mathewhe/aqua_rat huggingface dataset:
Question: What is the lowest positive integer that is divisible by each of the integers 1 through 10 inclusive?
(A) 420
(B) 840
(C) 1260
(D) 2520
(E) 5020
Rationale: We have to find the LCM of 1, 2, 3, 2^2, 5, 2*3, 7, 2^3, 3^2, and 2*5.
The LCM is 1*2^3*3^2*5*7= 2520
The answer is D.
Answer: (D) 2520
Question: Simplify: 1605 x 1605
(A) 2576025
(B) 2567025
(C) 2657025
(D) 2756025
(E) None of them
Rationale: = 1605 x 1605 = (1605)^2 = (1600 + 5)^2 = (1600)^2 + (5)^2 + 2 x 1600 x 5
= 2560000 + 25 + 16000 = 2576025.
Answer is A.
Answer: (A) 2576025
Question: Which of the following is a quadratic equation?
(A) x1/2 + 2x + 3 = 0
(B) x - 1)(x + 4) = x2 + 1
(C) x4 - 3x + 5 = 0
(D) (2x + 1)(3x - 4) = 2x2 + 3
(E) None of these
Rationale: Sol.(d) Equations in options (a) and (c) are not quadratic equations as in (a) max. power of x is fractional and in (c), it is not 2 in any of the terms.
For option (b), (x – 1)(x +4) = x2 + 1
or x2 + 4x - x + 4 = x2 + 1
or 3x - 5 = 0
which is not a quadratic equations but a linear.
For option (d), (2x + 1)(3x – 4) = 2x2 + 3
or 6x2 - 8x + 3x - 4 = 2x2 + 3
or 4x2 - 5x - 7 = 0
which is clearly a quadratic equation.
Answer D
Answer: (D) (2x + 1)(3x - 4) = 2x2 + 3
Question: Two trains having length of 140 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions (on parallel tracks). The time which they take to cross each other, is
(A) 10.8 s
(B) 12 s
(C) 9.8 s
(D) 8 s
(E) 7 s
Rationale: Explanation:
Distance = 140+160 = 300 m
Relative speed = 60+40 = 100 km/hr = (100×10)/36 m/s
Time = distance/speed = 300 / (100×10)/36 = 300×36 / 1000 = 3×36/10 = 10.8 s
Answer: Option A
Answer: (A) 10.8 s
Question: A thief is noticed by a policeman from a distance of 200 m. The thief starts running and the policeman chases him. The thief and the policeman run at the rate of 10 km and 11 km per hour respectively. What is the distance between them after 6 minutes?
(A) 100 m
(B) 150 m
(C) 190 m
(D) 200 m
(E) 220 m
Rationale: Explanation:
Relative speed of the thief and policeman = (11 – 10) km/hr = 1 km/hr
Distance covered in 6 minutes =1/60X6km=1/10km=100m
Distance between the thief and policeman = (200 – 100) m = 100 m.
ANSWER IS A
Answer: (A) 100 m
Question: Suppose you flip a fair coin six times. What is the probability that, in six flips, you get at least one head?
(A) 5/8
(B) 13/16
(C) 15/16
(D) 31/32
(E) 63/64
Rationale: Best way of solving an "at least 1" type of question is to compute "1 - probability of flipping 0 heads"
probability of flipping either a head or a tail = 1/2
probability of flipping 6 tails in a row (1/2)^6
probability of flipping at least 1 head = 1 - (1/2)^6 = 63/64 (answer E)
Answer: (E) 63/64
Question: How many 4 digit numbers are there, if it is known that the first digit is even, the second is odd, the third is prime, the fourth (units digit) is divisible by 3, and the digit 9 can be used only once?
(A) 20
(B) 150
(C) 225
(D) 304
(E) 320
Rationale: 4 options for the first digit: 2, 4, 6, 8;
5 options for the second digit: 1, 3, 5, 7, 9;
4 options for the third digit: 2, 3, 5, 7;
4 options for the fourth digit: 0, 3, 6, 9.
Four digit # possible without the restriction (about the digit 2): 4*5*4*4=320
Numbers with two 9-s, 9X9X 4*1*4*1=16.
