mathewhe/aqua_rat huggingface dataset:
Question: A can contains a mixture of liquids A and B is the ratio 7:5. When 9 litres of mixture are drawn off and the can is filled with B, the ratio of A and B becomes 7:9. How many liter W of liquid A was contained by the can initially?
(A) 10
(B) 20
(C) 21
(D) 25
(E) 27
Rationale: As A:B::7:5 ---> only option C is a multiple of 7 and hence it is a good place to start. Also A:B::7:5 means that , A = (712)*Total and B = (5/12)*Total
If A = 21 , B = 15 ---> remove 9 litres ---> you remove (7/12)*9 of A ---> A remaining = 21-(7/12)*9 = 63/4
Similarly, for B, you remove (5/12)*9 ---> B remaining = 15 - (5/12)*9 = 45/4 and then add 9 more litres of B ---> 9+45/4 = 81/4
Thus A/B (final ratio) = (45/4)/(81/4) = 7:9 , the same as the final ratio mentioned in the question.
Hence C is the correct answer.
A/B = 7/9 = (7x-(7/12)*9)/ (5x-(5/12)*9+9), where 7x and 5x are initial quantities of A and B respectively.
Thus, 7/9 = (7x-(7/12)*9)/ (5x-(5/12)*9+9) ---> giving you x=3. Thus A (original) W= 7*3 = 21.C
Answer: (C) 21
Question: If the arithmetic mean of seventy five numbers is calculated, it is 35. If each number is increased by 5, then mean of new number is?
(A) 22
(B) 40
(C) 28
(D) 21
(E) 27
Rationale: A.M. of 75 numbers = 35
Sum of 75 numbers = 75 * 35 = 2625
Total increase = 75 * 5 = 375
Increased sum = 2625 + 375 = 3000
Increased average = 3000/75
= 40.
Answer: B
Answer: (B) 40
Question: The simple interest on a sum of money will be Rs.600 after 10 years. If the principal is trebled after 5 years what will be the total interest at the end of the tenth year?
(A) 1203
(B) 2778
(C) 1200
(D) 2702
(E) 2871
Rationale: P --- 10 ---- 600
P --- 5 ----- 300
3P --- 5 ----- 900
------
=> 1200
Answer:C
Answer: (C) 1200
Question: A train travels from Albany to Syracuse, a distance of 120 miles, at the average rate of 50 miles per hour. The train then travels back to Albany from Syracuse. The total travelling time of the train is 5 hours and 30 minutes. What was the average rate of speed of the train on the return trip to Albany?
(A) 31
(B) 38.7
(C) 35
(D) 36
(E) 39
Rationale: 50*T =120 THEREFORE T = 120/50 =2.4
ON RETURN SPEED * ( 5.5 -2.4) =120 THEREFORE T = 120/3.1 =38.70
B
Answer: (B) 38.7
Question: There are 10 books on a shelf: 7 English books, 3 Spanish books and 2 Portuguese books. What is the probability of choosing 2 books in different languages?
(A) 31/90
(B) 3/10
(C) 1/3
(D) 41/45
(E) 28/90
Rationale: Probability = Favourable outcome / Total Outcome = 1- (Unfavourable outcome / Total Outcome)
Favourable Outcomes
Case-1: One book is English (out of 7 English books) and one book is Spanish (out of 3 Spanish books) i.e. 7C1*3C1
Case-2: One book is Spanish (out of 3 Spanish books) and one book is Portuguese (out of 2 Portuguese books) i.e. 3C1*2C1
Case-3: One book is English (out of 7 English books) and one book is Portuguese (out of 2 Portuguese books) i.e. 7C1*2C1
Total favourable Outcomes = 7C1*3C1+3C1*2C1+7C1*2C1 =21+6+14 = 41
Total Possible Outcomes = 10C2 = 45
i.e. Probability = 41/45
D
Answer: (D) 41/45
Question: If w, x, y, and z are four different prime numbers, which of the following is the smallest possible value of w + x + y + z?
(A) 15
(B) 17
(C) 19
(D) 21
(E) 23
Rationale: The sum of the four small smallest primes numbers is 2+3+5+7=17.
The answer is B.
