mathewhe/aqua_rat huggingface dataset:
Question: Murali travelled from city A to city B at a speed of 40 kmph and from city B to city C at 60 kmph. What is the average speed of Murali from A to C given that the ratio of distances between A to B and B to C is 2 : 3?
(A) 17 kmph
(B) 50 kmph
(C) 11 kmph
(D) 19 kmph
(E) 16 kmph
Rationale: Let the distances between city A to B and B to C be 2x km and 3x km respectively.
Total time taken to cover from A to C
= (2x)/40 + (3x)/60 = (6x + 6x)/120
= 12x/120 = x/10 Average speed
= (2x + 3x)/(x/10)
= 50 kmph.
Answer: B
Answer: (B) 50 kmph
Question: Adidas company has four empty trucks that will head out in the morning, all four to the same destination. The clerk has four different boxes to ship to that same destination. All four boxes could go on any one of the trucks, or the boxes could be split up into any groupings and given to the trucks in any combinations (ie. two to one truck, one to another, and one to another). In how many different ways could the boxes be put on the four trucks?
(A)  16
(B)  64
(C)  256
(D)  576
(E)  4096
Rationale: MAGOOSHOFFICIAL SOLUTION:
Adidas company has four empty trucks that will head out in the morning, all four to the same destination. Where we put one box has absolutely no bearing on where we put any of the other boxes. The placement of the four boxes is completely independent of one another. For each box, we have four choices.
N = 4*4*4*4 = 16*16 = 256
Answer = (C)
Answer: (C)  256
Question: Mr. John used to purchase certain number of mangoes for $360 Since the price of mangoes is reduced by 10% he got 12 more mangoes today. Find the original price of 130 mangoes.
(A) 360
(B) 380
(C) 400
(D) 406
(E) 433
Rationale: Mr. John used to purchase certain number of mangoes for $360 Since the price of mangoes is reduced by 10% he got 12 more mangoes today. Find the original price of 120 mangoes.
Method 1:
Let price per mango = x. Let number of mangoes be n. Then, nx = 360.
Now price = 0.9x; number of mangoes = n + 12. Total amount = 0.9x*(n+12) = 360.
nx = 0.9nx + 10.8x => 0.1nx = 10.8x => n = 108 => x = 360/108 = 3.33
Original price of 130 mangoes = 130*3.33 = 433.
Answer E
Answer: (E) 433
Question: A committee of three people is to be chosen from four teacher-student pairs. What is the number of different committees that can be chosen if two people who are married to each other cannot both serve on the committee?
(A) 16
(B) 24
(C) 26
(D) 30
(E) 32
Rationale: Each pair can send only one representative to the committee. Let's see in how many ways we can choose 3 pairs (as there should be 3 members) out of 4 to send only one representatives to the committee: 4C3=4.
But each of these 3 couples can send two persons (husband or wife): 2*2*2=2^3=8.
Total # of ways: 4C3*2^3=32.
Answer: E.
Answer: (E) 32
Question: A can do a piece of work in 10 days and B can do it in 15 days and C can do it 20 days. They started the work together and A leaves after 2 days and B leaves after 4 days from the beginning. How long will work lost?
(A) 09 2/3
(B) 10 2/3
(C) 11 2/3
(D) 12 2/3
(E) 16 2/3
Rationale: B
10 2/3
2/10 + 4/15 + x/20 = 1
x = 32/3 = 10 2/3
Answer: (B) 10 2/3
Question: In a race of 1000 m, A can beat by 100 m, in a race of 800m, B can beat C by 100m. By how many meters will A beat C in a race of 600 m?
(A) 236
(B) 127.5
(C) 267
(D) 268
(E) 281
Rationale: When A runs 1000 m, B runs 900 m and when B runs 800 m, C runs 700 m.
When B runs 900 m, distance that C runs = (900 * 700)/800 = 6300/8 = 787.5 m.
In a race of 1000 m, A beats C by (1000 - 787.5) = 212.5 m to C.
In a race of 600 m, the number of meters by which A beats C = (600 * 212.5)/1000 = 127.5 m
Answer: B
Answer: (B) 127.5
Question: Joe invested a certain sum of money in a simple interest bond whose value grew to $460 at the end of 3 years and to $560 at the end of another 5 years. What was the rate of interest in which he invested his sum?
