mathewhe/aqua_rat huggingface dataset:
Question: A fruit-salad mixture consists of apples, peaches, and grapes in the ratio 4:5:2, respectively, by weight. If 44 pounds of the mixture is prepared, the mixture includes how many more pounds of apples than grapes?
(A) 15
(B) 12
(C) 8
(D) 6
(E) 4
Rationale: We can first set up our ratio using variable multipliers. We are given that a fruit-salad mixture consists of apples, peaches, and grapes, in the ratio of 4:5:2, respectively, by weight. Thus, we can say:
apples : peaches : grapes = 4x : 5x : 2x
We are given that 39 pounds of the mixture is prepared so we can set up the following question and determine a value for x:
4x + 5x + 2x = 44
11x = 44
x = 4
Now we can determine the number of pounds of apples and of grapes.
pounds of grapes = (2)(4) = 8
pounds of apples = (4)(4) = 16
Thus we know that there are 16 – 8 = 8 more pounds of apples than grapes.
Answer is C.
Answer: (C) 8
Question: If 13x + < 2z and z + 3 = 5y2 then
(A) x is necessarily less than y
(B) x is necessarily greater than y
(C) x is necessarily equal to y
(D) None of the above is necessarily true
(E) Cannot be determined
Rationale: Explanation :
=> 13x + 1 < 2z and z + 3 = 5y2
=> 13x + 1 < 2(5y2 - 3).
=> 13x + 1 < 10y2 - 6.
=> 13x + 7< 10y2 , put x = 1
20 < 10y2 => y2 > 2
y2 > √2 => (y2 - 2)> 0.
Answer : D
Answer: (D) None of the above is necessarily true
Question: An electric motor makes 3,600 revolutions per minutes. How many degrees does it rotate in one second?
(A) 18.000 d/sec
(B) 28.000 d/sec
(C) 38.000 d/sec
(D) 21.600 d/sec
(E) 35.000 d/sec
Rationale: 3600 revolutions / minute
= 3600*360 degrees / 60 seconds
= 21600 degrees / second
D
Answer: (D) 21.600 d/sec
Question: When positive integer x is divided by 11, the quotient is y and the remainder is 4. When 2x is divided by 6, the quotient is 3y and the remainder is 1. What is the value of 7y – x ?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: (1) x = 11y + 4
(2) 2x = 18y + 1
Let's subtract equation (1) from equation (2).
7y - 3 = x
7y - x = 3
The answer is C.
Answer: (C) 3
Question: Because of the economic slowdown, a multinational company curtailed some of the allowances of its employees. John, the marketing manager of the company whose monthly salary has been reduced to Rs.42,000 is unable to cut more on his expenditure. He finds that there is a deficit of Rs.2,000 between his earning and expenses in the first month. This deficit, because of inflationary pressure, will keep on increasing by Rs.500 every month. John has a saving of Rs 60,000 which will be used to fill the deficit. After his savings get exhausted, John would start borrowing from his friends. How soon will he start borrowing?
(A) 1st months
(B) 10th months
(C) 11th months
(D) 12th months
(E) 13th months
Rationale: Let the Rashid 's savings will last till 'nn' months.
⇒n2[2×2000+(n−1)500]=60,000⇒n2[2×2000+(n−1)500]=60,000
[Expenditure every month increases by 500 rupees]
⇒n2+7n−200=0⇒n2+7n−200=0
n=12.38n=12.38
⇒ Rashid after Kartik's mother asked him to get the vegetables, milk and butter from the market and gave him the money in the denominator of 1 Rupee, 2 Rupee and 5 Rupee coins.
Kartik first goes to the grocery shop to buy vegetables. At the grocery shop he gives half of his 5 Rupee coins in return receives the same number of 1 Rupee coins.
Next he goes to the dairy shop to buy milk and butter and gives all 2 Rupee coins and in return get thirty 5 Rupee coins, which increase the number of five rupee coins by 75% more than the original number.
If the number of 1 rupee coins now is 50, the number of 1 rupee and 5 rupee coins originally were will start borrowing money from his friends.
E
Answer: (E) 13th months
Question: A bag contains 4 black, 5 yellow and 6 green balls. Three balls are drawn at random from the bag. What is the probability that all of them are yellow?
