mathewhe/aqua_rat huggingface dataset:
Question: A train passes a station platform in 32 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) 180 m
(B) 240 m
(C) 300 m
(D) 360 m
(E) 280 m
Rationale: Speed = 54 x	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 metres.
Then,	(x + 300)/32	= 15
x + 300 = 480
x = 180 m.Answer: Option A
Answer: (A) 180 m
Question: A man saves a certain portion of his income during a year and spends the remaining portion on his personal expenses. Next year his income increases by 25% but his savings increase by 100%. If his total expenditure in 2 years is double his expenditure in 1st year, What %age of his income in the first year did he save?
(A) 20%
(B) 25%
(C) 28.5%
(D) 30%
(E) 32%
Rationale: 1st year Income= I
1st year savings= S
1st year Expense= E1
2nd year Income = 1.25I
2nd year savings= 2S (100% increase)
2nd Year expense= E2
E1+ E2= 2E1
E2=E1
That means Expenses are same during both years. With increase of 25% income the savings increased by 100%.
or S= .25I
or S= 25% of Income
B is the answer
Answer: (B) 25%
Question: Vijay sells a cupboard at 10% below cost price. Had he got Rs.1500 more, he would have made a profit of 10%. What is the cost price of the cupboard?
(A) 7450
(B) 7500
(C) 7400
(D) 7500
(E) None of these
Rationale: Explanation:
Cost price = 1500/(0.10 + 0.10) = 1500/0.20
= Rs.7500
ANSWER B
Answer: (B) 7500
Question: A fruit drink is made of orange, watermelon, and grape juice, where 25 percent of the drink is orange juice and 40 percent is watermelon juice. If the drink is made with 70 ounces of grape juice, how many ounces is the drink total?
(A) 125
(B) 160
(C) 200
(D) 250
(E) 320
Rationale: Let the total number of ounces in the drink be x.
% of orange = 25%
% of watermelon = 40%
% of grape = 100% - 65% = 35%
0.35x = 70
x = 200
Therefore there are a total of 200 ounces in the drink.
The answer is C.
Answer: (C) 200
Question: 1/3 of certain journey is covered at the rate of 25kmph,one-fourth at the rate of 30kmph and the rest at 50 kmph.Find the avg speed for the whole journey.
(A) 23 kmph
(B) 25 kmph
(C) 33.333 kmph
(D) 35 kmph
(E) 37.133 kmph
Rationale: Average speed = total distance / total time
LCM = 3, 4 = 12
Average speed = 12 / (1/3*12*1/25 + ¼ * 12*1/30 +5/50)
= 12/ (4/25 + 3/30+ 5/30
= 150*12/54 = 33.333 kmph
C
Answer: (C) 33.333 kmph
Question: In a class there are 20 boys and 15 girls. In how many ways can a boy and a girl be selected?
(A) 288
(B) 500
(C) 277
(D) 266
(E) 300
Rationale: We can select one boy from 20 boys in 20 ways.
We select one girl from 15 girls in 15 ways
We select a boy and girl in 20 * 15 ways i.e.,
= 300 ways.
Answer: E
Answer: (E) 300
Question: Two trains start at same time from two stations and proceed towards each other at the rate of 20 km/hr and 25 km/hr respectively. When they meet, it is found that one train has traveled 65 km more than the other. What is the distance between the two stations?
(A) 585 km
(B) 767 km
(C) 276 km
(D) 178 km
(E) 176 km
Rationale: Explanation:
Let us assume that trains meet after 'x' hours
Distance = speed * Time
Distance traveled by two trains = 20x km and 25x km resp.
As one train travels 65 km more than the other,
25x â€“ 20x = 65
5x = 65
x = 13 hours
As the two trains are moving towards each other, relative speed = 20 + 25 = 45 km/hr
Therefore, total distance = 45*13 = 585 km.
