mathewhe/aqua_rat huggingface dataset:
Question: Jane spent $42 for shoes. This was $14 less than twice what she spent for a blouse. How much was the blouse?
(A) 10
(B) 25
(C) 14
(D) 16
(E) 28
Rationale: Every word problem has an unknown number. In this problem, it is the price of the blouse. Always let x represent the unknown number. That is, let x answer the question.
Let x, then, be how much she spent for the blouse. The problem states that "This" -- that is, $42 -- was $14 less than two times x.
Here is the equation:
2x − 14= 42.
2x= 42 + 14
= 56
x= 56/2
=28.
Ans is E
Answer: (E) 28
Question: Molly can do a task in 18 days while Sandy can do the task in 12 days. How many days will it take to complete the task if both work together?
(A) 6.2
(B) 6.6
(C) 7.2
(D) 7.8
(E) 8.4
Rationale: Each day, Molly can do 1/18 of the task.
Each day, Sandy can do 1/12 of the task.
Each day, they can do 1/18 + 1/12 = 5/36 of the task.
The task will be completed in 36/5 = 7.2 days.
The answer is D.
Answer: (D) 7.8
Question: There are 9 people and 9 chairs. In how many different ways people can occupy the chairs?
(A) 362880
(B) 340009
(C) 250909
(D) 345008
(E) 1000
Rationale: number of ways =9! = 362880
Answer is A
Answer: (A) 362880
Question: Two pipes A and B can fill a cistern in 10 and 15 minutes respectively. Both fill pipes are opened together,but at the end of 3 minutes, ‘B’ is turned off. How much time will the cistern take to fill ?
(A) 6 min
(B) 8 min
(C) 10 min
(D) 12 min
(E) None of these
Rationale: In one min, (A + B) fill the cistern = 1⁄10 + 1⁄15 = 1⁄6th
In 3 min, (A + B) fill the cistern = 3⁄6 = 1⁄2th
Remaining part = 1 - 1⁄2 = 1⁄2
∵ 1⁄10th part filled by A in one min.
∴ 1⁄2nd part filled by A in 10 × 1⁄2 = 5 min.
∴ Total time = 3 + 5 = 8 min.
Answer B
Answer: (B) 8 min
Question: The average of 26,29,n,35 and 43 lies between 25 and 35. If n is always an integer and greater than the average of the given integers then the value of n is :
(A) 36
(B) 29
(C) 33
(D) 28
(E) 21
Rationale: Explanation:
Average of 26,29,35 and 43 is 33.25 . Also the average of 26 , 29, n, 35 and 43 lies between 25 and 35 i.e,
Rightarrow 125 < 26+29+n+35+43 < 175
Rightarrow 125 < 133 + n < 175
Rightarrow n < 42
Since the value of n is an integer and greater than 33.25 then 33 < n < 42 for every integer n.
Answer: C
Answer: (C) 33
Question: For every $20 that a billionaire spends, a millionaire spends the equivalent of 20 cents. For every $6 that a millionaire spends, a yuppie spends the equivalent of $1. The ratio of money spent by a yuppie, millionaire, and billionaire can be expressed as
(A) 1 : 4 : 400
(B) 1 : 4 : 100
(C) 20 : 4 : 1
(D) 100 : 4 : 1
(E) 400 : 4 : 1
Rationale: millionaire 20 cents = 1/5 dollar ..therefore 1 dollar M = 100 dollar of B
therefore 6 dollar M = 600 dollar of B also 1 dollar Y
Y:M:B = 1:6:600
= 1:6:600
B
Answer: (B) 1 : 4 : 100
Question: Four car rental agencies A, B, C and D rented a plot for parking their cars during the night. A parked 15 cars for 12 days, B parked 12 cars for 20 days, C parked 18 cars for 18 days and D parked 16 cars for 15 days. If A paid Rs. 1125 as rent for parking his cars, what is the total rent paid by all the four agencies?
(A) Rs.6152
(B) Rs.6159
(C) Rs.6156
(D) Rs.6150
(E) Rs.6196
Rationale: The ratio in which the four agencies will be paying the rents = 15 * 12 : 12 * 20 : 18 * 18 : 16 * 15
= 180 : 240 : 324 : 240 = 45 : 60 : 81 : 60
Let us consider the four amounts to be 45k, 60k, 81k and 60k respectively.
The total rent paid by the four agencies = 45k + 60k + 81k + 60k= 246k
It is given that A paid Rs. 1125
45k = 1125 => k = 25
246k = 246(25) = Rs. 6150
Thus the total rent paid by all the four agencies is Rs.6150.
