mathewhe/aqua_rat huggingface dataset:
Question: A committee of four students has to be formed. There are five candidates: Jane, Joan, Paul, Stuart, and Jessica. If Paul and Stuart refuse to be in the committee together and Jane refuses to be in the committee without Paul, how many committees are possible?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 8
Rationale: Let's try a different problem with your approach. There are five people: A, B, C, D, E. Need to chose 3 for a committee. A and B cannot be chosen together. B and C cannot be chosen together. How many options?
Your approach: total 10 options, 5c3.
Now, assume the wrong scenario where A and B are chosen together. There are three such scenarios. (A and B are chosen, just need one more person.) So we have to subtract the three wrong options. Similarly, there are three wrong scenarios where B and C are chosen together.
This gives us 10-3-3=4 as the answer.
Yet this answer is wrong. There are five possibilities: ACD, ACE, ADE, BDE, CDE.
D
Answer: (D) 6
Question: Superman flies at a heroic rate of 10 miles per second- wow! What is his speed in kilometers per hour? [1km = 0.6 miles]
(A) 1,000
(B) 12,000
(C) 60,000
(D) 30,000
(E) 120,000
Rationale: To calculate the equivalent of kilometres in a mile
10 miles = 10*(0.6)^-1 = 16.6667 kilometres
In 1 hour there are 60 minutes
In 1 minute there are 60 seconds
So in 1 hour there are 3600 seconds
Speed in kmph = 16.6667 * 3600 = 60000
Correct answer - C
Answer: (C) 60,000
Question: A train met with an accident 90km away from station A. It completed the remaining journey at 5/6th of the original speed and reached station B 1hr 12mins late. Had the accident taken place 60km further, it would have been only 1hr late. what was the original speed of the train?
(A) 60 km/hr
(B) 55 km/hr
(C) 65 km/hr
(D) 90 km/hr
(E) 48 km/hr
Rationale: let the original speed be 6x. A/q, traveling 90 km at 5/6th of original speed costs him 12 minutes etc
90/5x =90/6x +12/90 -> x =10 , 9x= 90.
Ans D
Answer: (D) 90 km/hr
Question: What is the principal sum?
I. The sum amounts to Rs. 690 in 3 years at S.I.
II. The sum amounts to Rs. 750 in 5 years at S.I.
III. The rate of interest is 5% p.a.
(A) I and III only
(B) II and III only
(C) I and II only
(D) Any two of the three
(E) None of these
Rationale: Explanation:
Clearly, any of the three will give us the answer
Answer: D
Answer: (D) Any two of the three
Question: How many times in a day, are the hands of a clock in straight line but opposite in direction?
(A) 21
(B) 22
(C) 17
(D) 26
(E) 25
Rationale: B
22
The hands of a clock point in opposite directions (in the same straight line) 11 times in every 12 hours. (Because between 5 and 7 they point in opposite directions at 6 o'clcok only).
So, in a day, the hands point in the opposite directions 22 times.
Answer: (B) 22
Question: A committee is to be formed by randomly choosing 5 people from 7 candidates. If Alice and Bob are candidates, what is the probability that Alice will be selected but Bob will not?
(A) 3/7
(B) 4/7
(C) 5/21
(D) 6/21
(E) 9/42
Rationale: The total number of ways to form a committee is 7C5=21.
The number of committees which include Alice but not Bob is 5C4=5.
The probability that Alice is selected but Bob is not selected is 5/21.
The answer is C.
Answer: (C) 5/21
Question: What approximate value should come in place of the question mark (?) in the following equation?64.85 Ã— 12.25 â€“ 30.22 Ã— 8.95 = (52 + ?) Ã— 10
(A) 5.39435
(B) 3.39435
(C) 2.39435
(D) 0.39435
(E) 1.39435
Rationale: Solve using approximation
Answer D
Answer: (D) 0.39435
Question: One pipe can fill a pool 1.25 times faster than a second pipe. When both pipes are opened, they fill the pool in five hours. How long would it take to fill the pool if only the faster pipe is used?