(A) 3%
(B) 4%
(C) 5%
(D) 6%
(E) 7%
Rationale: In 5 years, the value grew $100, so the simple interest was $20 per year.
In 3 years, the total interest was 3*$20 = $60
The principal is $460 - $60 = 400.
The interest rate is $20/$400 = 5%
The answer is C.
Answer: (C) 5%
Question: 3(1/2) + 5(1/5) + ? + 2(1/4) = 11(1/3)
(A) 11/60
(B) 13/60
(C) 23/60
(D) 29/60
(E) None of these
Rationale: Explanation:
3(1/2) + 5(1/5) + ? + 2(1/4) = 11(1/3)
=> ? = 11(1/3) - [3(1/2) + 5(1/5) + 2(1/4)]
= 34/3 - [7/2 + 26/5 + 9/4]
= 34/3 - 219/20 = 23/60
Answer: Option C
Answer: (C) 23/60
Question: A number x is 11 times another number y. The percentage that y is less than x is
(A) 12.5%
(B) 90.9
(C) 91.7
(D) 11%
(E) 1%
Rationale: Say y=1 and x=11.
Then y=1 is less than x=11 by (11-1)/11*100=10/11*100=90.9%.
Answer: B.
Answer: (B) 90.9
Question: Two persons A and B take a field on rent. A puts on it 21 horses for 3 months and 15 cows for 2 months; B puts 15 cows for 6months and 40 sheep for 7 1/2 months. If one day, 3 horses eat as much as 5 cows and 6 cows as much as 10 sheep, what part of the rent should A pay?
(A) 1/3
(B) 1/8
(C) 1/4
(D) 1/1
(E) 1/2
Rationale: 3h = 5c
6c = 10s
A = 21h*3 + 15c*2
= 63h + 30c
= 105c + 30c = 135c
B = 15c*6 + 40s*7 1/2
= 90c + 300s
= 90c + 180c = 270c
A:B = 135:270
27:52
A = 27/79 = 1/3
Answer: A
Answer: (A) 1/3
Question: In the coordinate plane, a circle centered on point (-3, -4) passes through point (-1, 1). What is the area of the circle?
(A) 9π
(B) 18π
(C) 29π
(D) 37π
(E) 41π
Rationale: r^2=(-3+1)^2+(-4-1)^2=4+25=29
Area of circle=πr^2=29π
Answer : C
Answer: (C) 29π
Question: The cost price of a radio is Rs.1500 and it was sold for Rs.1230, find the loss %?
(A) 18%
(B) 17%
(C) 15%
(D) 11%
(E) 12%
Rationale: 1500 ---- 270
100 ---- ? => 18%
Answer: A
Answer: (A) 18%
Question: If 6 (A's capital) = 8 (B's capital) = 10 (C's capital). Then the ratio of their capitals is?
(A) 20:15:16
(B) 20:15:15
(C) 20:15:12
(D) 20:15:14
(E) 20:15:11
Rationale: 6A = 8B = 10 C
A:B:C = 1/6:1/8:1/10
= 20:15:12
Answer: C
Answer: (C) 20:15:12
Question: Murali travelled from city A to city B at a speed of 40 kmph and from city B to city C at 60 kmph. What is the average speed of Murali from A to C given that the ratio of distances between A to B and B to C is 2 : 3?
(A) 50 kmph
(B) 60 kmph
(C) 40 kmph
(D) 70 kmph
(E) 80 kmph
Rationale: A
Let the distances between city A to B and B to C be 2x km and 3x km respectively.
Total time taken to cover from A to C
= (2x)/40 + (3x)/60 = (6x + 6x)/120 = 12x/120 = x/10 Average speed = (2x + 3x)/(x/10) = 50 kmph.
Answer: (A) 50 kmph
Question: There is a circle of radius 2. What is the perimeter of the biggest rectangle that can be cut out of this circle?
