mathewhe/aqua_rat huggingface dataset:
Question: There are 30 girls in hostel whose average age is decreased by 2 months, when one girl 18 yrs is replaced by a new boy.Find the age of new girl.
(A) 1 year
(B) 1 year 2 months
(C) 2 years 5 months
(D) 5 years
(E) None
Rationale: Total decrease =30 * 2 = 60 month
= 5 years
D
Answer: (D) 5 years
Question: A thief is noticed by a policeman from a distance of 275 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) 50 meter
(B) 100 meter
(C) 175 meter
(D) 120 meter
(E) 130 meter
Rationale: Explanation:
Relative speed of the thief and policeman = (11 – 10) km/hr = 1 km/hr
Distance covered in 6 minutes =
1/60∗6=1/10=100meters
So distance between them after 6 minutes = 275 - 100
= 175 meters
Option C
Answer: (C) 175 meter
Question: When a is divided by b the remainder is 13.When c is divided by d the remainder is 12.
If a,b,c,d are all positive integers then which of these may be the value of b*d?
(A) 100
(B) 121
(C) 144
(D) 169
(E) 196
Rationale: b has to be greater than or equal to 14
d has to be greater than or equal to 13
b*d>=14*13
Only answer choice that satisfies above inequality is 625
ANSWER:E
Answer: (E) 196
Question: Ravi, Ram and Raj together started a business in partnership. The ratio of their capitals is 4:5:9.If their annual profit be Rs. 30600/-. What will be Raj’s share in this profit?
(A) Rs. 8500/-
(B) Rs. 6800/-
(C) Rs. 15030/-
(D) Rs. 15,300/-
(E) None of these
Rationale: Explanation:
Ravi : Ram : Raj = 4 : 5 : 9
Raj’s share = Rs(30600 * 9/18)
= Rs(30600 * 1/2) = 15300/-
Ram’s share = (30600 * 5/18) = 1700 * 5 = 8500/-
Ravi’s share = 6800/-
Answer: Option D
Answer: (D) Rs. 15,300/-
Question: A man saves Rs. 200 at the end of each year and lends the money at 5% compound interest. How much will it become at the end of 3 years?
(A) Rs.662.09
(B) Rs.662.18
(C) Rs.662.02
(D) Rs.662.01
(E) Rs.662.19
Rationale: Amount = [200(1 + 5/100)3 + 200(1 + 5/100)2 + 200(1 + 5/100)]
= [200 * 21/20(21/20 * 21/20 + 21/20 + 1)]
= Rs.662.02
Answer: C
Answer: (C) Rs.662.02
Question: Of the three numbers, the first is twice as second and three times the third. The average of the three numbers is 44, and the three numbers in order are?
(A) 116,58,36
(B) 98,49,33
(C) 72,36,24
(D) 108,54,36
(E) None of these
Rationale: Explanation :
Solution: Let A =x,
B =x/2, C = x/3.
=x + x/2 + x/3 / 3 = 44
By solving we will get x = 72.
Hence A= 72
B= 72/2= 36
C= 72/3 = 24
Answer : C
Answer: (C) 72,36,24
Question: The speed of a boat in still water is 60kmph and the speed of the current is 20kmph. Find the speed downstream and upstream?
(A) 22 kmph
(B) 40 kmph
(C) 78 kmph
(D) 15 kmph
(E) 23 kmph
Rationale: Speed downstream = 60 + 20 = 80 kmph
Speed upstream = 60 - 20
= 40 kmph
Answer:B
Answer: (B) 40 kmph
Question: Linda bought 3 notebooks at $1.20 each; a box of pencils at $1.50 and a box of pens at $1.70. How much did Linda spend?
(A) $3.80
(B) $6.80
(C) $7.80
(D) $10.80
(E) $9.80
Rationale: Linda spent
1.20*3 = $3.60 on notebooks
The total amount of money that Linda spent is equal to
3.60 + 1.50 + 1.70 = $6.80
correct answer B
Answer: (B) $6.80
Question: Rs.8000 become Rs.9261 in a certain interval of time at the rate of 5% per annum of C.I. Find the time?