ANSWER: A
Answer: (A) 585 km
Question: In case T, S and X are the only individuals sewing on committee B, the members of committee C should be:
(A) Z and Y
(B) Z and W
(C) Y and V
(D) Y and U
(E) Y and W
Rationale: Y and U Because in committee b the individuals are S and X so in committee c the individuals will be Y and U
ANSWER:D
Answer: (D) Y and U
Question: A can do a work in 12days. When he had worked for 3days, B joinedhim. If they complete the work in 3more days, in how manydays can Balone finish the work?
(A) 3 days
(B) 4 days
(C) 6 days
(D) 7 days
(E) 9 days
Rationale: sax Work done by Afar 3 days : i
J
.. Remzming war — 1
.Work done by (A + B) for 1 day :
. Work done by a for 1 day
6 days
C
Answer: (C) 6 days
Question: If below equations are true,
24 $ 6 = 64
35 $ 5 = 87
63 $ 7 = 99
Then based on similar logic what's the value of below equation
88 $ 8 = ?
(A) (8+8 = 16) (88/8 = 11)
(B) (8+8 = 16) (88/8 = 12)
(C) (8+8 = 16) (88/8 = 13)
(D) (8+8 = 16) (88/8 = 14)
(E) None of these
Rationale: Explanation:
The number on the right side is formed as (sum of digits of the 1st number)(number1/number2)
example,
24 $ 6 = 64 (2+4 = 6) (24/6 = 4)
35 $ 5 = 87 (3+5=8) (35/5 = 7)
63 $ 7 = 99 (6+3 =9) (63/7 =9)
Simillarly,
88 $ 8 = (8+8 = 16) (88/8 = 11)
Answer A
Answer: (A) (8+8 = 16) (88/8 = 11)
Question: At a supermarket, John spent 1/4 of his money on fresh fruits and vegetables, 1/3 on meat products, and 1/6 on bakery products. If he spent the remaining $6 on candy, how much did John spend at the supermarket?
(A)  $24
(B)  $80
(C)  $90
(D)  $120
(E)  $180
Rationale: Let's let T = total number of dollars spent at the supermarket. With this variable we can set up an equation and determine T.
We are given that John spent 1/4 of his money on fresh fruits and vegetables, or (1/4)T, 1/3 on meat products, or (1/3)T, and 1/6on bakery products, or (1/6)T. We are also given that he spent the remaining $6 on candy. Since we know where all his money was allocated, we can sum these values together and set the sum to T. So we have:
(1/4)T + (1/3)T + (1/6)T + 6 = T
To get rid of the fractions we can multiply the entire equation by 12, and we obtain:
3T + 4T + 2T + 72 = 12T
9T + 72 = 12T
72 = 3T
T = 24
John spent $24 at the supermarket.
Answer: A
Answer: (A)  $24
Question: Two pipes A and B can fill a tank in 20 and 30 minutes respectively. If both the pipes are used together, then how long will it take to fill the tank ?
(A) 12 min
(B) 15 min
(C) 25 min
(D) 50 min
(E) 55 min
Rationale: Part filled by A in 1 min = 1/20
Part filled by B in 1 min = 1/30
Part filled by (A + B) in 1 min =(1/20 + 1/30) = 1/12
so Both pipes can fill the tank in 12 minutes.
ANSWER:A
Answer: (A) 12 min
Question: Two numbers are less than third number by 30% and 37% respectively. How much percent is the second number less than by the first
(A) 8%
(B) 10%
(C) 9%
(D) 11%
(E) 12%
Rationale: Let the third number is x.
then first number = (100-30)% of x
= 70% of x = 7x/10
Second number is (63x/100)
Difference = 7x/10 - 63x/100 = 7x/10
So required percentage is, difference is what percent of first number
(7x/100 * 10/7x * 100 )% = 10% ANSWER :B
Answer: (B) 10%
Question: Find the unknown term 8,X,6,2,-4, -12
(A) 2
(B) 4
(C) 6
(D) 8
(E) 9
Rationale: 8,X,6,2,-4, -12
i guess each differ in d range of 2
8 - 8 = 0
8 - 6 = 2
6 - 2 = 4
2 - 6 = -4
-4 - 8 = -12
ANSWER:D
Answer: (D) 8
Question: A 25 cm wide path is to be made around a circular garden having a diameter of 4 meters. Approximate area of the path is square meters is?
