mathewhe/aqua_rat huggingface dataset:
Question: A train having a length of 240 m passes a post in 24 seconds. How long will it take to pass a platform having a length of 630 m?
(A) 120 sec
(B) 99 sec
(C) 89 sec
(D) 87 sec
(E) 85 sec
Rationale: Explanation:
v = 240/24 (where v is the speed of the train) = 10 m/s
t = (240+630)/10 = 87 seconds
Answer: Option D
Answer: (D) 87 sec
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) 25π
(D) 37π
(E) 41π
Rationale: r^2=(-3-1)^2+(4-1)^2=16+9=25
Area of circle=πr^2=25π
Answer : C
Answer: (C) 25π
Question: A coin is tossed two times. What is the probability that there is at the least one tail?
(A) 3/4
(B) 1/3
(C) 3/7
(D) 3/5
(E) 1/31
Rationale: Let P(T) be the probability of getting least one tail when the coin is tossed two times.
= There is not even a single tail.
i.e. all the outcomes are heads.
= 1/4 ; P(T) = 1 - 1/4
= 3/4
Answer: A
Answer: (A) 3/4
Question: Two-third of a positive number and 144/216 of its reciprocal are equal. The number is:
(A) 5/12
(B) 12/5
(C) 25/144
(D) 144/25
(E) 1
Rationale: Let the number be x. Then,
2/3 x = 144/216 * 1/x
x2 = 144/216 * 3/2 = 144/144
x = 1
ANSWER:E
Answer: (E) 1
Question: A son and father goes for boating in river upstream . After rowing for 1 mile son notices the hat of his father falling in the river. After 5 min he tells his father that his hat has fallen. So they turn round and are able to pick the hat at the point from where they began boating after 5min. Find the speed of river in miles/hours ?
(A) 7 mile/hr
(B) 6 mile/hr
(C) 8 mile/hr
(D) 1 mile/hr
(E) 2 mile/hr
Rationale: Explanation:
Let the speed of river and boat be 'r' m/min and 'b' m/min.
so relative speed in upstream (b-r)m/min and in downstream (b+r)m/min.
Now in upstream distnce covered in 5 min is 5(b-r)miles
so total distnce covered => 1 + 5(b-r)miles in upstream
In downstream distance covered in 5min is 5(b+r)miles
Now 1 + 5(b-r) = 5(b+r)
1+5b-5r = 5b+5r
1 = 10r
r = 1/10 mile/min => 6 mile/hr.
Answer: B
Answer: (B) 6 mile/hr
Question: The balance of a trader weighs 20% less than it should. Still the trader marks up his goods to get an overall profit of 30%. What is the mark up on the cost price?
(A) 4%
(B) 8%
(C) 25%
(D) 16.66%
(E) 9%
Rationale: The most natural way to deal with 'weights' questions is by assuming values.
Say the trader's balance shows 100 gms. It is actually 80 gms because it weighs 20% less. Say, the cost price is $80 ($1/gm). Since he gets a profit of 30%, the selling price must be 80+(30/100)*80 = $104
Since the cost price is actually supposed to be $100 (for 100 gms) and the selling price is $104, the mark up is simply 4%.
Ans : A
Answer: (A) 4%
Question: A bullet train 140 m long is running at 60 kmph. In how much time will it pass a platform 310 m long?
(A) 34 Seconds
(B) 22 Seconds
(C) 41 Seconds
(D) 24 Seconds
(E) 27 Seconds
Rationale: 27 Seconds
Distance travelled = 140 + 310m = 450m
Speed = 60 * 5/8 = 50/3m
Time = 450 * 3/50 = 27 Seconds
ANSWER E
Answer: (E) 27 Seconds
Question: If a and b are integers and (2^a)(3^b) is a factor of 180^40, what is the largest possible value of ab?
(A) 2a
(B) 5a
(C) 20a
(D) 40a
(E) 80a
Rationale: (2^a)(3^b) is a factor of 180^40
We need to find the largest possible value of ab.
We know that 180 = 2^2*5^1*3^2
Therefore 180^40 will have 2 powers of 3 in it.
Hence in (2^a)(3^b), b has to 2
Therefore value of ab = 2a
Correct Option: A
Answer: (A) 2a
Question: Weight of M, D and I is 74. Sum of D and I is 46 greater than M. I is 60% less than D. What is D's weight.