Answer: (B) 17
Question: The remainder when 1!+2!+3!...+50! divided by 3! will be
(A) 21
(B) 3
(C) 77
(D) 927
(E) 19
Rationale: The remainder when the terms greater than 3! are divided by 3! becomes 0 so we need to consider the terms upto 2!.
So remainder will be whatever is obtained by dividing 1!+2! with 3!.
So remainder is obtained by dividing (1+2)= 3 with 3! ( 9)
So remainder is 3.
Answer:B
Answer: (B) 3
Question: A retailer buys 140 pens at the market price of 36 pens from a wholesaler, if he sells these pens giving a discount of 1%, what is the profit % ?
(A) 105
(B) 155
(C) 125
(D) 185
(E) 285
Rationale: let the market price of each pen be $1
then, Cost Price of 140 pens = $ 36 Selling Price of 140 pens =99% of $140=$ 138.60
profit %=((102.60*100)/36) %=285%
Answer E
Answer: (E) 285
Question: Two circular signs are to be painted. If the radius of the larger sign is four times that of the smaller sign, how many times more paint is needed to paint the larger sign? (We can assume that a given amount of paint covers the same area on both signs.)
(A) 4
(B) 8
(C) 12
(D) 16
(E) 20
Rationale: Let R be the radius of the smaller sign.
The area A of the smaller sign is A = piR^2.
The area of the larger sign is pi(4R)^2=16piR^2=16A.
Since the area is 16 times larger, we need 16 times more paint for the larger sign.
The answer is D.
Answer: (D) 16
Question: A scuba diver descends at a rate of 30 feet per minute. a diver dive from a ship to search for a lost ship at the depth of 2400feet below the sea level..how long will he take to reach the ship?
(A) 70 minutes
(B) 72 minutes
(C) 80 minutes
(D) 76 minutes
(E) 77 minutes
Rationale: Time taken to reach = 2400/30= 80 minutes
ANSWER:C
Answer: (C) 80 minutes
Question: Richard has to paint a mural with seven horizontal stripes. He only has enough paint for four red stripes, four blue stripes, four white stripes. If his patron wants at most two different colors in the mural, how many different ways can he paint the wall?
(A) 210
(B) 350
(C) 700
(D) 2,520
(E) 5,040
Rationale: Number of ways to choose 2 colors among 3 - 3c2
Number of ways that the chosen colors can be painted for 7 horizontal stripes - 2 (either (4,3) or (3,4))
Now the order,
the number of ways in which a particular color among the 2 chosen colors can be painted for 4 stripes is - 7c4
[Note: We don't need to calculate the ways for the remaining 3 stripes as they are obvious and already counted under this]
Total number of combinations - 3c2 * 2* 7c4 = 210
A
Answer: (A) 210
Question: A shopkeeper bought 600 oranges and 400 bananas. He found 15% of oranges and 4% of bananas were rotten. Find the percentage of fruits in good condition?
(A) 92.5%
(B) 89.4%
(C) 85.2%
(D) 96.8%
(E) 78.9%
Rationale: Total number of fruits shopkeeper bought = 600 + 400 = 1000
Number of rotten oranges = 15% of 600
= 15/100 × 600
= 9000/100
= 90
Number of rotten bananas = 4% of 400
= 16
Therefore, total number of rotten fruits = 90 + 16= 106
Therefore Number of fruits in good condition = 1000 - 106 = 894
Therefore Percentage of fruits in good condition = (894/1000 × 100)%
= (89400/1000)%
= 89.4%
Answer:B
Answer: (B) 89.4%
Question: Cathy and Cara begin running at the same time and they start at the same place on a straight path. Cathy runs at 10 miles per hour, and Cara runs at 5 miles per hour. After 12 minutes, Cathy stops to stretch. If it takes Cathy 24 minutes to stretch and Cara continues to run during this time, how many minutes will it take Cathy to catch up to Cara?
(A) 10
(B) 12
(C) 14
(D) 16
(E) 18
Rationale: In 12 minutes, Cathy runs 2 miles.
In 36 minutes, Cara runs 3 miles.
Cathy can catch Cara at a rate of 5 miles per hour.