Thus there are 320-16=304 such numbers.
Answer: D.
Answer: (D) 304
Question: P and Q can complete a work in 80 days and 48 days respectively. P alone started the work and Q joined him after 16 days till the completion of the work. How long did the work last?
(A) 5 days
(B) 10 days
(C) 14 days
(D) 22 days
(E) 40 days
Rationale: Explanation :
Work done by P in 1 day = 1/80
Work done by Q in 1 day = 1/48
Work done by P in 16 days = 16 Ã— (1/80) = 1/5
Remaining work = 1 â€“ 1/5 = 4/5
Work done by P and Q in 1 day = 1/80 + 1/48=1/30
Number of days P and Q take to complete the remaining work = (4/5) / (1/30) = 24
Total days = 16 + 24 = 40
Answer : Option E
Answer: (E) 40 days
Question: A man sitting in a train which is travelling at 100 kmph observes that a goods train, travelling in opposite direction, takes 9 seconds to pass him. If the goods train is 280 m long, find its speed?
(A) 52 kmph.
(B) 62 kmph.
(C) 12 kmph.
(D) 80 kmph.
(E) None
Rationale: Solution
Relative Speed	= (280 / 9)m/sec
= (280/9 x 18/5)
= 112 kmph.
Speed of the train	= (112 - 100)kmph
= 12 kmph.
Answer C
Answer: (C) 12 kmph.
Question: Two trains, each 100 m long, moving in opposite directions, cross other in 12 sec. If one is moving twice as fast the other, then the speed of the faster train is?
(A) 26 km/hr
(B) 40 km/hr
(C) 60 km/hr
(D) 77 km/hr
(E) 46 km/hr
Rationale: Let the speed of the slower train be x m/sec.
Then, speed of the train = 2x m/sec.
Relative speed = ( x + 2x) = 3x m/sec.
(100 + 100)/12 = 3x => x = 50/9.
So, speed of the faster train = 100/9 = 100/9 * 18/5
= 40 km/hr.
Answer:B
Answer: (B) 40 km/hr
Question: Andy has 20 pairs of matched gloves. If he loses 16 individual gloves, which of the following is NOT a possible number of matched pairs he has left?
(A) 9
(B) 11
(C) 13
(D) 14
(E) 15
Rationale: We can solve this is second. The question isSelect an answer choice where there is no possibility of having a number as a matched pair
Case1: If 16 gloves are gone the maximum probability of losing maximum gloves is 16 pairs of gloves out of 20. This means i m having 4 pairs of gloves. [Minimum number of gloves i can have is 4 pairs]
Case2: If 16 gloves are gone the maximum probability of losing minimum gloves is 16/2 = 8 means i can lose 8 glove. in this scenario i will be having 12 gloves.
Hence10 < Available Glove Pair < 13
any given time I cant possess 13 glove pair for the above mentioned scenario. And thats the answer. C.
Answer: (C) 13
Question: A 20% stock yielding 12% is quoted at:
(A) Rs. 83.33
(B) Rs. 167
(C) Rs. 112
(D) Rs. 120
(E) Rs. 140
Rationale: Income of Rs 12 on investment of Rs 100
Income of Rs 20 on investment of ?
= (20*100)/12=167
ANSWER:B
Answer: (B) Rs. 167
Question: [( 3.241 x 14 ) / 100] = ?
(A) 0.045374
(B) 4.5388
(C) 453.88
(D) 473.88
(E) None of these
Rationale: Answer
Multiplying 3.241 x 14=4.5374
Now divide 4.5374 by 100
So, 4.5374 ÷ 100= 0.045374
∴ Shift the decimal two places to the left as 100
Correct Option: A
Answer: (A) 0.045374
Question: When positive integer n is divided by 5, the remainder is 1. When n is divided by 7, the remainder is 3. What is the smallest positive integer k such that k + n is a multiple of 36.
(A) 5
(B) 4
(C) 12
(D) 32
(E) 35
Rationale: First, let us say I have a number n which is divisible by 5 and by 7. We all agree that it will be divisible by 35, the LCM of 5 and 7.
