mathewhe/aqua_rat huggingface dataset:
Question: You make a cube that is made of 10 x 10 x 10 smaller cubes which sums up to a total of 1000 smaller cubes.
Now, if someone takes one layer of cubes, how many will remain?
(A) 357
(B) 834
(C) 500
(D) 512
(E) 216
Rationale: D
512
The cube that remains will be 8 x 8 x 8. This will make a total of 512. This is because, when a layer is taken, it will be taken from all sides of the cube which will reduce the dimension be two and not one.
Answer: (D) 512
Question: Two equal sums of money were invested, one at 4% and the other at 4.5%. At the end of 7 years, the simple interest received from the latter exceeded to that received from the former by 31.50. Each sum was :
(A) 1,200
(B) 600
(C) 750
(D) 900
(E) None of these
Rationale: Difference of S.I. = √31.50
Let each sum be x. Then
x×4 1/2×7 /100−x×4×7/100=31.50
or 7⁄100x × 1⁄2 = 63⁄2
or x = 900
Answer D
Answer: (D) 900
Question: A student must answer 6 out of 10 questions on an examination. If at least 3 of the first 5 questions must be answered, how many possible combinations of 6 questions are available to the student?
(A) 150
(B) 200
(C) 210
(D) 170
(E) 180
Rationale: as there is ONLY one possiblity of choosing 6 out of 10, while choosing less than 3 in first five
choose 2 in first 5 and all 4 from later half..
ways = 5C2 = 10..
total ways = 10C4 = 210
ans = 210-10 = 200
B
Answer: (B) 200
Question: Suppose 12 monkeys take 12 minutes to eat 12 bananas. How many monkeys would it take to eat 72 bananas in 72 minutes?
(A) 9
(B) 10
(C) 11
(D) 12
(E) 13
Rationale: One monkey takes 12 min to eat 1 banana , so in 72 mins 1 monkey will eat 6 bananas , so for 72 bananas in 72 min we need 72/6 =12 monkeys
ANSWER:D
Answer: (D) 12
Question: A shipment of 8 TV sets contains 4 black and white sets and 4 color sets. If 2 TV sets are to be chosen at random from this shipment, what is the probability that at least 1 of the 2 sets chosen will be a black and white set?
(A) 1/7
(B) 11/14
(C) 5/14
(D) 11/28
(E) 13/28
Rationale: 4/8 * 3/7 = 12/56
1-(12/56) = 44/56 = 11/14
Answer B
Answer: (B) 11/14
Question: If x and y are integers and x + y = 3, which of the following must be true?
(A) If x < 0, then y > 0.
(B) x and y are consecutive integers.
(C) If x > 0, then y < 0.
(D) Both x and y are even.
(E) Both x and y are less than 5.
Rationale: In option C if x > 0,then y<0 means x is +ve and y is -ve
In option B if x < 0, then y>0 means y is +ve and x is -ve, both are same and satisfying x+y = 5.
How option A is right could you explain
Answer: (A) If x < 0, then y > 0.
Question: What is the 4 digit number whose second digit is thrice the first digit and 3rd digit is sum of 1st and 2nd and last digit is thrice the second digit.
(A) 2674
(B) 1349
(C) 3343
(D) 3678
(E) 3679
Rationale: let four digits is a,b,c&d ...so by given
b is 3a
c is 4a
d is 9a so
ans is 1349
ANSWER:B
Answer: (B) 1349
Question: Solution X is 10 percent alcohol by volume, and solution Y is 30 percent alcohol by volume. How many milliliters of solution Y must be added to 250 milliliters of solution X to create a solution that is 25 percent alcohol by volume?
(A) 250/3
(B) 750
(C) 400
(D) 480
(E) 600
Rationale: we know that X is 10% , Y is 30% and W.Avg = 25% . what does this mean with respect to W.Avg technique ?
W.Avg is 1 portion away from Y and 3 portion away from X so for every 1 portion of X we will have to add 3 portions of Y.
