mathewhe/aqua_rat huggingface dataset:
Question: If four coins are tossed, the probability of getting two heads and two tails is -.
(A) 1/2
(B) 3/5
(C) 4/3
(D) 3/8
(E) 9/8
Rationale: Explanation:
Since four coins are tossed, sample space = 24
Getting two heads and two tails can happen in six ways.
n(E) = six ways
p(E) = 6/24 = 3/8
Answer:D
Answer: (D) 3/8
Question: Two trains 300m and 400m long run at the speeds of 40 kmph and 50kmph respectively in opposite Directions on parallel tracks. The time taken to cross each other?
(A) 28sec
(B) 20sec
(C) 30sec
(D) 15sec
(E) 25sec
Rationale: Length of two Trains = 300m + 400m = 700m
Total Speed= 40 Kmph + 50 Kmph (Opposite Direction)
= 90 Kmph
Time = Distance/Speed
Time = 700/ 90
Time = 28Sec
ANSWER A
Answer: (A) 28sec
Question: Which common no should be added or substracted to 17/24 to make it 1/2
(A) 3/24
(B) 4/24
(C) 5/24
(D) 6/24
(E) 7/24
Rationale: Since 17/24>1/2..the mumber is needed to be subtracted.
let the no. subtracted be x
so..17/24-x=1/2
17/24-1/2=x
therefore..x=5/24
ANSWER:C
Answer: (C) 5/24
Question: Townville has 100 residents, and 60 of them are females. If half of Townville’s male residents are smokers, and 1/2 of the female residents are smokers, which of the following represents the total number of Townville’s residents who are NOT smokers?
(A) 48
(B) 50
(C) 52
(D) 54
(E) 56
Rationale: Number of people =100
Females = 60
men = 100-60=40
Half of the men are smoker40/2=20, that means the remaining men 40-20=20 are non smokers.
1/2 females are smoker. i.e 1/2*60 = 30
60-30=30 females are non smokers
So, total number of non smokers in the town are 20+30 =50
Answer : B
Answer: (B) 50
Question: 0.009/x=0.025. find the value of X
(A) 0.0003
(B) 0.36
(C) 0.3
(D) 36
(E) 90
Rationale: x=0.009/0.36=0.25
ANSWER:C
Answer: (C) 0.3
Question: If Log 4 (x) = 12, then log 2 (x / 4) is equal to
(A) 23
(B) 25
(C) 21
(D) 22
(E) 26
Rationale: If Log 4 (x) = 12, then
x = 412
x / 4 = 411
Hence
log 2 (x / 4) = log 2 (411)
= log 2 ((22)11)
= log 2 (222)
= 22
answer D
Answer: (D) 22
Question: A person incurs 10% loss by selling a laptop for $900. At what price should the watch be sold to earn 10% profit?
(A) 1200
(B) 1000
(C) 1100
(D) 1050
(E) 1250
Rationale: Let the new S.P. = x
then (100-loss%): (1st S.P.) = (100+gain%): (2nd S.P.)
(100-10)/900 = (100+10)/x
x=110*900/90 = 1100
new price = $1100
correct option is C
Answer: (C) 1100
Question: Two plates and one cup costs $27. Three plates and four cups cost $58. Find the cost of a cup.
(A) 8
(B) 7
(C) 10
(D) 5
(E) 9.5
Rationale: Let cost of 1 plate = x, let cost of 1 cup = y
2x + y = 27
y = 27 - 2x
Again,
3x + 4y = 51
3x + 4(27 - 2x) = 58
3x + 108 - 8x = 58
3x + 108 = 58 + 8x
3x + 50 = 8x
50 = 5x
10 = x
Now plug x into initial equation:
2x + y = 27
2(10) + y = 27
20 + y = 27
y = 7
Answer: B
Answer: (B) 7
Question: Today Joelle opened an interest-bearing savings account and deposited $6,000. If the annual interest rate is 5 percent compounded interest, and she neither deposits nor withdraws money for exactly 2 years, how much money will she have in the account?