(A) 4 years
(B) 6 years
(C) 2 years
(D) 3 years
(E) 5 years
Rationale: 9261 = 8000(21/20)N
(21/20)3 = (21/20)N => N = 3
ANSWER:D
Answer: (D) 3 years
Question: Lexy walks 5 miles from point A to point K in one hour, then bicycles back to point A along the same route at 15 miles per hour. Ben makes the same round trip, but does so at half of Lexy’s average speed. How many minutes does Ben spend on his round trip?
(A) 40
(B) 80
(C) 120
(D) 160
(E) 180
Rationale: Lexy walks 5 miles from point A to point K in one hour, then bicycles back to point A along the same route at 15 miles per hour. Ben makes the same round trip, but does so at half of Lexy’s average speed. How many minutes does Ben spend on his round trip?
Average speed = total distance/total time
We know the total distance is 5+5 (going from A to K then from K to A)
Time = distance/speed
Time = 5/15
Time = 1/3 hour
Average speed = (10)/(1hr + 1/3hr)
Average speed (lexi) = 10 / 1.33
Therefore, if Ben's average speed is 1/2 of lexi's then his speed = 10/2.66.
This means it took him 2.66 hours to cover the same 10 miles Lexi did. 2.66 hours = roughly 160 minutes.
Answer: D). 160
Answer: (D) 160
Question: Find the odd man out. 856, 743, 633, 853, 871, 990, 532
(A) 532
(B) 990
(C) 528
(D) 633
(E) None of these
Rationale: Explanation :
In all numbers except 742, the difference of third and first digit is the middle digit. Answer : Option C
Answer: (C) 528
Question: After an ice began to melt out from the freezer, in the first hour lost 3/4, in the second hour lost 3/4 of its remaining. If after two hours, the volume is 0.3 cubic inches, what is the original volume of the cubic ice, in cubic inches?
(A) 2.5
(B) 3.0
(C) 4.8
(D) 6.5
(E) 8.0
Rationale: Let initial volume of ice be = x
Ice Remaining after 1 hour = x - 0.75x = 0.25x
Ice Remaining after 2 hour = (1/4)x - (3/4 * 1/4 * x) = (1/16)x
(1/16)x = 0.3
x = 4.8
Alternate solution: Try to backsolve.
Initial volume = 4.8
After one hour --> (1/4)4.8 = 1.2
After two hours --> (1/4)1.2 = 0.3
Answer: C
Answer: (C) 4.8
Question: a rabbit is tied to one end of an equilateral triangle of side 5 m with a rope length of 8 m.The rabbit is not allowed to travel inside the triangle then find the maximum area covered by the rabbit?
(A) (96/9)*pi
(B) (480/9)*pi
(C) (240/9)*pi
(D) (100/9)*pi
(E) cannot be determind
Rationale: The rabbit can graze upto 64*pi area if the triangle is not there.but the constraint here is,it should not enter the triangle so it must avoid grazing the sector of the circle which covers the triangular area also.each angle in the equilateral triangle is 60 degrees.so the area of the sector formed by 60 degrees and of radius 8m is (pi*8*8*60)/360
therefore maximum total area covered by the rabbit is given by=area of circle-area of sector
=(pi*8*8)-(pi*8*8*60)/360
=(480/9)*pi
ANSWER:B
Answer: (B) (480/9)*pi
Question: One card is drawn at random from a pack of 52 cards. What is the probability that the card drawn is a face card (Jack, Queen and King only)?
(A) 5/6
(B) 9/7
(C) 6/4
(D) 1/25
(E) 3/13
Rationale: Explanation:
Clearly, there are 52 cards, out of which there are 12 face cards.
P (getting a face card) =12/52=3/13
Answer: E
Answer: (E) 3/13
Question: A train passes a station platform in 38 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) 248 m
(B) 240 m
(C) 270 m
(D) 765 m
(E) 176 m
Rationale: Speed = (54 * 5/18) m/sec = 15 m/sec. Length of the train = (15 x 20)m = 300 m. Let the length of the platform be x meters. Then, (x + 300)/38 = 15 ==> x + 300 = 570 ==> x
= 270 m.
