mathewhe/aqua_rat huggingface dataset:
Question: A string of 15 light bulbs is wired in such a way that if any individual light bulb fails, the entire string fails. If for each individual light bulb the probability of failing during time period T is 0.06, what is the probability that the string of light bulbs will fail during the time period T?
(A) 1 - (0.94)^15
(B) (0.06)^15
(C) 1 - (0.06)^15
(D) (0.94)^15
(E) 0.06^150
Rationale: The string of light bulbs will fail if at least one light bulb fails. So, let's find the probability of the opposite event and subtract that value from 1.
The opposite event is when none of the 15 light bulbs fails, since the probability of each light bulb not to fail is 1-0.06=0.94 the probability that none of the 15 light bulbs fails is 0.94^15.
Hence, the probability that at least one light bulb fails is 1-0.94^15.
Answer: A.
Now, you should have spotted that your reasoning was not right because of one simple thing, consider the case when we have 100 light bulbs instead of 15, then according to your logic the probability that the string of light bulbs will fail would be 100*0.06=6, which is not possible since the probability of an event cannot be more than 1 (100%).
Answer: (A) 1 - (0.94)^15
Question: A train moves fast a telegraph post and a bridge 264 m long in 8 sec and 20 sec respectively. What is the speed of the train?
(A) 28.9 km/hr
(B) 89.9 km/hr
(C) 28.9 km/hr
(D) 79.2 km/hr
(E) 19.9 km/hr
Rationale: Let the length of the train be x m and its speed be y m/sec.
Then, x/y = 8 => x = 8y
(x + 264)/20 = y
y = 22
Speed = 22 m/sec = 22 * 18/5 = 79.2 km/hr.
Answer:D
Answer: (D) 79.2 km/hr
Question: Andrew purchased 7kg of grapes at the rate of 68 per kg and 9 kg of mangoes at the rate of 48 per kg. How much amount did he pay to the shopkeeper?
(A) 1000
(B) 908
(C) 930
(D) 1075
(E) 1080
Rationale: Cost of 7 kg grapes = 68 × 7 = 476.
Cost of 9 kg of mangoes = 48 × 9 = 432.
Total cost he has to pay = 476 + 432 = 908
B
Answer: (B) 908
Question: If x and y are different integers and x^2 = xy, which of the following must be true ?
I. y = 0
II. x = 0
III. x = y
(A) I only
(B) II only
(C) III only
(D) I and III only
(E) II, and III
Rationale: Answer choice A is correct.
The question gives you x^2=xy
you can simplify that as x^2-xy=0
x(x-y)=0 the solution will be either x=0 or x=y, since x and y are different integers x cannot equal y, that leaves you x=0 to be the only answer.
Answer E
Answer: (E) II, and III
Question: If f(x) = -*5 (x^4 - 1)/(x^2), what is f(1/x) in terms of f(x)?
(A) f(x)
(B) -f(x)
(C) 1/f(x)
(D) 5f(x)
(E) 2*f(x)
Rationale: -5*f(1/x) =-5* ((1/x)^4 - 1) / ((1/x)^2)
= -5*((1/x^4) - 1) / (1/x^2)
= -5*((1-x^4)/(x^4)) / (1/x^2)
= -5* (1-x^4)/(x^2)
= -5* ( (x^4) -1) / (x^2)
= 5f(x)
Answer is D.
Answer: (D) 5f(x)
Question: 4, 10, (?), 82, 244, 730
(A) 26
(B) 24
(C) 40
(D) 48
(E) 28
Rationale: 4 × 3 - 2 = 10
10 × 3 - 2 = 28
28 × 3 - 2 = 82
82 × 3 - 2 = 244
244 × 3 - 2 = 730
Answer is E.
Answer: (E) 28
Question: The cost of fencing a square field @ Rs. 20 per metre is Rs.10.080.How much will it cost to lay a three meter wide pavement along the fencing inside the field @ Rs. 50 per sq m
(A) 73828
(B) 73829
(C) 73811
(D) 73800
(E) 73129
Rationale: perimeter = total cost / cost per m = 10080 /20 = 504m
side of the square = 504/4 = 126m
breadth of the pavement = 3m
side of inner square = 126 - 6 = 120m
area of the pavement = (126 x126) - (120 x 120) = 246 x 6 sq m
cost of pavement = 246*6*50 = Rs. 73800
Answer: D
Answer: (D) 73800
Question: In an examination, a student scores 4 marks for every correct answer and loses 1 mark for every wrong answer. If he attempts all 50 questions and secures 130 marks, the no of questions he attempts correctly is :
(A) A)36
(B) B)38
(C) C)90
(D) D)88
(E) E)37
Rationale: Let the number of correct answers be X.