(A) 2/91
(B) 1/81
(C) 1/8
(D) 2/81
(E) 3/81
Rationale: Total number of balls = 4 + 5 + 6 = 15
Let S be the sample space.
n(S) = Total number of ways of drawing 3 balls out of 15 = 15C3
Let E = Event of drawing 3 balls, all of them are yellow.
n(E) = Number of ways of drawing 3 balls, all of them are yellow
= Number of ways of drawing 3 balls from the total 5 = 5C3
(∵ there are 5 yellow balls in the total balls)
P(E) = n(E)/n(S)
=5C3 /15C3=5C2 / 15C3 [∵ nCr = nC(n - r). So 5C3 = 5C2. Applying this for the ease of calculation]
=(5×42×1)/(15×14×13/3×2×1)=5×4/(15×14×13/3)=5×4/5×14×13=4/14×13=2/7×13=2/91
Answer is A
Answer: (A) 2/91
Question: In a certain store, the profit is 350% of the cost. If the cost increases by 25% but the selling price remains constant, approximately what percentage of the selling price is the profit?
(A) 72.2%
(B) 70%
(C) 100%
(D) 250%
(E) 120%
Rationale: Let C.P. = Rs. 100. Then, profit = Rs. 320, S.P. = Rs. 450
New C.P. = 125% of Rs. 100 = Rs. 125.
New S.P. = Rs. 420
Profit = 450 - 125 = Rs. 325
Required percentage = 295/420 * 100 = 72.2%
ANSWER:A
Answer: (A) 72.2%
Question: The Coen family consists of a father, a mother, two children and a dog. A photographer is about to take the family's picture. How many different arrangements (of standing in a row) does the photographer have, if it is known that the father insists of standing by his woman, as the song says?
(A) 12
(B) 24
(C) 48
(D) 60
(E) 120
Rationale: We need to find the number of arrangements of Father, Mother, Child-1, Child-2, and a Dog, so that F and M are always together.
Consider F and M to be one unit, then we would have total of four units: {FM}, {C1}, {C2}, {D}. The number of arrangements of these four units is 4!, but F and M within their unit can be arranged in 2 ways: {FM} or {MF}, so total number of arrangements is 4!*2=48.
Answer: C.
Answer: (C) 48
Question: A cistern 7m long and 4 m wide contains water up to a depth of 1 m 25 cm. The total area of the wet surface is:
(A) 49 m2
(B) 50 m2
(C) 53.5 m2
(D) 55.5 m2
(E) 57 m2
Rationale: Area of the wet surface	= [2(lb + bh + lh) - lb]
= 2(bh + lh) + lb
= [2 (4 x 1.25 + 7 x 1.25) + 7 x 4] m2
= 55.5 m2.
Answer: Option D
Answer: (D) 55.5 m2
Question: A man has Rs. 384 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?
(A) 90
(B) 70
(C) 72
(D) 80
(E) 60
Rationale: Let number of notes of each denomination be x.
Then x + 5x + 10x = 384
16x = 384
x = 24.
Hence, total number of notes = 3x = 72.
Answer is C.
Answer: (C) 72
Question: What is the divisor? The dividend is 76, the remainder is 8, the quotient is 4
(A) 32
(B) 48
(C) 67
(D) 17
(E) 26
Rationale: Divisor= Dividend - Remainder divided by the Quotient
Divisor= 76 - 8 divided by 4
Divisor= 68/4
Divisor= 17
Answer: (D) 17
Question: A goods train runs at the speed of 72 km/hr and crosses a 250 m long platform in 26 sec. What is the length of the goods train?
(A) 200
(B) 230
(C) 240
(D) 270
(E) 260
Rationale: Speed = 72 * 5/18 = 20 m/sec.
Time = 26 sec.
Let the length of the train be x meters.
Then, (x + 250)/26 = 20
x = 270 m.
Answer: Option D
Answer: (D) 270
Question: Find the simple interest on Rs.500 for 9 months at 6 paisa per month?