(A) 22
(B) 10
(C) 88
(D) 26
(E) 18
Rationale: M + D + I = 74 - - - (1)
(D + I) - M = 46 - - - (2)
I = 410410 D ⇒⇒ 5I = 2D ⇒⇒ I = 2D/5 - - - (3)
Adding (1) and (2) we get 2D + 2I = 120
Substituting the value of I in the above equation,
2D+2(2D5)=1202D+2(2D5)=120
⇒⇒ 14D = 600
⇒⇒ D = 300/7 = 42.8
Ans:B
Answer: (B) 10
Question: A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is:
(A) 10 km/hr
(B) 50 km/hr
(C) 14 km/hr
(D) 17 km/hr
(E) 77 km/hr
Rationale: Speed of the train relative to man = (125/10) m/sec = (25/2) m/sec. [(25/2) * (18/5)] km/hr = 45 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 45 ==> x = 50 km/hr.
Answer: B
Answer: (B) 50 km/hr
Question: A 300 meter long train crosses a platform in 39 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform?
(A) 177
(B) 166
(C) 350
(D) 198
(E) 161
Rationale: Speed = [300 / 18] m/sec = 50/3 m/sec.
Let the length of the platform be x meters.
Then, x + 300 / 39 = 50/3
3(x + 300) = 1950 è x = 350m.
Answer: C
Answer: (C) 350
Question: One fourth of one third of two fifth of a number is 15. What will be the 40% of that number is?
(A) 120
(B) 130
(C) 150
(D) 180
(E) 250
Rationale: (1/4) * (1/3) * (2/5) * x = 15 then x = 15 * 30 = 450
40% of 450 = 180
ANSWER D
Answer: (D) 180
Question: In a restaurant, the profit is 110% of the cost. If the cost increases by 12% but the selling price remains constant, approximately what percentage of the selling price is the profit?
(A) 30%
(B) 47%
(C) 90%
(D) 100%
(E) None of these
Rationale: Explanation :
Let C.P.= Rs. 100. Then, Profit = Rs. 110, S.P. = Rs. 210.
New C.P. = 112% of Rs. 100 = Rs. 112
New S.P. = Rs. 210.
Profit = Rs. (210 - 112) = Rs. 98.
Required percentage = (98 /210 *100) % = 47 % appox
Answer : B
Answer: (B) 47%
Question: A quadratic function f(x) attains a maximum of 3 at x = 1. The value of the function at x = 0 is 1. What is the value of f(x) at x = 10 ?
(A) -119
(B) -159
(C) -110
(D) -180
(E) -105
Rationale: Explanation :
Let, the quadratic equation be ax2 + bx + c. So, f(x) = ax2 + bx + c
At x = 0, the value of function is 1.
x = 0, f(x) = 1
ax2 + bx + c = a * 0 + b * 0 + c = c
c = 1.
At x = 1, f(x) = 3
x = 1, f(x) = 3
a *1 + b * 1 + c = 3
Since c = 1, a + b = 2.
Also, we know that f(x) is maximum when x = 1. If f(x) is maximum, (dx/dt)(f(x)) = 0
Differentiating f(x), we have d/dt (ax2 + bx + c) = 2ax + b
At x = 1, 2ax + b = 0.
2a + b = 0.
b = -2a.
Substituting we have a + b = 2, or a + -2a = 2. a = -2. So, b = 4.
So the equation is -2x2 + 4x + 1.
At x = 10, the value is -2 * 100 + 4 * 10 + 1 i.e -159.
Answer : B
Answer: (B) -159
Question: A began a business with Rs. 85,000. He was joined afterwards by B with Ks. 42,500. For how much period does B join, if the profits at the end of the year are divided in the ratio of 3 : 1 ?
(A) 4 months
(B) 5 months
(C) 6 months
(D) 8 months
(E) 7 months
Rationale: Suppose B joined for x months . Then, ( 85000 * 12 )/(42500 * x) = 3. or x = (85000 * 12) / (42500 * 3) = 8.