Answer: C
Answer: (C) 270 m
Question: In how many different number of ways 5 men and 2 women can sit on a shop which can accommodate persons?
(A) 180
(B) 190
(C) 200
(D) 210
(E) 220
Rationale: 7p3 = 7 × 6 × 5 = 210
Option 'D'
Answer: (D) 210
Question: A train 350 m long, running with a speed of 63 km/hr will pass a tree in?
(A) 15
(B) 16
(C) 17
(D) 18
(E) 20
Rationale: Speed = 63 * 5/18 = 35/2 m/sec
Time taken = 350 * 2/35 = 20 sec
Answer: Option E
Answer: (E) 20
Question: After decreasing 24% in the price of an article costs Rs.820. Find the actual cost of an article?
(A) 1400
(B) 1079
(C) 1200
(D) 1023
(E) 1523
Rationale: CP* (76/100) = 820
CP= 10.78 * 100 => CP = 1079
ANSWER:B
Answer: (B) 1079
Question: If x and y are positive integers, and y=x^2+8, the greatest common divisor of a and b CANNOT be
(A) 9
(B) 1
(C) 2
(D) 4
(E) 8
Rationale: If x is 1, 2, 4, or 8, then GCD of x and y is 1, 2, 4, and 8 respectively. So, by POE the answer must be A.
Still: if x is a multiple of 9, then y is 8 greater than a multiple of 9, so not a multiple of 9, so both of them cannot be divisive by 9.
Answer: A.
Answer: (A) 9
Question: An engineer undertakes a project to build a road 15 km long in 300 days and employs 55 men for the purpose. After 100 days, he finds only 2.5 km of the road has been completed. Find the (approximate) number of extra men he must employ to finish the work in time.
(A) a. 43
(B) b. 45
(C) c. 55
(D) d. 68
(E) e. 83
Rationale: 55 workers working already
Let x be the total men required to finish the task in next 200 days
2.5 km done hence remaining is 12.5 km
Also, work has to be completed in next 200 days (300 - 100 = 200)
We know that, proportion of men to distance is direct proportion
and, proportion of men to days is inverse proportion
Hence, X = (55 * 12.5 * 100) / (2.5 * 200)
thus, X = 137.5 that is approximately 138
Thus, more men needed to finish the task = 138-55=83
hence Answer is E
Answer: (E) e. 83
Question: The average age of three boys is 5 years and their ages are in proportion 3:5:7. What is the age in years of the youngest boy?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: 3x + 5x + 7x = 15
x =1
3x = 3
ANSWER:C
Answer: (C) 3
Question: Of the 100 athletes at a soccer club, 40 play defense and 62 play midfield. If at least 20 of the athletes play neither midfield nor defense, the number of athletes that play both midfield and defense could be any number between
(A) 10 to 20
(B) 10 to 40
(C) 22 to 40
(D) 30 to 70
(E) 40 to 70
Rationale: First of all notice that since only 40 athletes play defense, then the number of athletes that play both midfield and defense cannot possibly be greater than 40.Eliminate D and E.
{Total} = {defense} + {midfield} - {both} + {neither}
100 = 40 + 62 - {both} + {neither}
{both} = {neither} + 2.
Since the least value of {neither} is given to be 20, then the least value of {both} is 20+2=22.Eliminate A and B.
Answer: C.
Answer: (C) 22 to 40
Question: The ratio of 2 numbers is 3:4 and their H.C.F. is 4. Their L.C.M. is ?
(A) 20
(B) 24
(C) 48
(D) 36
(E) 60
Rationale: Let the numbers be 3x and 4x
Their H.C.F. = 4
so the numbers are 3*4 , 4*4 = 12,16
L.C.M. =48
Answer is C
Answer: (C) 48
Question: The volume of a cube is 1331 cc. Find its surface.