Now, if I have a number n which when divided by 5 gives a remainder 1 and when divided by 7 gives a remainder 1, we can say the number is of the form
n = 5a + 1 e.g. 5 + 1, 10 + 1, 15 + 1, 20 + 1, 25 + 1, 30 + 1, 35 + 1 etc
and
n = 7b + 1 e.g. 7 + 1, 14 + 1, 21 + 1, 28 + 1, 35 + 1 etc
So when it is divided by the LCM, 35, it will give 1 as remainder (as is apparent above)
Next, if I have a number n which when divided by 5 gives a remainder 1 and when divided by 7 gives a remainder 3, we can say the number is of the form
n = 5a + 1
and
n = 7b + 3
Now, the only thing you should try to understand here is that when n is divided by 5 and if I say the remainder is 1, it is the same as saying the remainder is -4. e.g. When 6 is divided by 5, remainder is 1 because it is 1 more than a multiple of 5. I can also say it is 4 less than the next multiple of 5, can't I? 6 is one more than 5, but 4 less than 10.
Therefore, we can say n = 5x - 4 and n = 7y - 4 (A remainder of 3 when divided by 7 is the same as getting a remainder of -4)
Now this question is exactly like the question above. So when you divide n by 36, remainder will be -4 i.e. n will be 4 less than a multiple of 36. So you must add 5 to n to make it a multiple of 36
A
Answer: (A) 5
Question: If 3^8 x 3^7 = 3^n what is the value of n?
(A) 20
(B) 18
(C) 17
(D) 16
(E) 15
Rationale: 3^8* 3^7 = 3^n
or 3 ^8+7 = 3^n
n =15
E
Answer: (E) 15
Question: Including Cara and Dan, there are seven members on the board of directors for a company. If the board is to be split up into a three-person subcommittee, what fraction of all the possible subcommittees that include Cara, also include Dan?
(A) 1/5
(B) 1/4
(C) 1/3
(D) 2/3
(E) 2/5
Rationale: The number of possible subcommittees with Cara is 6C2=15.
The number of possible subcommittees with Cara and Dan is 5C1=5.
The fraction of Cara's subcommittees which include Dan is 5/15=1/3.
The answer is C.
Answer: (C) 1/3
Question: Which of the following could be the sum of the reciprocals of two prime numbers?
(A) 7/13
(B) 11/12
(C) 11/30
(D) 23/50
(E) 13/22
Rationale: 13/22=(1/2) + (1/11)
Answer - E
Answer: (E) 13/22
Question: When a person aged 39 is added to a group of n people, the average age increases by 2. When a person aged 15 is added instead, the average age decreases by 1. What is the value of R?
(A)  7
(B)  8
(C)  9
(D)  10
(E)  11
Rationale: A simple and elegant solution.
As addition of 39, shifts mean by 2, and addition of 15, shifts mean by 1 to the other side, we have the mean lying between 3915, and in a ratio of 2:1
39-15 = 24
24 divide by 3 is 8.
Meaning mean of the n terms is 15+8 = 39-16 = 23
Now, from first statement, When a person aged 39 is added to a group of n people, the average age increases by 2.
R*23 +39 = 25*(R+1)
R = 7
Ans. (A)
Answer: (A)  7
Question: The ratio of the present age of Sandy to that of Molly is 7:2. Eight years from now, the ratio of the ages of Sandy to Molly will be 5:2. What was Sandy's age 6 years ago?
(A) 18
(B) 24
(C) 30
(D) 36
(E) 42
Rationale: Let the present age of Sandy be 7x years and that of Molly be 2x years.
(7x + 8) / (2x + 8) = 5 / 2
4x = 24
x = 6
Six years ago, Sandy's age was 7(6) - 6 = 36
The answer is D.
Answer: (D) 36
Question: In a certain company, a third of the workers do not have a retirement plan. 20% of the workers who do not have a retirement plan are women, and 40% of the workers who do have a retirement plan are men. If 176 of the workers of that company are men, how many of the workers are women?