Since Cara is ahead by 1 mile, it will take Cathy 1 / 5 hours = 12 minutes to catch Cara.
The answer is B.
Answer: (B) 12
Question: Everyone shakes hands with everyone else in a room. Total number of handshakes is 91. Number of persons=?
(A) 14
(B) 12
(C) 11
(D) 15
(E) 16
Rationale: In a room of n people, the number of possible handshakes is C(n,2) or n(n-1)/2
So n(n-1)/2 = 91 OR n(n-1)=182 OR n=14
Answer is (A)
Answer: (A) 14
Question: Rahul went to a shop and bought things worth Rs. 25, 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?
(A) 19.7
(B) 19.9
(C) 21
(D) 21.7
(E) 23
Rationale: Total cost of the items he purchased = Rs.25
Given that out of this Rs.25, 30 Paise is given as tax
=> Total tax incurred = 30 Paise = Rs.30/100
Let the cost of the tax free items = x
Given that tax rate = 6%
∴ (25−30/100−x)6/100 = 30/100
⇒ 6(25 −0.3 −x) = 30
⇒ (25 − 0.3 − x) = 5
⇒ x = 25 − 0.3 − 5 = 19.7
A)
Answer: (A) 19.7
Question: At a game of billiards, A can give B 15 points in 60 and A can give C to 20 points in 60. How many points can B give C in a game of 90?
(A) 22
(B) 98
(C) 10
(D) 77
(E) 28
Rationale: Explanation:
A : B = 60 : 45.
A : C = 60 : 40.
\inline \fn_jvn {\color{Black}\therefore \frac{B}{C}=\left ( \frac{B}{A} \times \frac{A}{C}\right )=\left ( \frac{45}{60}\times \frac{60}{40} \right )=\frac{45}{40}=\frac{90}{80}=90:80}
B can give C 10 points in a game of 90.
Answer: C) 10 points
Answer: (C) 10
Question: 50 men took a dip in a water tank 40 m long and 20 m broad on a religious day. If the average displacement of water by a man is 4 , then the rise in the water level in the tank will be:
(A) 22
(B) 25
(C) 32
(D) 99
(E) 88
Rationale: Explanation:
Total volume of water displaced =(4 x 50) = 200
Rise in water level = =0.25m = 25cm
Answer: B) 25 cm
Answer: (B) 25
Question: Ram and Shyam together can do a piece of work in 30 days. Ram having worked for 16 days, Shyam finishes the remaining work alone in 44 days. In how many days shall Shyam finish the whole work alone?
(A) 30 days
(B) 40 days
(C) 60 days
(D) 70 days
(E) 80 days
Rationale: Let us assume the total work to be done is 120 units.
According to the question,
Ram and Shyam finish the work in 30 days which implies 4 units of work is done by them in a single day, i.e.,
R + S = 4. ------ (1)
Also, Ram works for 16 days and the remaining work is finished by Shyam in 44 days, i.e.,
16R + 44S = 120 ------ (2)
Equating the equations (1) and (2), S = 2 units and R = 2 units.
Shyam alone finishes 2 units of work in one day.
Therefore, the number of days taken by Shyam alone to finish the whole work = 120/2 = 60 days.
ANSWER:C
Answer: (C) 60 days
Question: A fires 5 shots to B's 3 but A kills only once in 3 shots while B kills once in 2 shots. When B has missed 27 times, A has killed :
(A) 30 birds
(B) 60 birds
(C) 72 birds
(D) 90 birds
(E) 84 birds
Rationale: Explanation:
Let the no of shots be x. Then,
Shots fired by A = 5/8x
Shots fired by B = 3/8x
Killing shots by A = 1/3 of 5/8x= 5/24x
shots missed by B =1/2 of 3/8x =3/16x
therefore, 3/16x=27=> x=144
Birds killed by A = 5/24x=(5/24)x144=30
ANSWER IS A
Answer: (A) 30 birds
Question: find the number, difference between number and its 3/5 is 50.
(A) 120
(B) 123
(C) 124
(D) 125
(E) 359
Rationale: Explanation:
Let the number = x,
Then, x-(3/5)x = 50,
=> (2/5)x = 50 => 2x = 50*5,
=> x = 125
Option D
Answer: (D) 125
Question: A cycle is bought for Rs.900 and sold for Rs.1180, find the gain percent?