(A) 11.25
(B) 11.52
(C) 1.25
(D) 7.2
(E) 9
Rationale: Say the rate of the slower pipe is R pool/hour, then the rate of the faster pipe would be 1.25R=5R/4. Since when both pipes are opened, they fill the pool in five hours, then their combined rate is 1/5 pool/hour.
Thus we have that R + 5R/4 = 1/5 --> R = 4/45 pool/hour, faster pipe fills at 1.25R which is 5/4 * 4/45 = 1/9 --> time is reciprocal of rate thus it's 9/1 =9 hours.
Answer: E.
Answer: (E) 9
Question: After decreasing 24% in the price of an article costs Rs.320. Find the actual cost of an article?
(A) 400
(B) 520
(C) 651
(D) 525
(E) 421
Rationale: CP* (76/100) = 320
CP= 4.21 * 100 => CP = 421
ANSWER:E
Answer: (E) 421
Question: A man is 24 years older than his son. In two years, his age will be twice the age of his son. The present age of his son is:
(A) 21
(B) 19
(C) 23
(D) 25
(E) 26
Rationale: Let the son's present age be x years. Then, man's present age = (x + 28) years.
(x + 28) + 2 = 2(x + 2)
x + 30 = 2x + 4
x = 26.
ANSWER :E
Answer: (E) 26
Question: A can do a piece of work in 12 days. When he had worked for 2 days B joins him. If the complete work was finished in 8 days. In how many days B alone can finish the work?
(A) 2
(B) 4
(C) 18
(D) 6
(E) 9
Rationale: Explanation:
8/12 + 6/x = 1
X = 18 days
Answer:C
Answer: (C) 18
Question: A GOLF BALL HAS DIAMETER EQUAL TO 4.1CM. ITS SURFACE HAS 150 DIMPLES EACH OF RADIUS 2MM (0.2 CM) .CALCULATE TOTAL SURFACE AREA WHICH IS EXPOSED TO SURROUNDINGS ASSUMING THAT THE DIMPLES ARE HEMISPHERCAL.
(A) 81.62cm2
(B) 71.62cm2
(C) 61.62cm2
(D) 51.62cm2
(E) 41.62cm2
Rationale: the total surface area of the golf ball without considering the dimples is 4*3.14*sqrt(4.1/2).
Due to 150 pits on the surface a there will be a reduction in surface area of ball which will be equal to opening area of the dimples which is 150*3.04*sqrt(0.2). again due to formation of the pits there will be an increase in surface area due to hemispherical concave surface of the pits which will be 150*2*3.14*sqrt(0.2) .So, the total surface area will be 4*3.4*sqrt(4.1)-150*3.14*sqrt(.2)+150*2*3.14*sqrt(.2)=71.62cm2
ANSWER:B
Answer: (B) 71.62cm2
Question: A and B can do a work in 5 days and 10 days respectively. A starts the work and B joins him after 3 days. In how many days can they complete the remaining work?
(A) 4/3 days
(B) 2 days
(C) 8 days
(D) 3 days
(E) 9 days
Rationale: Work done by A in 3 days = 3/5
Remaining work = 2/5
Work done by both A and B in one day = 1/5 + 1/10 = 3/10
Remaining work = 2/5 * 10/3 = 4/3 days.
Answer: A
Answer: (A) 4/3 days
Question: Excluding stoppages, the speed of a train is 45 kmph and including stoppages it is 36 kmph. Of how many minutes does the train stop per hour?
(A) 18
(B) 77
(C) 12
(D) 99
(E) 12
Rationale: T = 9/45 * 60
= 12
Answer:C
Answer: (C) 12
Question: How many different combinations of clothes can rahul make if he have 2 pairs of pants, 4 shirts, and 3 jackets?
(A) 10
(B) 18
(C) 24
(D) 20
(E) 15
Rationale: number of ways rahul can make is 4*3*2=24
Answer:C
Answer: (C) 24
Question: If x and y are odd integers, which of the following must always be a non-integer?