(A) 864
(B) 726
(C) 255
(D) 287
(E) 267
Rationale: a3 = 1331 => a = 11
6a2 = 6 * 11 * 11 = 726
Answer:B
Answer: (B) 726
Question: The sum of two numbers is 96, and one of them is 12 more than the other. What are the two numbers?
(A) 36-48
(B) 50-34
(C) 60-24
(D) 42-54
(E) 21-63
Rationale: In this problem, we are asked to find two numbers. Therefore, we must let x be one of them. Let x, then, be the first number.
We are told that the other number is 12 more, x + 12.
The problem states that their sum is 96:
word problem = 96
The line over x + 12 is a grouping symbol called a vinculum. It saves us writing parentheses.
We have:
2x = 96 âˆ’ 12
= 84.
x = 84/2
= 42.
This is the first number. Therefore the other number is
x + 12 = 42 + 12 = 54.
The sum of 42 + 54 is 96.
D
Answer: (D) 42-54
Question: At the end of three years what will be the compound interest at the rate of 10% p.a. on an amount of Rs.20000?
(A) Rs.6620
(B) Rs.6500
(C) Rs.6800
(D) Rs.6400
(E) Rs.5400
Rationale: A = 20000(11/10)3
= 26620
= 20000
----------
6620
ANSWER:A
Answer: (A) Rs.6620
Question: The population of a town increased from 1,75,000 to 2,62,500 in a decade. What is the average percent increase of population per year?
(A) 4%
(B) 6%
(C) 5%
(D) 50%
(E) None of these
Rationale: Explanation :
Increase in the population in 10 years = 2,62,500 - 1,75,000 = 87500
% ncrease in the population in 10 years = (87500/175000) × 100 = 8750/175 = 50%
Average % increase of population per year = 50%/10 = 5%
Answer : Option C
Answer: (C) 5%
Question: The distance between Delhi and Mathura is 140 kms. A starts from Delhi with a speed of 24 kmph at 7 a.m. for Mathura and B starts from Mathura with a speed of 46 kmph at 8 a.m. from Delhi. When will they meet?
(A) 11
(B) 23 3/4
(C) 16 1/2
(D) 9 1/2
(E) 98
Rationale: D = 140 – 24 = 116
RS = 46 + 24 = 70
T = 116/70 = 1.6 hours
8 a.m. + 1.6 = 9 1/2 a.m..Answer: D
Answer: (D) 9 1/2
Question: Five booksâ€ Math, Physics, Chemistry, Biology and Commerceâ€ are going to place on each other. The math book & biology book should not be together, and the others can placed in any order. How many possible configurations are there for the books?
(A) 110
(B) 112
(C) 48
(D) 60
(E) 68
Rationale: the total no. of configuration for placing books are permutation of five item
5p5=5!=120
now the no. of ways in which math and biology will come together is 4Ã—2=8.
so by subtracting 8 to total no. of configuration give us the value in which math and biology book will not come together.
120-8=112.
answer B
Answer: (B) 112
Question: Elena’s bread recipe calls for 8 ounces of butter for each 14 cups of flour used. She needs to make 4 times the original recipe. If 12 ounces of butter is used, then how many cups of flour are needed?
(A) 1
(B) 4
(C) 9
(D) 13
(E) 56
Rationale: Solving through algebra route:
8B + 14F = x amount
If we multiply this equation with 4 we get:
32B + 56F =4X
Therefore, we got 32 ounces of butter and 4X amount of quantity when we use 56 ounces of floor.
Ans:E
Answer: (E) 56
Question: A train traveled at an average speed of 100 km/hr, stopping for 3 minutes after every 75 km. How
long did it take to reach its desƟnaƟon 600 km from the starting point
(A) 6 hours 24 mins
(B) 6 hours 21 mins
(C) 6 hours 18 mins
(D) 6 hours 15 mins
(E) None of these
Rationale: Explanation:
Time taken to cover 600 km = 6 hours [because train speed is 100 km/hr]
Number of stops =
begin{aligned}
frac{600}{75} - 1 = 7 \
text{Total Ɵme on stops =}7*3 = 21 mins
end{aligned}
Total Ɵme taken by train = 6 hours 21 mins
Answer: B
Answer: (B) 6 hours 21 mins
Question: If 8 ∙ 2x = 5(y+8), then when y = -8, x =
(A) 8
(B) 2
(C) 6
(D) 0
(E) 7
Rationale: 8 ∙ 2x = 5(y+8).
or, 8 ∙ 2x = 5(-8+8).
or, 2x = 50.
or, 2x = 1 [anything to the power 0 is 1 then, 50 = 1].
