mathewhe/aqua_rat huggingface dataset:
Question: Machine X can complete a job in half the time it takes Machine Y to complete the same job, and Machine Z takes 50% longer than Machine X to complete the job. If all three machines always work at their respective, constant rates, what is the ratio J of the amount of time it will take Machines X and Z to complete the job to the ratio of the amount of time it will take Machines Y and Z to complete the job?
(A) 5 to 1
(B) 10 to 7
(C) 1 to 5
(D) 7 to 10
(E) 9 to 10
Rationale: Solutioning this exercise can be facilitated by using a R T W (rate time work) table:
We translate the exercise into the table:
R T W
X t/2 1
Y t 1
Z (t/2*3/2 =3t/4) 1
From this table we find the rates
Rx = 2/t
Ry = 1/t
Rz = 4/3t
The Q is what is the ratio of (Tx + Ty) / (Ty + Tz)
Rx + Ry = 2/t + 4/3t = 6/3t+4/3t = 10/3t
Ry+Rz = 1/t + 4/3t = 3/3t + 4/3t = 7/3t
The (10/3t)/(7/3t) = 10/7 then the work ratios is 10 to 7
Since Time Ratio J is the inverse of work, the the answer is 7 to 10
CORRECT ANSWER D
Answer: (D) 7 to 10
Question: A certain number of workers can do a work in 45 days. If there were 10 workers more it could be finished in 10 days less. How many workers are there?
(A) 25
(B) 30
(C) 28
(D) 24
(E) 35
Rationale: number of workers = 10* (45-10)/10 = 35
Answer is E
Answer: (E) 35
Question: A train 575 m long crosses a tunnel of length 325 in 90 sec. What is the speed of the train in kmph.
(A) 28
(B) 32
(C) 36
(D) 24
(E) 30
Rationale: Total distance traveled = Length of train + Length of tunnel = 575 + 325 = 900
Time taken to cross the tunnel = 90 sec.
Speed in kmph = distance/time *18/5 = 900/90 * 18/5
= 180/5 = 36 kmph
ANSWER:C
Answer: (C) 36
Question: If X and Y are both positive two-digit integers and share no digits, and X > Y, what is the smallest possible value of X - Y?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 9
Rationale: Answer = B = 1
20 - 19 = 30-29 = 40-39 = 50-49 = 1
Answer: (B) 1
Question: Find the average of first 4 multiples of 9?
(A) 10
(B) 12.6
(C) 22.5
(D) 31.3
(E) 40.8
Rationale: average = (9+18+27+36)/4 = 22.5
Answer is C
Answer: (C) 22.5
Question: A table is bought for Rs.500/- and sold at a loss of 10% find its selling price
(A) s.450/-
(B) s.530/-
(C) s.540/-
(D) s.600/-
(E) s.700/-
Rationale: 100 % ------> 500 (100 * 5 = 500)
90 % ------> 450 (90 * 5 = 450)
Selling price = Rs.450/-
A
Answer: (A) s.450/-
Question: If the remainder is 11 when the integer n is divided by 20, what is the remainder when 2n is divided by 10?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: n = 20k+11
2n = 2(20k+11) = 4k*10 + 22 = 4k*10 + 2*10 + 2 = 10j + 2
The answer is C.
Answer: (C) 2
Question: The average age of 15 students of a class is 15 years. Out of these, the average age of 5 students is 14 years and that of the other 9 students is 16 years. Tee age of the 15th student is?
(A) 11 years
(B) 17 years
(C) 67 years
(D) 14 years
(E) 12 years
Rationale: Age of the 15th student
=[15 * 15 - (14 * 5 + 16 * 9)]
= (225 - 214)
= 11 years.
Answer:A
Answer: (A) 11 years
Question: On Children's Day, sweets were to be equally distributed among 175 children in a school. Actually on the Children's Day, 35 children were absent and therefore each child got 4 sweets extra. Total how many sweets were available for distribution ?
(A) 2400
(B) 2480
(C) 2680
(D) 2800
(E) 2900
Rationale: Let take X is the sweets received by each student.
Actually on the Children's Day, 35 children were absent and therefore each child got 4 sweets extra. means
35*x = 140*4 = 560. X= 16. total Sweets are 175*16 = 2800
ANSWER:D
Answer: (D) 2800
Question: A circular well with a diameter of 6 metres , is dug to a depth of 24 metres. What is the volume of the earth dug out?