(A) 4âˆš8
(B) 4âˆš5
(C) 2âˆš6
(D) 16
(E) 5
Rationale: The largest rectangle to be cut out of a circle would be a square, with a diagonal of 4 (Radius*2 2*2=4)
Using the Pythagorean theorem a^2+b^2=c^2; in a square this is 2a^2 because this is a right triangle/half of a square, so 2a^2=4^2
2a^2=16
a^2=8
a=âˆš8
Area of a square = side * 4 so perimeter= 4âˆš8
Answer is A
Answer: (A) 4âˆš8
Question: Yearly subscription to professional magazines cost a company $940.00. To Make a 20% cut in the magazine budget, how much less must be spent?
(A) 654
(B) 752
(C) 656
(D) 657
(E) 658
Rationale: total cost 940
940*20/100=188
so the cut in amount is 188
the less amount to be spend is 940-188=752
ANSWER:B
Answer: (B) 752
Question: 24 * 22 = ? / 8
(A) 4224
(B) 2224
(C) 5374
(D) 2434
(E) 4254
Rationale: A
4224
?/8 = 24*22
? = 24 * 22 * 8
? = 4224
Answer: (A) 4224
Question: The speed of a boat in still water in 30 km/hr and the rate of current is 7 km/hr. The distance travelled downstream in 36 minutes is:
(A) 18.4 km
(B) 20.6 km
(C) 21.4 km
(D) 1111 km
(E) 22.2 km
Rationale: Explanation:
Speed downstream = (30 + 7) = 37 kmph
Time = 36 minutes = 36/60 hour = 3/5 hour
Distance travelled = Time × speed = (3/5)×37 = 22.2 km
Answer: Option E
Answer: (E) 22.2 km
Question: The speed of a train is 90 kmph. What is the distance covered by it in 15 minutes?
(A) 15
(B) 66
(C) 22.5
(D) 52
(E) 42
Rationale: 90 * 15/60 = 22.5 kmph
Answer:C
Answer: (C) 22.5
Question: A certain library assesses fines for overdue books as follows. On the first day that a book is overdue, the total fine is $0.08. For each additional day that the book is overdue, the total fine is either increased by $0.30 or doubled, whichever results in the lesser amount. What is the total for a book on the fourth day it is overdue?
(A) $0.62
(B) $0.70
(C) $0.80
(D) $0.90
(E) $1.00
Rationale: 1st day fine - 0.08
2nd day fine - 0.08*2 = 0.16 (as doubling gives lower value)
3rd day fine - 0.16*2 = 0.32 (as doubling gives lower value)
4th day fine - 0.32 + 0.3 = 0.62 (as doubling gives higher value we add 0.3 this time)
Answer: A.
Answer: (A) $0.62
Question: A sock drawer contains 4 socks, each one a different solid color. The colors of the socks are green, blue, indigo, and violet. If a person reaches into the drawer and pulls out two socks, how many different color combinations are possible in the selected pair of socks?
(A) 12
(B) 15
(C) 6
(D) 36
(E) 42
Rationale: Since the order in which we select the socks does not matter we can use combinations.
We can select 2 socks from 4 socks in 4C2 ways.
4C2 = 6
Answer : C
Answer: (C) 6
Question: The marks obtained by Polly and Sandy are in the ratio 5:6 and those obtained by Sandy and Willy are in the ratio of 9:7. The marks obtained by Polly and Willy are in the ratio of...?
(A) 9:8
(B) 11:10
(C) 13:12
(D) 15:14
(E) 17:16
Rationale: Polly : Sandy = 5:6 = 15:18
Sandy : Willy = 9:7 = 18:14
Polly : Sandy : Willy = 15:18:14
Polly : Willy = 15:14
The answer is D.
Answer: (D) 15:14
Question: If a man lost 4% by selling oranges at the rate of 12 a rupee at how many a rupee must he sell them to gain 44%?
(A) 5
(B) 8
(C) 9
(D) 5
(E) 1
Rationale: 96% ---- 12
144% ---- ?
96/144 * 12 = 8
Answer: B
Answer: (B) 8
Question: During the first week of performances of a certain play, 5,400 tickets were sold, all at reduced price. During the remaining weeks of performances, 5 times as many tickets were sold at full price as were sold at reduced price. If the total number of tickets sold W was 25,200, how many of them were sold at full price?