Number of incorrect answers = (60 – X).
4x – (50 – x) = 130
=> 5x = 180
=> x = 36
Answer:A
Answer: (A) A)36
Question: How many cones of radius 4 m, height 2 m can be formed from a cylinder of 12 m radius, 10 m height:
(A) 135
(B) 125
(C) 145
(D) 115
(E) 155
Rationale: (Cylinder volume)/(Cone volume)
(πr(power2)h)/(1/3 πr(power2)h)
= (π × 12 × 12 × 10)/(1/3 π × 4 × 4 × 2) = 135
Answer is A.
Answer: (A) 135
Question: A sum at simple interests at 13 ½ % per annum amounts to Rs.2502.50 after 4 years find the sum.
(A) Rs.1645.
(B) Rs.1675.
(C) Rs.1625.
(D) Rs.1635.
(E) Rs.1655.
Rationale: Let sum be Rs. x then , S.I.=Rs.(x*(27/2) *4*(1/100) ) = Rs.27x/50
amount = (Rs. x+(27x/50)) = Rs.77x/50
77x/50 = 2502.50  x = (2502.50 * 50)/77 = 1625
Hence , sum = Rs.1625.
Answer is C.
Answer: (C) Rs.1625.
Question: Frank is 14 years younger then John. In 5 years John will be twice as old as Frank. How old will Frank be in four years?
(A) 8
(B) 10
(C) 13
(D) 14
(E) 16
Rationale: Frank is 15 years younger then John --> F+14=J;
In 5 years John will be twice as old as Frank (in 5 year John will be J+5 years old and Frank will be F+5 years old) --> J+5=2*(F+5) --> (F+14)+5=2*(F+5) --> F=9;
In 4 years Frank will be 9+4=13 years old.
Answer: C.
Answer: (C) 13
Question: A room contains 160 people, 20 percent of whom are women. A group of people, 30 percent of whom are women, leaves the room. Of the people remaining in the room, 10 percent are women. How many people left the room?
(A) 10
(B) 20
(C) 40
(D) 60
(E) 80
Rationale: Say group of x people left the room.
# of women in the room was 0.2*160=32;
# of women in the group that left 0.3x;
# of women in the room after the group left it is 0.1(160-x);
So, 32-0.3x= 0.1(160-x) --> x=80.
Answer: E.
Answer: (E) 80
Question: A 250 m long train is running at a speed of 55 Km/hr. It crossed a platform of length 520 m in ?
(A) 41.1 sec
(B) 20.2 sec
(C) 31.8 sec
(D) 50.4 sec
(E) none of the above
Rationale: Speed = 55 Km/hr
(to convert km/hr in to M/s)
= 55 x 5/18 M/s
Distance = 250 m + 520 m ( If questions is about train crossing a post you need to consider only the length of Train, )
= 770 m
Time = Distance / Speed
= 770 x 18 / (5 x 55)
= 50.4 sec
Ans is :D
Answer: (D) 50.4 sec
Question: The age of father 10 years ago was thrice the age of his son. Ten years hence, father's age will be twice that of his son. The ratio of their present ages is:
(A) 5:2
(B) 7:3
(C) 9:2
(D) 10:4
(E) 13:4
Rationale: Let the ages of father and son 10 years ago be 3x and x years respectively.
Then, (3x + 10) + 10 = 2[(x + 10) + 10]
3x + 20 = 2x + 40
x = 20.
Required ratio = (3x + 10):(x + 10) = 70:30 = 7:3.
Answer: Option B
Answer: (B) 7:3
Question: In Arun’s opinion, his weight is greater than 65 kg but less than 72 kg. His brother doest not agree with Arun and he thinks that Arun’s weight is greater than 60 kg but less than 70 kg. His mother’s view is that his weight cannot be greater than 68 kg. If all are them are correct in their estimation, what is the average of different probable weights of Arun?
(A) 67 kg.
(B) 68 kg.
(C) 69 kg.