If X = 250 then Y = 750
ANSWER:B
Answer: (B) 750
Question: Marge has 3 pumps for filling her swimming pool. When all 3 pumps work at their maximum rates, the swimming pool is filled in 66 minutes. Pump 1's maximum rate is twice the maximum rate of pump 2 and four times the maximum rate of pump 3. How long would it take Marge to fill the pool if she used only pump 3 at its maximum rate ?
(A) 2hrs, 48mins
(B) 6hrs, 32mins
(C) 7hrs, 12mins
(D) 13hrs, 4mins
(E) 7hrs, 42mins
Rationale: The rate of pump 1 = 4x job/minute.
The rate of pump 2 = 2x job/minute.
The rate of pump 3 = x job/minute.
Given that x+2x+4x=1/66 --> x=1/462 --> (time) = (reciprocal of rate) = 462 minutes = 7 hours and 42 minutes.
Answer: E
Answer: (E) 7hrs, 42mins
Question: For any non-zero a and b that satisfy |ab| = ab and |a| = -a
|b + 4| + |ab - b| = ?
(A) a) ab - 4
(B) b) 2b - a - 4
(C) c) ab - 2b - 4
(D) d) ab - 2b + 4
(E) e) 4 - ab
Rationale: |a| = -a Suggests that 'a' is Negative
|ab| = ab Suggests that 'ab' is Positive
'ab' is Positive Suggests that 'a' and 'b' have same Sign i.e. either both positive or both negative
But since 'a' is Negative therefore 'b' is Negative too.
Since b is negative so |b - 4| = -b-4
Since ab is Positive and b is Negative so |ab - b| = ab - b
i.e. |b + 4| + |ab - b| = -b-4 + ab - b =ab - 2b - 4
Answer: Option C
Answer: (C) c) ab - 2b - 4
Question: A can finish a piece of work in 5 days. B can do it in 10 days. They work together for two days and then A goes away. In how many days will B finish the work?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
Rationale: 2/5 + (2 + x)/10 = 1 => x = 4 days
Answer: A
Answer: (A) 4
Question: Fox jeans regularly sell for $15 a pair and Pony jeans regularly sell for $18 a pair. During a sale these regular unit prices are discounted at different rates so that a total of $9 is saved by purchasing 5 pairs of jeans: 3 pairs of Fox jeans and 2 pairs of Pony jeans. If the sum of the two discounts rates is 22 percent, what is the discount rate on Pony jeans?
(A) 9%
(B) 10%
(C) 11%
(D) 12%
(E) 13%
Rationale: Let X be the percentage decrease in fox jeans
pony jeans = 22- X
(15*x/100)*3 + (18(22-X)/100)*2 = 9 ........... given
45X/100 + 792-36x/100 = 9
9x+792/100 = 9
9x+ 792 = 900
9x= 108
X = 12 = fox jeans
hence pony jeans = 22-12 = 10
ANSWER:B
Answer: (B) 10%
Question: A certain sum is invested at simple interest at 18% p.a. for two years instead of investing at 12% p.a. for the same time period. Therefore the interest received is more by Rs. 240. Find the sum?
(A) 7000
(B) 7029
(C) 2778
(D) 2800
(E) 2000
Rationale: Let the sum be Rs. x.
(x * 18 * 2)/100 - (x * 12 * 2)/100 = 240 => 36x/100 - 24x/100 =240
=> 12x/100 = 240 => x = 2000.Answer:E
Answer: (E) 2000
Question: The workforce of Company nokia is 60% female. The company hired 20 additional male workers, and as a result, the percent of female workers dropped to 50%.How many employees did the company have after hiring the additional male workers?
(A) 130
(B) 135
(C) 150
(D) 145
(E) 140
Rationale: let x be the total worker then 0.6x =female worker and 0.4x is male worker then 20 male worker added
06x/(0.4x +20) = 50/100 or 60x = 50*( 0.4x+100) = 20x+ 5000 or 40x = 5000 , x = 125
total worker = 125 +20= 145
D
Answer: (D) 145
Question: For a lottery, three numbers are drawn, each from 1 to 40. A player can win if the product of his or her three numbers is odd. Initially, the same number may be picked up to three times. Later, the rules are changed so that each number may only be picked once. Approximately how much does this reduce a person's probability of winning?