(A) 3.34 sq m
(B) 3.37 sq m
(C) 3.84 sq m
(D) 7.34 sq m
(E) 3.24 sq m
Rationale: Area of the path = Area of the outer circle - Area of the inner circle
= ∏{4/2 + 25/100}2 - ∏[4/2]2
= ∏[2.252 - 22] = ∏(0.25)(4.25) { (a2 - b2
= (a - b)(a + b) }
= (3.14)(1/4)(17/4) = 53.38/16
= 3.34 sq m
Answer:A
Answer: (A) 3.34 sq m
Question: Q is a set of four distinct prime numbers. If the sum of the integers in Q is odd and the number x is a member of Q, then what is the least value that x can be?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 7
Rationale: 2 + 3 + 5 + 7 = 17 ( sum is ODD)
Least number = 2
A
Answer: (A) 2
Question: In a lottery, there are 10 prizes and 10 blanks. A lottery is drawn at random. What is the probability of getting a prize?
(A) 1/10
(B) 2/5
(C) 2/7
(D) 5/7
(E) 1/2
Rationale: Solution
P(getting a prize)	= 10 / (10+10)
‹=› 10 / 20
‹=› 1 / 2.
Answer E
Answer: (E) 1/2
Question: A cat leaps 5 leaps for every 4 leaps of a dog, but 2 leaps of the dog are equal to 3 leaps of the cat. What is the ratio of the speed of the cat to that of the dog?
(A) 5:6
(B) 3:2
(C) 4:8
(D) 1:2
(E) 7:8
Rationale: Given;
2 dog = 3 cat;
Or, dog/cat = 3/2;
Let cat's 1 leap = 2 meter and dogs 1 leap = 3 meter.
Then, ratio of speed of cat and dog = 2*5/3*4 = 5:6.''Answer: 5:6;
Answer: (A) 5:6
Question: If a man buys 50 fish for $150 and sold them for $2.5 dollars each determine his loss.
(A) $ 35
(B) $ 30
(C) $ 25
(D) $ 20
(E) $ 38
Rationale: Cost of 50 fishes = $150
Sold each fish for $2.5
So he sold 50 fishes for $(50 × 2.5) = $125
Loss = $(150 – 125) = $25
Therefore, loss = $ 25.
Answer:C
Answer: (C) $ 25
Question: A cistern 2 meters wide and 4 meters long contains water up to a depth of 1 meter 25 cm. What is the total area of the wet surface?
(A) 49
(B) 87
(C) 23
(D) 66
(E) 19
Rationale: Area of the wet surface = [2(lb + bh + lh) - lb]
= 2(lh + bh) + lb
= [2 (4 x 1.25 + 2 x 1.25) + 2 x 4]
= 23
The answer is C.
Answer: (C) 23
Question: An express traveled at an average speed of 100 km/hr, stopping for 3 min after every 75 kn. How long did it take to reach its destination 600 km from the starting point?
(A) 6 hrs 21 min
(B) 6 hrs 91 min
(C) 6 hrs 01 min
(D) 6 hrs 23 min
(E) 3 hrs 21 min
Rationale: Time taken to cover 600 km = 600/100 = 6 hrs.
Number of stoppages = 600/75 - 1 = 7
Total time of stoppages = 3 * 7 = 21 min
Hence, total time taken = 6 hrs 21 min.
Answer:A
Answer: (A) 6 hrs 21 min
Question: Train X crosses a stationary train Y in 60 seconds and a pole in 25 seconds with the same speed. The length of the train X is 300 m. What is the length of the stationary train Y?
(A) 620 m
(B) 120 m
(C) 420 m
(D) 250 m
(E) 550 m
Rationale: C
420 m
Let the length of the stationary train Y be LY
Given that length of train X, LX = 300 m
Let the speed of Train X be V.
Since the train X crosses train Y and a pole in 60 seconds and 25 seconds respectively.
=> 300/V = 25 ---> ( 1 )
(300 + LY) / V = 60 ---> ( 2 )
From (1) V = 300/25 = 12 m/sec.