(A) 21,000
(B) 19,800
(C) 16,500
(D) 15,800
(E) 8,700
Rationale: Given:
The question tells us about the number of tickets sold in the first week at reduced price = 5,400. It also tells us that during the remaining weeks, the number of tickets sold at full price was 5 times the no. of tickets sold at reduced price. The total tickets sold was 25,200, and we are asked to find the number of tickets that where sold at full price.
Approach:
The question asks us to find the number of ticket sold at full price. We know that the number of tickets sold at full price was 5 times the no. of tickets sold at reduced price in remaining weeks. Hence, assuming tickets sold at reduced price in remaining weeks to be x would give us the no. of tickets sold at full price to be 5x.
Tickets sold in first week + Tickets sold in remaining weeks = Total no. of tickets soldi.e.
Tickets sold in first week + Tickets sold at full price in remaining weeks + Tickets sold at reduced price in remaining weeks = Total no. of tickets sold
We know the no. of tickets sold during first week and the total no. of tickets sold. We will use this relation to get to our answer.
Working Out:
Tickets sold in first week + Tickets sold at full price in remaining weeks + Tickets sold at reduced price in remaining weeks = Total no. of tickets sold
Substituting values in the equation, we get
5,400 + 5x + x = 25,200
x= 3,300
Tickets sold at full price = 5x = 16,500
Answer: Option C
Answer: (C) 16,500
Question: In how many ways can 3 postcards can be posted in 5 postcards?
(A) 50
(B) 120
(C) 125
(D) 130
(E) 100
Rationale: First card can go into any of the five boxes, Second can go into any of the five boxes.
Third card also can go into any of the five boxes
Number of ways=5*5*5=125 ways
Answer:C
Answer: (C) 125
Question: If a/b = 1/7, b/c = 3, c/d = 2/3, d/e = 2 and e/f = 1/2, then what is the value of abc/def ?
(A)  72/21
(B)  27/85
(C)  34/47
(D)  13/81
(E)  16/21
Rationale: Say a = 1. Then:
a/b = 1/7 --> b = 7;
b/c = 3 --> c = 7/3;
c/d = 2/3 --> d = 7/2;
d/e = 2 --> e = 7/4;
e/f = 1/2 --> f = 7/2.
abc/def = (1*7*7/3)/(7/2*7/4*7/2) = 16/21.
Answer: E.
Answer: (E)  16/21
Question: Six computers, each working at the same constant rate, together can process a certain amount of data in 12 days. How many additional computers, each working at the same constant rate, will be needed to process the same amount of data in 4 days?
(A) 3
(B) 5
(C) 6
(D) 9
(E) 12
Rationale: Explanation: If six computers require 12 days to process the data, thats
a total of 72 computer-days the product of 6 and 12. If you change the number
of computers or the number of days, 90 will have to remain the product, whether
that means 72 days of one computer or one day with 72 computers.
In 4 days, the number of computers is:
4c = 72
c = 18
18 computers is 12 more than the 6 that it took to do the job in 12 days, so
the correct choice is (E).
Answer: (E) 12
Question: Find a sum for 1st 5 prime no.'s?
(A) 23
(B) 28
(C) 30
(D) 32
(E) 34
Rationale: Required sum = (2 + 3 + 5 + 7 + 11) = 28
Note: 1 is not a prime number
Option B
Answer: (B) 28
Question: What will be the cost of building a fence around a square plot with area equal to 289 sq ft, if the price per foot of building the fence is Rs. 58?
(A) 3944
(B) 2882
(C) 2999
(D) 2667
(E) 2121
Rationale: Let the side of the square plot be a ft.
a2 = 289 => a = 17
Length of the fence = Perimeter of the plot = 4a = 68 ft.
Cost of building the fence = 68 * 58 = Rs. 3944.
Answer: A
Answer: (A) 3944
Question: If 9975 kg of wheat is packed in 95 bags, how much wheat will each bag contain?