Answer: D
Answer: (D) Rs.6150
Question: The ratio of the length and the breadth of a rectangle is 4 : 3 and the area of the rectangle is 6912 sq cm. Find the ratio of the breadth and the area of the rectangle?
(A) 1: 96
(B) 1: 97
(C) 1: 98
(D) 1: 99
(E) 1: 92
Rationale: Let the length and the breadth of the rectangle be 4x cm and 3x respectively.
(4x)(3x) = 6912
12x2 = 6912
x2 = 576 = 4 * 144 = 22 * 122 (x > 0)
=> x = 2 * 12 = 24
Ratio of the breadth and the areas = 3x : 12x2 = 1 : 4x = 1: 96.
Answer: Option A
Answer: (A) 1: 96
Question: Given that 268x74= 19732, find the value of 2.68x.74.
(A) 1.9732
(B) 1.0025
(C) 1.5693
(D) 1.0266
(E) None
Rationale: Solution
Sum of decimals places	=(2+2)
= 4.
Therefore,	= 2.68×.74
= 1.9732
Answer A
Answer: (A) 1.9732
Question: A man can row his boat with the stream at 12 km/h and against the stream in 8 km/h. The man's rate is?
(A) 2 kmph
(B) 6 kmph
(C) 7 kmph
(D) 4 kmph
(E) 9 kmph
Rationale: Explanation:
DS = 12
US = 8
S = ?
S = (12- 8)/2 =2 kmph
Answer: A
Answer: (A) 2 kmph
Question: A and B enter into a partnership. A contributed Rs.5000 for 8 months and B Rs.6000 for 5 months. Find A's share in a total profit of rs.8400.
(A) Rs. 4800
(B) Rs. 2400
(C) Rs. 3600
(D) Rs. 5600
(E) None of these
Rationale: Explanation:
Ratio of capitals of A and B
= Ratio of their investments
= 5000 × 8 : 6000 × 5
= 40000 : 30000 = 4 : 3
.: A's share = Rs. [(4/7) × 8400] = Rs. 4800
Answer: Option A
Answer: (A) Rs. 4800
Question: On a ferry, there are 22 cars and 10 trucks. The cars have an average mass of 1200 kg and the trucks have an average mass of 3000 kg. What is the average mass of all 32 vehicles on the ferry?
(A) 1686.5
(B) 1762.5
(C) 1824.5
(D) 1878.5
(E) 1906.5
Rationale: The total mass of the vehicles is 22*1200+10*3000=56400
The average mass is 56400/32=1762.5
The answer is B.
Answer: (B) 1762.5
Question: factor: 3y (x-3)-2(x-3)
(A) (x-3)-2(x-3)
(B) (x-3)power2
(C) (x-3)(3y-2)
(D) 3y(x-3)
(E) x-3
Rationale: 3y(x-3)-2(x-3), = (x-3)(3y-2). Answer: (C)
Answer: (C) (x-3)(3y-2)
Question: fill in the blank space.
1, 9, 25, 49, 81, ?
(A) 100
(B) 121
(C) 144
(D) 169
(E) 172
Rationale: The series consists of squares of consecutive prime numbers.
Answer : B.
Answer: (B) 121
Question: The number N is 5,2H4, where H represents the ten's digit. If N is divisible by 3, what is the value of H?
(A) 2
(B) 3
(C) 5
(D) 4
(E) 9
Rationale: Integer is divisible by 3 - Sum of digits is divisible by 3
Answer: D
Answer: (D) 4
Question: How many 3-digit numbers can be formed from the digits 2, 3, 5, 6, 7 and 9, which are divisible by 5 and if the repetition is allowed?
(A) 20
(B) 5
(C) 10
(D) 36
(E) 25
Rationale: Since, each desired number is divisible by 5, so we must have 5 at the unit place.
So , the tens place can now be filled by any of the remaining 6 digits (2, 3, 6, 7, 9, 5)
therefore the 3-digit no can be formed by (6 * 6 * 1) = 36 ways ------(since repetition is allowed)
Ans- D
Answer: (D) 36
Question: Excluding stoppages, the speed of a bus is 54 kmph and including stoppages, it is 45 kmph. For how many minutes does the bus stop per hour?
(A) 70 min
(B) 16 min
(C) 20 min
(D) 10 min
(E) 40 min
Rationale: D
10 min
Due to stoppages, it covers 9 km less.