So, B joined for 8 months.Answer: D
Answer: (D) 8 months
Question: Potato chips are on sale, buy 2 get 1 free. There are only 9 bags of chips left (4 plain and 5 bbq). A shopper randomly grabs 3 bags. What is the probability the shopper will grab exactly 3 bags of bbq chips?
(A) 2/3
(B) 1/3
(C) 1/5
(D) 5/42
(E) 7/42
Rationale: Combination Probability Formula: nCr = n!/[r!(n-r)!]
Total possible, select 3 bags from 9 bags = 9C3 = 9!/[3!(9 - 3)!] = 84.
To have 3 bbq there must be 0 plain, select 0 plain from 4 = 4C0 = 1.
And, select 3 bbq from 5 = 5C3 = 10.
3 bbq and 0 plain = (1)(10) = 10
Probability = (number outcomes favorable)/(total number outcomes) = 10/84 = 5/42
Answer: D
Answer: (D) 5/42
Question: A train 180 m long passed a pole in 3 sec. How long will it take to pass a platform 330 m long?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
Rationale: Speed = 180/3
= 60 m/sec.
Required time
= (180 + 300)/60
= 8 sec.
Answer:D
Answer: (D) 8
Question: The average temperature of Monday, Tuesday, Wednesday and Thursday was 38∘ and that of Tuesday, Wednesday, Thursday and Friday was 40∘. If the temperature on Monday was 32∘, the temperature of Friday was :
(A) 40∘
(B) 39∘
(C) 38∘
(D) 30∘
(E) None of these
Rationale: Explanation:
M+T+W+Th=(4×38)=152
Monday temperature is 32. So T+W+Th=(152-32)=120
T+W+Th+F=(4×40)=160
F = (160-120)=40∘
Correct Option: A
Answer: (A) 40∘
Question: The probability of a lottery ticket being a prized ticket is 0.2. When 4 tickets are purchased, the probability of winning a prize on atleast one ticket is?
(A) 0.5909
(B) 0.5904
(C) 0.5902
(D) 0.5907
(E) 0.5901
Rationale: P(winning prize atleast on one ticket)
= 1 - P("Losing on all tickets")
= 1 - (0.8)4 = (1 + (0.8)2)(1 - (0.8)2)
= (1.64)(0.36) = 0.5904
Answer:B
Answer: (B) 0.5904
Question: 18 beavers, working together in a constant pace, can build a dam in 12 hours. How many hours will it take 12 beavers that work at the same pace, to build the same dam?
(A) 2.
(B) 4.
(C) 5.
(D) 6
(E) 18.
Rationale: Total Work = 18*12= 216 Beaver hours
12 Beaver * x =216Beaver hours
x=216 / 12=18
ANSWER:E
Answer: (E) 18.
Question: The length of a train and that of a platform are equal. If with a speed of 90 k/hr, the train crosses the platform in one minute, then the length of the train (in meters) is?
(A) 299
(B) 266
(C) 299
(D) 750
(E) 261
Rationale: Speed = [90 * 5/18] m/sec = 25 m/sec; Time = 1 min. = 60 sec.
Let the length of the train and that of the platform be x meters.
Then, 2x/60 = 25 è x = 25 * 60 / 2 = 750
Answer: D
Answer: (D) 750
Question: A train running at the speed of 60 km/hr crosses a pole in 36 seconds. What is the length of the train?
(A) 186 m
(B) 176 m
(C) 100 m
(D) 600 m
(E) 765 m
Rationale: Speed=(60 * 5/18) m/sec = (50/3) m/sec Length of the train
= (Speed x Time) = (50/3 * 36) m
= 600 m.
Answer: D
Answer: (D) 600 m
Question: What is the measure of the angle Y made by the diagonals of the any adjacent sides of a cube.
(A) 30
(B) 45
(C) 60
(D) 75
(E) 90
Rationale: C.. 60 degrees
All the diagonals are equal. If we take 3 touching sides and connect their diagonals, we form an equilateral Triangle. Therefore, each angle would be 60.C
Answer: (C) 60
Question: A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 40 years now, the son's age five years back was:
(A) A)15
(B) B)67
(C) C)56
(D) D)89
(E) E)34
Rationale: Let the son's present age be x years. Then, (40 - x) = x
2x = 40.
x = 20.
Son's age 5 years back (20 - 5) = 15 years.