(D) Data inadequate
(E) None of these
Rationale: EXPLANATION
Let Arun’s weight by X kg.
According to Arun, 65 < X < 72
According to Arun’s brother, 60 < X < 70.
According to Arun’s mother, X <= 68
The values satisfying all the above conditions are 66, 67 and 68.
Required Average =( 66 + 67 + 68 /3 )= (201/3) = 67 kg
Answer A
Answer: (A) 67 kg.
Question: A crate of apples contains 1 bruised apple for every 30 apples in the crate. Two out of every 4 bruised apples are considered not fit to sell, and every apple that is not fit to sell is bruised. If there are 12 apples not fit to sell in the crate, how many apples are there in the crate?
(A) 720
(B) 360
(C) 480
(D) 600
(E) 840
Rationale: as given 2 out of every 4 bruised apple is not fit to sell
or, 50% of the bruised apples are not fit to sell.
as per the question 12 are not fit to sell
or,
0.0.5x=12
x=1200/50=24
thus total number of bruised apples =24
total number of apples =30*24=720
Answer:A
Answer: (A) 720
Question: A library has an average of 510 visitors on Sundays and 240 on other day. The average number of visitors in a month of 5 days starting with sunday is
(A) 1215
(B) 1314
(C) 2900
(D) 1710
(E) 2750
Rationale: Explanation:
As the month begin with sunday, so there will be five sundays in the month. So result will be:
=(510×5+240×25/30)=(8550/5)=1710
Answer: Option D
Answer: (D) 1710
Question: If 2n+4 - 2n+2 = 3, then n is equal to :
(A) 2
(B) -2
(C) 1
(D) -1
(E) None
Rationale: Sol.
2n+4 - 2n+2 = 3 ⇔ 2n+2 (22 - 1) = 3 ⇔ 2n+2 = 1 = 20
⇔ n+2 = 0 ⇔ n= -2.
Answer B
Answer: (B) -2
Question: (935421 x 625) = ?
(A) 584625125
(B) 584626125
(C) 584629125
(D) 584637125
(E) 584638125
Rationale: 935421 x 625 = 935421 x 54 = 935421 x 10 4
2
=	935421 x 104	=	9354210000
24	16
= 584638125
E)
Answer: (E) 584638125
Question: Which of the following is true about 0<|x|-x/2<5?
(A) -1<x<0
(B) 0<x<1
(C) 1<x<2
(D) 2<x<3
(E) 3<x<4
Rationale: when can be |x|-4x be greater than 0..
NEVER when x is positive..
ONLY A is left..
you can also substitute any value within the given range to check for answer
Example - put x as -0.5 for A. -1<x<0..
so |x|-x/2 = |-0.5|- (-0.5)/2 = 0.75 and it satisfies 0<|x|-4x<5
A
Answer: (A) -1<x<0
Question: A man rows his boat 85 km downstream and 45 km upstream, taking 2 1/2 hours each time. Find the speed of the stream?
(A) 6 kmph
(B) 5 kmph
(C) 2 kmph
(D) 8 kmph
(E) 1 kmph
Rationale: Speed downstream = d/t = 85/(2 1/2) = 34 kmph
Speed upstream = d/t = 45/(2 1/2) = 18 kmph
The speed of the stream = (34 - 18)/2 = 8 kmph
Answer:D
Answer: (D) 8 kmph
Question: In a games hour 4 different types of players came to the ground? cricket 22, hokey 15, football 21, softball 19. How many players are present in the ground?
(A) 70
(B) 52
(C) 62
(D) 77
(E) 79
Rationale: total number of players= 22+15+21+19= 77
Answer is D
Answer: (D) 77
Question: A man buy a book in Rs50 & sale it Rs90. What is the rate of profit ???
(A) 10%
(B) 80%
(C) 30%
(D) 25%
(E) 28%
Rationale: cp=50
sp=90
profit=90-50=40
%=40/50*100=80%
ANSWER:B
Answer: (B) 80%
Question: A train can travel 50% faster than a car. Both start from point A at the same time and reach point B at 75 kms away from A at the same time. On the way, however, the train lost about 12.5 minutes while stopping at the stations. The speed of the car is?
(A) 179 km/hr
(B) 197 km/hr
(C) 120 km/hr
(D) 109 km/hr
(E) 187 km/hr
Rationale: Let speed of the car be x km/hr.