(A) 105
(B) 109
(C) 119
(D) 218
(E) 288
Rationale: Solution:
Since 95 bags contain wheat 9975 kg
Therefore, 1 bag contains wheat (9975 ÷ 95) kg
= 105 kg
ANSWER IS A
Answer: (A) 105
Question: An assembly line produces 30 cogs per hour until an initial order of 60 cogs is completed. The speed of the assembly line is then immediately increased so that it can produce 60 cogs per hour until another 60 cogs are produced. What is the overall average output, in cogs per hour, for the assembly line during this whole time?
(A) 40
(B) 44
(C) 48
(D) 52
(E) 56
Rationale: The time to produce the first 60 cogs is 60/30 = 2 hours.
The time to produce the next 60 cogs is 60/60 = 1 hour.
The average output is 120 cogs / 3 hours = 40 cogs per hour.
The answer is A.
Answer: (A) 40
Question: The average age of a group of 10 persons was decreased by 3 years when one person, whose age was 44 years, was replaced by a new person. Find the age of the new person?
(A) 18
(B) 56
(C) 12
(D) 17
(E) 14
Rationale: Initial average age of the 10 persons be P.
Age of the new person Q.
Sum of the ages of the initial 10 persons = 10P
New average
= (P-3) 10(P-3)
= 10P - 44 + Q
=> Q = 14
Answer:E
Answer: (E) 14
Question: x is a set containing 8 different positive odd numbers. y is a set containing 7 different numbers, all of which are members of S. Which of the following statements CANNOT be true?
(A) The range of y is even.
(B) The mean of x is even.
(C) The mean of y is even.
(D) The range of x is equal to the range of y.
(E) The median of y is equal to the mean of y.
Rationale: Given: x is a set containing 8 different positive odd numbers
Easily inferred: y is a set containing 7 differentoddnumbers
(A) The range of y is even. - Always even, since it is a difference of two odd numbers
(B) The mean of x is even. - can be. suppose 8 numbers consist of 4 pairs of (16n-1,16n+1) for different values of n. Adding these will give a multiple of 16, which when divided by 8 (to arrive at mean), will give an even number
(C) The mean of y is even. - Cannot be. Mean = (sum of 7 odd numbers)/7 = Odd number/odd number thus cannot be even.
(D) The range of x is equal to the range of y.
(E) The median of y is equal to the mean of y
Option C
Answer: (C) The mean of y is even.
Question: The H.C.F and L.C.M of two numbers are 84 and 21 respectively. If the ratio of the two numbers is 1 : 4 , then the larger of the two numbers is
(A) 32
(B) 37
(C) 84
(D) 29
(E) 21
Rationale: Explanation:
Let the numbers be x and 4x. Then, \inline \fn_jvn x\times 4x =84\times 21\: \: \Leftrightarrow \: \: x^{2}=\frac{84\times 21}{4} \: \: \Leftrightarrow \: \: x=21
Hence Larger Number = 4x = 84
Answer: C) 84
Answer: (C) 84
Question: A horse is tethered to one corner of a rectangular grassy field 36 m by 20 m with a rope 18 m long. Over how much area of the field can it graze?
(A) 154 cm2
(B) 308 m2
(C) 254 m2
(D) 260 m2
(E) None of these
Rationale: Area of the shaded portion
= 1⁄4 × π × (18)2 = 254 m2
Answer C
Answer: (C) 254 m2
Question: Jo's collection contains US, Indian and British stamps. If the ratio of US to Indian stamps is 5 to 2 and the ratio of Indian to British stamps is 5 to 1, what is the ratio of US to British stamps?
(A) 10 : 5
(B) 15 : 2
(C) 20 : 2
(D) 25 : 2
(E) None of these
Rationale: Explanation:
Indian stamps are common to both ratios. Multiply both ratios by factors such that the Indian stamps are represented by the same number.
US : Indian = 5 : 2, and Indian : British = 5 : 1. Multiply the first by 5, and the second by 2.