Answer:A
Answer: (A) A)15
Question: If the average of w, b, c, 14 and 15 is 12. What is the average value of w, b, c and 29
(A) 12
(B) 13
(C) 14
(D) 15
(E) 16
Rationale: w+b+c+14+15 = 12*5 = 60
=>w+b+c = 60-29 = 31
w+b+c+29 = 31+29= 60
Average = 60/4 = 15
Answer D
Answer: (D) 15
Question: A train passes a station platform in 36 sec and a man standing on the platform in 20 sec. If the speed of the train is 54 km/hr. What is the length of the platform?
(A) 120 m
(B) 240 m
(C) 300 m
(D) 500 m
(E) 550 m
Rationale: Speed = 54 * 5/18 = 15 m/sec.
Length of the train = 15 * 20 = 300 m.
Let the length of the platform be x m . Then,
(x + 300)/36 = 15 => x = 240 m.
ANSWER B
Answer: (B) 240 m
Question: n is an integer chosen at random from the set
{5, 7, 9, 11 }
p is chosen at random from the set
{2, 4, 10, 14, 18}
What is the probability that n + p = 13 ?
(A) 0.15
(B) 0.2
(C) 0.25
(D) 0.3
(E) 0.4
Rationale: Set N: there is 4 ways to chose a number
Set P: there is 5 ways to chose a number
so total outcome is 4*5 = 20 which is represent 20 pairs of number
now we have 3 pairs can give us 13 which are (7,6), (9,4) and (11,2) .
3/20 = 0.15
Answer A
Answer: (A) 0.15
Question: A tank contains 10,000 gallons of a solution that is 5 percent sodium chloride by volume. If 3,000 gallons of water evaporate from the tank, the remaining solution will be approximately what percent sodium chloride?
(A) 6.28%
(B) 7.14%
(C) 7.86%
(D) 8.25%
(E) 8.63%
Rationale: The amount of sodium chloride is 0.05*10,000 = 500 gallons
500/7000 = 1/14 which is about 7.14%
The answer is B.
Answer: (B) 7.14%
Question: At a dinner party every two guests used a bowl of rice between them, every three guests used a bowl of dal between them and every four used a bowl of meat between them. There were altogether 65 dishes. How many guests were present at the party ?
(A) 60
(B) 65
(C) 90
(D) 95
(E) None of these
Rationale: no. of rice bowl=x
no. of dal bowl=y
no. of meat bowl=z
then, x+y+z=65(eq 1)
also, 2x=3y=4z
substituting value of y&z in terms of x in eq 1, x=30.
as 1 rice bowl is shared between 2 guests, therefore there are 60 guests...
ANSWER:A
Answer: (A) 60
Question: Sylvia can buy watches at a price of M dollars per watch, which she marks up by a certain percentage before selling. If she makes a total profit of X by selling Y watches, then in terms of M and X and Y, what is the percent of the markup from her buy price to her sell price?
(A) 100*(YM)
(B) 100X*(YM)
(C) 100X/(YM)
(D) 100X-(YM)
(E) 100X+(YM)
Rationale: Algebraic Solution:If she makes a total profit of X for Y watches, then that must be a profit of X/Y for each watch. That must be the markup above cost on each watch, the amount of the increase. Well, percent increase = (amount of increase)/(starting amount) x 100% = (X/Y)/M *100 = 100X/(YM)
Answer : C
Answer: (C) 100X/(YM)
Question: What profit percent is made by selling an article at a certain price, if by selling at 2/3rd of that price, there would be a loss of 14%?
(A) 20%
(B) 29%
(C) 13 1/30%
(D) 12%
(E) 13%
Rationale: SP2 = 2/3 SP1
CP = 100
SP2 = 86
2/3 SP1 = 86
SP1 = 129
100 --- 29 => 29%
ANSWER:B
Answer: (B) 29%
Question: Find the smallest four-digit number which is a multiple of 112.
(A) 896
(B) 1008
(C) 1120
(D) 1024
(E) None of these
Rationale: The smallest four digit number is 1000. If 1000 is divided by 112, the remainder is 104.
112 - 104 = 8, if 8 is added to 1000, it will become the smallest four digit number and a multiple of 112.
ANSWER:B
Answer: (B) 1008
Question: 25% of 30% of 45% is equal to?