(A) 01
(B) 025
(C) 115
(D) 125
(E) 5
Rationale: (1/2)∗(1/2)∗(1/2))−((1/2)∗(19/39)∗(18/38))((1/2)∗(1/2)∗(1/2))−((1/2)∗(19/39)∗(18/38))
((1/8)−(9/78))((1/8)−(9/78))
(0.125−approx.0.1111)(0.125−approx.0.1111)
Approximately 0.010.01
ANSWER :A
Answer: (A) 01
Question: In a car company, the company made A type cars numbering 20% of B type cars. What is the number of B type of cars as a percentage of A type cars?
(A) 7%
(B) 5%
(C) 8%
(D) 16%
(E) 12%
Rationale: A type cars made in a company is 20% of B type of cars
If B type of cars=10
A type of cars=2
We are asked to find the number of B type of cars as a percentage of A type of cars
B/A=10/2=5%
Answer is B
Answer: (B) 5%
Question: If 2^(2w) = 8^(w−1), what is the value of w?
(A) 3
(B) 6
(C) 9
(D) 12
(E) 15
Rationale: 2^(2w) = 8^(w−1)
2^(2w) = 2^(3*(w−1))
2^(2w) = 2^(3w-3)
Let's equate the exponents as the bases are equal.
2w = 3w-3
w = 3
The answer is A.
Answer: (A) 3
Question: Two, trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 16 hours respectively. The ratio of their speeds is:
(A) 2 : 3
(B) 4 : 3
(C) 6 : 7
(D) 9 : 16
(E) 9 : 14
Rationale: Let the slower train have speed of 1 unit and faster train a speed of
r units of speed.
Let t = time to when the trains meet.
rt 1t
Howrah|-----------------------|----------| Patna
meet
They meet rt units from Howrah and 1t units from Patna
For the second part of the journey the fast train at speed r has 1t
unit of distance and 9 hours to do it
So 1t/r = 9
Slow train has rt units of distance at speed of 1 unit and 16 hours
to do it.
rt/1 = 16
So rt/1 16
----- = ---- giving r^2 = 16/9
1t/r 9
r = 4/3
ANSWER:B
Answer: (B) 4 : 3
Question: The jogging track in a sports complex is 528 m in circumference. Deepak and his wife start from the same point and walk in opposite directions at 4.5 km/hr and 3.75 km/hr respectively. They will meet for the first time in?
(A) 5.29 min
(B) 3.84 min
(C) 5.08 min
(D) 9.28 min
(E) 5.988 min
Rationale: Clearly, the two will meet when they are 528 m apart.
To be (4.5 + 3.75) = 8.25 km apart, they take 1 hour.
To be 528 m apart, they take (100/825 * 528/1000) hrs = (528/8250 * 60) min = 3.84 min.
Answer: B
Answer: (B) 3.84 min
Question: There are three guys who have equal number of bullets. All of them shoot 8 bullets. The remaining bullets are equal to the total number of bullets remaining is equal to the bullets each had after division. What was the original number of bullets each one had?
(A) 18
(B) 19
(C) 27
(D) 31
(E) 36
Rationale: let initially each was having x bullets
they shot 8 bullets
so 3x-24=x
x=12
so each was having 12 bullets.
total was 36.
ANSWER:E
Answer: (E) 36
Question: In a certificate by mistake a candidate gave his height as 25% more than actual height. In the interview panel, he clarified that his height was 5feet 10 inches. Find the % correction made by the candidate from his stated height to his actual height?
(A) 10
(B) 20
(C) 17.5
(D) 43
(E) 50
Rationale: His height was = 5 feet 5 inch = 10 + 60 = 70 inch. Required % correction =70*(1.25-1) = 17.5
C
Answer: (C) 17.5
Question: The length of the bridge, which a train 155 metres long and travelling at 45 km/hr can cross in 30 seconds, is:
(A) 220 m
(B) 225 m
(C) 245 m
(D) 250 m
(E) 270 m
Rationale: Let the length of the bridge:L
The equation now is L+155/12.5m/s(45km/hr or12.5m/s)=30
Solving, L =220m
ANSWER:A
Answer: (A) 220 m
Question: If x = -14/17 and y = -11/3, what is the value of the expression -2x – y^2?