(A) $6715
(B) $5615
(C) $6415
(D) $6615
(E) $6315
Rationale: Interest for 1st year = 6000*5/100 = 300
Interest for 2nd year = 6300 *5/100 = 315
Total =6000+300+315 = 6615
Answer : D
Answer: (D) $6615
Question: A trader marked the price of a car 20% above the cost price and allowed the purchaser 5% discount on the marked price there by gained Rs.8400. Find the cost price of the car?
(A) 1028
(B) 1026
(C) 1023
(D) 1029
(E) 1021
Rationale: Given that, the question paper consists of five problems. For each problem, one or two or three or none of the choices can be attempted.
Hence, the required number of ways = 45 - 1.
= 210 - 1 = 1024 - 1 = 1023
Answer: C
Answer: (C) 1023
Question: loga (ab) = x, then log b (ab) is :
(A) 1/x
(B) x/ (x+1)
(C) x/(1-x)
(D) x/(x-1)
(E) x/(x-2)
Rationale: loga (ab) = x => log b/ log a = x => (log a + log b)/ log a = x
1+ (log b/ log a) = x => log b/ log a = x-1
log a/ log b = 1/ (x-1) => 1+ (log a/ log b) = 1 + 1/ (x-1)
(log b/ log b) + (log a/ log b) = x/ (x-1) => (log b + log a)/ log b = x/ (x-1)
=>log (ab)/ log b = x/(x-1) => logb (ab) = x/(x-1)
ANSWER:D
Answer: (D) x/(x-1)
Question: A certain school principal must choose 5 students to attend a field trip out of a group of 9 students. In addition, out of the 5 chosen students, the principal must select a note-taker and a treasurer. How many different ways are there for the principal to select the 5 students and then select the treasurer and the note-taker?
(A) 1,260
(B) 2,520
(C) 5,040
(D) 6,020
(E) 10,080
Rationale: 5 students can be selected out of 9 students in 9C5 ways.
out of the remaining 5 students,Note taker can be chosen in 5 ways.
Finally only 4 students remain from which we can choose a treasurer in 4 ways.
Total number of ways = 126 * 5 *4 = 2520
correct answer - B
Answer: (B) 2,520
Question: A train covers a distance of 18 km in 10 min. If it takes 9 sec to pass a telegraph post, then the length of the train is?
(A) 120m
(B) 180m
(C) 270m
(D) 220m
(E) 280m
Rationale: Speed = (18/10 * 60) km/hr = (108 * 5/18) m/sec = 30 m/sec.
Length of the train = 30 * 9 = 270 m.
ANSWER:C
Answer: (C) 270m
Question: If A's salary is 20% less than B's salary, by how much percent is B's salary more than A's?
(A) 5%
(B) 10%
(C) 15%
(D) 25%
(E) None
Rationale: Solution
Required percentage
‹=› [20 / (100 - 20) x 100]%
‹=› 25%
Answer D
Answer: (D) 25%
Question: what is the ratio of two no. 5xy and 8xy.
(A) 2:5
(B) 3:4
(C) 5:8
(D) 2:3
(E) 1:2
Rationale: 5xy/8xy
=5:8
answer C
Answer: (C) 5:8
Question: Alfred buys an old scooter for $4700 and spends $600 on its repairs. If he sells the scooter for $5800, his gain percent is?
(A) 5.45%
(B) 6.23%
(C) 7%
(D) 9.43%
(E) 10%
Rationale: C.P. = 4700+600 = $5300
S.P. = $5800
Gain = 5800-5300 = $500
Gain% = 500/5300 * 100 = 9.43%
Answer is D
Answer: (D) 9.43%
Question: A committee has 5 men and 6 women. What are the number of ways of selecting 2 men and 3 women from the given committee?
(A) 127
(B) 200
(C) 882
(D) 272
(E) 323
Rationale: The number of ways to select two men and three women
= ⁵C₂ * ⁶C₃
= (5 *4 )/(2 * 1) * (6 * 5 * 4)/(3 * 2)
= 200
Answer: B
Answer: (B) 200
Question: If there is an equal probability of a child being born a boy or a girl, what is the probability that a couple who have 8 children have two children of the same sex and one of the opposite sex?