Taking log on both sides,
log 2x = log 1.
or, x log 2 = 0 [since log 1 = 0].
or, x = 0/log 2 [dividing log 2 on both sides].
Therefore, x = 0.
Answer:D
Answer: (D) 0
Question: In a 1000 m race, A beats B by 200 meters or 25 seconds. Find the speed of B?
(A) 8 m/s
(B) 9 m/s
(C) 5 m/s
(D) 3 m/s
(E) 6 m/s
Rationale: Since A beats B by 200 m or 25 seconds, i
t implies that B covers 200 m in 25 seconds.
Hence speed of B = 200/25
= 8 m/s.
Answer:A
Answer: (A) 8 m/s
Question: 5354 x 51 = ?
(A) 273054
(B) 273243
(C) 273247
(D) 273250
(E) 273258
Rationale: 5354 x 51	= 5354 x (50 + 1)
= 5354 x 50 + 5354 x 1
= 267700 + 5354
= 273054
A
Answer: (A) 273054
Question: The side of a rhombus is 25 m and length of one of its diagonals is 10 m. The area of the rhombus is?
(A) 244.85
(B) 224.95
(C) 244.85
(D) 224.95
(E) 244.95
Rationale: area of the rhombus = 1/2 * p * √4(a)2 - (p)2
a= 25 ; p = 10
A=1/2 * 10 *√4(25)2 - (10)2
=1/2 * 10 *√2500 - 100
=1/2 * 10 *√2400
A =244.95
Answer : E
Answer: (E) 244.95
Question: John gets on the elevator at the 14th floor of a building and rides up at the rate of 84 floors per minute. At the same time, Vinod gets on an elevator at the 58th floor of the same building and rides down at the rate of 92 floors per minute. If they continue travelling at these rates, then at which floor will their paths cross?
(A) 31
(B) 32
(C) 33
(D) 34
(E) 35
Rationale: Let their paths cross after x minutes
Then,
84x + 92x = 58 - 14
=> 176x = 44
⇒x=44/176=1/4
Number of floors covered by John in these 1/4 minute=84×1/4=21
Hence, their path cross at 14 + 21 = 35, i.e., at 35th floor
Answer is E.
Answer: (E) 35
Question: In a certain warehouse, 40 percent of the packages weigh less than 75 pounds, and a total of 48 packages weigh less than 25 pounds. If 80 percent of the packages weigh at least 25 pounds, how many of the packages weigh at least 25 pounds but less than 75 pounds?
(A) 8
(B) 64
(C) 48
(D) 102
(E) 144
Rationale: If 80% of the packages weigh at least 25 pounds
This means that 20% of the packages weigh LESS THAN 25 pounds
Let T = TOTAL number of packages
So, 20% of T = # of packages that weigh LESS THAN 25 pounds
48 packages weigh LESS THAN 25 pounds
GREAT. So, 20% of T = 48
Rewrite to get: 0.2T = 48
Solve:T = 240
40% of the packages weigh less than 75 pounds
So, 40% ofT= number of packages that weigh less than 75 pounds
40% of240=96, so96packages weigh less than 75 pounds
OF THOSE96packages that weigh less than 75 pounds,48packages weigh less than 25 pounds.