(A) -1023/754
(B) 1456/514
(C) 1364/153
(D) 153/1805
(E) -1805/153
Rationale: x = -14/17 and y = -11/3
==> -2(-14/17) - (-11/3)^2 = 28/17 - 121/9 = -1805/153
Ans: E
Answer: (E) -1805/153
Question: If (6)(x^2) has four different prime factors, at most how many different prime factors does x have?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: x can have at most 4 prime factors, namely the prime factors 2 and 3, plus 2 others.
If x had more than this number of prime factors, then (6)(x^2) would have more than 4 prime factors.
The answer is D.
Answer: (D) 4
Question: In an election between two candidates, one got 55% of the total valid votes, 20% of the votes were invalid. If the total number of votes was 7000, the number of valid votes that the other candidate got, was:
(A) 2800
(B) 2700
(C) 2900
(D) 2200
(E) 2520
Rationale: E
Number of valid votes = 80% of 7000 = 5600.
Valid votes polled by other candidate = 45% of 6000
= (45/100 x 5600) = 2520.
Answer: (E) 2520
Question: The average age of 20 men in the class is 16.6 years. Five new men join and the new average becomes 15.56 years. What was the average age of five new men?
(A) 15.5
(B) 15.4
(C) 15.25
(D) 15.3
(E) 11.4
Rationale: Total age of 20 men = 16.6 x 20 = 332
Now, total age of 25 men = 389.
Total age of five men added later = 389 - 332 = 57.
Hence, the total average of five men = 57/5 = 11.4
ANSWER:E
Answer: (E) 11.4
Question: In the formula P = 3/(r+3)^3, if r is halved, then P is multiplied by
(A) 125/64
(B) 125
(C) 1/64
(D) 64/125
(E) 1/125
Rationale: Say r=2 => P1 = 3/125
when r=1; P2 = 3/64
P2 = 125/64*P1.
Answer : A
Answer: (A) 125/64
Question: If a 3-member subcommittee is to be formed from a certain 9-member committee, how many different such subcommittee are possible?
(A) 6
(B) 18
(C) 84
(D) 108
(E) 216
Rationale: 1st member can be selected in 9 ways
2nd can be selected in 8 ways
3rd can be selected in 7 ways
So total ways : 504
But to avoid the similar scenarios 504/3!=84
ANS:C
Answer: (C) 84
Question: Sam invested Rs. 15000 @ 10% per annum for one year. If the interest is compounded half-yearly, then the amount received by Sam at the end of the year will be?
(A) Rs. 16,500
(B) Rs. 16,525.50
(C) Rs. 16,537.50
(D) Rs. 18,150
(E) Rs. 19,150
Rationale: P = Rs. 15000; R = 10% p.a. = 5% per half-year; T = 1 year = 2 half-year
Amount = [15000 * (1 + 5/100)2]
= (15000 * 21/20 * 21/20) = Rs. 16537.50
ANSWER:C
Answer: (C) Rs. 16,537.50
Question: 1/2, 1/4, 1/8, 1/16, 1/32, 1/64, ....
In the sequence above each term after after the first one-half the previous term. If x is the tenth term of the sequence, then x satisfies which of the following inequalities?
(A) 0.1 < x < 1
(B) 0.01 < x < 0.1
(C) 0.001 < x < 0.01
(D) 0.0001 < x < 0.001
(E) 0.00001 < x < 0.0001
Rationale: In the Sequence notice that the sequence is just the 1/(2^n) ...
so for 1st term=1/2^1=1/2
2nd term=1/(2^2)1/4, 3rd term=1/(2^3)=1/8 and so on...
Thus the 10th term will be 1/(2^10)=1/1024
Roughly, 1/1024 can be 1/1000=0.001 but since denominator is a bit more than 1000 therefore the actual value will be a bit less than 0.001.
thus the ans will lie btw. 0.00001 and 0.0001.(E)
Answer: (E) 0.00001 < x < 0.0001
Question: A train covers a distance at a speed of 150kmph in 3 hours. To cover the same distance in 1 hours, it must travel at a speed of?