(A) 11
(B) 31
(C) 99
(D) 77
(E) 18
Rationale: 900 ---- 280
100 ---- ? => 31%
Answer: B
Answer: (B) 31
Question: A can do a work in 60days and B in 12 days.Then A and B together do the work in,how many days?
(A) 5 days
(B) 4 days
(C) 10 days
(D) 2 days
(E) 6 days
Rationale: Explanation:
A's 1day's work = 1/60
B's 1day's work = 1/12
They work together = 1/60 + 1/12 = 10 days
Answer: Option C
Answer: (C) 10 days
Question: An engineer designed a ball so that when it was dropped, it rose with each bounce exactly one-half as high as it had fallen. The engineer dropped the ball from a 20-meter platform and caught it after it had traveled 52.5 meters. How many times did the ball bounce?
(A) 5
(B) 6
(C) 7
(D) 3
(E) 2
Rationale: Going down = 20 m
Going Up = 10 --> Total = 30
Going down = 10 --> Total = 40
Going Up = 5 --> Total = 45
Going down = 5 --> Total = 50
Going up = 2.5 --> Total = 52.5 (Caught)
No of bouncing = 3
Answer : D
Answer: (D) 3
Question: The volume of a cube is 1000 cc. Find its surface.
(A) 900
(B) 700
(C) 600
(D) 500
(E) 800
Rationale: a3 = 1000 => a = 106a2 = 6 * 10 * 10 = 600Answer: C
Answer: (C) 600
Question: At Company K, 15 percent of the employees are secretaries and 60 percent are salespeople. If there are 35 other employees of Company K, how many employees does Company K have?
(A)  140
(B)  180
(C)  190
(D)  200
(E)  400
Rationale: Let the total number of employees in the company be x
% of secretaries = 15%
% of salespeople = 60%
% of of employees other than secretaries and salespeople = 100 - 75 = 25%
But this number is given as 35
so 25% of x = 35
x = 140
Therefore there a total of 140 employees in the company K
Correct answer - A
Answer: (A)  140
Question: The average of 1st 3 of 4 numbers is 16 and of the last 3 are 15. If the sum of the first and the last number is 13. What is the last numbers?
(A) 5
(B) 7
(C) 8
(D) 9
(E) 12
Rationale: Explanation:
A + B + C = 48
B + C + D = 45
A + D = 13
A – D = 3
A + D = 13
2D = 10
D = 5
A)
Answer: (A) 5
Question: If a, b, and c are integers and a*b^2/c is a positive even integer, which of the following must be true?
I. c is even
II. ab > 0
III.ab is even
(A) III only
(B) II only
(C) I and II
(D) I and III
(E) I, II, and III
Rationale: Two ways this can happen: 1- Even/ Even= Even or 2- Even/Odd= Even
So Ab MUST be even, with either A or B being even, Ab does not have to be positive, as B could be negative and once it is raised to 2 it becomes positive again, and of course, C could be Odd or Even as described above.
III only.letter A
Answer: (A) III only
Question: The area of a parallelogram is 72 sq m and its altitude is twice the corresponding base. Then the length of the base is?
(A) 6
(B) 16
(C) 8
(D) 36
(E) none
Rationale: 2x * x = 72 => x
= 6
Answer:A
Answer: (A) 6
Question: A person spends 1/3rd of the money with him on clothes, 1/5th of the remaining on food and 1/4th of the remaining on travel. Now, he is left with Rs 400. How much did he have with him in the beginning?
(A) s 200
(B) s 1000
(C) s 300
(D) s 450
(E) s 550
Rationale: Suppose the amount in the beginning was Rs ’x’
Money spent on clothes = Rs 1x/3 Balance = Rs 2x/3
Money spent on food = 1/5 of 2x/3 = Rs 2x/15
Balance = 2x/3 - 2x/15 = Rs 8x/15
Money spent on travel = 1/4 of 8x/15 = Rs 2x/15 = 8x/15 - 2x/15 = 6x/15 = Rs2x/5
Therefore 2x/5 = 400 = 1000
ANSWER:B
Answer: (B) s 1000
Question: If p is the product of the integers from 1 to 34, inclusive, what is the greatest integer k for which 3^k is a factor of p?