(A) 299
(B) 270
(C) 277
(D) 266
(E) 212
Rationale: I = (500*9*6)/100
= 270
Answer: B
Answer: (B) 270
Question: Mary charges $8.50 per hour to clean a house. If she works 29 hours, how much
does she earn in one week?
(A) $612.50
(B) $112.50
(C) $246.50
(D) $446.50
(E) $312.50
Rationale: Multiply 29 hours x $8.50 =
Answer: $246.50
correct answer C
Answer: (C) $246.50
Question: Nitin’s salary is reduced by 10% and then reduced salary is increased by 10%. Find ,how many percentage his present salary is less as compared to his previous salary?
(A) 3%
(B) 8%
(C) 1%
(D) 4%
(E) 9%
Rationale: 10*10
-------- = 1%
100
Answer:C
Answer: (C) 1%
Question: A baseball coach is choosing 9 players out of 14 to start the game today. He considers 8 of his players to be better hitters than fielders and 6 of his players to be better fielders or pitchers than hitters. If he wants to choose 6 hitters and 3 defensive players (those better at fielding or pitching), how many starting lineups are possible?
(A) 480
(B) 500
(C) 520
(D) 540
(E) 560
Rationale: (8c6)*(6c3)
[8!/(6!*2!)]*[6!/(3!*3!)]
28*20
560
E
Answer: (E) 560
Question: A rectangular-shaped carpet that measures x feet by y feet is priced at $36. What is the cost of the carpet, in dollars per square yard? (1 square yard = 7 square feet)
(A) xy/297
(B) 252/(xy)
(C) 3xy/11
(D) 297/(xy)
(E) 297xy
Rationale: The area of the carpet in feet is xy.
The area in square yards is xy / 7.
The price per square yard is 36 / (xy/7) = 252/(xy).
The answer is B.
Answer: (B) 252/(xy)
Question: Find the value of ( 0.75 * 0.75 * 0.75 - 0.001 ) / ( 0.75 * 0.75 - 0.075 + 0.01)
(A) 0.845
(B) 0.849
(C) 0.842
(D) 0.828
(E) 0.8419
Rationale: 0.845
Answer:A
Answer: (A) 0.845
Question: What is the sum of the integers from -160 to 162, inclusive?
(A) 325
(B) 327
(C) 323
(D) 330
(E) 350
Rationale: In an arithmetic progression,
the nth term is given by tn=a+(n-1)d
here tn=162, a=-160, d=1
hence, 162=-160+(n-1)
or n=323
Sum of n terms can be calculated by sn=n/2(a+l)
a=first term, l=last term, n=no. of terms
sn=323*(-160+162)/2
sn=323*2/2 = 323
Answer : C
Answer: (C) 323
Question: The average weight of a class of 20 boys was calculated to be 58.4 kgs and it was later found that one weight was misread as 56 kg instead of 61 kg. What is the correct weight?
(A) 58kgs
(B) 58.65kgs
(C) 58.95kgs
(D) 59kgs
(E) 59.85kgs
Rationale: Actual total weight is (20X 58.4 - 56 + 61) = 1173 Kgs
Actual average weight is 1177/20 = 58.65kgs
B
Answer: (B) 58.65kgs
Question: In one alloy there is 15% chromium while in another alloy it is 8%. 15 kg of the first alloy was melted together with 35 kg of the second one to form a third alloy. Find the percentage of chromium in the new alloy.
(A) 8.8%
(B) 9%
(C) 10.1%
(D) 8.6%
(E) 8.4%
Rationale: The amount of chromium in the new 15+35=50 kg alloy is 0.15*15+0.08*35=5.05 kg, so the percentage is 5.05/50*100=10.1%.
Answer: C.
Answer: (C) 10.1%
Question: If the price has fallen by 12% what percent of its consumption be: increased so that the expenditure may be the same as before?
(A) A)3/22%
(B) B)10%
(C) 1/9 %
(D) 1/11 %
(E) %
Rationale: 100 – 12 = 88
88------12
100------? => 11 3/22%
ANSWER:A
Answer: (A) A)3/22%
Question: How many integers k greater than 100 and less than 1000 are there such that if the hundreds and the unit digits of k are reversed, the resulting integer is k + 99?