(A) 80
(B) 95
(C) 105
(D) 120
(E) 154
Rationale: Set up equation:
x = total number of workers
176 = 0,4 * 2/3 * x + 0,8 * 1/3 * x
176 = 16/30 x
x = 330
330 - 176 = 154
Answer E
Answer: (E) 154
Question: The average mark of the students of a class in a particular exam is 80. If 5 students whose average mark in that exam is 40 are excluded, the average mark of the remaining will be 90. Find the number of students who wrote the exam.
(A) 22
(B) 27
(C) 25
(D) 99
(E) 21
Rationale: Let the number of students who wrote the exam be x.
Total marks of students = 80 x.
Total marks of (x - 5) students = 90(x - 5)
80x - (5 * 40) = 90(x - 5)
250 = 10x => x = 25.Answer: C
Answer: (C) 25
Question: What will be the cost of building a fence around a rectangle plot with area equal to 289 sq ft, and a = 1.7*b if the price per foot of building the fence is Rs. 58?
(A) A)Rs.3944
(B) B)Rs.3948
(C) C)Rs.3988
(D) D)Rs.4082.65
(E) E)Rs.3923
Rationale: Let the side of the rectangle plot be a ft.
a*b = 289 =>1.7 b*b = 289
b = 13.03
a = 22.17
Length of the fence = Perimeter of the plot = 2(a+b) = 70.39 ft.
Cost of building the fence = 70.39 * 58 = Rs.4082.65
Answer: D
Answer: (D) D)Rs.4082.65
Question: Set S has a mean of 16 and a standard deviation of 1.5. We are going to add two additional numbers to Set S. Which pair of numbers would decrease the standard deviation the most?
(A) {2, 10}
(B) {9, 11}
(C) {16, 16}
(D) {10, 18}
(E) {7, 13}
Rationale: answer A,B,D, and E mean is not 16 therefore not accepted . C mean is 16 but S.D is more. therefore accepted
answer is C mean is 16 and S.D decreases minimum.
C
Answer: (C) {16, 16}
Question: In Country C, the unemployment rate among construction workers dropped from 16 percent on September 1, 1992, to 9 percent on September 1, 1996. If the number of construction workers was 20 percent greater on September 1, 1996, than on September 1, 1992, what was the approximate percent change in the number of unemployed construction workers over this period?
(A) 50% decrease
(B) 30% decrease
(C) 15% decrease
(D) 30% increase
(E) 55% increase
Rationale: September 1, 1992
The total number of construction workers = 1,000 (assume);
16% are unemployed, thus the number of unemployed workers = 160.
September 1, 1996
The total number of construction workers = 1,200 (20% greater);
9% are unemployed, thus the number of unemployed workers = 108.
Decrease is 52, which is approximately 30% of 160.
Answer: B.
Answer: (B) 30% decrease
Question: A and B started business in partnership investing Rs. 20,000 and Rs. 15,000 respectively. After six months, C joined them with Rs. 20,000. What will be B's share in the total profit of Rs. 25,000 earned at the end of 2 years from the starting of the business?
(A) Rs. 7500
(B) Rs. 9000
(C) Rs. 9500
(D) Rs. 10,000
(E) None of these
Rationale: Explanation:
A:B:C = (20000 * 24) : (15000 * 24) : (20000 * 18) = 4:3:3
B's share = 25000 * 3/10 = Rs. 7500.
ANSWER IS A
Answer: (A) Rs. 7500
Question: A started a business with an investment of Rs. 70000 and after 6 months B joined him investing Rs. 120000. If the profit at the end of a year is Rs. 52000, then the share of B is?
(A) 33888
(B) 24000
(C) 27778
(D) 27772
(E) 81122
Rationale: Ratio of investments of A and B is (70000 * 12) : (120000 * 6) = 7 : 6
Total profit = Rs. 52000
Share of B = 6/13 (52000) = Rs. 24000
Answer: B
Answer: (B) 24000
Question: A certain company assigns employees to offices in such a way that some of the offices can be empty and more than one employee can be assigned to an office. In how many ways can the company assign 2 employees to 4 different offices?