Then, speed of the train = 150/100 x = 3/2 x km/hr.
75/x - 75/(3/2 x) = 125/(10 * 60)
75/x - 50/x = 5/24 = 120 km/hr.
Answer: C
Answer: (C) 120 km/hr
Question: A car has been driven with an average speed of 30 kilometers per hour during the first 30 kilometers of a journey. Upon reaching the 30th kilometer, the car then travels at 45 kilometers per hour for the next 30 kilometers. Find out the average speed of the car if it has not been stopped at all during the journey.
(A) 35
(B) 36
(C) 37.5
(D) 38
(E) 40
Rationale: Avg speed = Total distance/ total time taken
= 60 km/ 100 min
= .6 km/m
= .6 * 60 per hour
= 36 km
ANSWER:B
Answer: (B) 36
Question: If k > 0, x + k = y, and y + 5k = z, what is the ratio between z - x and y - x ?
(A) 2 to 1
(B) 3 to 1
(C) 4 to 1
(D) 5 to 1
(E) 6 to 1
Rationale: y-x = k
z-y = 5k
Let's add the two equations together:
z-x = 6k
The ratio of z-x to y-x is 6:1.
The answer is E.
Answer: (E) 6 to 1
Question: For how many integers n is 1^n+2 = (n+2)^1?
(A) 0
(B) 1
(C) 2
(D) None of these
(E) 3
Rationale: If n=0
1^0+2 = (0+2)^1
1^2 = 1 ; 2^1 =2 not ok
If n=1
1^1+2 =1 ; (1+2)^1=3^1=3 not OK
So, Answer : D
Answer: (D) None of these
Question: How many different sevevn letter words can be formed (the words need not be meaningful) using the letters of the word MEDITERRANEAN such that the first letter is E and the last letter is R?
(A) 65
(B) 11!/(2!*2!*2!)
(C) 56
(D) 23
(E) 11!/(3!*2!*2!*2!)
Rationale: E- -R
We are left with the following 11 letters: {M, D, I, T, R, EE, AA, NN} out of which 8 are distinct: {M, D, I, T, R, E, A, N}.
We should consider two cases:
1. If the two middle letters are the same, we'd have 3 words: EEER, EAAR and ENNR.
2. If the two middle letters are distinct, then we are basically choosing 2 letters out of 8 when the order of the selection matters, so it's 8P2 = 56.
Total = 56 + 3 = 65.
Answer: A.
Answer: (A) 65
Question: The average age of A and B is 22 years. If C were to replace A, the average would be 44 and if C were to replace B, the average would be 33. What are the age of A, B and C?
(A) 11,33,55
(B) 20, 20, 18
(C) 22, 44, 33
(D) 44, 88, 66
(E) None of the above
Rationale: Given A + B = 44â€¦(i)
C + B = 88 â€¦ (ii)
A + C = 66â€¦(iii)
(i) + (ii) + (iii) â‡’ A + B + C =99 â€¦(iv)
from (i) and (iv), we get
C = 55 years
âˆ´ B = 33 years and A = 11years
Answer A
Answer: (A) 11,33,55
Question: Of the 70 house in a development, 50 have a two-car garage, 40 have an in-the-ground swimming pool, and 35 have both a two-car garage and an in-the-ground swimming pool. How many houses in the development have neither a two-car garage nor an in-the-ground swimming pool?
(A) 10
(B) 15
(C) 20
(D) 25
(E) 30
Rationale: Neither Car nor Garage
= Total - Garage - (Swim - Common)
= 70 - 50 - (40-35) = 70-55 = 15
Answer B
Answer: (B) 15
Question: In how many different ways can the letters of the word ‘SMART’ be arranged?
(A) 120
(B) 354
(C) 126
(D) 214
(E) 124
Rationale: A
120
The word SMART has 5 distinct letters.
Number of arrangements = 5!
= 5 × 4 × 3 × 2 × 1 = 120
Answer: (A) 120
Question: A, B and C invested Rs.6300, Rs.4200 and Rs.10500 respectively, in a partnership business. Find the share of A in profit of Rs.14200 after a year?
(A) 3630
(B) 9232
(C) 4260
(D) 2387
(E) 2813
Rationale: 6300:4200:10500
3:2:5
3/10 * 14200 = 4260
Answer: C
Answer: (C) 4260
Question: Donna, Chris, and Austin have a total of $93 in their wallets. Donna has $7 more than Chris. Austin has 3 times what Donna has. How much do they have in their wallets?