(A) 1/3
(B) 2/3
(C) 1/4
(D) 1/16
(E) 3/5
Rationale: No of ways of selecting a gender - 2C1
No of ways of selecting any 2 children out of 8 = 8C2
Total possible outcomes - 2^8 (each child can be either a girl or a boy)
Probability=2C1*8C2/2^8= 2*8/2*2*2*2*2*2*2*2=16/256=1/16
Ans=D
Answer: (D) 1/16
Question: A man goes from A to B at a speed of 20 kmph and comes back to A at a speed of 30 kmph. Find his average speed for the entire journey?
(A) 30 kmph
(B) 38 kmph
(C) 24 kmph
(D) 34 kmph
(E) 04 kmph
Rationale: Distance from A and B be 'd'
Average Speed = total distance/total time
Average Speed = (2d)/[(d/20) + (d/30)]
= (2d)/[5d/60) => 34 kmph.
ANSWER:D
Answer: (D) 34 kmph
Question: If P(A) = 2/5 and P (B) = 2/5, find P (A n B) if A and B are independent events.
(A) 7/25
(B) 4/25
(C) 8/25
(D) 2/13
(E) 3/17
Rationale: P (A n B) = P(A) . P(B)
P (A n B) = 2/5 . 2/5
P (A n B) = 4/25.
B
Answer: (B) 4/25
Question: The average weight of a group of boys is 30 kg. After a boy of weight 35 kg joins the group, the average weight of the group goes up by 1 kg. Find the number of boys in the group originally ?
(A) 7
(B) 6
(C) 4
(D) 8
(E) 9
Rationale: Let the number of boys in the group originally be x.
Total weight of the boys = 30x
After the boy weighing 35 kg joins the group, total weight of boys = 30x + 35
So 30x + 35 + 31(x + 1) = > x = 4.
Answer: C
Answer: (C) 4
Question: Which of the following has the most number of divisors?
(A) 99
(B) 101
(C) 176
(D) 182
(E) 107
Rationale: 99 = 1 x 3 x 3 x 11
101 = 1 x 101
176 = 1 x 2 x 2 x 2 x 2 x 11
182 = 1 x 2 x 7 x 13
So, divisors of 99 are 1, 3, 9, 11, 33, .99
Divisors of 101 are 1 and 101
Divisors of 176 are 1, 2, 4, 8, 11, 16, 22, 44, 88 and 176
Divisors of 182 are 1, 2, 7, 13, 14, 26, 91 and 182.
Answer: Option C
Hence, 176 has the most number of divisors.
Answer: (C) 176
Question: If two balls are randomly selected from a green urn containing 4 black and 4 white balls and placed into a yellow urn initially containing 5 black and 3 white balls. What is the probability that the yellow urn will contain an equal number of black and white balls after the change?
(A) A.3/14
(B) B.4/9
(C) C.5/9
(D) D.1/3
(E) E.1/9
Rationale: To have equal number of black and white balls, the yellow urn must have 5 black and 5 white balls. So the balls we select out of the green urn must be both white.
Probability (first ball is white) = 4/8
Probability(second ball is white) = 3/7
Probability (both balls are white) = (4/8)*(3/7) = 3/14
Answer A
Answer: (A) A.3/14
Question: A reduction of 30% in the price of salt enables a lady to obtain 10kgs more for Rs.100, find the original price per kg?
(A) 2.8
(B) 2.3
(C) 2.5
(D) 2.1
(E) 4.3
Rationale: 100*(30/100) = 30 --- 10
? --- 1 => Rs.3
100 --- 70
? --- 3 => Rs.4.3
Answer: E
Answer: (E) 4.3
Question: In a committee there are 15 men and 10 women. If three members are selected randomly then what is the probability that 1 women and 2 men are selected?
(A) 20/35
(B) 21/31
(C) 21/46
(D) 11/21
(E) 11/23
Rationale: Let S be the sample space and E be the event of selecting 1 girl and 2 boys.
Then, n(S)	= Number ways of selecting 3 students out of 25
= 25C3 `
=	(25 x 24 x 23)
(3 x 2 x 1)
= 2300.
n(E)	= (10C1 x 15C2)
= 10 x	(15 x 14)
(2 x 1)
= 1050.
P(E) =	n(E)	=	1050	= 21/46
n(S)	2300
C
Answer: (C) 21/46
Question: For which of the following values of s is (70+s)/s an integer?