From (2) (300 + LY)/12 = 60
=> 300 + LY = 60 (12) = 720
=> LY = 720 - 300 = 420 m
Length of the stationary train = 420 m
Answer: (C) 420 m
Question: Students at a school were on average 180 cm tall. The average female height was 170 cm, and the average male height was 185 cms. What was the ratio of men to women?
(A)  5:2
(B)  5:1
(C)  4:3
(D)  2:1
(E)  3:1
Rationale: We're given a few facts to work with:
1) The average height of the females is 170cm
2) The average height of the males is 185cm
3) The average of the GROUP is 180cm
We're asked for the RATIO of men to women.
W = number of Women
M = number of Men
(170W + 185M)/(W+M) = 180
170W + 185M = 180W + 180M
5M = 10W
M = 2W
M/W = 2/1
The ratio of men to women is 2 to 1.
D
Answer: (D)  2:1
Question: A boat running downstream covers a distance of 16 km in 4 hours while for covering the same distance upstream,it takes 8 hours.What is the speed of the boat in still water ?
(A) 3 km/hr
(B) 6 km/hr
(C) 8 km/hr
(D) Data inadequate
(E) None of these
Rationale: Solution
Rate downstream =(16/4) kmph = 4 kmph, Rate upstream =(16/8) = 2 kmph.
∴ Speed in still water =1/2(4+2) kmph = 3 kmph.
Answer A
Answer: (A) 3 km/hr
Question: The principal that amounts to Rs. 4913 in 3 years at 6 1/4 % per annum C.I. compounded annually, is?
(A) 288
(B) 267
(C) 200
(D) 4096
(E) 2771
Rationale: Principal = [4913 / (1 + 25/(4 * 100))3]
= 4913 * 16/17 * 16/17 * 16/17 = Rs. 4096.
Answer: D
Answer: (D) 4096
Question: A hiker walking at a constant rate of 4 kilometers per hour is passed by a cyclist travelling in the same direction along the same path at a constant rate of 24 kilometers per hour. The cyclist stops and waits for the hiker 5 minutes after passing her while the hiker continues to walk at her constant rate. How many minutes must the cyclist wait until the hiker catches up?
(A) 10
(B) 15
(C) 20
(D) 25
(E) 30
Rationale: In 5 minutes, the cyclist travels a distance of (5/60)*24 = 2 km.
The time it takes the hiker to complete this distance is 2/4 hours = 30 minutes
The cyclist needs to wait 30 - 5 = 25 minutes
The answer is D.
Answer: (D) 25
Question: On the coordinate plane , points P and O are defined by the coordinates (-1,0) and (3,3), respectively, and are connected to form a chord of a circle which also lies on the plane. If the area of the circle is (25/4) π , what are the coordinates of the center of the circle ?
(A)  (1.5,1)
(B)  (2,-5)
(C)  (0,0)
(D)  (1,1.5)
(E)  (2,2)
Rationale: Although it took me 3 mins to solve this question using all those equations, later I thought this question can be solved easily using options.
One property to keep in mind - A line passing through the centre of the circle bisects the chord (or passes from the mid point of the chord).
Now mid point of chord here is (-1+3)/2, (3+0)/2 i.e. (1,1.5) now luckily we have this in our Ans. choice. so definitely this is the ans. It also indictaes that PO is the diameter of the circle.
There can be a case when PO is not a diameter but in that case also the y-coordinate will remain same as it is the midpoint of the chord and we are moving up in the st. line to locate the centre of the circle.
If ans choices are all distinct (y cordinates) ONLY CHECK FOR Y CORDINATE and mark the ans=D
Answer: (D)  (1,1.5)
Question: There are 8 women and 9 men in a certain club. If the club is to select a committee of 2 women and 2 men, how many different such committees are possible?
(A) 120
(B) 720
(C) 1,008
(D) 1,520
(E) 1,980
Rationale: Answer is E. Can somebody tell me what answer I may have found if I had added the 8C2 and 9C2 (28+36=64)?
I'm guessing that would've been the number of 2-member committees which had men and women separately. Is that right?