(A) Donna $10 -Chris $45 -Austin $90
(B) Donna $20-Chris $13 -Austin $60
(C) Donna $30 -Chris $34-Austin $70
(D) Donna $40 -Chris $56 -Austin $100
(E) Donna $50 -Chris $23 -Austin $80
Rationale: Let the amount in Chris’s wallet be $x
Donna has $7 more than Chrish's wallet = $(x + 7)
Austin has 3 times than Donna's wallet = $3(x + 7)
According to the problem, Donna, chris, and Austin have a total of $93 in their wallets.
Therefore,
x + (x + 7) + 3(x + 7) = 93
x + x + 7 + 3x + 21 = 93
5x + 28 = 93
- 28 -28 (subtract 28 from both sides)
5x = 65
or, 5x/5 = 65/5 (Divide both sides by 5)
x = 13
Amount in Chris wallet = $x = $13
Amount in Donna's wallet = $(x + 7) = $(13 + 7) = $20
Amount in Austin 's wallet = $3(x + 7) = $3(13 + 7) = $3(20) = $ 60
Answer: Amount in Chris’s wallet: $13
Amount in Donna's wallet: $20
Amount in Austin's wallet: $60
correct answer B
Answer: (B) Donna $20-Chris $13 -Austin $60
Question: if m is a positive integer greater than 8, which of the following must be divisible by 4?
(A)  m(m-1)(m+2)(m+3)
(B)  m(m-1)(m+3)(m+4)
(C)  m(m-3)(m+2)(m+4)
(D)  m(m-3)(m+2)(m+3)
(E)  m(m+1)(m+3)(m+4)
Rationale: D.
For any integer m, D is the only answer choice which will always be divisible by 4.
A product of 4 consecutive integers will always be divisible by 4. Since, none of the answer choices are a product of 4 consecutive integers, we have to ensure at least one of the integers is always a multiple of 4. The best way to do that is to ensure the answer choice ism* [(m-1)OR(m+3)] * [(m-2)OR(m+2)] * [(m-3)OR(m+1)]. (answer D)
Answer: (D)  m(m-3)(m+2)(m+3)
Question: An athlete runs 200 metres race in 24 seconds. What is his speed?
(A) 20 km/hr
(B) 30 km/hr
(C) 25 km/hr
(D) 35 km/hr
(E) 40 km/hr
Rationale: speed = dist/time = 200/24
200/24 * 18/5 = 40*3/4 = 30 km/hr
ANSWER B
Answer: (B) 30 km/hr
Question: A train running at the speed of 90 km/hr crosses a pole in 9 sec. What is the length of the train?
(A) 288
(B) 225
(C) 277
(D) 272
(E) 150
Rationale: Speed = 90 * 5/18 = 25 m/sec
Length of the train = speed * time = 25 * 9
= 225 m
Answer: B
Answer: (B) 225
Question: A bag contains 9 red and 5 white balls. One ball is drawn at random. What is the probability that the ball drawn is white?
(A) 4/7
(B) 2/3
(C) 5/8
(D) 9/14
(E) 5/7
Rationale: Total number of balls = 9+5 = 14
number of white balls = 9
Probability = 9/14
Answer is D
Answer: (D) 9/14
Question: Find the cost of fencing around a circular field of diameter 36 m at the rate of Rs.3.50 a meter?
(A) 438
(B) 395
(C) 378
(D) 279
(E) 222
Rationale: 2 * 22/7 * 18 = 113
113 * 3 1/2
= Rs.395
Answer: B
Answer: (B) 395
Question: A trader sells 45 meters of cloth for Rs. 4500 at the profit of Rs. 12 per metre of cloth. What is the cost price of one metre of cloth?
(A) Rs. 80
(B) Rs. 85
(C) Rs. 88
(D) Rs. 100
(E) None of these
Rationale: SP of 1m of cloth = 4500/45 = Rs. 100
CP of 1m of cloth = SP of 1m of cloth - profit on 1m of cloth
= Rs. 100 - Rs. 12 = Rs. 88.
ANSWER:C
Answer: (C) Rs. 88
Question: If 4 women can colour 48 m long cloth in 2 days, then 6 men can colour 36 m long cloth in?