(A) 678.6 m3
(B) 36 m3
(C) 40 m3
(D) 44 m3
(E) None
Rationale: Solution
Volume	= πr2h
‹=› (22 /7 ×3×3×24)m3
‹=›678.6 m3.
Answer A
Answer: (A) 678.6 m3
Question: Two men started from the same place walk at the rate of 10kmph and 12kmph respectively. What time will they take to be 30 km apart, if they walk in the same direction?
(A) 15hours
(B) 6hours
(C) 8hours
(D) 10hours
(E) 12hours
Rationale: To be 2km apart they take 1 hour
To be 10km apart they take = 1/2 * 30 =15 hours
Answer is A
Answer: (A) 15hours
Question: A total of 3000 chocolates were distributed among 120 boys and girls such that each boy received 2 chocolates and each girl received 3 chocolates. Find the respective number of boys and girls?
(A) 97
(B) 60
(C) 91
(D) 26
(E) 21
Rationale: Let the number of boys be x.
Number of girls is 120 - x.
Total number of chocolates received by boys and girls = 2x + 3(120 - x) = 300
=> 360 - x = 300 => x = 60.
So, the number of boys or girls is 60.
Answer: B
Answer: (B) 60
Question: A boat having a length 3 m and breadth 2 m is floating on a lake. The boat sinks by 1 cm when a man gets on it. The mass of the man is:
(A) 12 kg
(B) 60 kg
(C) 72 kg
(D) 80 kg
(E) 96 kg
Rationale: Volume of water displaced	= (3 x 2 x 0.01) m3
= 0.06 m3.
Mass of man	= Volume of water displaced x Density of water
= (0.06 x 1000) kg
= 60 kg. Answer: Option B
Answer: (B) 60 kg
Question: A person sold two cows each for Rs.9900. If he gained 10% on one and lost 20% on the other, then which of the following is true?
(A) He Gained Rs. 200
(B) He lost Rs. 200
(C) He neither gained nor lost
(D) None of the above
(E) He lost Rs. 400
Rationale: Explanation:
The CP of profitable cow = 9900/1.1=9000
and profit = Rs. 900
The CP of loss yielding cow = 9900/0.8=12375
and loss = Rs. 2475
so, the net loss = 2475 - 900 = 1575. Answer: D
Answer: (D) None of the above
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?
(A) 18:11
(B) 18:15
(C) 18:10
(D) 18:12
(E) 18:13
Rationale: 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
Answer: (A) 18:11
Question: A train travels at an average of 50 miles per hour for 2 1/2 hours and then travels at a speed of 70miles per hour for 1 1/2 hours. How far did the train travel in the entire 4 hours?
(A) 200miles
(B) 230miles
(C) 250miles
(D) 150miles
(E) 300miles
Rationale: Total distance traveled = (50*2 1/2)+(70*1 1/2) = 125+105 = 230 miles
Answer is B
Answer: (B) 230miles
Question: In an examination, 35% candidates failed in one subject and 42% failed in another subject while 15% failed in both the subjects. If 2500 candidates appeared at the end of the examination how many passed in either subject but not in both?
(A) 975
(B) 1020
(C) 1175
(D) 1243
(E) 1525
Rationale: Failed in 1st subject = 35*2500/100 = 875
Failed in 2nd subject = 42*2500/100 = 1050
Failed in both = 15*2500/100 = 375
Failed in 1st subject only = 875-375 = 500
Failed in 2nd subject only = 1050-375 = 675
Passed in either subject but not in both = 675+500 = 1175
Answer is C
Answer: (C) 1175
Question: 12 men work 8 hours per day to complete the work in 10 days. To complete the same work in 10 days, working 12 hours a day, the number of men required?
(A) 10 days
(B) 9 days
(C) 6 days
(D) 8 days
(E) 7 days
Rationale: That is, 1 work done = 12 × 8 × 10
Then, 12 8 × 10 = ? × 12 × 10
? (i.e. No. of men required) = 12 × 8 × 10/12× 10 = 8 days
D)
Answer: (D) 8 days
Question: Which of the following numbers is not prime?