So, the number of packages that weight BETWEEN 25 and 75 pounds =96-48= 48 = C
Answer: (C) 48
Question: In a flower shop there were 6 flowers in each bouquet. If the seller has doubled the number of flowers in each bouquet then the new average of flowers in each bouque is
(A) 12
(B) 3
(C) 8
(D) 9
(E) None of these
Rationale: Answer
Now required average
= old average x Multiplicand
= 6 x 2 = 12
Correct Option: A
Answer: (A) 12
Question: If a quarter kg of onions costs 80 paise, how many paise will 100 gm cost?
(A) 32 paise
(B) 65 paise
(C) 56 paise
(D) 87 paise
(E) 15 paise
Rationale: Explanation:
Let the required cost be x paise.
Less weight, Less cost (Direct proportion)
250 : 100 : : 80 : x
250 * x = (100 * 80)
x = (100 * 80) / 250
x = 32
ANSWER: A
Answer: (A) 32 paise
Question: 39! is divided by 41. Then what is the remainder?
(A) 1
(B) 3
(C) 4
(D) 6
(E) 9
Rationale: Substituting p = 41 in the wilson's theorem, we get
40!+141=0
40×39!+141=0
−1×39!41=−1
Cancelling -1 on both sides,
39!41=1
A
Answer: (A) 1
Question: A library contains 90671 books in English and 405063 books in other languages. What is the total number of books available in the library?
(A) 494947
(B) 494044
(C) 495734
(D) 493734
(E) 493923
Rationale: Number of English Books = 90671
Number of in other Language Books = 405063
total number of books 90671 + 405063 = 495734 books
answer :C
Answer: (C) 495734
Question: what is probabability that 5 envelope can not put in to the right envelope?
(A) 11/30
(B) 12/30
(C) 13/30
(D) 14/30
(E) 15/30
Rationale: Number of derangements = n! (1/2! - 1/3! + 1/4! + ... + ((-1)^n)/n!)
Given 5 letters A, B, C, D and E:
Total number of derangements = 5! (1/2! - 1/3! + 1/4! - 1/5!) = 60-20+5-1 = 44.
Total possible arrangements = 5! = 120.
P(no letter is in the correct position) = 44/120 = 11/30.
ANSWER:A
Answer: (A) 11/30
Question: There are 15 students in a class. On the day the test was given, Cara was absent. The other 14 students took the test and their average was 76. The next day, Cara took the test, and with this grade included, the new average was 77. What was Cara's grade on the test?
(A) 89
(B) 90
(C) 91
(D) 92
(E) 93
Rationale: 14*76+Cara's grade=15*77
Cara's grade is 15*77-14*76=91.
The answer is C.
Answer: (C) 91
Question: If the quantity (p + 5) is 5 times the quantity (q − 5), then what is the relationship between p and q?
(A) p = 5q + 30
(B) p = 5q − 30
(C) 5p = q + 20
(D) p = 5q
(E) p = 5q − 20
Rationale: p+5=5(q-5)
p+5=5q-25
p=5q-30
option B
Answer: (B) p = 5q − 30
Question: In a camp, there is a meal for 120 men or 200 children. If 120 children have taken the meal, how many men will be catered to with remaining meal?
(A) 30
(B) 42
(C) 40
(D) 57
(E) 63
Rationale: There is a meal for 200 children.
120 children have taken the meal.
Remaining meal is to be catered to 70 children.
Now, 200 children 120 men.
70 children = (120/200)x 70 = 42 men.
B
Answer: (B) 42
Question: From a pack of cards two cards are drawn one after the other, with replacement. The probability that the first is a red card and the second is a king is ?
(A) 1/26
(B) 1/25
(C) 1/21
(D) 1/29
(E) 1/23
Rationale: Let E1 be the event of drawing a red card.
Let E2 be the event of drawing a king .
P(E1 ∩ E2) = P(E1) . P(E2)
(As E1 and E2 are independent)
= 1/2 * 1/13 = 1/26
Answer:A
Answer: (A) 1/26
Question: In a friendship gang Andrew has 8 gang, in how many ways can he invite one or more of the gang to his house?
(A) 245
(B) 255
(C) 260
(D) 268
(E) 270
Rationale: Andrew can select one or more than one of his 8 gang.