(A) 3
(B) 4
(C) 9
(D) 11
(E) 70
Rationale: This problem has to be solved by checking the options
(70 + s)/s
For this entity to be an integer, 50 + s should be divisible by s
Option A: 73/3 - Not an Integer
Option B: 74/4 - Not an Integer
Option C: 79/9 - Not an integer
Option D: 81/11 - Not an integer
Option E - 140/70 - Integer
Correct Option: E
Answer: (E) 70
Question: What is the greatest number of four digits which is divisible by 15, 25, 40 and 75 ?
(A) 9800
(B) 9600
(C) 9400
(D) 9500
(E) 9200
Rationale: Greatest number of four digits = 9999
LCM of 15, 25, 40 and 75 = 600
9999 ÷ 600 = 16, remainder = 399
Hence, greatest number of four digits which is divisible by 15, 25, 40 and 75
= 9999 - 399 = 9600
answer :B
Answer: (B) 9600
Question: A, B and C started a partnership business by investing Rs.24000, Rs.32000, Rs.36000 respectively. At the end of the year , the profit were distributed among them. If C's share of profit is 36000, What is the total profit?
(A) 70000
(B) 60000
(C) 80000
(D) 92000
(E) 50000
Rationale: A:B:C =24000:32000:36000
=6:8:9
Let total profit =p
Then pÃ—9/23=36000
p=(36000Ã—23)/9=92000
Answer is D.
Answer: (D) 92000
Question: The sum of two numbers is 8 and the sum of their squares is 120. Find the product of the two numbers.
(A) 25
(B) 24
(C) 23
(D) 21
(E) 28
Rationale: Let a and b be the two numbers(a+b)^2=a^2+2ab+b^2Given (a+b)=8 a^2+b^2=120So, 8^2=120+2ab2ab=120-642ab=56ab=28Ans E
Answer: (E) 28
Question: In Arun's opinion, his weight is greater than 65 kg but leas than 72 kg. His brother does 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 of them are correct in their estimation, what is the average of diferent probable weights of Arun ?
(A) 16.5 kg
(B) 66.5 kg
(C) 26.5 kg
(D) 56.5 kg
(E) 86.5 kg
Rationale: Let Arun's weight be 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 and 67.
Required average = (66 + 67) / 2 = 66.5 kg
Answer: B
Answer: (B) 66.5 kg
Question: What will the ratio of simple interest earned by certain amount at the same rate of interest for 12 years and that for 10 years.
(A) 6:5
(B) 2:3
(C) 2:5
(D) 4:3
(E) None of these
Rationale: Explanation:
Let the principal be P and rate be R
then
ratio = [(P∗R∗12/100) /(P∗R∗10/100)]
=12PR /10PR=6:5
Option A
Answer: (A) 6:5
Question: The roots of the equation ax2 + 3x + 6 = 0 will be reciprocal to each other if the value of a is
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: Explanation :
If roots of ax2 + bx + c = 0 are α and ß are roots then
=> α + ß = b/a
and α × ß = c/a .
Now α = 1/ß.
Then α × ß = α and 1/ß × ß = 1 .
=> c/a = 1
i.e. c = a.
Here, c = 6, so
a = 6.
Answer : D
Answer: (D) 6
Question: A BUS is running at a speed of 40 km/hr and it crosses a post in 18 seconds. What is the length of the BUS?
(A) metres
(B) metres
(C) metres
(D) metres
(E) metres
Rationale: Explanation:
Speed of the BUS , v = 40 km/hr = 40000/3600 m/s = 400/36 m/s
Time taken to cross, t = 18 s
Distance Covered, d = vt = (400/36)× 18 = 200 m
Distance covered is equal to the length of the BUS = 200 m
Answer: Option C
Answer: (C) metres
Question: 5% of men have unlisted phone numbers and 4% of women have unlisted phone numbers. Population ratio of men : women in the city of gpuzzles is 4:3. If we select randomly 100 people from the phone directory, Can you tell us how many people selected will definitely have unlisted phone numbers?
(A) 0%
(B) 1%
(C) 2%
(D) 3%
(E) 4%
Rationale: Solution:
0%
Explanation:
In the number is in the phone directory, it means the number is listed and therefore if we pick any number from phone directory than number is surely listed.