(A) 5+6
(B) 20-1
(C) 3+4
(D) 59-6
(E) 9+6
Rationale: Choice A is excluded because 5 can not be factored. Choice B is excluded because 1 has no factors. In Choice C, the number 3 is not able to be factored. Choice D 59 can not be factored. Notice we can factor 3 out of both 9+6. --> 9+6= 3*(3+2). The correct answer is E.
Answer: (E) 9+6
Question: If A's height is 30% less than that of B, how much percent B's height is more than that of A?
(A) 42.85%
(B) 66.68%
(C) 66.766%
(D) 86.66%
(E) 66.65%
Rationale: Excess of B's height over A's = [(30/(100 - 30)] x 100%
= 42.85%
Answer: A)
Answer: (A) 42.85%
Question: There are 8 magazines lying on a table; 4 are movie magazines and the other 4 are education magzines. If 3 magazines are to be selected at random from the 8 magazines, what is the probability that at least one of the movie magazine will be selected?
(A) 9/14
(B) 11/14
(C) 13/14
(D) 1/14
(E) 3/14
Rationale: 1- (4c3/8c3) = 13/14
Answer : C
Answer: (C) 13/14
Question: A is thrice as efficient as B and is, therefore, able to finish a piece of work 10 days earlier than B. In how many days A and B will finish it together?
(A) 87 days
(B) 77 days
(C) 8 days
(D) 5 days
(E) 6 days
Rationale: WC = 3:1
WT = 1:3
x 3x
1/x – 1/3x = 1/10
x = 20/3
3/20 + 1/20 = 1/5 => 5 days
Answer: D
Answer: (D) 5 days
Question: 5n + 2 > 12 and 7n - 12 < 44; n must be between which numbers?
(A) 2 and 8
(B) 2 and 6
(C) 0 and 9
(D) 2 and 7
(E) 2 and 9
Rationale: 5n+2 > 12
5n > 10
n > 2
7n-12 < 44
7n < 56
n < 8
So n must be between 2 and 8
2 < n < 8
correct answer A
Answer: (A) 2 and 8
Question: A cistern is filled by pipe A in 8 hours and the full cistern can be leaked out by an exhaust pipe B in 12 hours. If both the pipes are opened, in what time the cistern is full?
(A) 24hrs
(B) 60hrs
(C) 70hrs
(D) 80hrs
(E) 90hrs
Rationale: time taken to full the cistern=(1/8-1/12)hrs
=1/24
=24hrs
ANSWER:A
Answer: (A) 24hrs
Question: When sold at a 60% discount, a sweater nets the merchant a 20% profit on the wholesale cost at which he initially purchased the item. By what % is the sweater marked up from wholesale at its normal retail price?
(A) 20%
(B) 40%
(C) 66.67%
(D) 80%
(E) 100%
Rationale: we should be careful about what are we measuring % on/what is the base..
let the Marked up price =100..
Selling price= 100-60%of 100=40..
profit= 20%..
therefore the wholesale purchase cost= x.... 1.2x=40
or x=33.33...
marked price was 100 so ...
so answer is 66.67%..
C
Answer: (C) 66.67%
Question: A bag contains 2 red, 3 green and 2 blue balls. Two balls are drawn at random. What is the probability that none of the balls drawn is blue?
(A) 10/21
(B) 10/29
(C) 10/20
(D) 10/22
(E) 10/24
Rationale: Explanation:
Total number of balls = (2 + 3 + 2) = 7.
Let S be the sample space.
Then, n(S) = Number of ways of drawing 2 balls out of 7 = = 21
Let E = Event of drawing 2 balls, none of which is blue.
n(E) = Number of ways of drawing 2 balls out of (2 + 3) balls = = 10
Therefore, P(E) = n(E)/n(S) = 10/ 21.
Answer: A) 10/21
Answer: (A) 10/21
Question: Exactly 36% of the numbers in set Q are even multiples of 3. If 40% of the even integers in set Q are not multiples of 3, what percent of the numbers in set Q are not even integers?
(A)  76%
(B)  60%
(C)  50%
(D)  40%
(E)  24%
Rationale: Everything is correct except the red part with a typo: it should be N=0.6Q --> even numbers are 60% of Q --> 40% of Q are not even integers.
Answer: D.
Answer: (D)  40%
Question: If |x - 16| = 2x, then x=?