(A) 0.03375
(B) 0.03372
(C) 0.0337
(D) 0.03377
(E) 0.03376
Rationale: (25/100) * (30/100) * (45/100)
1/4 * 3/10 * 9/20
27/800 = 0.03375
Answer:A
Answer: (A) 0.03375
Question: A watch which gains uniformly ,is 5 min,slow at 8 o'clock in the morning on sunday and it is 5 min 48 sec.fast at 8 p.m on following sunday. when was it correct?
(A) 28 min past 7pm on wednesday
(B) 20 min past 7pm on wednesday
(C) 20 min past 8pm on wednesday
(D) 29 min past 7pm on wednesday
(E) 20 min past 5pm on wednesday
Rationale: Explanation:
This sunday morning at 8:00 AM, the watch is 5 min. Slow, and the next sunday at 8:00PM it becomes 5 min 48 sec fast. The watch gains min in a time of (7×24)+12 = 180 hours.
To show the correct tine, it has to gain 5 min.
Answer: B) 20 min past 7pm on wednesday
So the correct time will be shown on wednesdy at 7:20 PM
Answer: (B) 20 min past 7pm on wednesday
Question: Tom, who has 50 math questions, will get 7 points per question if he chooses a correct answer. If he chooses a wrong answer to a question or skips one, he will lose 2 points per question. Then, which of the following can be the score if he solves all the 50 questions?
(A) 192
(B) 193
(C) 194
(D) 195
(E) 197
Rationale: Let x be the correctly answered questions. y be the wrongly answered/ skipped ones.
We have x + y = 50;
Score = 7x-2y
2x+2y = 100; 7x-2y = Score;
==> 9x = 100+Score;
check for answer choices where 100+Score is divisible by 9
Choice (E) 197 fits the equation !
Answer: (E) 197
Question: In how many different number of ways 5 boys and 3 girls can sit on a bench?
(A) 700
(B) 40320
(C) 720
(D) 730
(E) 740
Rationale: npn = n!
8p8 = 8 X 7 X 6 Ã— 5 Ã— 4 Ã— 3 Ã— 2 Ã— 1 = 40320
B
Answer: (B) 40320
Question: If selling price of an article is Rs. 250, profit percentage is 25%. Find the ratio of the cost price and the selling price
(A) 4:5
(B) 3.:2
(C) 2:1
(D) 9:3
(E) 4:2
Rationale: selling price = 250
Profit=25%
cost price =250*100/125=200
Required ratio =200:250=4:5
Answer: Option A
Answer: (A) 4:5
Question: If n is a natural number, then 6n^ 2 + 6n is always divisible by?
(A) 6 only
(B) 6 and 12
(C) 12 only
(D) 18 only
(E) 20 only
Rationale: 6n^2 + 6n = 6n(n+1), which is always divisible by 6 and 12 both, since n(n+1) is always even.
Answer is B
Answer: (B) 6 and 12
Question: If the sum of two numbers is 45 and the H.C.F and the sum of the reciprocals of the numbers are 3 and 103/100 respectively, then the LCM of the numbers is equal to:
(A) 460
(B) 300
(C) 245
(D) 100
(E) 200
Rationale: Let the numbers be a and b and LCM be x,
Then, a + b = 45 and ab = 3 * x = 3x
Required sum = 1/a + 1/b = (a + b)/ab = 103/300
103/300=45/3x
x=100
ANSWER:D
Answer: (D) 100
Question: A lemonade stand sold only small and large cups of lemonade on Tuesday. 2/5 of the cups sold were small and the rest were large. If the large cups were sold for 7/6 as much as the small cups, what fraction of Tuesday's total revenue was from the sale of large cups?
(A) (a) 7/16
(B) (b) 7/11
(C) (c) 10/21
(D) (d) 17/35
(E) (e) 1/2
Rationale: A simpler way i guess would be to think that in total 5 cups were sold. Out of which 2 are small and 3 are large. Now let the small ones cost $6. so the large ones would cost $7.
So,
2*6=12 and 3*7=21.