(A) 16
(B) 6
(C) 7
(D) 8
(E) 9
Rationale: Ans. Each employee can go into any of the two offices. Thus we have
=> 4* 4=16
Answer : A
Answer: (A) 16
Question: The average of first five prime numbers greater than 37 is?
(A) 32.2
(B) 32.98
(C) 42.3
(D) 48.6
(E) 32.4
Rationale: 41 + 43 + 47 + 53 + 59
= 243/5
= 48.6
Answer: D
Answer: (D) 48.6
Question: If we write 1/7 as a decimal, what number holds the 50th digit's place to the right of the decimal?
(A) 7
(B) 8
(C) 2
(D) 1
(E) 4
Rationale: Writing 1/7 as a decimal we get 1/7 = 0.142857142857... ( the "142857" repeats forever)
This is an infinitely repeating decimal with 6 digits repeating, and 50 = (6)(8) + 2, so 4 is the 50th digit.
Answer: E
Answer: (E) 4
Question: A rectangular box of volume x has width, depth and height in the ratio of 2:3:3 (in that order). What is the width as a function of x?
(A) (2x/12)^(1/2)
(B) (x/2)^(1/2)
(C) (x/3)^(1/2)
(D) (2x/9)^(1/2)
(E) (x)^(1/2)
Rationale: We are given width = 2, depth = 3, height = 3
Then Volume x = Width x Depth x Height = 2*3*3 = 18
i.e. x = 18
i.e. The correct option should result in 2 on substituting the value of x=18
Checking options with x=18
A) (2x/12)^(1/2) = (2*18/12)^(1/2) = 3^(1/2) INCORRECT ANSWER
B) (x/2)^(1/2) = (18/2)^(1/2) = 9^(1/2) = 3 INCORRECT ANSWER
C) (x/3)^(1/2) = (18/3)^(1/2) INCORRECT ANSWER
D) (2x/9)^(1/2) = (2*18/9)^(1/2) = 4^(1/2) = 2 CORRECT ANSWER
E) (x)^(1/2) = (18)^(1/2) INCORRECT ANSWER
Answer: Option D
Answer: (D) (2x/9)^(1/2)
Question: What is the probability that a 4 person committee chosen at random from a group consisting of 6 men, 4 women, and 5 children contains exactly 1 woman?
(A) 44/91
(B) 77/832
(C) 11/77
(D) 308/1411
(E) 22/832
Rationale: Total possible selections = 4 out of 15 group members = 15C4
Favorable selections = 1 out of 4 women and 3 out of 11 (= 6 men + 5 children) = 4C1 * 11C3
Thus the required probability = 4C1*11C3 / 15C4 = 44/91. Thus A is the correct answer.
Answer: (A) 44/91
Question: A and B started a business in partnership investing Rs.20,000 and Rs.15,000 respectively. After six months, C joined them with Rs.20,000. What will be B's share in the total profit of Rs.26,000 earned at the end of 2 years from the starting of the business?
(A) Rs.7800
(B) Rs.9000
(C) Rs.9500
(D) Rs.10,000
(E) None
Rationale: Solution
A : B : C	=(20000×24):(15000×24):(20000×18)
=4 :3 :3
B's share	=Rs.(26000×3/10)
= Rs.7800.
Answer A
Answer: (A) Rs.7800
Question: A certain box has 9 cards and each card has one of the integers from 1 to 9 inclusive. Each card has a different number. If 2 different cards are selected at random, what is the probability that the sum of the numbers written on the 2 cards is less than the average (arithmetic mean) of all the numbers written on the 9 cards?
(A) 1/36
(B) 1/15
(C) 1/18
(D) 1/9
(E) 2/9
Rationale: The average of the numbers is 5.
The total number of ways to choose 2 cards from 9 cards is 9C2 = 36.
The ways to choose 2 cards with a sum less than the average are: {1,2},{1,3}
The probability is 2/36 = 1/18
The answer is C.
Answer: (C) 1/18
Question: You collect pens. Suppose you start out with 20. Mike gives you another 22 pens. Since her father makes pens, Cindy decides to double your pens. Since you're nice, you give Sharon 19 pens. How many pens do you have at the end?
(A) 39
(B) 40
(C) 65
(D) 42
(E) 43
Rationale: Solution
Start with 20 pens.