(A) 10
(B) 15
(C) -16
(D) 16
(E) 5
Rationale: |x - 16| = 2x ...(given)
x^2 - 32x + 256 = 4x^2
3*x^2 + 32*x -256 = 0 ....(by solving above eq. we get) , x = -16 or 5.33 ===> Ans - C
Answer: (C) -16
Question: The areas, in kilometers squared, of some countries are given below. USA: 9,629,091, Russia: 17,098,242, China: 9,598,094, Canada: 9,984,670, the UK: 242,400 and India: 3,287,263.
What is the difference between the areas of Russia and China?
(A) 8,500,148 kilometers squared
(B) 9,500,148 kilometers squared
(C) 7,500,148 kilometers squared
(D) 4,500,148 kilometers squared
(E) 1,500,148 kilometers squared
Rationale: the difference between the areas of Russia and China is given by
17,098,242 - 9,598,094 = 7,500,148 kilometers squared
correct answer C
Answer: (C) 7,500,148 kilometers squared
Question: A, B and C invested Rs.6300, Rs.4200 and Rs.10500 respectively, in a partnership business. Find the share of A in profit of Rs.12100 after a year?
(A) 3630
(B) 8289
(C) 356E3
(D) 3778
(E) 838
Rationale: 6300:4200:10500
3:2:5
3/10 * 12100
= 3630
AnswerA
Answer: (A) 3630
Question: 54671 - 14456 - 31466 = ?
(A) 2449
(B) 5449
(C) 8749
(D) 8449
(E) 6468
Rationale: C
If we calculate we will get 8749
Answer: (C) 8749
Question: Insert the missing number
121, 112, ..., 97, 91, 86
(A) 102
(B) 108
(C) 99
(D) 104
(E) 114
Rationale: first and second number difference is starting from 9, and further decresed by 1 by each iteration.
121, 112, ..., 97, 91, 86....
Dfference between two numbers Will be as 9, 8, 7, 6, 5,...
ANSWER:D
Answer: (D) 104
Question: The distance between two stars is 2.5 × 10^5 light years. What is the distance between the two stars in parsecs? (1 parsec = 3.26 light years)
(A) 5.5 × 10^3
(B) 3.3 × 10^4
(C) 7.7 × 10^4
(D) 9.9 × 10^5
(E) 1.1 × 10^6
Rationale: 2.5 × 10^5 ly / (3.26 ly/parsec) = (2.5/3.26) x 10^5 = 0.77 x 10^5 = 7.7 x 10^4 parsec
The answer is C.
Answer: (C) 7.7 × 10^4
Question: A can complete a work in 12days and B can do the same work in 6days. If A after doing 3days, leaves the work, find in how many days B will do the remaining work?
(A) 2 1/2days
(B) 4 1/2days
(C) 6 1/2days
(D) 7 1/2days
(E) 10 1/2days
Rationale: The required answer = (12-3)*6 / 12 = 54/12 = 4 1/2days
Answer is B
Answer: (B) 4 1/2days
Question: Two numbers are respectively 20% and 25% more than a third number. The percentage that is first of the second is?
(A) 76%
(B) 86%
(C) 96%
(D) 56%
(E) 92%
Rationale: I II III
120 125 100
125----------120
100-----------? => 96%
Answer:C
Answer: (C) 96%
Question: After decreasing 24% in the price of an article costs Rs.912. Find the actual cost of an article?
(A) 1288
(B) 1238
(C) 1200
(D) 1233
(E) 1234
Rationale: CP* (76/100) = 912
CP= 12 * 100 => CP
= 1200
Answer:C
Answer: (C) 1200
Question: Paul earns $12000 an year from his job. His income increased and now makes $13500 an year. What is the percent increase?
(A) 25%
(B) 20%
(C) 15.5%
(D) 12.5%
(E) 10.5%
Rationale: Increase = (1500/12000)*100 = (1/8)*100 = 12.5%.
D
Answer: (D) 12.5%
Question: A tank is filled in eight hours by three pipes A, B and C. Pipe A is twice as fast as pipe B, and B is twice as fast as C. How much time will pipe B alone take to fill the tank?