Total revenue was 12+21=33
and Large cup sales as found above is 21
Therefore answer is 21/33 i.e 7/11
B
Answer: (B) (b) 7/11
Question: Light glows for every 15 seconds . How many times did it between 1:57:58 and 3:20:47 am
(A) 381
(B) 332
(C) 383
(D) 334
(E) 385
Rationale: the diff in sec between 1:57:58 and 3:20:47 is 4969 sec, 4969/13 = 331.
so total 332 times light ll glow
ANSWER:B
Answer: (B) 332
Question: A 250m long train is travelling at 30km/hr. Another 200m long train travelling at 40km/hr in the same direction overtakes it. How long would it take to pass the first train completely?
(A) 2min32secs.
(B) 1min32secs.
(C) 3min42secs.
(D) 2min42secs,
(E) 4min12secs.
Rationale: Relative speed =x-y x,y are their speeds. Distance =(250+200)m =450m Relative speed = (40-30)km/hr =450m =25/9 m/s Time taken to cover 450m = 450*9/25 secs. =162 secs. =2min.42sec. Answer : D
Answer: (D) 2min42secs,
Question: A boy is traveling from his house to school at 3km/hr and reached school 9minutes late. Next day he traveled 4km/hr and reached 6minutes early. Then find the distance between house and school?
(A) 3km
(B) 4.5km
(C) 5km
(D) 2.5km
(E) 6km
Rationale: Let distance be x
S1 = 3km/hr
S2 = 4km/hr
T1 = x/3hr
T2 = x/4hr
Difference in time = 9+6 = 15m = 1/4hr
(x/3)-(x/4) = 1/4
x = 3km
Answer is A
Answer: (A) 3km
Question: A, B, C, D and E play a game of cards. A says to B, "If you give me three cards, you will have as many as E has and if I give you three cards, you will have as many as D has." A and B together have 10 cards more than what D and E together have. If B has two cards more than what C has and the total number of cards be 133, how many cards does B have ?
(A) 37
(B) 23
(C) 25
(D) 29
(E) 17
Rationale: Clearly, we have :
B-3 = E ...(i)
B + 3 = D ...(ii)
A+B = D + E+10 ...(iii)
B = C + 2 ...(iv)
A+B + C + D + E= 133 ...(v)
From (i) and (ii), we have : 2 B = D + E ...(vi)
From (iii) and (vi), we have : A = B + 10 ...(vii)
Using (iv), (vi) and (vii) in (v), we get:
(B + 10) + B + (B - 2) + 2B = 133 5B = 125 B = 25.
Answer: C
Answer: (C) 25
Question: There are r red ball, b blue ball and w white ball in a bag. What is the ratio of the number of blue ball to the total no. of ball in terms of r, b and w.?
(A) (r + b + w)
(B) r / (r + b + w)
(C) r * (r + b + w)
(D) r / (r + b )
(E) r / (r + w)
Rationale: The total number of marbles is
r + b + w
The total ratio of blue marbles to the total number of marbles is
r / (r + b + w)
B
Answer: (B) r / (r + b + w)
Question: What is the total number of X integers between 100 and 200 that are divisible by 3?
(A)  33
(B)  32
(C)  31
(D)  30
(E)  29
Rationale: yes there is a different way of arriving at that answer ....
u can also use airthmetic progression to get the answer
since the first term to be divisble by 3 is 102 ..take that as A .. the starting no
and since 198 is the last digit to be divisible by 3 take that as N ...
since the difference is 3 take that as D
no u have to find what term is 198 take that as nth term
the formula for that is N = A + (n-1) * d
198 = 102 +(n-1) * 3
from this u get n =33
Answer: (A)  33
Question: Half of the workers in Palabras bookstore have read the latest book by J. Saramago, and 1/6 of the workers have read the latest book by H. Kureishi. The number of workers that have read neither book is one less than the number of the workers that have read the latest Saramago book and have not read the latest Kureishi book. If there are 42 workers in the Palabras bookstore, how many of them have read both books?
(A) 3
(B) 12
(C) 9
(D) 8
(E) 7
Rationale: There are total 42 workers.
Half of the workers in Palabras bookstore have read the latest book by J. Saramago,
So 21 have read Saramago.
1/6 of the workers have read the latest book by H. Kureishi.
So (1/6) * 42 = 7 have read Kureishi
The number of workers that have read neither book is one less than the number of the workers that have read the latest Saramago book and have not read the latest Kureishi book
If B workers have read both books, 20 - B have read Saramago but not Kureishi.