Time taken to cover 9 km = (9/54 x 60) min = 10 min
Answer: (D) 10 min
Question: If ‘POOJA’ is coded as ‘SRRMD’, then ‘PRIYA’ is coded as
(A) THGFE
(B) GVFED
(C) FREDCV
(D) SULBD
(E) SUUNF
Rationale: P= 16 = 16+3 = 19 = S
O = 15 =15+3 =18 = R
SIMILARLY,
P = 16 = 16+3 = 19 = S
R = 18 = 18+3 = 21 = U
I = 9 = 9+3 = 12 = L
Y = 25 = 25 +3 = 28 = B
A = 1 = 1+3 = 4 = D
SO ANS IS
SULBD
Answer: (D) SULBD
Question: In the sea there are 3 fishers in a boat and they take 4 hours to complete one third of a fish container. They went to rest and were supplanted by 8 fishers. If they continue to fish at the same rate, how many hours will take to all of the fishers complete all the container?
(A)  16 hours
(B)  12 hours
(C)  8 hours
(D)  7 hours
(E)  5 hours
Rationale: We have that: 3 fishers ----- 4 hours, 8F ----- xhr, that is: (Xhr/ 3F) = (4hr/8F), then: Xhr = (4hr/8F)3F = (3/2)hr. Is to say, they did the same work in 3/2 hours; it is only one third of the container. Then, all the container is: C = C1 + C2 + C3 = 4 hr + (3/2) hr + (3/2) hr = (4 + 3) hr = 7 hr. Answer D.
Answer: (D)  7 hours
Question: By using the numbers 0, 1, 3, 5 and 6 only once, how many five digit numbers can be made that are divisible by 15?
(A) 12
(B) 18
(C) 24
(D) 36
(E) 42
Rationale: A number to be divisible by 15 must end with 15, 30, 45,60,75 or 70.
So, there are the following cases possible:
035-15 --> the first three digits can be arranged in 3=6 ways.
156-30 --> the first three digits can be arranged in 3=6 ways.
135-60 --> the first three digits can be arranged in 3=6 ways.
Total = 6+6+6= 18.
Answer:B.
Answer: (B) 18
Question: How many three digit numbers E are divisible by 78 or 91?
(A) 17
(B) 19
(C) 20
(D) 21
(E) 22
Rationale: The answer will be 19.
Explanation:
78= 2*3*13 now multiples of 78, 156 ....780, now 1000-780 = 220 only two more muktiples of 78 can exists. So total number of 3 digit Multiples of 78 are 9+2=11
91= 13*7--Total number of three digit multiples --9
No remember we have a common multiples as well-- 13*7*6=91*6=546
So total number of multiples E--11+9 -1 =19.
Hence Answer is 19.B
Answer: (B) 19
Question: Nine people are planning to share equally the cost of a rental van. If one person withdraws from the arrangement and the others share equally the cost of the rental van, then the share of each of the remaining people will increase by...?
(A) 1 / 9
(B) 1 / 8
(C) 1 / 7
(D) 7 / 8
(E) 8 / 7
Rationale: Let P = total cost of the rental van.
The original share per person is P/9.
The new share per person is P/8.
P/8 = P/9 * 9/8 = (1 + 1/8)*original share
The answer is B.
Answer: (B) 1 / 8
Question: The G.C.D of 1.08, 0.36 and 0.9 is
(A) 0.03
(B) 0.9
(C) 0.18
(D) 0.108
(E) None
Rationale: Solution
Given numbers are 1.08 , 0.36 and 0.90.
H.C.F of 108 ,36 and 90 is 18.
‹=› H.C.F of given numbers = 0.18.
Answer C
Answer: (C) 0.18
Question: A man can row upstream at 25 kmph and downstream at 35 kmph, and then find the speed of the man in still water?
(A) 65
(B) 86
(C) 30
(D) 78
(E) 38
Rationale: US = 25
DS = 35
M = (35 + 25)/2
= 30
Answer: C
Answer: (C) 30
Question: A person buys an article at Rs.500. At what price should he sell the article so as to make a profit of 25%?
(A) 600
(B) 887
(C) 625
(D) 654
(E) 712
Rationale: Cost price = Rs.500
profit = 25% of 500 = Rs.125
Selling price = Cost price + Profit
= 500 + 125 = 625
Answer: C
Answer: (C) 625
Question: Find compound interest on Rs. 8000 at 15% per annum for 2 years 4 months, compounded annually.
(A) Rs 400
(B) Rs 300
(C) Rs 3109
(D) Rs 250
(E) Rs 400
Rationale: Time = 2 years 4 months = 2(4/12) years = 2(1/3) years.
Amount = Rs'. [8000 X (1+¬(15/100))2 X (1+((1/3)*15)/100)]
=Rs. [8000 * (23/20) * (23/20) * (21/20)]
= Rs. 11109.	.