Answer A
Answer: (A) 0%
Question: The cost price of 20 books is the same as the selling price of ’X’ books. If the profit is 32%, then the value of X is ?
(A) 25
(B) 18
(C) 11.9
(D) 15
(E) 14
Rationale: let S.P. of X books = Rs 100 = C.P. of 20 books
Therefore, C.P. of one book = Rs 6.4
Profit = 32 %
Therefore, S.P of one book = 8.4
S.P of X articles = 8.4 X
8.4 X = 100 => X = 11.9
ANSWER:C
Answer: (C) 11.9
Question: In a triangle, one side is 6 Cm and another side is 9 Cm. which of the following can be the perimeter of the triangle?
(A) 18.
(B) 25.
(C) 30.
(D) 32.
(E) 34.
Rationale: Given : one side is 6 Cm and another side is 9 Cm. So the 3rd side will be > 3 and < 15.
Thus the perimeter will be : 18 < perimeter < 30.
Only option satisfying this condition is 25.
Hence B.
Answer: (B) 25.
Question: The first flight out of Phoenix airport had a late departure. If the next three flights departed on-time, how many subsequent flights need to depart from Phoenix on-time, for the airport's on-time departure rate to be higher than 60%?
(A) 5
(B) 4
(C) 6
(D) 8
(E) 7
Rationale: We need on-time departure rate to be higher than 6/10, so it should be at least 7/11, which means that 7 out of 11 flights must depart on time. Since for now 3 out of 4 flights departed on time then 7-3=4 subsequent flights need to depart on-time.
Answer: B
Answer: (B) 4
Question: There has been successive increases of 30% and then 20% in the price of gas from the previous month. By what percentage should a driver reduce gas consumption so that the expenditure does not change?
(A) 20%
(B) 24%
(C) 28%
(D) 32%
(E) 36%
Rationale: Let P be the original price per unit of gas.
Let x be the original gas consumption.
Let y be the reduced gas consumption.
y*1.2*1.3*P = x*P
y = x / (1.2*1.3) which is about 0.64x which is a decrease of about 36%.
The answer is E.
Answer: (E) 36%
Question: If population of certain city increases at the rate of 5%. If population in 1981 was 138915, then population in 1978 was?
(A) 120000
(B) 120002
(C) 120082
(D) 120028
(E) 120039
Rationale: X * (105/100) * (105/100) * (105/100) = 138915
X = 138915/1.157625
X = 120000
Answer: A
Answer: (A) 120000
Question: In ΔPQS above, if PQ =6 and PS = 7, then
(A)  9/4
(B)  12/5
(C)  16/5
(D)  15/4
(E) 21/4
Rationale: there are two ways to calculate area of PQS. area remains same, so both are equal.
6*7/2 = PR*8/2
PR = 21/4
E
Answer: (E) 21/4
Question: The famous church in the city of Kumbakonnam has a big clock tower and is said to be over 300 years old. Every Monday 10.00 A M the clock is set by Antony, doing service in the church. The Clock loses 6 mins every hour. What will be the actual time when the faulty clock shows 3 P.M on Friday?
(A) 2.19
(B) 2.12
(C) 2.13
(D) 2.11
(E) 2.1
Rationale: Total time passed in the faulty clock = Monday 10 am to Friday 3 pm = 24 x 4 + 5 hours = 96 and 5 hours = 101 hrs
54 min in the faulty clock = 60 minutes of the correct clock
101 hrs in the faulcty clock = ?
10154×6010154×60 = 112.2 Hrs.
96 Hrs + 16.2 Hrs
Friday 10 am + 16 hrs = Saturday 2am
0.2 x 60 min = 12 min
So Saturday 2.12 min AM
Answer:B
Answer: (B) 2.12
Question: Three investors, A, B, and C, divide the profits from a business enterprise in the ratio of 5 : 7 : 8, respectively. If investor A earned $ 2,500, how much money did investors B and C earn in total?