Hence the two ratios can be combined and US : British = 25 : 2
Now US : Indian = 25 : 10, and Indian : British = 10 : 2 Answer: D
Answer: (D) 25 : 2
Question: The average weight of A, B and C is 43 kg. If the average weight of A and B be 48 kg and that of B and C be 42 kg, then the weight of B is:
(A) 55 kg
(B) 53 kg
(C) 49 kg
(D) 52 kg
(E) 51 kg
Rationale: EXPLANATION
Let A, B, C represent their respective weights. Then, we have:
A + B + C = (43 x 3) = 129 â€¦. (i)
A + B = (48 x 2) = 96 â€¦. (ii)
B + C = (42 x 2) = 84 â€¦.(iii)
Adding (ii) and (iii), we get: A + 2B + C = 180 â€¦. (iv)
Subtracting (i) from (iv), we get : B = 51.
Bâ€™s weight = 51 kg.
Answer E
Answer: (E) 51 kg
Question: The average of six numbers is 3.95. The average of two of them is 3.3, while the average of the other two is 3.85. What is the average of the remaining two numbers?
(A) 4.5
(B) 4.6
(C) 4.7
(D) 4.8
(E) 4.9
Rationale: Sum of the remaining two numbers
= (3.95 × 6) – [(3.3 × 2) + (3.85 × 2)]
= 23.70 – (6.6 + 7.7)
= 23.70 – 14.3 = 9.40
∴ Required average = (9.4⁄2) = 4.7
Answer C
Answer: (C) 4.7
Question: For the positive numbers, n+3, n + 4, n + 6, n + 8, and n + 9, the mean is how much greater than the median?
(A) 0
(B) 1
(C) n+l
(D) n+2
(E) n+3
Rationale: Let’s first calculate the mean (arithmetic average).
mean = sum/quantity
mean = (n + 3+n + 4 + n + 6 + n + 8 + n + 9)/5
mean = (5n + 30)/5
mean = n + 6
Next, we determine the median. The median is the middle value when the terms are ordered from least to greatest. The terms ordered from least to greatest are as follows:
n+3, n + 4, n + 6, n +8, n + 9
The median is n + 6
Finally we are asked how much greater the mean is than the median. To determine the difference we can subtract the smaller value (the median) from the larger value (the mean) and we get:
n + 6 – (n + 6) = n + 6 – n – 6 = 0
The answer is A
Answer: (A) 0
Question: The average of first six prime numbers which are odd is?
(A) 15.5
(B) 15.7
(C) 9.3
(D) 15.8
(E) 15.1
Rationale: Sum of first 6 prime no. which are odd = 56
Average = 56/6 = 9.3
Answer:C
Answer: (C) 9.3
Question: Two stations A and B are 110 km apart on a straight line. One train starts from A at 7 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet?
(A) 12
(B) 13
(C) 16
(D) 10
(E) 15
Rationale: Suppose they meet x hours after 7 a.m.
Distance covered by A in x hours = 20x km.
Distance covered by B in (x - 1) hours = 25(x - 1) km.
Therefore 20x + 25(x - 1) = 110
45x = 135
x = 3.
So, they meet at 10 a.m.
Answer: D
Answer: (D) 10
Question: A can do a piece of work in 4 days. B can do it in 5 days. With the assistance of C they completed the work in 2 days. Find in how many days can C alone do it?
(A) 23 days
(B) 18 days
(C) 20 days
(D) 22 days
(E) 28 days
Rationale: C
20 days
C = 1/2 - 1/4 - 1/5 = 1/20 => 20 days
Answer: (C) 20 days
Question: A certain fruit stand sold apples for $0.70 each and bananas for $0.60 each. If a customer purchased both apples and bananas from the stand for a total of $6.30, what total number of apples and bananas did the customer purchase?
(A) 8
(B) 9
(C) 10
(D) 11
(E) 12
Rationale: Let's start with 1 apple for $0.70.
Let's subtract $0.70 from $6.30 until we get a multiple of $0.60.
$6.30, $5.60, $4.90, $4.20 = 7*$0.60
The customer purchased 7 bananas and 3 apples.
The answer is C.
Answer: (C) 10
Question: Sagar purchased 10 kg of rice at the rate of Rs. 15 per kg and 25 kg of rice at the rate Rs. 14 per kg. He mixed the two and sold the mixture. Approximately at what rate per kg should he sell the mixture to make 40 % profit in the transaction?