Mike gives you 22 pens: 20 + 22 = 42 pens.
Cindy doubles the number of pens you have: 42 Ã— 2 = 84 pens.
Sharon takes 19 pens from you: 84 - 19 = 65 pens.
So you have 65 at the end.
Correct answer: C
Answer: (C) 65
Question: 6 workers should finish a job in 8 days. After 3 days came 4 workers join them. How many days M do they need to finish the same job?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: Let Rate of one worker be R
=> (6*R)*8 = 1 (Rate * Time = work)
=> R = 1/48
=> Work remaining after 3 days
1 - (3*6)/48 = 30/48
After 4 ppl joined in
((6+4)*Time)/48 = 30/48
Time M= 3 days to finish the task
IMO A
Answer: (A) 3
Question: For any 5 given numbers, which of the following is always equivalent to adding the 3 numbers together and then dividing the sum by 3?
I. Ordering the 3 numbers numerically, from highest to lowest, and then selecting the middle number.
II. Dividing each of the numbers by 3 and then adding the results together.
III. Multiplying each number by 6, adding the resulting products together, and then dividing the sum by 9.
(A) I only
(B) II only
(C) I and II only
(D) II and III only
(E) None of the above
Rationale: Let the 3 numbers be x, y and z.
Question: Which of the following is equivalent to (x + y + z)/3
I. Ordering the 3 numbers numerically, from highest to lowest, and then selecting the middle number. --> Not always equivalent Eg: 111 and 141
II. Dividing each of the numbers by 3 and then adding the results together. --> x/3 + y/3 + z/3 = (x + y + z)/3 --> Equivalent
III. Multiplying each number by 6, adding the resulting products together, and then dividing the sum by 9. --> (6x + 6y + 6z)/9 = 2(x + y + z)/3 --> Not equivalent
Answer: C
Answer: (C) I and II only
Question: The length of a rectangle is two - fifths of the radius of a circle. The radius of the circle is equal to the side of the square, whose area is 400 sq.units. What is the area (in sq.units) of the rectangle if the rectangle if the breadth is 5 units?
(A) 40 sq.units
(B) 158 sq.units
(C) 187 sq.units
(D) 607 sq.units
(E) 815 sq.units
Rationale: Given that the area of the square = 400 sq.units
=> Side of square = √400= 20 units
The radius of the circle = side of the square = 20 units
Length of the rectangle = 2/5 * 20 = 8 units
Given that breadth = 5 units
Area of the rectangle = lb = 8 * 5 = 40 sq.units
Answer: A
Answer: (A) 40 sq.units
Question: 200 college students were asked in a survey if they preferred Windows or Mac brand computers. 70 Students claimed that they preferred Mac to Windows brand computers. One third as many of the students who preferred Mac to Windows, equally preferred both brands. 80 of the students had no preference. How many of the students in the survey preferred Windows to Mac brand computers?
(A) 25
(B) 50
(C) 57
(D) 60
(E) 75
Rationale: 200 = 70(Mac) + x(Window) + 80(both) => x=50
ANSWER:B
Answer: (B) 50
Question: I bought two books; for Rs.300. I sold one at a loss of 15% and other at a gain of 19% and then I found each book was sold at the same price. Find the cost of the book sold at a loss?
(A) 175
(B) 280
(C) 189
(D) 278
(E) 268
Rationale: x*(85/100)
= (300 - x)119/100
x = 175
Answer: A
Answer: (A) 175
Question: If the simple interest on a sum of money for 5 years at 9% per annum is Rs. 800, what is the compound interest on the same sum at the rate and for the same time?
(A) Rs. 947.55
(B) Rs. 957.55
(C) Rs. 857.55
(D) Rs. 657.55
(E) Rs. 357.55
Rationale: Sum = (800 * 100) / (5 * 9) = Rs. 1,777.78
C.I. on Rs. Rs. 1,777.78 for 5 years at 9% = Rs. 2,735.33.