(A) xy
(B) x/y
(C) y/x
(D) xy/2
(E) -xy
Rationale: A) xy: (1)(1) = 1 and 1 is an integer. ELIMINATE
B. x/y: 1/1 = 1 and 1 is an integer. ELIMINATE
C. y/x: 1/1 = 1 and 1 is an integer. ELIMINATE
D. xy/2
E. -xy: -(1)(1) = -1 and -1 is an integer. ELIMINATE
As X and Y are odd, multiplication of x and y would result in odd integer
(Odd Integer)/2 will always be non integer
ANSWER:D
Answer: (D) xy/2
Question: A work can be finished in 11 days by forty women. The same work can be finished in eleven days by four men. The ratio between the capacity of a man and a woman is
(A) 4:1
(B) 3:4
(C) 2:3
(D) 3:2
(E) 4:5
Rationale: Work done by 40 women in 1 day = 1/11
Work done by 1 woman in 1 day = 1/(40Ã—11)
Work done by 4 men in 1 day = 1/11
Work done by 1 man in 1 day = 1/(4Ã—11)
Ratio of the capacity of a man and woman =1/(4Ã—11) : 1/(40Ã—11) = 1/4 : 1/40
= 1/1:1/4 = 4:1
Answer is A.
Answer: (A) 4:1
Question: Find the sum lend at C.I. at 5 p.c per annum will amount to Rs.441 in 2 years?
(A) 200
(B) 400
(C) 378
(D) 883
(E) 732
Rationale: 441 = P(21/20)2
P = 400
Answer: B
Answer: (B) 400
Question: A train passes a station platform in 40 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
(A) 328
(B) 279
(C) 240
(D) 288
(E) 300
Rationale: Speed = [54 * 5/18] m/sec = 15 m/sec.
Length of the train = (15 * 20) m = 300 m.
Let the length of the platform be x meters.
Then, x + 300 / 40 = 15
x + 300 = 600
x = 300 m. Answer:E
Answer: (E) 300
Question: A crate of mangoes contains one bruised mango for every thirty mango in the crate. If three out of every four bruised mango are considerably unsalable and there are 12 unsaleable mangoes in the crate then how many mango are there in the crate?
(A) 180
(B) 280
(C) 380
(D) 480
(E) 580
Rationale: Let the total no of mangoes in the crate be x
Then the no of bruised mango = 1/30 x
Let the no of unsalable mangoes =3/4 (1/30 x)
1/40 x =12
x=480
ANSWER D
Answer: (D) 480
Question: The ratio of radius of a circle and the side of a square is 2 : 7. Find the ratio of their areas:
(A) 2 : 1
(B) 4 : 7
(C) 8 : 77
(D) 4 : 49
(E) None
Rationale: radius/side = 2/7
â‡’ area of circle/area of square= 4/49
Answer: D
Answer: (D) 4 : 49
Question: How many members are there between 1 to 100 which are divisible by 9 and the sum of two digits is 9?
(A) 13
(B) 11
(C) 7
(D) 9
(E) 10
Rationale: 9,18,27,36,45,54,63,72,81,90,99
9 is not a two digit number
99 sum is 18;
ans=9
ANSWER:D
Answer: (D) 9
Question: A patient is given exactly 750 milliliters of a mixture of two medications daily. Medication A contains 40% pain killer and medication B contains 20% pain killer. If the patient receives exactly 215 milliliters of pain killer daily, how many milliliters of medication B are in the mixture?
(A) 150
(B) 225
(C) 325
(D) 425
(E) 550
Rationale: Let there be A milliliters of Medication A
and B milliliters of Medication B
A+B = 750 -- 1
Medication A contains 40% pain killer and medication B contains 20% pain killer.
(40/100)*A + (20/100)*B = 215
=> (2/5)*A + (1/5)*B = 215
Multiplying by 5 , we get
2A + B = 1075 -- 2
Equation 2- Equation 1 , we get
A = 325
B = 425
Answer D
Answer: (D) 425
Question: The volumes of two cubes are in the ratio 27: 125, what shall be the ratio of their surface areas?
(A) 6:25
(B) 3:5
(C) 9:25
(D) 16:25
(E) 19:25
Rationale: a13 : a23 = 27 : 125
a1 : a2 = 3 : 5
6 a12 : 6 a22
a12 : a22 = 9 : 25
ANSWER:C
Answer: (C) 9:25
Question: Fifteen participants are participating in a competition. In how many ways can the first three prizes be won?