(A) 11
(B) 13
(C) 15
(D) 17
(E) 19
Rationale: 34! has 3, 6, 9,....30, 33 as factors, which are 11 multiples of 3.
We need to add 4 more to these 11 because of 9, 18, and 27.
The greatest integer of k is 15.
The answer is C.
Answer: (C) 15
Question: In Mr. Mehta's family, there are one grandfather, two fathers, two mothers, one father-in-law, one mother-in-law, one brother, two sisters, two sons, two daughters, etc. You have to give the minimal number of members
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
Rationale: one grandfather and his wife.
grandfather's first son and his wife.
grandfather's second son alone.
2 daughters from first son.
total minimal no =7.
ANSWER:D
Answer: (D) 7
Question: If P(A) = 5/7 and P (B) = 2/5, find P (A n B) if A and B are independent events.
(A) 7/25
(B) 3/25
(C) 8/25
(D) 2/7
(E) 3/17
Rationale: P (A n B) = P(A) . P(B)
P (A n B) = 5/7 . 2/5
P (A n B) = 2/7.
D
Answer: (D) 2/7
Question: A is three times as fast as B. If B alone can do a piece of work in 12 days, in what time can A and B together complete the work?
(A) 5
(B) 8
(C) 3
(D) 2
(E) 12
Rationale: A can do the work in 12/3 i.e., 4 days.
A and B's one day's work = 1/4 + 1/12 = (3+ 1)/12 = 1/3
So A and B together can do the work in 3 days.
Answer:C
Answer: (C) 3
Question: . A car covers a distance of 495 km in 5 hours. Find its speed?
(A) 99
(B) 100
(C) 102
(D) 288
(E) 2761
Rationale: 495/5 = 99 kmph
Answer: A
Answer: (A) 99
Question: (753 x 753 + 247 x 247 - 753 x 247)/(753 x 753 x 753 + 247 x 247 x 247)=?
(A) 1 / 1000
(B) 1 / 506
(C) 253 / 500
(D) 253 / 1000
(E) None of these
Rationale: Given Exp. =(a^2 + b^2 - ab)/(a^3 + b^3)	= 1/(a + b) = 1/(753 + 247) =1/1000
Answer:A
Answer: (A) 1 / 1000
Question: 1/2 is what percent of 1/3
(A) 150%
(B) 200%
(C) 250%
(D) 300%
(E) 400%
Rationale: Explanation:
1/2/1/3 * 100 = 1/2 * 3/1 * 100 = 150 %
Answer: Option A
Answer: (A) 150%
Question: 4 friends want to buy a company from the $150 000 cost. However, they have only $20 000 to be put in the company. How much partner will they have to fetch in more and which will be the equal value for every partner (The value should not contain of decimals) ?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: 4 friends * $ 20 000 = $ 100 000 total
$150 000 - $ 100 000 = $ 50 000 / $ 20 000 = 2.5 partners (impossible and not equal)
1+5+0+0+0+0 = 6 (even) so the answer have to be even (2 partners, 4 partners, 6 partners)
$150 000/ (4 actuals partners + 2 new partners) = $25 000 but they can only afford $ 20 000. The option is reject
$150 000/ (4 actuals partners + 4 new partners) = $ 18 750
We don't need to go further because $18 750 is the close number to $20 000. Answer is C, 4 more partners
Correct option: C) 4 partners
Answer: (C) 4
Question: A man took a loan from a bank at the rate of 13% p.a. simple interest.After 3 years he had to pay Rs. 5400 interest only for the period.The principal amount borrowed by him was :
(A) Rs. 12,000.15
(B) Rs. 13846.15
(C) Rs. 15,000.15
(D) Rs. 20,000.15
(E) None
Rationale: Solution
Principal = Rs.(100x5400/13x3)= Rs. 13846.15.
Answer B
Answer: (B) Rs. 13846.15
Question: A peacock of flying speed 5 km/h is sitiing on a top of a wooden pole of height 10m. There is a hole in the pole downwards and a snake is approaching that hole which is 21m away from the snake.How much time it will take for the peacock to catch the snake before it enters the hole.