:. C.I. = Rs. (11109 - 8000) = Rs. 3109.
ANSWER C Rs 3109
Answer: (C) Rs 3109
Question: How many ways could two people sit at a table with four seats in which two of the four seats will remain empty?
(A) 60
(B) 12
(C) 112
(D) 118
(E) 120
Rationale: ways in which 2 seats out 4 can be selected = 4C2
ways in which 2 people can be arranged in 2 seats = 2!
Total ways of arrangement = 4C2*2!
=4*3
=12
Ans = B
Answer: (B) 12
Question: A person covered one-fourth of the total distance at 26 kmph and remaining distance at 24 kmph. What is the average speed for the total distance?
(A) 21 (1/9)
(B) 21 (1/3)
(C) 21 (1/2)
(D) 21 (5/3)
(E) 21 (1/6)
Rationale: Let the total distance be x km
total time taken = (x/4)/16 + (3x/4)/24 = x/64 + x/32 = 3x/64
Average speed = x/(3x/64) = 64/3kmph = 21 (1/3)kmph.'
Answer: B
Answer: (B) 21 (1/3)
Question: A chair is bought for Rs.600/- and sold at a loss of 10% find its selling price
(A) Rs.500/-
(B) Rs.510/-
(C) Rs.515/-
(D) Rs.530/-
(E) Rs.540/-
Rationale: 100 % ------> 600 (100 * 6 = 600)
90 % ------> 540 (90 * 6 = 540)
Selling price = Rs.540/-
E
Answer: (E) Rs.540/-
Question: Real-estate salesman Z is selling a house at a 25 percent discount from its retail price. Real-estate salesman X vows to match this price, and then offers an additional 5 percent discount. Real-estate salesman Y decides to average the prices of salesmen Z and X, then offer an additional 30 percent discount. Salesman Y's final price is what fraction of salesman X's final price?
(A) 21/34
(B) 55/71
(C) 25/34
(D) 26/34
(E) 27/34
Rationale: Let the retail price be = x
Selling price of Z = 0.75x
Selling price of X = 0.95*0.75x = 0.71x
Selling price of Y = ((0.75x + 0.71x)/2)*0.70 = 0.73x * 0.75 = 0.55x
0.55x = k * 0.71x
k = 0.55/0.71 = 55/71
Answer: B
Answer: (B) 55/71
Question: Combine terms: 12a + 26b -4b – 16a.
(A) 4a + 22b
(B) -28a + 30b
(C) -4a + 22b
(D) 28a + 30b
(E) 5a + 30b
Rationale: Solution:
12a + 26b -4b – 16a.
= 12a – 16a + 26b – 4b.
= -4a + 22b.
Answer: (C)
Answer: (C) -4a + 22b
Question: An eccentric casino owner decides that his casino should only use chips in $5 and $8 denominations. Which of the following amount cannot be paid out using these chips?
(A) $34
(B) $27
(C) $31
(D) $29
(E) $24
Rationale: Yes, the number of 5 or/and 8 dollar chips can be zero, however both being zero mean that the casino is paying out $0, which is not realistic.
Each option but B can be represented as the sum of a multiple of 5 and a multiple of 8:
A. $34 = 8*3 + 5*2
B. $31 = 8*2 + 5*3
C. $29 = 8*3 + 5*1
E. $24 = 8*3
Answer: B.
Answer: (B) $27
Question: A reduction of 40% in the price of bananas would enable a man to obtain 64 more for Rs.40, what is reduced price per dozen?
(A) 6
(B) 5
(C) 4
(D) 3
(E) 2
Rationale: 40*(40/100)
= 16 --- 64
? --- 12
=> Rs.3
Answer: D
Answer: (D) 3
Question: Mary passed a certain gas station on a highway while traveling west at a constant speed of 50 miles per hour. Then, 15 minutes later, Paul passed the same gas station while traveling west at a constant speed of 80 miles per hour. If both drivers maintained their speeds and both remained on the highway for at least 2 hours, how long after he passed the gas station did Paul catch up with Mary?
(A) 35
(B) 15
(C) 20
(D) 25
(E) 30
Rationale: d = rt
M: r = 50mph, t = t + 1/4hr
d = 50 (t + 1/4)
P: r = 80, t = t
d = 80t
since they went the same distance:
50t + 50/4 = 80t
30t = 50/4 = 50/120 *60 =25 min
t = 25 min
D
Answer: (D) 25
Question: The banker's gain on a sum due 6 years hence at 12% per annum is Rs. 900. What is the banker's discount?