(A) 920
(B) 680
(C) 2730
(D) 720
(E) 620
Rationale: Out of 15 participants, the first three prizes can be won in,
15P3 = 15! / (15 - 3)!
= 15 x 14 x 13
= 2730 ways
ANSWER:C
Answer: (C) 2730
Question: If x is equal to the sum of the integers from 20 to 40, inclusive, and y is the number of even integers from 20 to 40, inclusive, what is the value of x + y?
(A) 601
(B) 611
(C) 621
(D) 631
(E) 641
Rationale: x = 20 + 21 +...+ 40 = 21(30) = 630
y = 11
x+y = 641
The answer is E.
Answer: (E) 641
Question: A man spend 1/5 of his salary on food , 1/10 of his salary on house rent and 3/5 salary on clothes. he still has $16000 left with him. find salary..
(A) $10800
(B) $18000
(C) $160000
(D) $1800
(E) None
Rationale: [1/(x1 / y1 + x2/y2 + x3/y3)] * Total amount= Balance amount
[1-(1/5 + 1/10 + 3/5)} * total salary= $16000, = [1-9/10] * Total salary = $16000, Total salary = $16000*10 = $160000, correct answer (C)
Answer: (C) $160000
Question: Katie has 9 employees that she must assign to 3 different projects. If 3 employees are assigned to each project and no one is assigned to multiple projects, how many different combinations S of project assignments are possible?
(A) 252
(B) 1,680
(C) 2,340
(D) 362,880
(E) 592,704
Rationale: The ways to select three employees out of 9 for first project = 9C3
The ways to select three employees out of Remaining 6 for Second project = 6C3
Third Project already has the group of three to be assigned to it so need to select that
So total ways to assign 3 employees to each of 3 projects S= 9C3 * 6C3 * 1 = 1,680
Answer: Option B
Answer: (B) 1,680
Question: A car travels the first 1/3 of certain distance with a speed of 10km/hr the next 1/3 distance with a speed of 20 km/hr, and the last 1/3 distance with a speed of 10 km/hr. the average speed of the car for the whole journey is?
(A) 12km/hr
(B) 18km/hr
(C) 89km/hr
(D) 52km/hr
(E) 79km/hr
Rationale: Let the whole distance travelled be x km
and the average speed of the car for he whole journey be y km/hr
then (x/3)/10+(x/3)/20+(x/3)/10=x/y
x/30+x/60+x/30=x/y
1/12y=1
y=12km/hr
Answer(A)
Answer: (A) 12km/hr
Question: Of the goose eggs laid at a certain pond, 2/3 hatched and 3/4 of the geese that hatched from those eggs survived the first month. Of the geese that survived the first month, 3/5 did not survive the first year. If 125 geese survived the first year and if no more than one goose hatched from each egg, how many goose eggs were laid at the pond?
(A)  280
(B)  400
(C)  540
(D)  625
(E)  840
Rationale: Of the goose eggs laid at a certain pond, 2/3 hatched and 3/4 of the geese that hatched from those eggs survived the first month:
2/3*3/4 = 1/2 survived the first month.
Of the geese that survived the first month, 3/5 did not survive the first year:
(1-3/5)*1/2 = 1/5 survived the first year.
120 geese survived the first year:
1/5*(total) = 125 --> (total) = 625.
Answer: D.
Answer: (D)  625
Question: y =2x^2 +2bx + 512 cuts the x axis at (h, 0) and (k, 0). If h and k are integers, what is the least value of b?
(A) 256
(B) -256
(C) -128
(D) -64
(E) -257
Rationale: As the curve cuts the x-axis at (h,0) and (k,0). Therefore h,k are the roots of the quadratic equation.
For the quadratic equation is in the form ofax^2+bx+c=0,
The product of the roots =c/a= 512/2=256 and the sum of the roots =-b/a=-b
256 can be expressed as product of two numbers in the following ways:
1 * 256
2 * 128
4 * 64
8 * 32
16 * 16
The sum of the roots is maximum when the roots are 1 and 256 and the maximum sum is 1 + 256 = 257.