(A) 14.73 seconds
(B) 16.73 seconds
(C) 15.73 seconds
(D) 17.73 seconds
(E) 18.73 seconds
Rationale: Speed of the peacock = 5 km/h(given)
Distance of the pole = 10m(given)
Distance between the pole hole and snake = 21m(given)
Therefore, we have to first find the distance between the peacock and the snake.
This can be done by using Pythagora's Theorem,
Therefore, 21^2 + 10^2 = 23.26 metre(approx)
Speed of the peacock = 5 km/h or 1.39 metre/sec(approx)
Now, we know can find the time for peacock to catch the snake by,
Time = Distance/Speed
= 23.26/1.39
= 16.73 seconds(approx)
Therefore, the required time for peacock to catch the snake before it enters the hole of the pole is 16.73 seconds.
ANSWER:B
Answer: (B) 16.73 seconds
Question: Machine Y takes 2 more hours than machine B to make 20 widgets. If working together, the machines can make 25 widgets in 3 hours, how long will it take machine Y to make 40 widgets?
(A)  5
(B)  6
(C)  8
(D)  10
(E)  12
Rationale: i approached this one by plugging in numbers...started with C.
if 40 are made in 8 hours, then 20 are made in 4 hours. so time of Y is 4, and time of B is 2.
rate together: 20/4 + 20/2 = 5+10 = 15. so in 1 hour, together make 15 widgets. in 3 hours = 45. way too much. we can eliminate right away C, B, and A - because B and Y reduces the time - the total # of widgets made will be even higher.
now between D and E -> try only one ..if it doesn't work, then the other one is the answer.
i picked E:
12h to make 40 widgets, and 6 hours to make 20. this is the time of Y. time of B=4 hours.
20/6 + 20/4 = 10/3 + 20/4
find LCM of 3 and 4 = 12. multiply first by 4, and second by 3:
40+60/12 = 100/12
divide by 4:
25/3
so this is the rate given.
E is the correct answer
Answer: (E)  12
Question: One-quarter of one-seventh of a land is sold for Rs. 30,000. What is the value of an eight thirty-fifth of load?
(A) Rs. 1,92,2300.
(B) Rs. 1,92,2450.
(C) Rs. 1,92,2400.
(D) Rs. 1,92,2000.
(E) none of these
Rationale: One-quarter of one-seventh = 1/4 x 1/7
= 1/28
Now, 1/28 of a land costs = Rs. 30,000
Thus, 8/35 of the land will cost = 30,000 x 28 x 8/35
= Rs. 1,92,2000.
ANSWER:D
Answer: (D) Rs. 1,92,2000.
Question: A sells his goods 50% cheaper than B but 50% dearer than C. The cheapest is?
(A) 33.9
(B) 33.6
(C) 33.3
(D) 33.1
(E) 33.2
Rationale: Let B = 100
A = 50
C * (150/100) = 50
3C = 100
C = 33.3 then 'C' Cheapest
Answer: C
Answer: (C) 33.3
Question: From the below series find the remainder? 1201 × 1203 ×1205 × 1207 is divided by 6
(A) 3
(B) 4
(C) 6
(D) 7
(E) 8
Rationale: If you don't know the above rule, this problem is really calculation intensive.
But by applying the above rule, when 1201, 1201, 1203, 1204 divided by 6, leaves remainders 1, 3, 5, 1. The product of these remainders = 15.
When 15 is divided by 6, Remainder is 3
A
Answer: (A) 3
Question: An book was sold after a discount of 20% and there was a gain of 20%. If the profit made on it was $6 less than the discount offered on it, find its selling price?
(A) $66
(B) $38
(C) $77
(D) $72
(E) $63
Rationale: D
$72
Let CP = $100x
SP = $120x
MP = 120x/80 * 100 = $150x
D = $150x - $120x = $30x
D - P = 30x - 20x = $6, 10x = $6
120x = 120/10 * 6 = $72
Answer: (D) $72
Question: Two same glasses are respectively 1/4th 1/5th full of milk. They are then filled with water and the contents mixed in a tumbler. The ratio of milk and water in the tumbler is?