(A) Rs. 20.00
(B) Rs. 19.50
(C) Rs. 15
(D) Rs. 17.5
(E) None of these
Rationale: By 40% profit on cost price,
Selling price of mixture = 140/100 * 500
= Rs. 700
Therefore, selling price per kg of mixture = 700/35 = Rs. 20
ANSWER A
Answer: (A) Rs. 20.00
Question: The cost of 3 pens and 5 pencils is Rs.200. Also the cost of one pen and one pencil is in the ratio of 5:1 respectively. What is the cost of one dozen pens?
(A) Rs.200
(B) Rs.250
(C) Rs.300
(D) Rs.150
(E) Rs. 600
Rationale: Explanation:
Let the cost of one pen is ‘5x’ and pencil is ‘x’
3 X 5x + 5x = Rs.200
15x + 5x = Rs.200
X = 200/20 = 10
:. Cost of 1 pen = 5x = 5 x 10 = 50
:. Cost of 12 pens, i.e. (one dozen) = 50 x 12 = Rs.600
Answer: Option E
Answer: (E) Rs. 600
Question: The sum of two numbers is 16. The difference is 4. What are the two numbers?Let x be the first number. Ley y be the second number
x + y = 16
x - y = 4
(A) 10 and 6
(B) 10 and 5
(C) 10 and 4
(D) 10 and 3
(E) 10 and 2
Rationale: Solution
Let x be the first number. Ley y be the second number
x + y = 16
x - y = 4
Solve the system of equations by elimination
Adding the left sides and the right sides gives:
x + x + y + -y = 16 + 4
2x = 20
x = 10
Since x + y = 16, 10 + y = 16
10 + y = 16
10 - 10 + y = 16 - 10
y = 6
The numbers are 10 and 6
Answer A
Answer: (A) 10 and 6
Question: There are 28 balls which are red, blue or green. If 12 balls are green and the sum of red balls and green balls is less than 24, at most how many red balls are there?
(A) 10
(B) 12
(C) 11
(D) 13
(E) 14
Rationale: r+g+b=28
g=12
r + g < 24
=> r + 12 < 24
=> r < 12
=> at most 11 red balls
ANSWER:C
Answer: (C) 11
Question: At a certain restaurant, 30 percent of the servers reported their tips, while 40 percent of the servers who were tipped didn't report their tips. What percent of the servers were tipped?
(A) 30%
(B) 60%
(C) 50%
(D) 70%
(E) 80%
Rationale: Statement: 30% of Servers (S) Reported their Tips (RT). Of the servers who were tipped (T) 40% didn't report their tips (notRT). [Note: A Venn Diagram is useful to visualize the problem.]
Solution: Sample space is 100%.
S = 100%
RT/S = 30%
notRT/T = 40% => 100% - 40% => RT/T = 60%
T/S = (30)/(60)% = 50%
Answer: C
Answer: (C) 50%
Question: The value of a machine depreciates at the rate of 10% per year. If its present is Rs.1,62,000 what will be its worth after 2 years ? What was the value of the machine 2 years ago ?
(A) 50000
(B) 100000
(C) 150000
(D) 200000
(E) None of them
Rationale: Value of the machine after 2 years
=Rs.[162000*(1-(10/100))^2] = Rs.[162000*(9/10)*(9/10)]
=Rs. 131220
Value of the machine 2 years ago
= Rs.[162000/(1-(10/100)^2)]=Rs.[162000*(10/9)*(10/9)]=Rs.200000
Answer is D.
Answer: (D) 200000
Question: In the first 10 overs of a cricket game, the run rate was only 4.6. What should be the run rate in the remaining 40 overs to reach the target of 282 runs?
(A) 4.25
(B) 5.9
(C) 6.25
(D) 7
(E) 7.5
Rationale: Required run rate = 282 - (4.6x 10) =	236 236/40= 5.9
B)
Answer: (B) 5.9
Question: A group of students decided to collect as many paise from each member of group as is the number of members. If the total collection amounts to Rs. 98.01, the number of the member is the group is:
(A) 57
(B) 67
(C) 77
(D) 99
(E) 97
Rationale: Money collected = (98.01 x 100) paise = 9801 paise.
Number of members =Square root of 9801 = 99.
Answer: Option D
Answer: (D) 99