(A) $4,000
(B) $4,900
(C) $7,500
(D) $9,500
(E) $10,500
Rationale: Let profit for A = 5x
profit for B = 7x
profit for C = 8x
Investor A earned = 2500
5x = 2500=>x=500
Total profit for B and C = 7x+ 8x = 15x
Therefore , 15x = 15*500 = 7,500
Answer C
Answer: (C) $7,500
Question: The average of 11 results is 50, if the average of first six results is 49 and that of the last six is 52. Find the sixth result?
(A) 46
(B) 56
(C) 66
(D) 76
(E) 74
Rationale: 1 to 11 = 11 * 50 = 550
1 to 6 = 6 * 49 = 294
6 to 11 = 6 * 52 = 312
6th = 294 + 312 – 550 = 56
Answer:B
Answer: (B) 56
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) 10
(B) 14
(C) 15
(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: Find the average of all prime numbers between 50 and 70
(A) 90
(B) 45
(C) 60
(D) 90
(E) 26
Rationale: Prime numbers between 50 and 70 are 53, 59, 61, 67
Required average = (53+ 59+ 61+ 67)/4 = 240/4 = 60
Answer is C
Answer: (C) 60
Question: A triangle marked A,B and C on its three sides . Three colors, grey, violet, and purple are used to paint the three sides of the triangle. If the adjacent faces are painted with the different colors, in how many ways can the triangle sides be painted?
(A) 3
(B) 8
(C) 6
(D) 12
(E) 36
Rationale: If the base of the triangle is grey, then in order the adjacent faces to be painted with the different colors . Then 2 sides can be painted in Violet-Purple-Violet-Purple OR Purple-Violet- Purple-Violet (2 options).
But we can have the base painted in either of the three colors, thus the total number of ways to paint the triangle is 3*1=3.
Answer: A.
Answer: (A) 3
Question: What is the greatest integer m for which the number 30!/10^m is an integer?
(A) 7
(B) 8
(C) 9
(D) 10
(E) 11
Rationale: 10^m = 2^m*5^m.
Let's figure out how many 5's are in the prime factorization of 30!
The multiples of 5 are: 5, 10, 15, 20, 5*5, 30.
Thus 5^7 will divide 30! but 5^8 will not.
Clearly 2^7 will divide 30!
So m=7 is the largest possible integer.
The answer is A.
Answer: (A) 7
Question: To get to a business meeting, John drove m miles in h hours, and arrived 1/2 hour early. At what rate should he have driven to arrive exactly on time?
(A) m/2h
(B) 2m/(2h+1)
(C) 2m/(2h-1)
(D) 2m-h/2h
(E) none of these
Rationale: m miles in h - 1/2 = (2h - 1)/2 hours
=> 2m/(2h - 1) miles per hours
ANSWER:C
Answer: (C) 2m/(2h-1)
Question: A train passes a station platform in 36 seconds and a man standing on the platform in 22 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
(A) 37
(B) 240
(C) 210
(D) 267
(E) 211
Rationale: Speed = (54 * 5/18) m/sec = 15 m/sec. Length of the train = (15 x 22)m = 330 m. Let the length of the platform be x meters. Then, (x + 330)/36 = 15 ==> x + 330 = 540 ==> x = 210 m.Answer: C
Answer: (C) 210
Question: An outlet pipe empties a tank which is full in 10 hours. If the inlet pipe is kept open, which lets water in at the rate of 4 litres/min then outlet pipe would take 6 hours longer. Find the capacity of the tank.
(A) 8600 litres
(B) 6400 litres
(C) 12800 litres
(D) 11200 litres
(E) 13200 litres
Rationale: Let the rate of outlet pipe be x liters/hour;
Rate of inlet pipe is 4 litres/min, or 4*60 = 240 liters/hour;
Net outflow rate when both pipes operate would be x-240 liters/hour.
Capacity of the tank = x*10 hours = (x-240)*(10+6) hours
10x=(x-240)*16 --> x=640 --> capacity = 10x = 6400 liters.
Answer: B.
Answer: (B) 6400 litres
Question: What decimal of an hour is a second?
(A) .0025
(B) .0256
(C) .00027
(D) .000126
(E) None
Rationale: Solution
Required decimal	= 1/ 60 x 60
= 1/ 3600
= .00027.