C
Answer: (C) 1,008
Question: A person decided to build a house in 100days. He employed 100men in the beginning and 100 more after 25 days and completed the construction in stipulated time. If he had not employed the additional men , how many days behind schedule would it have been finished?
(A) 7
(B) 5
(C) 2
(D) 3
(E) 1
Rationale: 200 men do the rest of the work in 100-25 = 75 days
100 men can do the rest of the work in 75*200/100 = 75days
Required number of days = 75-80 = 5 days
Answer is B
Answer: (B) 5
Question: If the wheel is 14 cm then the number of revolutions to cover a distance of 1232 cm is?
(A) A)15
(B) B)10
(C) C)14
(D) D)12
(E) E)11
Rationale: 2 * 22/7 * 14 * x = 1232 => x = 14
ANSWER:C
Answer: (C) C)14
Question: If e>0, which of the following must be true?
(A) 1 < e
(B) 0 < e < 2
(C) -1 < e < 1
(D) -10 <e
(E) 1/100 < e
Rationale: All we know is that e is some positive number. Right away we can see that D must be true: if e is positive then it MUST be true that it's greater than -10. Still let's check each option.
A. 1 < e. We don't know whether the number is greater than 1, it could be a positive number less than or equal to 1. Discard.
B. 0 < e < 2. The same here: we don't know whether the number is less than 2, it could be more than or equal to 2. Discard.
C. -1 < e < 1. The same as A. Discard.
E. 1/100 <e. We don't know whether the number is greater than 1/100, it could be a positive number less than or equal to 1/100. Discard.
Answer: D.
Answer: (D) -10 <e
Question: An analyst will recommend a combination of 3 industrial stocks, 2 transportation stocks, and 2 utility stocks. If the analyst can choose from 7 industrial stocks, 4 transportation stocks, and 3 utility stocks, how many different combinations of 7 stocks are possible?
--
(A) 12
(B) 19
(C) 60
(D) 180
(E) 630
Rationale: 7C3 * 4C2 * 3C2 = 35*6*3 = 630.
Answer: E.
Answer: (E) 630
Question: If the average marks of three batches of 72, 60 and 45 students respectively is 50, 55, 60, then the average marks of all the students is
(A) 54.48
(B) 54.68
(C) 54.6
(D) 54.23
(E) None of these
Rationale: Explanation:
(72Ã—50)+(60Ã—55)+(45Ã—60) / 72+60+45
9600 / 177=54.23
Option D
Answer: (D) 54.23
Question: There r 4 prime numbers in ascending order. The multiplication of first 3 is 385 and that of last 3is 1001. what is the last number is
(A) 12
(B) 16
(C) 19
(D) 13
(E) 17
Rationale: Explanation:
abcbcd=3851001=>ad=513
abcbcd=3851001=>ad=513
So d = 13
D
Answer: (D) 13
Question: A candidate got 35% of the votes and lost to the rival by 2400 votes. How many votes were cast?
(A) 7700
(B) 8000
(C) 8300
(D) 8600
(E) 8900
Rationale: 35%-----------L
65%-----------W
------------------
30% = 2400
10% = 800
100% of the votes = 8000
Answer: B
Answer: (B) 8000
Question: If 4 tic equals 3 tacs and 6 tacs equal 4 tocs, what is the ratio of one tic to one toc?
(A) 15/2
(B) 6/5
(C) 5/6
(D) 3/10
(E) 2/1
Rationale: 4Tic=3*Tac and 6*Tac=4*Toc;
24*Tic=18*Tac and 18*Tac=12*Toc --> 24*Tic=12*Toc --> Tic/Toc=24/12=2/1.
Answer: E.
Answer: (E) 2/1
Question: A hall is 15 meters long and 10 meters wide. If the sum of the areas of the floor and the ceiling is equal to the sum of the areas of four walls, what is the volume of the hall (in cubic meters)?
(A) 600
(B) 700
(C) 800
(D) 900
(E) 1000
Rationale: 2HL + 2HW = 2LW
H = LW / (L+W)
Volume = LWH = (LW)^2 / (L+W) = 900
The answer is D.