The least value possible for b is therefore -257.
E
Answer: (E) -257
Question: Calculate the share of profit made by 2 business partners, who invested $800 and $1200 respectively in a business if the profit made is $600.
(A) $241,$360
(B) $240,$2260
(C) $240,$360
(D) $230,$360
(E) $220,$360
Rationale: A:B = 800:1200
A:B = 2 : 3
A's share = 600*2/5 = $240
B's share = 600*3/5 = $360
Answer is C
Answer: (C) $240,$360
Question: What is the average of xx, 2x2x, and 66?
(A) x+2
(B) x+3
(C) x+2x+2
(D) x+4
(E) 2x+5
Rationale: By the definition of an average, we get:
x+2x+63=3x+63x+2x+63=3x+63
=3(x+2)3=x+2.=3(x+2)3=x+2.
Hence, the answer is x+2x+2 or Option C
Answer: (C) x+2x+2
Question: If the average (arithmetic mean) of x, x + 2, and x + 4 is 73, what is the value of x?
(A) 71
(B) 75
(C) 85
(D) 83
(E) 82
Rationale: AM of x, x + 2, and x + 4 = x + (x + 2) + (x + 4) / 3 = 3x + 6 /3 = x + 2
Given that x + 2 = 73
x = 71
Answer : A
Answer: (A) 71
Question: The ratio of number of students studying Arts, Commerce and Science in a College is 3 : 5 :4. What is the new ratio of the number of students studying Arts, Commerce and Science respectively if there is an increase of 20%, 40% and 25% in the number of students studying Arts, Commerce and Science?
(A) 18 : 35 : 50
(B) 3 : 10 : 10
(C) 4 : 8 : 5
(D) 8 : 35 : 25
(E) None of these
Rationale: Suppose the number of students studying Arts, Commerce and Science be 3x, 5x and 4x respectively.
When their numbers are increased by 20%, 40% and 25% respectively the new ratio becomes
3x × 120% : 5x × 140% :
4x × 125% = 36 : 70 : 50
= 18 : 35 : 25
Answer D
Answer: (D) 8 : 35 : 25
Question: The ratio of money with Ram and Gopal is 7 : 17 and that with Gopal and Krishan is 7: 17. If Ram has Rs. 539, Krishan has ?
(A) s. 2890
(B) s. 2330
(C) s. 1190
(D) s. 1620
(E) s. 3179
Rationale: Ram : Gopal = 7 : 17 = 49 : 119
Gopal : Krishan = 7 : 17 = 119 : 289
Ram : Gopal : Krishan = 49 : 119 : 289
Ram : Krishan = 49 : 289
Thus, 49 : 289 = 539 : N
&there N = 289 x 539 / 49
= Rs. 3179
Answer :E
Answer: (E) s. 3179
Question: Find the Missing Number 1, 5, 13, 25, ?
(A) 41
(B) 44
(C) 23
(D) 26
(E) 29
Rationale: 5-1=4
13-5=8
25-13=12
So,
41-25=16
ans- 41
ANSWER:A
Answer: (A) 41
Question: Lucy deposited $62500 in an investment fund that provided 22 percent annual return compounded quarterly. If she made no other transactions with the fund, in how much time, in years, did her investment earn a total interest of $5100?
(A) 1/2
(B) 1/7
(C) 3
(D) 6
(E) 6.1
Rationale: A = P + I = 62500 + 5100 = 67600
67600 = 62500(1 + 22/4*100)^(4t)
t = 1/7 yrs
Answer: B
Answer: (B) 1/7
Question: What is the greatest prime factor of 5^6 - 1?
(A) 29
(B) 31
(C) 37
(D) 41
(E) 43
Rationale: 5^6-1 = (5^3-1)(5^3+1) = 124*126 = 4*31*3*42
The answer is B.
Answer: (B) 31
Question: Which of the following inequalities has a solution set, when graphed on the number line, is a single line segment of finite length?