(A) 1/5 day
(B) 1 day
(C) 2 days
(D) 3 days
(E) 4 days
Rationale: The length of cloth painted by one woman in one day = 48 / 4 × 2 = 6 m
No. of days required to paint 36 m cloth by 6 women = 36/ 6 × 6 = 1 day.
B)
Answer: (B) 1 day
Question: If n is the product of three consecutive integers, and n is divisible by 3, which of the following is not necessarily a divisor of n ?
(A) 18
(B) 20
(C) 24
(D) 22
(E) 26
Rationale: IF ONE NO. IS 4 THEN OTHER CONSEQUTIVE NO. ARE 1*2*3=6 , 2*3*4=24 , 3*4*5 =60
24 IS NOT A DIVISOR OF N
C
Answer: (C) 24
Question: After Naomi received her order, she found that she could make a scarf from one skein of the yarn
that cost $5.99 a skein. After taking into account the discount, taxes, and shipping for the yarn, how
much would it cost to make five scarves?
(A) $40.45
(B) $60.45
(C) $10.45
(D) $20.45
(E) $30.45
Rationale: $5.99 x 5 = $29.95
.10 x $29.95 = 2.995 rounds to $3.00
$29.95 - $3.00 = $26.95 discounted price
$26.95 x 1.13 = $30.45 with tax and shipping
correct answer E
Answer: (E) $30.45
Question: In the above number, A and B represent the tens and units digits, respectively. If the above number is divisible by 25, what is the greatest possible value of B x A?
(A) 0
(B) 15
(C) 20
(D) 25
(E) 35
Rationale: I also was confused when I was looking forabove number:D
As far as I understood, 25 is a factor of AB. In other words, the values of B (units digits can be 5 or 0. Better to have option for 5 in this case to havebigger result). Now let's try 25x1 (A=2, B=5 respectively we have =10). But we don't have this number in answer choices, move on. (avoid even multiples of 2,4,6,8 etc (we will have 0 in units thus making our result 0)
25x3 = 75 (A=7 B=5 respectively. Hey! that's 35. This is the greatest possible value of B x A
IMO E.
Answer: (E) 35
Question: The area of sector of a circle whose radius is 12 metro and whose angle at the center is 38° is?
(A) 30m2
(B) 40m2
(C) 47.7m2
(D) 50m2
(E) 55m2
Rationale: 38/360 * 22/7 * 12 * 12
= 47.7 m2
Answer:C
Answer: (C) 47.7m2
Question: A shopkeeper buys two articles for Rs.1000 each and then sells them, making 20% profit on the first article and 20% loss on second article. Find the net profit or loss percent?
(A) neither profit nor loss
(B) 1%
(C) 2%
(D) 3%
(E) 4%
Rationale: Profit on first article = 20% of 1000 = 200.
This is equal to the loss he makes on the second article. That, is he makes neither profit nor loss.
ANSWER:A
Answer: (A) neither profit nor loss
Question: How many numbers from 2 to 9 are exactly divisible by 2?
(A) A)2
(B) B)3
(C) C)5
(D) D)4
(E) E)8
Rationale: 2/2 = 1 and 9/2 = 4
4 - 1 = 3
3 + 1 = 4 Numbers.
Answer : D
Answer: (D) D)4
Question: 18.05 Ã— 0.001 = ?
(A) 0.1805
(B) 0.01805
(C) 1.805
(D) 0.001805
(E) None of these
Rationale: 18.05 Ã— 0.001 = ?
or,? = 0.01805
Answer B
Answer: (B) 0.01805
Question: If the operation Ø is defined for all positive integers x and w by x Ø w = (2^x)/(2^w) then (4 Ø 2) Ø 2 = ?
(A) 2
(B) 4
(C) 8
(D) 16
(E) 32
Rationale: 4 Ø 2 = 2^4/2^2 = 4
4 Ø 2 = 2^4/2^2 = 4
The answer is B.
Answer: (B) 4
Question: The average of 10 numbers is calculated as 21. It is discovered later on that while calculating the average, one number namely 36 was wrongly read as 26. The correct average is?
(A) A)16
(B) B)18
(C) C)19
(D) D)22
(E) E)24
Rationale: Explanation:
10 * 21 + 36 – 26 = 220=>220/10 = 22
D)
Answer: (D) D)22
Question: Danny obtained 76, 65, 82, 67 and 75 marks (out of 100) in English, Mathematics, Physics, Chemistry and Biology. What are his average marks?