Answer: (D) 900
Question: A heap of coconuts is divided into groups of 2, 5 and 7 and each time one coconut is left over. The least number of Coconuts in the heap is?
A. 31 B. 41 C. 51 D. 61
(A) A)31
(B) B)41
(C) C)51
(D) D)61
(E) E)71
Rationale: LCM = 70
=> 70 + 1 = 71
ANSWER:E
Answer: (E) E)71
Question: 3 buffaloes eat as much as 4 cows or 2 oxen. At a farm there are 15 buffaloes, 8 oxen and 24 cows. The fodder for these cattle is available for 24days. If 8 more cows & 9 more buffaloes are brought in, how long will the fodder last?
(A) 13
(B) 15
(C) 16
(D) 18
(E) 21
Rationale: Sol. 2 oxen = 3 buffaloes = 4 cows 8 oxen = 16 cows and 15 buffaloes = 20 cows 16 cows + 20 cows + 24 cows = 60 cows Since fodder is available for 60 cows for 24 days
So fodder will be available for (60 + 8 + 12) = 80 cows c 24x60 .0 .
for-^—=18 days.
D
Answer: (D) 18
Question: Karen places a bet with Tom that she will beat Tom in a car race by 4 miles even if Karen starts 4 minutes late. Assuming that Karen drives at an average speed of 60 mph and Tom drives at an average speed of 45 mph, how many W miles will Tom drive before Karen wins the bet?
(A) 15
(B) 18
(C) 21
(D) 24
(E) 27
Rationale: Let K and T be the speeds of Karen and Tom respectively.
t be the time that Karen will travel ----> t+4/60 will be the total time Tom will travel by the time the distance between Karen and Tom is 4 miles.
Thus, per the question , K(t) - T(t+4/60) = 4 ---> t = 7/15 hours
Thus the distance traveled by Tom when Karen is 4 miles ahead of him W: T*(t+4/60) = 45 (7/15+4/60) = 24 miles. D is the correct answer.
Answer: (D) 24
Question: What is the 50th digit to the right of the decimal point in the decimal form of 48/88?
(A) 6
(B) 7
(C) 9
(D) 11
(E) 4
Rationale: We have to use some long division. This long division allows us to get 48/88 in decimal form, which is 0.545454… where “54” is repeating.
We can see that the 1st, 3rd, 5th digit to the right of the decimal point is a 5 and that the 2nd, 4th, 6th digit to the right of the decimal point is a 4. In other words, each odd-positioned digit is a 5, and each even-positioned digit is a 4.
Then about the 50 digit to the right of the decimal point and we see that 50 is even, we know that the 50th digit is a 4.
Answer E.
Answer: (E) 4
Question: In how many ways can a supermarket manager display 5 brands of cereals in 3 spaces on a shelf?
(A) 120
(B) 30
(C) 60
(D) 40
(E) 20
Rationale: This is asking for the number of permutations, since we don't want repetitions. The number of ways is:
5P3 = 60
Ans- C
Answer: (C) 60
Question: A relay has a series of 5 circuits in a line. The even-numbered circuits are control circuits; the odd are buffer circuits. If both a control circuit and the buffer circuit immediately following it both fail in that order, then the relay fails. The probability of circuit one failing is 3/8; circuit two, 3/8; circuit three, 3/10; circuit four, 3/4; and circuit five, 2/5 .What is the probability that the relay fails?
(A) 9/80
(B) 3/10
(C) 303/800
(D) 35/80
(E) 497/800
Rationale: The relay fails when "2 and 3 fail" or "4 and 5 fail".
P(2 and 3 fail) = (3/8)*(3/10) = 9/80
P(4 and 5 fail) = (3/4)*(2/5) = 3/10
Both these cases include the cases in which all 4 circuits fail. So we need to subtract that probability once out of the sum.
P(2, 3, 4 and 5 fail) = (9/80)*(3/10) = 27/800
P(Relay fails) = 9/80 + 3/10 - 27/800 = 303/800
Answer (C)
Answer: (C) 303/800
Question: A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?