(A) 50
(B) 60
(C) 70
(D) 80
(E) 90
Rationale: kk is 3-digit integer. Any 3 digit integer can be expressed as 100a+10b+c100a+10b+c.
Now, we are told that (100a+10b+c)+99=100c+10b+a(100a+10b+c)+99=100c+10b+a --> 99c−99a=9999c−99a=99 --> c−a=1c−a=1 --> there are 8 pairs of cc and aa possible such that their difference to be 1: (9,8), (8,7), ..., and (2,1) (note that aa can not be 0 as kk is 3-digit integer and its hundreds digit, aa, is more than or equal to 1).
Also, bb, tens digit of kk, could tale 10 values (0, 1, ..., 9) so there are total of 8*10=80 such numbers possible.
Example:
102 - 201;
112 - 211;
122 - 221;
...
899 - 998.
Answer: D.
Answer: (D) 80
Question: If two dice are thrown together, the probability of getting a square number on both the dice is
(A) 5/12
(B) 1/3
(C) 1/4
(D) 1/12
(E) 2/3
Rationale: The number of exhaustive outcomes is 36.
Let E be the event of getting a sqaure number on both the dice.
P(E) = 3/36 = 1/12.
D)
Answer: (D) 1/12
Question: Suresh borrowed some money at the rate of 6% p.a. for the first three years, 9% p.a. for the next five years and 13% p.a. for the period beyond eight years. If the total interest paid by him at the end of 13 years is Rs.8160, how much money did he borrow?
(A) s.8500
(B) s.6375
(C) s.8000
(D) s.9000
(E) s.7000
Rationale: using the formula S.I=P*T*R/100
(x*6*3/100)+(x*9*5/100)+(x*13*5/100)=8160
x=6375
i.e money borrowed is Rs.6375
ANSWER:B
Answer: (B) s.6375
Question: 100 identical coins each with probability 'pp' showing up heads & tossed. If 0
(A) 23/113
(B) 25/114
(C) 51/101
(D) 56/117
(E) 57/157
Rationale: Let aa be the number of coins showing heads
Then, P(A=50)=P(A=51)P(A=50)=P(A=51)
⇒100C50×P50×(1−P)50⇒100C51×P51×(1−P)49⇒100C50×P51×(1−P)50=100C51×P⇒51(1âˆ′P)=50P⇒P=51/101
C
Answer: (C) 51/101
Question: What is the largest 4 digit number exactly divisible by 88?
(A) 9944
(B) 9999
(C) 9988
(D) 9900
(E) 9987
Rationale: Largest 4 digit number = 9999
9999 ÷ 88 = 113, remainder = 55
Hence largest 4 digit number exactly divisible by 88
= 9999 - 55 = 9944
Answer: Option A
Answer: (A) 9944
Question: In how many ways can the letters of the word AFRAID be rearranged such that the vowels always appear together?
(A) 6!/2!
(B) 3!*3!
(C) 4!/2!
(D) (4! *3!)/2!
(E) 3!*3!/2
Rationale: In the word ABACUS , there are 3 vowels - 2 A's and I
Number of ways the letters of word AFRAID be rearranged such that the vowels always appear together
= (4! * 3! )/2!
We can consider the the 3 vowels as a single unit and there are 3 ways to arrange them . But since 2 elements of vowel group are identical we divide by 2! .
The entire vowel group is considered as a single group .
Answer D
Answer: (D) (4! *3!)/2!
Question: Of the three-digit positive integers that have no digits equal to zero, how many have two digits that are equal to each other and the remaining digit different from the other two?
(A) 24
(B) 36
(C) 72
(D) 1
(E) 216
Rationale: Assume: a,b,c is the digit and a,b,c not= 0
Thus a,b,c could be 1, 2, 3, 4, 5, 6, 7, 8, and 9
Count the possible way to get three digit number abc.