(A) 2 <= 8x+10 <= 6
(B) 2 <= 34x+4 <= 6
(C) 2 <= 3x+4 <= 6
(D) 2 <= 3465x+4 <= 6
(E) 2 <= 346x+4 <= 6
Rationale: The key words in the stem are:a singleline segment offinite length
Now, answer choices A, B, and C can not be correct answers as solutions sets for these exponential functions are not limited at all (>= for even powers and <= for odd power) and thus can not be finite (x can go to + or -infinity for A and C and x can got to -infinity for B). As for D: we have thatabsolute valueof x is between two positive values, thus the solution set for x (because of absolute value) will be two line segments which will be mirror images of each other.
Answer: C.
Answer: (C) 2 <= 3x+4 <= 6
Question: In a series of eight football matches between Germany and Argentina , the probability of Germany winning a match is 1/3 and the probability that the match ends in a draw is 1/4. If a win gets the team 2 points, a draw 1 point and a loss 0 Points, What is the probability that Germany will end up in 8 draws in the series?
(A) 24/576
(B) 125/864
(C) 1/25
(D) 1/65536
(E) 1/5
Rationale: Since the probability of a draw is 1/4, then the probability of 8 draws in 8 matches is (1/4)^8=1/65536.
Answer: D.
Answer: (D) 1/65536
Question: The perimeter of a rectangle is equal to the perimeter of aright-angled triangle of height 12 cm. If the base of the triangle is equal to the breadth of the rectangle, what is the length of the rectangle”
(A) 18 cm
(B) 24 cm
(C) 22 cm
(D) Data inadequate
(E) None of these
Rationale: P = 2(l + b) = L + B + h = L + b + 12.
Data inadequate.
Answer D
Answer: (D) Data inadequate
Question: At a meeting, 25 attendants used a pencil and 15 attendants used a pen. If exactly 20 attendants used only one of the two types of writing tools, how many attendants wrote with both types of writing tools?
(A) 10
(B) 6
(C) 7
(D) 4
(E) 14
Rationale: Say x attendants wrote with both writing tools.
(25 - x) + (15 - x) = 20 --> x = 10.
Answer: A.
Answer: (A) 10
Question: A numberais squared and then multiplied by negative 3. The result of this operation E is equal to three times the sum of three timesaand two. What is one possible value ofa?
(A) -3
(B) -2
(C) 1
(D) 2
(E) 3
Rationale: E=-3*a^2=3(3a+2)
a= -2 or -1
a=-2=B
Answer: (B) -2
Question: There are 10person among whom 2are brother. The total no.of ways in which these persons can be seated around a round table so that exactly 1person sit between the brothers, is equal to?
(A) 7!*3!
(B) 7!*2!
(C) 6!*3!
(D) 5!*2!
(E) 8!*3!
Rationale: Total number of ways = 7!*2!.
B
Answer: (B) 7!*2!
Question: A person can row at 9 kmph and still water. He takes 4 1/2 hours to row from A to B and back. What is the distance between A and B if the speed of the stream is 1 kmph?
(A) 28
(B) 26
(C) 25
(D) 21
(E) 20
Rationale: Let the distance between A and B be x km.
Total time = x/(9 + 1) + x/(9 - 1) = 4.5
=> x/10 + x/8 = 9/2 => (4x + 5x)/40 = 9/2 => x = 20 km.
Answer:E
Answer: (E) 20
Question: Two stations A and B are 65 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) 9
(B) 10
(C) 11
(D) 12
(E) 8
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) = 65
45x = 90
x = 2.
So, they meet at 9 a.m.
Answer: Option A
Answer: (A) 9
Question: A completes a work in 6 days and B complete the same work in 12 days. If both of them work together, then the number of days required to complete the work will be
(A) 8 days
(B) 9 days
(C) 10 days
(D) 12 days
(E) 4 days
Rationale: If A can complete a work in x days and B can complete the same work in y days, then, both
of them together can complete the work in x y/ x+ y days
Therefore, here, the required number of days = 6 × 12/ 18 = 4days.
Answer : E
Answer: (E) 4 days
Question: If the population of a certain country increases at the rate of Two person every 60 seconds, by how many persons does the population increase in 100 minutes?