Answer C
Answer: (C) .00027
Question: A bus started its journey from Chennai and reached Mumbai in 50 min with its average speed of 60 km/hr. If the average speed of the bus is increased by 6 km/hr, how much time will it take to cover the same distance?
(A) 45 min.
(B) 55 min.
(C) 65 min.
(D) 60 min.
(E) 50 min.
Rationale: Sol. Distance between Mumbai and Pune=(60*50)/60=50
Average speed of the bus is increased by 6 km/hr then the
speed of the bus = 66 km/hr
Required time = 50*66/60 = 55min.
B
Answer: (B) 55 min.
Question: What will be the income tax payable by a person getting a taxable income of Rs. 30,000 during the year if the first Rs. 18000 is not taxable and the tax rates arc 25% of the next Rs. 25000 ?
(A) Rs. 3000
(B) Rs. 3250
(C) Rs. 3500
(D) Rs. 3750
(E) None of these
Rationale: T.I.=30,000, N.T.I.=18000
Taxable 12000, Income Tax = 25% of Taxable Income
= 1/4 ×: 12000 = RS.3000
Answer: A.
Answer: (A) Rs. 3000
Question: The equation w = 2y2 + 5y - 17, describes a parabola in the xy coordinate plane. If line l, with slope of 3, intersects the parabola in the upper-left quadrant at w = -5, the equation for l is
(A) + y + 15 = 0
(B) - 3x - 11 = 0
(C) + y - 16.5 = 0
(D) - y - 7 = 0
(E) + y + 13.5 = 0
Rationale: Is optionC: -3w + y -6.5= 0=C
Answer: (C) + y - 16.5 = 0
Question: Three bells chime at intervals of 18 min., 24 min. and 32 min. respectively. At a certain time they begin together. What length J of time will elapse before they chime together again?
(A) 2 hr. and 24 min.
(B) 4 hr. and 48 min.
(C) 1 hr. and 36 min.
(D) 5 hr.
(E) 2 hr.
Rationale: It should be simple. All the three bells will chime again together whenver their time intervals intersect eachother.
So the LCM of the three time intervals (18, 24,32) would be the answer.
LCM (18, 24, 32) J= 288 => 4 hours 48 mins.B
Answer: (B) 4 hr. and 48 min.
Question: Two pipes P and Q can fill a cistern in 10 and 15 minutes respectively. Both are opened together, but at the end of 4 minutes the first is turned off. How many more minutes will it take for the cistern to fill after the first pipe is turned off?
(A) 3.5
(B) 4
(C) 4.5
(D) 5
(E) 5.5
Rationale: Let x be the total time it takes for the cistern to fill.
4/10 + x/15 = 1
x/15 = 3/5
x = 9
After the first pipe is turned off, it takes 5 more minutes to fill the cistern.
The answer is D.
Answer: (D) 5
Question: If n is an integer greater than 7, which of the following must be divisible by 3 ?
(A) n(n + 1)(n – 4)
(B) n(n + 5)(n – 6)
(C) n(n + 2)(n – 1)
(D) n(n + 3)(n – 5)
(E) n(n + 5)(n – 6)
Rationale: If n= 8 then n+1 is divisible by 3
A
Answer: (A) n(n + 1)(n – 4)
Question: Two trains of equal length, running with the speeds of 60 and 100 kmph, take 50 seconds to cross each other while they are running in the same direction. What time will they take to cross each other if they are running in opposite directions?
(A) 10
(B) 6.25
(C) 7.35
(D) 2.62
(E) 2.28
Rationale: RS = 60 -40 = 20 * 5/18 = 100/18
T = 50
D = 50 * 100/18 = 2500/9
RS = 60 + 100 = 160 * 5/18
T = 2500/9 * 18/800= 6.25 sec.Answer: B
Answer: (B) 6.25
Question: The length of the bridge, which a train 120 meters long and travelling at 45 km/hr can cross in 30 seconds, is?
(A) 266
(B) 288
(C) 245
(D) 255
(E) 232
Rationale: Speed = (45 * 5/18) m/sec = (25/2) m/sec. Time = 30 sec. Let the length of bridge be x meters. Then, (120 + X)/30 = 25/2 ==> 2(120 + X) = 750 ==> X
= 255 m.
Answer:D
Answer: (D) 255