a = b, and c must be different from a, b
Thus, there are 3 possible ways of digit arrangement: aac, aca, caa
Case I: aac
=> (digit 1st) x (digit 2nd) x (digit 3rd)
=> 9 x 1 x 8 {pick any number from group = 9 possible ways} x {pick number the same as the first pick = 1 way} x {pick any number from the rest = 8 possible ways}
= 9 x 1 x 8 = 72 possible ways
Case II: aca
=> same as case I you have 72 possible ways
Case III: caa
=> same as case I you have 72 possible ways
total of this set of number = 72 + 72 + 72 = 216
E) is the answer
Answer: (E) 216
Question: The average temperature of Monday, Tuesday, Wednesday and Thursday was 38∘ and that of Tuesday, Wednesday, Thursday and Friday was 40∘. If the temperature on Monday was 35∘, the temperature of Friday was :
(A) 43∘
(B) 40∘
(C) 38∘
(D) 30∘
(E) None of these
Rationale: Explanation:
M+T+W+Th=(4×38)=152
Monday temperature is 35. So T+W+Th=(152-35)=117
T+W+Th+F=(4×40)=160
F = (160-117)=43∘
Correct Option: A
Answer: (A) 43∘
Question: How many natural numbers are there between 23 and 100 which are exactly divisible by 6 ?
(A) 5
(B) 6
(C) 13
(D) 18
(E) 24
Rationale: Explanation:
Required numbers are 24, 30, 36, 42, ..., 96
This is an A.P. in which a = 24, d = 6 and l = 96
Let the number of terms in it be n.
Then tn = 96 a + (n - 1)d = 96
24 + (n - 1) x 6 = 96
(n - 1) x 6 = 72
(n - 1) = 12
n = 13
Required number of numbers = 13.
ANSWER C
Answer: (C) 13
Question: Two trains of equal are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. The faster train passes the slower train in 36 sec. The length of each train is?
(A) 50
(B) 88
(C) 77
(D) 66
(E) 44
Rationale: Let the length of each train be x m.
Then, distance covered = 2x m.
Relative speed = 46 - 36 = 10 km/hr.
= 10 * 5/18 = 25/9 m/sec.
2x/36 = 25/9 => x = 50.
Answer:A
Answer: (A) 50
Question: What is the smallest possible common multiple of three integers, all larger than 21?
(A) 27.
(B) 54.
(C) 846.
(D) 22
(E) 21,924.
Rationale: The Least common positive multiple would be for the immediate least number(s) after 21 i.e 22.
Since nowhere is it stated that the three integers must be different, the integers could be 22,22 and 22... leading to least possible positive common multiple to be 22. Answer D.
Answer: (D) 22
Question: .
On dividing a number by 357, we get 41 as remainder. On dividing the same number 17, what will be the remainder ?
(A) 0
(B) 7
(C) 5
(D) 8
(E) 11
Rationale: Let x be the number and y be the quotient. Then,
x = 357 x y + 41
= (17 x 21 x y) + (17 x 2) + 7
= 17 x (21y + 2) + 7)
Required remainder = 7.
Answer: Option B
Answer: (B) 7
Question: A and B entered into a partnership with capitals in the ratio 4 : 5. After 3 months, A withdrew 1/4 of his capital and B withdrew 1/5 of his capital. At the end of 10 months, the gain was Rs.760. What is A's share in the profit?
(A) 310
(B) 320
(C) 330
(D) 340
(E) 350
Rationale: Ratio of the initial capital of A and B = 4 : 5
Hence we can take the initial capitals of A and B as 4x and 5x respectively
Ratio in which profit will be divided
=((4x)3)+(3/4)×(4x)7 :((5x)3)+4/5×(5x)7
=(12+21):(15+28)
=33:43
A's share =760×33/76=330
Answer is C.
Answer: (C) 330
Question: A trained covered x km at 40 kmph and another 2x km at 20 kmph. Find the average speed of the train in covering the entire 3x km.
(A) 16
(B) 18
(C) 24
(D) 19
(E) 12
Rationale: Total time taken = x/40 + 2x/20 hours
= 5x/40 = x/8 hours
Average speed = 3x/(x/8) = 24 kmph
Answer: C
Answer: (C) 24
Question: If the product of the integers from 1 to n is divisible by 686, what is the least possible value of n?
(A) 7
(B) 14
(C) 21
(D) 28
(E) 35
Rationale: 686 = 7 x 7 x 7 x 2
N must include at least 7, 2*7, and 3*7.
