
C. 5673
D. 6530
E. 8154
Let's think step by step. | Area of the four walls = 2h(l + b)
Since there are doors and WINDOWS, area of the walls = 2 * 12 (15 + 25) - (6 * 3) - 3(4 * 3) = 906 sq.ft.
Total cost = 906 * 9 = Rs.8154
Answer: Option E | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: At a party, everyone shook hands with everybody else. There were 66 handshakes.
How many people were at the party?
Choices:
A. 15
B. 18
C. 11
D. 12
E. 19
Let's think step by step. | D
12
If there are n people,
the first person will shake hand with n-1 persons,
the second with n-2,
the third with n-3,
and
the (n-1)th person with n-(n-1)=1 person means the last person.
Hence, total handshakes are (n-1)+(n-2)+(n-3)+….+3+2+1
Which can be equated using n(n-1)/2=66
Hence, n=12 | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: A profit of Rs. 600 is divided between X and Y in the ratio of 1/2:1/3 . What is the difference between their profit shares ?
Choices:
A. s. 220
B. s. 120
C. s. 320
D. s. 50
E. s. 90
Let's think step by step. | A profit of Rs. 600 is divided between X and Y in the ratio of 1/2 : 1/3 or 3:2.
so profits are 360 and 240.
difference in profit share = 360-240=120
ANSWER:B | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: What will come in place of the x in the following Number series? 2, 7, 32, 157, 782, x
Choices:
A. 3707
B. 3790
C. 3910
D. 3907
E. 3970
Let's think step by step. | 2
2 x 5 - 3 = 7
7 x 5 - 3 = 32
32 x 5 - 3 = 157
157 x 5 - 3 = 782
782 x 5 - 3 = 3907
D | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: Find large number from below question The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder
Choices:
A. 1234
B. 1345
C. 1564
D. 1670
E. 1635
Let's think step by step. | Let the smaller number be x. Then larger number = (x + 1365).
x + 1365 = 6x + 15
5x = 1350
x = 270
Large number = 270+1365 = 1635
E | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: A rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered. If the area of the field is 680 sq. feet, how many feet of fencing will be required?
Choices:
A. 34
B. 40
C. 68
D. 88
E. 98
Let's think step by step. | Explanation:
We have: l = 20 ft and lb = 680 sq. ft.
So, b = 34 ft.
Length of fencing = (l + 2b) = (20 + 68) ft = 88 ft.
Answer: D | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: A gardener wants to plant trees in his garden in such a way that the number of trees in each row should be the same. If there are 4 rows or 5 rows or 6 rows, then no tree will be left. Find the least number of trees required.
Choices:
A. 30
B. 60
C. 120
D. 240
E. 480
Let's think step by step. | The least number of trees that are required = LCM(4, 5, 6) = 60.
ANSWER:B | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: A number when divided by 5 gives a number which is 8 more than the remainder obtained on dividing the same number by 34. Such a least possible number V is
Choices:
A. 74
B. V=75
C. V=175
D. V=680
E. 690
Let's think step by step. | I solved this question by plugging in numbers from the answer choices.
A.) 74
Starting with answer choice A, I immediately eliminated it because 74 is not even divisible by 5.
B.) 75
I divide 75/5 and get 15 as an answer. I divide 75/34 and get a remainder of 7.
15-7 = 8 so I know the correct answer isB | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: A train is 485 meter long is running at a speed of 45 km/hour. In what time will it pass a bridge of 140 meter length
Choices:
A. 20 seconds
B. 30 seconds
C. 40 seconds
D. 50 seconds
E. None of these
Let's think step by step. | Explanation:
Speed = 45 Km/hr = 45*(5/18) m/sec
= 25/2 m/sec
Total distance = 485+140 = 625 meter
Time = Distance/speed
=625∗2/25=50seconds
Option D | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: What is the functional unit of compact bone?
Choices:
A. the canton
B. the boron
C. the auteron
D. the osteon
Let's think step by step. | Bone matrix provides bones with their basic structure. Notice the spongy bone in the middle, and the compact bone towards the outer region. The osteon is the functional unit of compact bone. Therefore the final answer is D | https://huggingface.co/datasets/allenai/sciq |
Question: The average of six numbers is 3.95. The average of two of them is 3.1, while the average of the other two is 3.85. What is the average of the remaining two numbers?
Choices:
A. 4.5
B. 4.6
C. 4.7
D. 4.8
E. 4.9
Let's think step by step. | Sum of the remaining two numbers
= (3.95 × 6) – [(3.1 × 2) + (3.85 × 2)]
= 23.70 – (6.1 + 7.7)
= 23.70 – 13.9 = 9.80
∴ Required average = (9.8⁄2) = 4.9
Answer E | https://huggingface.co/datasets/deepmind/aqua_rat |
Question: A bicyclist travels uphill from town A to town B for 2 hours at an average speed of 4 miles per hour and returns along the same road at an average speed of 5 miles per hour. What is the bicyclist’s average speed for the round trip, in miles per hour?
Choices:
A. (a. 24/5
B. (b. 5
C. (c. 40/9
D. (d. 27/5
E. (e. 28/5
Let's think step by step. | from the uphill we can find out the distance = 4*2 = 8
average speed = total distance/total time
= 16/ (2+ (8/5)) = 40/9
Answer is C. | https://huggingface.co/datasets/deepmind/aqua_rat |
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