(A) 3:7
(B) 9:31
(C) 7:21
(D) 9:25
(E) 7:6
Rationale: 1/4 : 3/4 = (1:3)5 = 5:15
1/5 : 4/5 = (1:4)4 = 4:16 = > 9:31
ANSWER B
Answer: (B) 9:31
Question: Twelve kilograms of oranges contained 98% of water. If the next day the concentration of water decreased by 2%, what was the new weight of the oranges, in kilograms?
(A)  6
(B)  4.8
(C)  2.5
(D)  2
(E)  1
Rationale: Twelve kilograms of oranges contained 98% of water. If the next day the concentration of water decreased by 2%, what was the new weight of the oranges, in kilograms?
(A) 6
(B) 4.8
(C) 2.5
(D) 2
(E) 1
If A is the answer, then the question means that the concentration of water the newt day became 96%.
Out of 12 kilograms 98%, or 11.76 kilograms was water and 0.24 kilograms was non-water.
The next day, after some water evaporated, oranges became 96% water and 4% of non-water, so the next day 0.24 kilograms of non-water composed 4% of oranges, which means that the new weight of the oranges was x*0.04=0.24 --> x=6 kilograms.
Answer: A.
Answer: (A)  6
Question: The greatest number of four digits which is divisible by 21, 25, 40 and 75 is:
(A) 9000
(B) 8400
(C) 9600
(D) 9800
(E) 9200
Rationale: Greatest number of 4-digits is 9999.
L.C.M. of 21, 25, 40 and 75 is 4200.
On dividing 9999 by 4200, the remainder is 1599.
Required number (9999 - 1599) = 8400.
Answer: Option B
Answer: (B) 8400
Question: On a certain test, Bill scored 20 more points than John, but half as many points as Sue. If the sum of the scores of the three students was 220 points, how many points did Bill receive?
(A) 30
(B) 40
(C) 50
(D) 60
(E) 100
Rationale: consider john's points as x
so bill's points are x +20
So sue's points are 2x +40
total of all three students is 4x +60, but this total is given as 220
x = 40
so bill's points = 40 +20 = 60
correct answer option D
Answer: (D) 60
Question: In how many ways can a cricket eleven be chosen out of a batch
of 15 players.
(A) 1255
(B) 1355
(C) 1340
(D) 1365
(E) 1300
Rationale: Required number of ways
= 15C 11 = 15C (15-11)
= 15 C 4
15C4 = 15 * 14 * 13 * 12 / 4 * 3 * 2 *1
= 1365
ANSWER D
Answer: (D) 1365
Question: Joe had an average of 95 on his first 5 tests. He had an average score of 90 on his first 6 tests. What did he score on the 6th test?
(A) 95
(B) 85
(C) 65
(D) 45
(E) 30
Rationale: The sum of Joe's first 5 tests is 95 * 5 and the sum of his first 6 tests is 90*6, so he received 90*6 - 95*5 on his 6th test. You can do the arithmetic and the correct answer is C.
Answer: (C) 65
Question: Rory and Roxy, both house cats, love to hunt and chase insects. Since Rory only has three paws, Roxy is able to catch approximately 2.5 times more insects than Rory in one day.
After 3 days of hunting, Roxy was able to catch 23 insects. Assuming that both cats had an equal amount of hunting time, how many total insects can the two of them catch after 18 days of hunting?
Please round to the nearest whole number.
(A) 143
(B) 193
(C) 111
(D) 194
(E) 138
Rationale: 18 (total days) is divisible by 3 (initial data given days) 6 times,
therefore we can easily find Roxy's total for the 18 day period is 23 x 6 = 138 insects
Taking Roxy's total, we can then find Rory's total by dividing 138 by 2.5 = 55.2 insects
To find the pair's total, we add 138 + 55.2 = 193.2
This number rounded to nearest whole number is 193, answer B.
You could also divide 23 by 2.5 to get 9.2, which would be Rory's total for the first 3 days.
You could then multiply again, (23x6) + (9.2x6) = 138 + 55.2 = 193.2
Answer: (B) 193