(A) 120
(B) 150
(C) 240
(D) 220
(E) 200
Rationale: Answer = 2 * 100 = 200
Answer = E
Answer: (E) 200
Question: A wheel that has 6 cogs is meshed with a larger wheel of 14 cogs. When the smaller wheel has made 21 revolutions, then the number of revolutions mad by the larger wheel is:
(A) 49
(B) 4
(C) 12
(D) 9
(E) 27
Rationale: Let the required number of revolutions made by larger wheel be x.
Then, More cogs, Less revolutions (Indirect Proportion)
14 : 6 :: 21 : x 14 * x = 6 x 21
x =	(6 x 21)/14
x = 9.
Answer is D.
Answer: (D) 9
Question: The average age of a husband, wife and their child 3 years ago was 27 years and that of wife and the child 5 years ago was 20 years. The present age of the husband is:
(A) 10
(B) 19
(C) 20
(D) 25
(E) 17
Rationale: Sum of the present ages of husband, wife and child = (23 * 2 + 5 * 2) = 57 years.
Required average = 57/3 = 19 years.
ANSWER B
Answer: (B) 19
Question: Rectangle ABCD is constructed in the coordinate plane parallel to the x- and y-axes. If the x- and y-coordinates of each of the points are integers which satisfy 2 ≤ x ≤ 11 and -5 ≤ y ≤ 5, how many possible ways are there to construct rectangle ABCD?
(A) 396
(B) 1260
(C) 2475
(D) 7920
(E) 15840
Rationale: As the rectangle is parallel to coordinate axes, the coordinates of the points of the rectangle would be
(X1, Y1), (X2, Y1), (X2, Y2), (X1,Y2)
given that X1, X2 lie between 2 and 11..ie., 10 possible numbers
Possible combinations for X1,X2 would be 10C2 = 45
Similarly, Possible combinations for Y1, Y2 would be 11C2 = 55
Possible ways of constructing rectangle is by selecting any of the combination of X1,X2 and Y1,Y2
= 45 * 55 = 2475
Ans. C
Answer: (C) 2475
Question: The average monthly income of P and Q is Rs. 2050. The average monthly income of Q and R is Rs. 5250 and the average monthly income of P and R is Rs. 6200. The monthly income of P is:
(A) 3050
(B) 3000
(C) 4000
(D) 4050
(E) 3100
Rationale: Explanation:
Let P, Q and R represent their respective monthly incomes. Then, we have:
P + Q = (2050 x 2) = 4100 .... (i)
Q + R = (5250 x 2) = 10500 .... (ii)
P + R = (6200 x 2) = 12400 .... (iii)
Adding (i), (ii) and (iii), we get: 2(P + Q + R) = 27000 or P + Q + R = 13500 .... (iv)
Subtracting (ii) from (iv), we get P = 3000.
P's monthly income = Rs. 3000.
Answer: B
Answer: (B) 3000
Question: The number which exceeds 16% of it by 42 is?
(A) 50
(B) 25
(C) 52
(D) 58
(E) 60
Rationale: Let the number be x.
Then, x - 16% of x = 42.
x - 16/100 x = 42
x = (42 * 25)/21 = 50
ANSWER:A
Answer: (A) 50
Question: Rs.1430 is divided so that 4 times the first share, thrice the 2nd share and twice the third share amount to the same. What is the value of the third share?
(A) s.528
(B) s.542
(C) s.528
(D) s.540
(E) s.660
Rationale: A+B+C = 1430
4A = 3B = 2C = x
A:B:C = 1/4:1/3:1/2 = 3:4:6
6/13 * 1430 = Rs.660
Answer: E
Answer: (E) s.660
Question: There are 5 more women than there are men on a local co-ed softball team. If there are a total of 15 players on the team, what is the ratio of men to women?
(A) 10/16
(B) 6/16
(C) 5/10
(D) 6/10
(E) 4/10
Rationale: w = m+5
w+m = 15
m+5+m = 15
2m = 10
m = 5
w = 10
ratio:5:10
Ans: C
Answer: (C) 5/10