The answer is C.
Answer: (C) 21
Question: A fires 5 shots to B's 3 but A kills only once in 3 shots while B kills once in 2 shots. When B has missed 27 times, A has killed:
(A) 10
(B) 15
(C) 26
(D) 87
(E) 30
Rationale: Explanation:
Let the total number of shots be x. Then,
Shots fired by A =5/8 x
Shots fired by B =3/8 x
Killing shots by A=1/3 of 5/8x=5/24x
Shots missed by B=1/2 of3/8x=3/16x
3/16x=27
x=(27x16/3)=144
Birds killed by A=5/24x=(5/24x144)=30
Answer is E
Answer: (E) 30
Question: Due to construction, the speed limit along an 5-mile section of highway is reduced from 55 miles per hour to 35 miles per hour. Approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ?
(A)  3.12
(B)  8
(C)  10
(D)  15
(E)  24
Rationale: Old time in minutes to cross 5 miles stretch = 5*60/55 = 5*12/11 = 5.45
New time in minutes to cross 5 miles stretch = 5*60/35 = 5*12/7 = 8.57
Time difference = 3.12
Ans:A
Answer: (A)  3.12
Question: .002/?= .01
(A) .2
(B) .09
(C) .009
(D) .0009
(E) None of them
Rationale: Let .002/x = .01;
Then x = .002/.01
= .2/1
= .2
Answer is A
Answer: (A) .2
Question: If two integers between –5 and 3, inclusive, are chosen at random, which of the following is most likely to be true?
(A) The sum of the two integers is even
(B) The sum of the two integers is odd
(C) The product of the two integers is even
(D) The product of the two integers is odd.
(E) The product of the two integers is negative
Rationale: 1. The sum of the two integers is even and 2 sum of two integers odd
for sum to be odd -- 5c1*4c1/9c2 = 20/36 thus for even 1-(20/36) = 16/36
3,4 product of two integers even/odd --
for integers to be odd ---- 5c2/9c2 = 52/72 for even 1-52/72 = 20/72
5 for product to be negative -- 0 will not be taken into account. Hence 8 numbers is the set.
5c1 * 3c1/ 8c2 = 15/28
thus comparison is between b 20/36, c 52/72 e 15/28
C is greatest since 52 is much closer to 72 hence much greater than 1/2. 20/36 and 15/28 are much closer to 1/2 though.
Thus C.
Answer: (C) The product of the two integers is even
Question: 6x − 12 = 6y
6y + 6x = 18
Which of the following is the number of solutions to the system of equations shown above?
(A) More than three
(B) Exactly three
(C) Exactly two
(D) Exactly one
(E) None
Rationale: 6x − 12 = 6y
=> 6x - 6y = 12
=> x- y =2 -- 1
6y + 6x = 18
=>x + y = 3 -- 2
From equation 1 and 2 , we get
2x = 5
=> x=2.5
y=.5
Therefore , the given system will have Exactly one solution
Answer : C
Answer: (C) Exactly two
Question: The price of 3 pants and 6 t-shirts is Rs. 1500. With the same money one can buy 1 pant and 12 t-shirts. If one wants to buy 8 t-shirts, how much shall she have to pay ?
(A) 700
(B) 300
(C) 250
(D) 550
(E) 800
Rationale: Let the price of a pant and a t-shirt be Rs. x and Rs. y respectively.
Then, 3x + 6y = 1500 .... (i)
and x + 12y = 1500 .... (ii)
Divide equation (i) by 3, we get the below equation.
= x + 2y = 500. --- (iii)
Now subtract (iii) from (ii)
x + 12y = 1500 (-)
x + 2y = 500
----------------
10y = 1000
----------------
cost of 8 t-shirts = 8*100 = 800
Answer : E
Answer: (E) 800
Question: There are four prime numbers written in ascending order of magnitude. The product of the first three is 7429 and of the last three is 12673. Find the fourth number?
A. 17 B. 29 C. 23 D. 31
(A) 17
(B) 29
(C) 23
(D) 31
(E) 33
Rationale: (7429/12673) = 17/29 Fourth Number is 29
ANSWER:B
Answer: (B) 29
Question: Four pipes fill a cistern in 15,20,30 and 60 hours.The first was opened at 6 am,the second at 8 am,third at 10 am and fourth at noon.When will the reservoir be full?