(A) 150 m
(B) 175 m
(C) 120 m
(D) 145 m
(E) 165 m
Rationale: Speed=(60 * 5/18) m/sec = (50/3) m/sec
Length of the train= (Speed x Time) = (50/3 * 9) m = 150 m.
Answer: A
Answer: (A) 150 m
Question: Rose is two years older than Bruce who is twice as old as Chris. If the total of the age of Rose, Bruce and Chris be 42 years, then how old is Bruce ?
(A) 7 years
(B) 16 years
(C) 12 years
(D) 13 years
(E) 14 years
Rationale: Let Chris's age be x years. Then, Bruce's age = 2x years.Rose's age = (2x + 2) years.
(2x + 2) + 2x + x = 42
5x = 40
x = 8
Hence, Bruce's age = 2*8 = 16 years.
Answer : B
Answer: (B) 16 years
Question: The set S has 36 different subsets each of which contains exactly two elements. How many subsets of S could contain exactly eight elements each?
(A) 27
(B) 18
(C) 16
(D) 8
(E) 9
Rationale: nC2 = 36
=> n*(n-1)/2 = 36 , by middle term factor
=> n = 9
nC3 = 9C8 = 9
So, Answer is E.
Answer: (E) 9
Question: A thief is noticed by a policeman from a distance of 200 m. The thief starts running and the policeman chases him. The thief and the policeman run at the rate of 10 km and 11 km per hour respectively. What is the distance between them after 4 minutes?
(A) 150 m
(B) 200 m
(C) 170 m
(D) 133 m
(E) 250 m
Rationale: Relative speed of the thief and policeman = 11 - 10 = 1 km/hr.
Distance covered in 6 minutes = 1/60 * 4 = 1/15 km = 67 m.
Distance between the thief and policeman = 200 - 67 = 133 m
D
Answer: (D) 133 m
Question: Find the compound interest on $800 for 1year at 10% p.a. if CI is component yearly?
(A) $40
(B) $400
(C) $840
(D) $800
(E) $80
Rationale: A = P(1 + R/100)^T
= 800(1 + 10/100)^1
= 800*21/20
=$840
CI = A-P = 840-800 = $40
Answer is A
Answer: (A) $40
Question: Given the two equations 3x + 2y = 16 and 5x + 3y = 26, by how much does r exceed s?
(A) 3
(B) 4
(C) 5
(D) 1
(E) 2
Rationale: Solve by Simultaneous Equations.
My Answer is E.
x=4
y=2
Answer: (E) 2
Question: A can do a piece of work in 20 days, B can do a piece of work in 12 days,both are working together for 3 days after A left the job,then how many days B requires to complete the remaining work?
(A) 6 Days
(B) 5 Days
(C) 3 Days
(D) 7 Days
(E) 12 Days
Rationale: First take LCM of (20,12) = 60; Total work = 60; A's one day work = 60/20 =3; B's one day work =60/12 = 5; One day work of both A+B= 3+5 = 8; Total work completed in 3 days = 8*3=24; remaining work is = 60 - 24=36; remaining work completed by B in = 36/12= 3 days.Answer =C
Answer: (C) 3 Days
Question: Klaudia can choose any two of four different candles and any 8 of 9 different flowers for a centerpiece arrangement. Given these choices, how many candle + flower groupings can she select?
(A) 54
(B) 72
(C) 96
(D) 144
(E) 432
Rationale: Klaudia can choose any two of four different candles and any 8 of 9 different flowers for a centerpiece arrangement.2 candles from 4 candles: 4C2: 6
8 flowers from 9 flowers: 9C8 : 9
So total grouping
9*6= 54.
Answer is A.
Answer: (A) 54
Question: A group of medical interns at Bohemus Medical School want to go on dates. There are 7 girls and 7 guys. Assuming girls go on dates with guys, how many possible ways can these 14 medical interns date each other?
(A) A)4640
(B) B)4740
(C) C)4840
(D) D)4940
(E) E)5040
Rationale: 1st girl can go with 7 guys
2nd girl can go with remaining 6
3rd girl can go with remaining 5 and so on
so the total ways are 7!= 5040
E should be the answer
Answer: (E) E)5040