= Rs. 2,735.33 - 1,777.78 = Rs. 957.55
ANSWER:B
Answer: (B) Rs. 957.55
Question: Ratio between length and breath of a rectangle is 25:16. The area of the rectangle is same with a square whose side is 200. Find the breadth and length of the rectangle?
(A) 150,200
(B) 140,300
(C) 100,300
(D) 160,250
(E) 100,200
Rationale: Let length l = 25x and breadth b = 16x
Area of the square = 200^2 = 40000
16x*25x = 40000
400x^2 = 40000
x^2 = 100
x = 10
length = 25*10 = 250
breadth = 16*10 = 160
Answer :D
Answer: (D) 160,250
Question: P and Q are both positive integers. When P is divided by Q, the remainder is some positive integer D, and when P is divided by (Q + 3), the remainder is also D. If P/Q = 1020.75 and P/(Q + 3) = 816.6, then which of the following gives the correct set of {D, Q}?
(A) {6, 12}
(B) {6, 15}
(C) {9, 12}
(D) {9, 15}
(E) {15, 24}
Rationale: Here, we have to use
decimal part of decimal quotient ={remainder/divisor}
to translate each act of division. The first one tells us 0.75 = D/Q, and the second one tells us that 0.60 = D/(Q + 3). These are also two simultaneous equations. Multiply both to get rid of the fractions.
D = 0.75*Q
D = 0.60*(Q + 3) = 0.60*Q + 1.80
Both are equal to D, so set them equal to each other and solve for Q.
0.75*Q = 0.60*Q + 1.80
0.15*Q = 1.80
Q = 1.80/0.15 = 180/15 = 60/5 = 12
Now that we know Q = 12, we can find D = 0.75*Q = (3/4)*12 = 9. So D = 9 and Q = 12. Answer = C.
Answer: (C) {9, 12}
Question: 110 people are attending a newspaper conference. 45 of them are writers and more than 38 are editors. Of the people at the conference, x are both writers and editors and 2x are neither. What is the largest possible number of people who are both writers and editors?
(A) 34
(B) 32
(C) 30
(D) 26
(E) 28
Rationale: {Total}={Writers}+{Editors}-{Both}+{Neither}.
{Total}=110;
{Writers}=45;
{Editors}>38;
{Both}=x;
{Neither}=2x;
110=45+{Editors}-x+2x --> x=65-{Editors}. We want to maximize x, thus we should minimize {Editors}, minimum possible value of {Editors} is 39, thus x={Both}=65-39=26.
Answer: D.
Answer: (D) 26
Question: A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for Rs. 3200. With the help of C, they completed the work in 3 days. How much is to be paid to C?
(A) 375
(B) 400
(C) 600
(D) 800
(E) 550
Rationale: C's 1 day's work =1/3-1/6	+1/7	=1/3	-7/24=1/24	.
A's wages : B's wages : C's wages =	1/6 : 1/8 : 1/24= 4 : 3 : 1.
C's share (for 3 days) = Rs. 3 x	1/24	x 3200 = Rs. 400.
Option B
Answer: (B) 400
Question: If y = 30p, and p is prime, what is the greatest common factor of y and 18p, in terms of p?
(A) p
(B) 2p
(C) 5p
(D) 6p
(E) p^2
Rationale: Y=30p
other number is 18p
then GCF(30p,18P)=6P; D is the correct answer
Answer: (D) 6p
Question: In a college, the ratio of the number of boys to girls is 8 : 5. If there are 160 girls, the total number of students in the college is
(A) 2447
(B) 377
(C) 667
(D) 416
(E) 871
Rationale: Explanation:
Let the number of boys and girls be 8x and 5x.
Total number of students = 13x = 13 * 32 = 416.
Answer: D
Answer: (D) 416
Question: A five-member committee is to be formed from a group of five military officers and nine civilians. If the committee must include at least two officers and two civilians, in how many different ways can the committee be chosen?
(A) 119
(B) 1,200
(C) 3,240
(D) 3,600
(E) 14,400
Rationale: To meet the conditions we can have only 2 cases:
2 officers and 3 civilians: C25∗C39=840
3 officers and 2 civilians: C35∗C29=360
Total: 840+360=1,200.
Answer: B.
Answer: (B) 1,200