(A) 320
(B) 250
(C) 560
(D) 400
(E) 450
Rationale: Distance = 150*3 = 450km
Required speed = 450/1 =450 km/hr
Answer is E
Answer: (E) 450
Question: Two trains X and Y (80 km from each other) are running towards each other on the same track with a speed of 40km/hr. A bird starts from the train X and travels towards train Y with constant speed of 100km/hr. Once it reaches train Y, it turns and starts moving toward train X. It does this till the two trains collides with each other. Find the total distance traveled by the bird?
(A) 120
(B) 100
(C) 240
(D) 232
(E) 221
Rationale: B
100 km
Velocity of approach for the two trains = (40 + 40) km/hr
Total time the trains will take to collide = 80km/80km/hr = 1 hour
Total distance travelled by the bird = 100km/hr * 1hr = 100 km.
Answer: (B) 100
Question: A local bank that has 18 branches uses a two-digit code to represent each of its branches. The same integer can be used for both digits of a code, and a pair of two-digit numbers that are the reverse of each other (such as 17 and 71) are considered as two separate codes. What is the fewest number of different integers required for the 18 codes?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 18( 5 integers 25 codes
Rationale: Pick any two integer.
Integers: 12
Code: 11, 12, 21, 22 = 4 Codes
Add one more integer: 3
13, 31, 33, 23, 32 = 5 Codes
Add one more integer: 4
44, 14, 41, 24, 42, 34, 43 = 7 Codes
Add one more integer: 5
55, 15,51, 25,52,35,53,45,54 =9 codes
Total = 25 Codes. Enough. Answer: E
5 integers create 25 codes.
E
Answer: (E) 18( 5 integers 25 codes
Question: For what value of â€œkâ€ will the equation (2kx2 + 7kx +2)=0 have equal roots?
(A) 2/7
(B) 16/49
(C) 16/25
(D) 7/1
(E) 7/2
Rationale: for a 2nd degree equation ax2+bx_c=0 has equal roots the condition is b2-4ac =0
in the given equation
(7k)^2-4*2k*2=0
by solving this equation
we get k=0, k=16/49
ANSWER:B
Answer: (B) 16/49
Question: A train travels from station A to station B. If it travels at a speed of 100 miles per hour, it ends up reaching the station 30 minutes late. If it travels at 110 miles per hour, it reaches the station 15 minutes early. What is the amount of time that the train is scheduled to take for the journey and what is the distance between the stations?
(A) 	2 hours, 225 miles
(B) 	3 hours, 350 miles
(C) 	4 hours, 450 miles
(D) 	5 hours, 550 miles
(E) 	8 hours, 850 miles
Rationale: Let t be the usual time and x be the distance between AB. So we need to find t and Distance x. The question gives us 2 combinations of speedtime, but the distance remains the same for both condition.
Equation 1 - x= 100 (t+.5) (converted 30 mins into hr) added .5 hrs because it is late or took more time than usual.
Equation 2 - x= 110 (t-.25) subtracted .25 hrs because it is early or took less time than usual.
Now equating 12 we get 100(t+.5)=120(t-.25)
=> 10t +5 = 11t - 3
=> t=8 => t= 8 hrs.
Hence x= 100(8+.5) =>100 X 8.5 => 850 miles.
Hence correct answer E
Answer: (E) 	8 hours, 850 miles
Question: Ed throws a blue die and a red die. How many combinations are there in which the two dice do not yield the same result and the sum of the results is not 9?
(A) 10
(B) 24
(C) 26
(D) 30
(E) 36
Rationale: Total number of combination is 6*6 = 36..
Condition 1: we shouldn't get the same number... (1,1)(2,2)(3,3)(4,4)(5,5)(6,6) - 6 combinations.
condition 2: We shouldn't get the 9 as the sum (4,5)(5,4)(3,6)(6,3) - 4 combinations...
Total = 36 - 10 = 26.
ANS option C.