(A) 56 hours
(B) 28 hours
(C) 55 hours
(D) 66 hours
(E) 47 hours
Rationale: 1/A + 1/B + 1/C = 1/8 (Given)
Also given that A = 2B and B = 2C
=> 1/2B + 1/B + 2/B = 1/8
=> (1 + 2 + 4)/2B = 1/8
=> 2B/7 = 8
=> B = 28 hours.
Answer: B
Answer: (B) 28 hours
Question: (9568422 x 558) = ?
(A) 5846381256
(B) 5339179476
(C) 5346381356
(D) 5846381406
(E) 5346381456
Rationale: 9568422 x 558=5339179476Ans B
Answer: (B) 5339179476
Question: A number is missing from the number series below.
Can you find it ?
84, ?, 258, 399 , 584, 819.
(A) 155
(B) 350
(C) 399
(D) 421
(E) 449
Rationale: A
The missing number is 155.
84 = 4^3 + 3^2 + 4
258 = 6^3 + 6^2 + 6
399 = 7^3 + 7^2 + 7
584 = 8^3 + 8^2 + 8
819 = 9^3 + 9^2 + 9
Thus,
155 = 5^3 + 5^2 + 5
Answer: (A) 155
Question: 5 men are equal to as many women as are equal to 8 boys. All of them earn Rs.75 only. Menâ€™s wages are?
(A) 6Rs
(B) 7Rs
(C) 8Rs
(D) 5Rs
(E) 1Rs
Rationale: 5M = xW = 8B
5M + xW + 8B ----- 75 Rs.
5M + 5M + 5M ----- 75 Rs.
15M ------ 75 Rs. => 1M = 5Rs.
Answer:D
Answer: (D) 5Rs
Question: If in a certain sequence of consecutive multiples of 100, the median is 750, and the greatest term is 1200, how many terms that are smaller than 650 are there in the sequence?
(A) 6
(B) 7
(C) 8
(D) 12
(E) 13
Rationale: Since the median is 750 we know there must be a even number of integers
So the list around 750 must go. 700 (750) 800 900 1000 1100 ,1200
Since we know there are 5 numbers greater than 750 then there must be 5 numbers less then 750
C
Answer: (C) 8
Question: Pipe A fills a tank in 56 minutes. Pipe B can fill the same tank 7 times as fast as pipe A. If both the pipes are kept open when the tank is empty, how many minutes will it take to fill the tank?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
Rationale: A's rate is 1/56 and B's rate is 1/8.
The combined rate is 1/56 + 1/8 = 1/7
The pipes will fill the tank in 7 minutes.
The answer is D.
Answer: (D) 7
Question: If x and y are distinct prime numbers less than ten, what must be true about the product of x and y?
(A) xy is even
(B) xy is odd
(C) xy < 0
(D) xy < 36
(E) xy > 6
Rationale: Prime numbers less than 10 = 2, 3, 5, 7. x and y can take any oth the values
On checking the options
A. xy is even
xy can be even or odd both
B. xy is odd
xy can be even or odd both
C. xy < 0
Product of two prime numbers can never be < 0
Prime numbers are always positive
D. xy < 36
The maximum value of multiplication can be 5*7 = 35.
Hence this is true always
E. xy > 6
x = 2, y = 3
In this case, xy = 6. FALSE
Correct Option: D
Answer: (D) xy < 36
Question: One side of a rectangle is 3 cm shorter than the other side. If we increase the length of each side by 1 cm, then the area of the rectangle will increase by 24 cm2. Find the lengths of all sides.
(A) 10 and 3
(B) 7 and 10
(C) 10 and 7
(D) 3 and 10
(E) 13 and 10
Rationale: Let x be the length of the longer side x>3, then the other side's length is x−3 cm. Then the area is S1 = x(x - 3) cm2. After we increase the lengths of the sides they will become (x+1) and (x−3+1)=(x−2) cm long. Hence the area of the new rectangle will be A2=(x+1)⋅(x−2) cm2, which is 24 cm2 more than the first area. Therefore
A1+24=A2
x(x−3)+24=(x+1)(x−2)
x2−3x+24=x2+x−2x−2
2x=26
x=13. So, the sides of the rectangle are 13 cm and (13−3)=10 cm long.
So answer is E.
Answer: (E) 13 and 10
Question: The angles of a triangle are in the ratio 1:3:8. Find the measurement of the three angles of triangle.