So, (21 - B - 1) have read neither.
Total = n(A) + n(B) - Both + Neither
42 = 21 + 7 - B + (21 - B - 1)
B = 3
Answer (A)
Answer: (A) 3
Question: In how many ways can a group of 5 men and 2 women be made out of a total of 7 men and 3 women?
(A) 33
(B) 63
(C) 22
(D) 29
(E) 177
Rationale: Explanation:
Required number of ways = \inline {\color{Black}(7C_{5}\times 3C_{2})=(7C_{2}\times 3C_{1})=63}
Answer: B) 63
Answer: (B) 63
Question: The surface area of a sphere is same as the curved surface area of a right circular cylinder whose height and diameter are 12 cm each. The radius of the sphere is:
(A) 4cm
(B) 6cm
(C) 8cm
(D) 10cm
(E) 9cm
Rationale: Explanation:
Curved surface area of sphere =4/πr2Surface area of cylinder =2πrh
=>4/πr2=2πrh
=>r2=6∗12/2
=>r2=36
=>r=6
Note: Diameter of cylinder is 12 so radius is taken as 6.
Option B
Answer: (B) 6cm
Question: If cost of sugar increases by 52%. How much percent consumption of sugar should be decreased in order to keep expenditure fixed?
(A) 34.21
(B) 35.15
(C) 36.32
(D) 28.21
(E) 26.54
Rationale: 100
152
-----
152 ----- 52
100 ------ ? => 34.21%
Answer:A
Answer: (A) 34.21
Question: Three numbers are in the ratio 1:4:8 and their H.C.F is 3. The numbers are?
(A) 3, 15, 24
(B) 3, 12, 27
(C) 3, 12, 22
(D) 3, 12, 24
(E) 3, 12, 21
Rationale: Let the required numbers be x, 4x and 8x. Then, their H.C.F = x. So, x = 3.
The numbers are 3, 12, 24.
Answer: D
Answer: (D) 3, 12, 24
Question: Compound interest earned on a sum for the second and the third years are Rs.1200 and Rs.1440 respectively. Find the rate of interest?
(A) 80% p.a
(B) 10% p.a
(C) 20% p.a
(D) 28% p.a
(E) 30% p.a
Rationale: Rs.1440 - 1200 = Rs.240 is the interest on Rs.1200 for one year.
Rate of interest = (100 * 240) / (100 * 1) = 20% p.a
Answer:C
Answer: (C) 20% p.a
Question: In a class of 40 students 26 play football and play 20 long tennis, if 17 play above, many play neither?
(A) 6
(B) 8
(C) 10
(D) 11
(E) 14
Rationale: 26 + 20 - 17 = 29
40 - 29 = 11 play neither
Answer is D
Answer: (D) 11
Question: Express 20 mps in kmph?
(A) 23
(B) 88
(C) 90
(D) 72
(E) 21
Rationale: 20 * 18/5 = 72 kmph
Answer:D
Answer: (D) 72
Question: Edward is a trail runner who decides to take a day off work to run up and down a local mountain. He runs uphill at an average speed of 6 miles per hour and returns along the same route at an average speed of 9 miles per hour. Of the following, which is the closest to his average speed, in miles per hour, for the trip up and down the mountain?
(A)  5.5
(B)  5.8
(C)  6.0
(D)  6.3
(E)  7.2
Rationale: to calculate average of 2 speeds a and b when distance is constant
Formula - 2ab/(a+b)
Here Edward's uphill speed = 6 mph
Edward's downhill speed = 9 mph
2*6*9/(6+9) = 108/15 = 7.2
Correct answer - E
Answer: (E)  7.2
Question: The length of a room is 5.5 m and width is 3.75 m. Find the cost of paving the floor by slabs at the rate of Rs. 1400 per sq. metre.
(A) Rs. 15000
(B) Rs. 15550
(C) Rs. 15600
(D) Rs. 28875
(E) None of these
Rationale: Solution
Area of the floor = (5.5 × 3.75) m2 = 20.625 m2
∴ Cost of paving = Rs. (1400 × 20.625) = 28875. Answer D
Answer: (D) Rs. 28875