Answer: (C) 26
Question: A contractor undertakes to do a piece of work in 40 days. He engages 100 men at the begining and 100 more after 35 days and completes the work in stipulated time. If he had not engaged the additional men, how many days behind schedule would it be finished?
(A) 1
(B) 5
(C) 7
(D) 8
(E) 2
Rationale: Explanation:
\inline \fn_jvn [(100\times 35)+(200\times 5)] men can finish the work in 1 day
\inline \fn_jvn \therefore 4500 men can finish the work in 1 day. 100 men can finish it in \inline \fn_jvn \frac{4500}{100} = 45 days.
This is 5 days behind Schedule
Answer: B
Answer: (B) 5
Question: A goods train runs at the speed of 72 kmph and crosses a 280 m long platform in 26 seconds. What is the length of the goods train?
(A) 230 m
(B) 270m
(C) 240m
(D) 832m
(E) 270m
Rationale: Speed =	(72 x	5/18)m/sec	= 20 m/sec.
Time = 26 sec.
Let the length of the train be x metres.
Then,	x + 280/26	= 20
x + 280 = 520
x = 240.
Answer:C
Answer: (C) 240m
Question: In one year, the population, of a village increased by 10% and in the next year, it decreased by 10%. If at the end of 2nd year, the population was 7920, what was it in the beginning?
(A) 8002
(B) 8000
(C) 2869
(D) 2790
(E) 2760
Rationale: x*110/100 * 90/100 = 7920
X*0.99=7920
X=7920/0.99
=> 8000
Answer:B
Answer: (B) 8000
Question: Two cyclist start from the same places in opposite directions. One is going towards north at 10kmph and the other is going towards south 25kmph. What time will they take to be 50km apart?
(A) 1.42hr
(B) 2.22hrs
(C) 3.24hrs
(D) 5hrs
(E) 6.02hrs
Rationale: To be (10+25) km apart, they take 1 hour
To be 50 km apart, they take 1/35*50 = 1.42 hrs
Answer is A
Answer: (A) 1.42hr
Question: A started a business with 4500 and another person B joined after some period with 3000. Determine this period after B joined the business if the profit at the end of the year is divided in the ratio 2 : 1
(A) After 3 months
(B) After 4 months
(C) After 6 month
(D) After 2 1⁄2 months
(E) None of these
Rationale: Let B joined after x months.
Then, 4500 × 12 : 3000 (12 – x) = 2 : 1
Ratio of their investments
4500×12/3000(12−x)=21=21 ⇒ x = 3
Answer A
Answer: (A) After 3 months
Question: If J is the least positive integer that is divisible by every integer from 10 to 15 inclusive, then J/26 is =
(A)  1155
(B)  2310
(C)  4620
(D)  30030
(E)  60060
Rationale: The integer should be divisible by: 10, 11, 12, 13, 14 and 15, that is 5*2, 11, 3*2^2, 13, 2*7, and 3*5. The least common multiple of these integers is the product of 13, 11, 7, 5, 3 and 2^2. Then, R/26 is (13 * 11 * 7 * 5 * 3 * 2^2)/2 * 13 = 11*7*5*3*2 = 2310.
Answer: B.
Answer: (B)  2310
Question: Naomi was ordering yarn from a discount web site. If she ordered more than $50 worth of
yarn labeled “discountable”, she could take an extra 10% from the price of that yarn. Only
some of the yarn she ordered was eligible for the discount. Here is what Naomi ordered:
2 skeins at $2.50 per skein (not discountable)
8 skeins at $8.40 per skein (discountable)
7 skeins at $5.99 per skein (discountable)
Tax is 5% and shipping is 8%. How much did Naomi pay for her yarn?
(A) $116.64
(B) $216.64
(C) $316.64
(D) $416.64
(E) $516.64
Rationale: 8 x $8.40 = $67.20 (All money is rounded to hundredths at each step.)