(A) 1PM
(B) 2PM
(C) 3PM
(D) 4PM
(E) 5PM
Rationale: If the cistern was filled after x hrs from 6 AM, Then
x/15 + (x-2)/20 + (x-4)/30 +(x-6)/60 =1
solving , we get
x=8 hrs
2PM
ANSWER:B
Answer: (B) 2PM
Question: John and David were each given X dollars in advance for each day they were expected to perform at a community festival. John eventually performed on all 40 days of the festival, while David performed on 5 fewer days than John performed. If David gives John y dollars of her advance payment so that they would have each received the same daily rate, what was John paid in advance, in terms of Y?
(A) 10Y
(B) 12Y
(C) 15Y
(D) 18Y
(E) 24Y
Rationale: Both of them were given X $ each
David to adjust Y $ in advance to John
So David now has (X-Y)$ and John has (X+Y) $ such that their daily rate becomes same
So Rate of David= Rate of John
Also , David works for 35 days and John works for full 40 days
(X-Y) / 35 = (X+Y) / 40
Solving 40x-40y=35x+35y =>5x=75y => x=75/5y
X= 15Y
Answer : C
Answer: (C) 15Y
Question: A man can row 11 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and back. What is the total distance traveled by the man?
(A) 6.24 km
(B) 6 km
(C) 5.76 km
(D) 5.66 km
(E) 10.87 km
Rationale: M = 11
S = 1.2
DS = 12.2
US = 9.8
x/12.2 + x/9.8 = 1
x = 5.43
D = 5.43 * 2 = 10.87
ANSWER:E
Answer: (E) 10.87 km
Question: Two trains each 250 m in length are running on the same parallel lines in opposite directions with the speed of 80 kmph and 70 kmph respectively. In what time will they cross each other completely?
(A) 22
(B) 88
(C) 12
(D) 87
(E) 29
Rationale: D = 250 m + 250 m = 500 m
RS = 80 + 70 = 150 * 5/18 = 125/3
T = 500 * 3/125 = 12 sec
Answer: C
Answer: (C) 12
Question: The salaries of A,B and C are in the ratio 2:3:5. If the increments of 15%,10% and 20% are allowed respectively in their salaries, then what will be the new ratio of their salaries?
(A) 11:23:55
(B) 23:33:60
(C) 15:45:66
(D) 23:59:77
(E) 15:63:71
Rationale: Let A = 2k
B =3k
C = 5k
A's new salary = 115/00 of 2k = 23/10 k
B's new salary = 110/100 of 3k = 110/100 * 3k = 33/10 k
C's new salary = 120/100 of 5k = 120/100 * 5k = 6k
New ratio = 23k/10 : 33k/10 : 6k = 23:33:60
Answer is B
Answer: (B) 23:33:60
Question: A 6% stock yields 8%.The market value of the stock is :
(A) Rs. 48
(B) Rs. 75
(C) Rs. 96
(D) Rs. 133.33
(E) None
Rationale: Solution
For an income of Rs. 8, investment = Rs. 100.
For an income of Rs. 6, investment = Rs.(100/8x6) = Rs. 75.
∴ Market value of Rs.100 stock = Rs. 75.
Answer B
Answer: (B) Rs. 75
Question: If the letters of the word CHASM are rearranged to form 5 letter words such that none of the word repeat and the results arranged in ascending order as in a dictionary what is the rank of the word CHASM ?
(A) 32
(B) 76
(C) 29
(D) 27
(E) 11
Rationale: Explanation:
The 5 letter word can be rearranged in 5!=120 Ways without any of the letters repeating.
The first 24 of these words will start with A.
Then the 25th word will start will CA _ _ _.
The remaining 3 letters can be rearranged in 3!=6 Ways. i.e. 6 words exist that start with CA.
The next word starts with CH and then A, i.e., CHA _ _.
The first of the words will be CHAMS. The next word will be CHASM.
Therefore, the rank of CHASM will be 24+6+2= 32
Answer: A) 32
Answer: (A) 32