(A) 90°
(B) 100°
(C) 120°
(D) 140°
(E) 160°
Rationale: If the ratio of the three angles is 1:3:8, then the measures of these angles can be written as x, 3x and 8x. Also the sum of the three interior angles of a triangle is equal to 180°. Hence
x + 3x + 8x = 180
Solve for x
12x = 180
x = 15
The measures of the three angles are
x = 15°
3x = 3 × 15 = 45°
8x = 8 × 15 = 120°
C
Answer: (C) 120°
Question: A sun is divided among X, Y and Z in such a way that for each rupee X gets, Y gets 45 paisa and Z gets 30 paisa. If the share of Y is RS. 27, what is the total amount?
(A) 228
(B) 105
(C) 288
(D) 267
(E) 168
Rationale: x:y:z = 100:45:30
20:9:6
9 --- 27
35 --- ? => 105
Answer:B
Answer: (B) 105
Question: Cost of 16 mirror and 8 comb is Rs.360 and the cost of 4 mirror and 4 comb is Rs.96. Find the cost of each mirror?
(A) 10
(B) 12
(C) 20
(D) 21
(E) 22
Rationale: Let the cost of each pen and pencil be 'p' and 'q' respectively.
16m + 8c = 360 --- (1)
4m + 4c = 96
8m + 8c = 192 --- (2)
(1) - (2) => 8p = 168
=> m = 21
D
Answer: (D) 21
Question: A 90-liter solution of cool-drink is made from 5% jasmine water. If 6.5 liters of jasmine and 13.5 liters of water were added to the solution, what percent of the solution is jasmine?
(A) 8%
(B) 8.5%
(C) 9%
(D) 9.5%
(E) 10%
Rationale: The percent of jasmine in the resulting solution is: (amount of jasmine) / (total volume)
(0.05(90) + 6.5) / 110 = 11/110 = 10%
The answer is E.
Answer: (E) 10%
Question: In a market, a dozen eggs cost as much as a pound of rice, and a half-liter of kerosene costs as much as 6 eggs. If the cost of each pound of rice is $0.24, then how many cents does a liter of kerosene cost? [One dollar has 100 cents.]
(A)  0.20
(B)  0.24
(C)  20
(D)  24
(E)  55
Rationale: A dozen eggs cost as much as a pound of rice --> 12 eggs = 1 pound of rice = 24 cents;
A half-liter of kerosene costs as much as 6 eggs --> 6 eggs = 1/2 liters of kerosene.
How many cents does a liter of kerosene cost --> 1 liter of kerosene = 12 eggs = 12/12*24 = 24 cents.
Answer: D.
Answer: (D)  24
Question: A jogger running at 9 km/hr along side a railway track is 240 m ahead of the engine of a 120 m long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger?
(A) 22
(B) 88
(C) 36
(D) 88
(E) 27
Rationale: Speed of train relative to jogger = 45 - 9 = 36 km/hr.
= 36 * 5/18 = 10 m/sec.
Distance to be covered = 240 + 120 = 360 m.
Time taken = 360/10 = 36 sec.
Answer: C
Answer: (C) 36
Question: How many months are in 3 years?
(A) 48
(B) 12
(C) 30
(D) 36
(E) 30
Rationale: D. 36 months
Answer: (D) 36
Question: What will be the fraction of 10%
(A) 1/4
(B) 1/5
(C) 1/10
(D) 1/11
(E) None of above
Rationale: Explanation:
It will 10*1/100 = 1/10
Option C
Answer: (C) 1/10
Question: The number of arrangements that can be made with the letters of the word COPY so that the vowels occupy the even places?
(A) 6
(B) 144
(C) 777
(D) 992
(E) 221
Rationale: The word MEADOWS has 7 letters of which 3 are vowels.
-V-V-V-
As the vowels have to occupy even places, they can be arranged in the 1 even places in 1! i.e., 1 ways. While the consonants can be arranged among themselves in the remaining 3 places in 3! i.e., 6 ways.
Hence the total ways are 1 * 6 = 6.
Answer:A
Answer: (A) 6
Question: A bowl has only 6 apples and 6 bananas. If one piece of fruit is selected from the bowl at random, and a second piece is selected from the bowl without replacing the first, what is the probability that both pieces of fruit chosen are apples?