(A) A)87
(B) B)99
(C) C)68
(D) D)82
(E) E)73
Rationale: Average = (76 + 65 + 82 + 67 + 75)/5
= 365/5
= 73.
Answer:E
Answer: (E) E)73
Question: In an examination, 300 students appeared. Out of these students; 29 % got first division, 54 % got second division and the remaining just passed. Assuming that no student failed; find the number of students who just passed.
(A) 51
(B) 37
(C) 54
(D) 99
(E) 01
Rationale: The number of students with first division = 29 % of 300 = 29/100 × 300 = 8700/100 = 87
And, the number of students with second division = 54 % of 300
= 54/100 × 300
=16200/100
= 162
Therefore, the number of students who just passed = 300 – (87 + 162) = 51
Answer:A
Answer: (A) 51
Question: 1,245
1,254
1,425
.....
....
+5,421
The addition problem above shows four of the 24 different integers that can be formed by using each of the digits 1,2,4,5 exactly once in each integer. What is the sum of these 24 integers?
(A) 74,446
(B) 79,992
(C) 83,338
(D) 86,662
(E) 91,114
Rationale: In each of the units, tens, hundreds, and thousands place, each digit will appear 6 times.
Then the sum equals 6(1111)+6(2222)+6(4444)+6(5555) = 79,992
The answer is B.
Answer: (B) 79,992
Question: A man spends 15% of his income in house rent, 25% of the rest on his children’s education, 20% of the rest miscellaneous causes. If he now posses Rs. 2988 then his income is?
(A) A)Rs.3625
(B) B)Rs.4625
(C) C)Rs.4585
(D) D)Rs.5655
(E) E)Rs.6225
Rationale: X * (85/100) * (75/100) * (80/100) = 2988
X * 0.85 * 0.75 * 0.8=2988
X = 2988/0.48
X = 6225
ANSWER:E
Answer: (E) E)Rs.6225
Question: How many times do the hands of a clock coincide in a day?
(A) 29
(B) 28
(C) 22
(D) 88
(E) 27
Rationale: Explanation:
The hands of a clock coincide 11 times in every 12 hours (Since between 11 and 1, they
coincide only once, i.e., at 12 o'clock).
The hands overlap about every 65 minutes, not every 60 minutes.
The hands coincide 22 times in a day.
Answer: C) 22
Answer: (C) 22
Question: A bat is bought for Rs.410 and sold at a gain of 20% find its selling price
(A) s.430/-
(B) s.492/-
(C) s.400/-
(D) s.580/-
(E) s.600/-
Rationale: 100 % ------> 410
120 % ------> 120*410/100
Selling price = Rs.492/-
B
Answer: (B) s.492/-
Question: The speed of a car is 10 km in the first hour and 60 km in the second hour. What is the average speed of the car?
(A) 79 kmph
(B) 85 kmph
(C) 35 kmph
(D) 23 kmph
(E) 14 kmph
Rationale: S = (10 + 60)/2
= 35 kmph
Answer:C
Answer: (C) 35 kmph
Question: If 0.10 of a number is equal to 0.070 of another number, the ratio of the numbers is :
(A) 2 :3
(B) 3 :4
(C) 7:10
(D) 20 : 3
(E) 30:7
Rationale: 0.10A = 0.070B
-> A/B = 0.07/0.10 = 7/10
:. A : B = 7 : 10
ANSWER:C
Answer: (C) 7:10
Question: Mr. Smith calculated the average of 10three digit numbers. But due to a mistake he reversed the digits of a number and thus his average increased by 49.5. The difference between the unit digit and hundreds digit of that number is :
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: Since the average increased by 49.5 and there were a total of 10 numbers, it means the incorrect number was 49.5 greater than the correct number.
Say, the correct number was abc (where a, b and c are the digits of the 3 digit number)
Then the incorrect number was cba.
100c + 10b + a - (100a + 10b + c) = 495
99c - 99a = 99(c - a) = 495
495 = 99*5 = 99(c - a)
So c - a = 5
Answer (C)
Answer: (C) 5
Question: A man is 28 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) 20 years
(B) 21 years
(C) 22 years
(D) 24 years
(E) 26 years
Rationale: Explanation:
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
So, x = 26
Answer: Option E
Answer: (E) 26 years