=> Required number of ways = 28 – 1= 255.
B
Answer: (B) 255
Question: John bought 2 shares and sold them for $36 each. If he had a profit of 20% on the sale of one of the shares but a loss of 20% on the sale of the other share, then on the sale of both shares John had
(A) a profit of $10
(B) a profit of $3
(C) a loss of $3
(D) a loss of $10
(E) neither a profit nor a loss
Rationale: Loss% = (%age Profit or loss / 10)^2 = (20/10)^2 = 4% loss
Total Selling Price = 36*2 = $72
Total Cost Price = 72/(0.96) = $75
Loss = 75-72 = $3
Answer: Option C
Answer: (C) a loss of $3
Question: A library branch originally contained 18360 volumes, 30% of which were fiction novels. 1/3 of the volumes were transferred to another location and 1/5 of the volumes transferred were fiction novels. What percent of the remaining collection was fiction novels?
(A) 2.5%
(B) 17.67%
(C) 28.3%
(D) 36%
(E) 73.6%
Rationale: Fiction Novels = 5,508
Transferred to another location = 6,120
Transferred fiction novels =1,101
Non Transferred Fiction Novels = 4,407
Percent of the remaining collection was fiction novels = 4,407/(18360 - 6120 ) * 100 => 36.004...%
Hence answer will be (D)
Answer: (D) 36%
Question: Two trains are moving in the same direction at 72 kmph and 36 kmph. The faster train crosses a man in the slower train in 10 seconds. Find the length of the faster train?
(A) 270
(B) 288
(C) 100
(D) 299
(E) 126
Rationale: Relative speed = (72 - 36) * 5/18 = 2 * 5 = 10 mps.
Distance covered in 27 sec = 10 * 10 = 100 m.
The length of the faster train = 100 m.
Answer: C
Answer: (C) 100
Question: Roberto has three children: two girls and a boy. All were born on the same date in different years. The sum of the ages of the two girls today is smaller than the age of the boy today, but a year from now the sum of the ages of the girls will equal the age of the boy. four years from today, the difference between the age of the boy and the combined ages of the girls will be
(A) 1
(B) 2
(C) 3
(D) –3
(E) –1
Rationale: Approach I (Plugin's)
Girl I ............... Girl II ................ Boy
1 ....................... 1 ........................ 3 (Assume the current ages)
1 + 1 < 3 .......... (Satisfies the given condition)
1 Year later there ages are
2 ....................... 2 ......................... 4
2 + 2 = 4 ............ (Satisfies the given condition)
After 4 years there ages are
5 ....................... 5 ............................ 7
Difference = 7 - (5+5) = 7 - 10 = -3
Answer = D
Answer: (D) –3
Question: A coin is tossed 3 times. What is the probability of getting exactly 2 heads?
(A) 1/2
(B) 1/4
(C) 3/8
(D) 5/8
(E) 3/16
Rationale: The number of possible outcomes is 2^3 = 8
There are 3 ways to get exactly 2 heads.
P(exactly 2 heads) = 3/8
The answer is C.
Answer: (C) 3/8
Question: A can do a piece of work in 5 days and B can do it in 4 days how long will they both work together to complete the work?
(A) 6/11
(B) 8/11
(C) 7/9
(D) 2/9
(E) 10/11
Rationale: Explanation:
A’s one day work = 1/5
B’s one day work = 1/4
(A+B)’s one day work = 1/5 + 1/4 = 9/20 => time = 20/9 = 2 2/9 days
Answer: Option D
Answer: (D) 2/9
Question: Find the probability that a non leap year selected at random will have 53 Wednesdays.
(A) 6/7
(B) 5/7
(C) 1/7
(D) 3/7
(E) 2/7
Rationale: There are 365 days in a leap year: 52 weeks and 1 more days. So, 52 Sundays and 1 days.
This 1 days can be {Mon, Tue, Wed, Thu, Fri, Sat,Sun} (7 cases). In order to have 53 Mondays we should have Mon case.
The probability of that is 1/7.
Answer: C.
Answer: (C) 1/7