(A) 1/10
(B) 1/5
(C) 2/9
(D) 30/131
(E) 1/2
Rationale: 6/12 * 5/11
=30/131
D. 30/131
Answer: (D) 30/131
Question: If n ≠ 0, which of the following must be greater than n?
I. 4n
II. n^2
III. 2 - n
(A) II only
(B) I only
(C) I and II only
(D) II and III only
(E) None
Rationale: n ≠ 0 => n = negative or n = positive
if n = negative:
2n < n (n = -1 then 2n = -2 => -2 < -1)
n^2 > n (n =-1 then n^2 = 1 => n^2 > n)
2 - n > n (n = -1 then 2--1 = 2+1=3 => 2-n > n)
but if n = positive:
n^2 > n (n = 2 then n^2 = 4 => n^2 > n) => II
2 - n < n(n =2 then 2-2 = 0)
=> only II
=>answer is A
Answer: (A) II only
Question: A train 250 m long running at 72 kmph crosses a platform in 30 sec. What is the length of the platform?
(A) 350m
(B) 200m
(C) 250m
(D) 270m
(E) 300 m
Rationale: D = 72 * 5/18 = 30 = 600 â€“ 250 = 350m
ANSWER:A
Answer: (A) 350m
Question: A train 300 m long passed a pole in 22 sec. How long will it take to pass a platform 725 m long?
(A) 12 sec
(B) 59 sec
(C) 73 sec
(D) 67 sec
(E) 76 sec
Rationale: Speed = 300/22
= 14 m/sec.
Required time = (300 + 725)/14
= 73 sec.
Answer: C
Answer: (C) 73 sec
Question: From 5 positive numbers and 6 negative numbers, how many groups of 4 numbers, yielding a positive product, can be formed?
(A) 170
(B) 625
(C) 30
(D) 960
(E) 255
Rationale: The number of ways to choose 4 positive numbers is 5C4 = 5.
The number of ways to choose 4 negative numbers is 6C4 = 15.
The number of ways to choose 2 positive and 2 negative numbers is 5C2*6C2 = 10*15 = 150.
The total number of groups is 5+15+150 = 170.
The answer is A.
Answer: (A) 170
Question: A man can row a boat at 14 kmph in still water. If the speed of the stream is 5 kmph, what is the time taken to row a distance of 80 km downstream?
(A) 85/19
(B) 90/18
(C) 80/19
(D) 70/19
(E) 60/19
Rationale: Speed downstream = 14 + 5 =19 kmph.
Time required to cover 80 km downstream = d/s = 80/19
= 80/19 hours.
Answer: C
Answer: (C) 80/19
Question: Working simultaneously at their respective constant rates, Machines A and B produce 800 nails in x hours. Working alone at its constant rate, Machine A produces 800 nails in q hours. In terms of x and q, how many hours does it take Machine B, working alone at its constant rate, to produce 800 nails?
(A) x/(x+y)
(B) y/(x+y)
(C) xy/(x+y)
(D) xy/(x-y)
(E) xq/(q-x)
Rationale: Pick some smart numbers for x and q.
Say x=1 hour and q=2 hours (notice that q must be greater than x, since the time for machine A to do the job, which is q hours, must be more than the time for machines A and B working together to do the same job, which is x hours).
In this case, the time needed for machine B to do the job must also be 2 hours: 1/2+1/2=1.
Now, plug x=1 and q=2 in the options to see which one yields 2. Only option E fits.
Answer: E.
Answer: (E) xq/(q-x)
Question: 2 men and 3 boys can do a piece of work in 10 days while 3 men and 2 boys can do the same work in 8 days.In how many days can 2 men and 1 boy do the work?
(A) 29/2
(B) 21/2
(C) 27/2
(D) 23/2
(E) 25/2
Rationale: Let 1 man’s 1 day’s work = x and 1 boy’s 1 day’s work = y.
Then, 2x+3y = 1/10 and 3x+2y = 1/8
Solving,we get: x = 7/200 and y = 1/100
(2 men + 1 boy)’s 1 day’s work = (2 x 7/200 + 1 x 1/100 ) = 16/200 = 2/25
So, 2 men and 1 boy together can finish the work in 25/2 days
Answer is E.
Answer: (E) 25/2