7 x $5.99 = $41.93
$67.20 + $41.93 = $109.13 discountable
$109.13 x .10 = $10.91 (rounded)
$109.13 - $10.91 = $98.22 for discounted yarn
2 x $2.50 = $5.00 for un-discounted
$98.22 + $5.00 = $103.22 cost of yarn
$103.22 x 1.13 = $116.64 with tax and shipping
(5% + 8% = 13%)
correct answer A
Answer: (A) $116.64
Question: A rectangular tiled patio is composed of 50 square tiles. The rectangular patio will be rearranged so that there will be 2 fewer columns of tiles and 4 more rows of tiles. After the change in layout, the patio will still have 50 tiles, and it will still be rectangular. How many rows are in the tile patio before the change in layout?
(A) 5
(B) 6
(C) 10
(D) 13
(E) 28
Rationale: r*c=50 and (6+4)(7-2)=50 --> r=6 and c=7.
Answer: B.
Answer: (B) 6
Question: How many ways can Jason sit with his five friends in a row of six seats with an aisle on either side of the row, if Jason insists on sitting next to one of the aisles?
(A) 120
(B) 240
(C) 360
(D) 540
(E) 720
Rationale: Jason can select his seat in 2 Ways (two aisles)
His 1st of 4 friends have 5 seats to select =>
His 2nd of remaining 3 friends will have 4 seat to chose from...and so on
Total ways => 2*5*4*3*2*1 = 240
ANS:B
Answer: (B) 240
Question: Two trains of length 100 m and 200 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 54 kmph and 72 kmph. After how much time will the trains meet?
(A) 20/8 sec
(B) 22/7 sec
(C) 20/7 sec
(D) 20/2 sec
(E) 30/7 sec
Rationale: They are moving in opposite directions, relative speed is equal to the sum of their speeds.
Relative speed = (54 + 72)*5/18 = 7*5
=35 mps.
The time required = d/s
= 100/35
=20/7 sec.
Answer:C
Answer: (C) 20/7 sec
Question: A sum of Rs. 125000 amounts to Rs. 15500 in 4 years at the rate of simple interest. What is the rate of interest?
(A) 7%
(B) 8%
(C) 3%
(D) 6%
(E) 1%
Rationale: S.I. = (15500 - 12500) = Rs. 3000\
Rate = (100 * 3000) / (12500 * 4) = 6%
Answer: D
Answer: (D) 6%
Question: If 4 (A's capital) = 6 (B's capital) = 10 (C's capital), then out of a profit of Rs. 4650, C will receive ?
(A) Rs.980
(B) Rs.228
(C) Rs.900
(D) Rs.287
(E) Rs.921
Rationale: Let 4A = 6B = 1OC = k. Then, A = k/4, B = k/6, and C =k/10 .
A : B :C = k/4 : k/6 : k/10 = 15 : 10 : 6.
Hence, C's share (4650 * 6/31) = Rs, 900.
Answer: C
Answer: (C) Rs.900
Question: Rabin has 3 cows in his farm. If he he decide to arrange the cows in every possible combination and moved just one cow every 5 minute, how long would it taken by him ?
(A) 12 minutes
(B) 15 minutes
(C) 40 minutes
(D) 10 minutes
(E) 30 minutes
Rationale: Explanation:
Clearly, number of ways of arranging 3 cows = 3 ! = 3 x 2 x 1 = 6.
So, total time taken = 6*5 minutes = 30 minutes
Answer: E
Answer: (E) 30 minutes
Question: A rainstorm increased the amount of water stored in State J reservoirs from 160 billion gallons to 200 billion gallons. If the storm increased the amount of water in the reservoirs to 50 percent of total capacity, approximately how many billion gallons of water were the reservoirs short of total capacity prior to the storm?
(A) 240
(B) 250
(C) 260
(D) 270
(E) 300
Rationale: Let total capacity be x
we know 200 = 0.50x
x = 200/0.50 = 400
Prior to storm, we had 160 bn gallons
400-160 = 240
Answer : A
Answer: (A) 240
Question: A courtyard is 25 meter long and 16 meter board is to be paved with bricks of dimensions 20 cm by 10 cm. The total number of bricks required is
(A) 16000
(B) 18000
(C) 20000
(D) 22000
(E) 24000
Rationale: Explanation:
Number of bricks =Courtyard area/1 brick area
=(2500×160020×10)=20000
Answer: Option C
Answer: (C) 20000