(A) 1240
(B) 1120
(C) 1190
(D) 2150
(E) None of these
Rationale: Explanation :
TD = (BG ×100)/TR = (900×100)/(6×12) = Rs. 1250
BG = BD – TD
=> 900 = BD - 1250
=> BD = 2150 Answer : Option D
Answer: (D) 2150
Question: At a certain supplier, a machine of type A costs $20,000 and a machine of type B costs $40,000. Each machine can be purchased by making a 20 percent down payment and repaying the remainder of the cost and the finance charges over a period of time. If the finance charges are equal to 40 percent of the remainder of the cost, how much less would 2 machines of type A cost than 1 machine of type B under this arrangement?
(A) $14,000
(B) $11,200
(C) $12,000
(D) $12,800
(E) $13,200
Rationale: 1 machine of type B will cost: 20% down payment of 40,000 = 8,000plusremaining sum (50,000-8,000=42,000) with 40% of finance charges 42,000*1.4=58,800 --> 8,000+58,800=66,800;
2 machine of type A will cost: 20% down payment of 2*20,000 = 8,000plusremaining sum (40,000-8,000=32,000) with 40% of finance charges 32,000*1.4=44,800 --> 8,000+44,800=52,800;
Difference = 66,800 - 52,800 = 14,000.
Answer: A.
Answer: (A) $14,000
Question: Running 3/4th of his usual rate, a man is 9min late. Find his usual time in hours ?
(A) 6/4 hrs
(B) 3/4 hrs
(C) 9/20 hrs
(D) 3/4 hrs
(E) 1/4 hrs
Rationale: Explanation:
Walking at 3/4th of usual rate implies that time taken would be 4/3th of the usual time. In other words, the time taken is 1/3rd more than his usual time
so 1/3rd of the usual time = 9min
or usual time = 3 x 9 = 27min = 27/60 hrs = 9/20 hrs.
Answer: C
Answer: (C) 9/20 hrs
Question: A rectangular wall is covered entirely with two kinds of decorative tiles: regular and jumbo. 1/3 of the tiles are jumbo tiles, which have a length three times that of regular tiles and have the same ratio of length to width as the regular tiles. If regular tiles cover 90 square feet of the wall, and no tiles overlap, what is the area of the entire wall?
(A) 160
(B) 240
(C) 360
(D) 495
(E) 560
Rationale: The number of jumbo tiles = x.
The number of regular tiles = 2x.
Assume the ratio of the dimensions of a regular tile is a:a --> area = a^2.
The dimensions of a jumbo tile is 3a:3a --> area = 9a^2.
The area of regular tiles = 2x*a^2 = 90.
The area of jumbo tiles = x*9a^2 = 4.5(2x*a^2 ) = 4.5*90 =405.
Total area = 90 + 405 = 495
Answer: D.
Answer: (D) 495
Question: A man bought some mangoes at Rs12 per dozen and bought the same number of at Rs 10 per kg. He sold these mangoes at Rs 13 per dozen and gained Rs 160.The total number of mangos bought by him are
(A) 40dozens
(B) 60dozens
(C) 70dozens
(D) 80dozens
(E) 90dozens
Rationale: let total no of mangoes is 2x..
then we profit=sp-cp
160=13*2x-(12x+10x)
160=4x
x=40
hence 2x=80
so total no are 80dozens
ANSWER:D
Answer: (D) 80dozens
Question: In how many ways can you line up 7 cars in a row if one of them cannot be in the middle or at the either end?
(A) 82
(B) 92
(C) 1,750
(D) 2,880
(E) 982
Rationale: Since the car cannot be placed in the middle or at either end (3 spots), then he can choose 4 spots to sit. The remaining 6 apples can be placed in in 6! ways. Thus the # of arrangements is 4*6! = 2,880.
Answer: D.
Answer: (D) 2,880
Question: The averge score of a cricketer for ten matches is 35 runs. If the average for the first six matches is 23. Then find the average for the last four matches?
(A) 58
(B) 53
(C) 64.25
(D) 55
(E) 57
Rationale: sum of last 4 matches = (10 × 35) – (6 × 23)=212
Average = 212/4
= 53
ANSWER:B
Answer: (B) 53
Question: In a village ,50% of the students play football, 60% of the student play basketball,40% of the student play cricket. 20% play both football and basketball ,20% play both football and cricket,25% play both cricket and baseketball.5% of the student play all the three games and 100 students play none of the games.How many students are there in the college?
(A) 700
(B) 800
(C) 900
(D) 1000
(E) 1100
Rationale: the student play all three games=5%
the student play only both football n bsketball=(20-5)%=15%
the student play only both football n cricket=(20-5)%=15%
the student play only both basketball n cricket=(25-5)=20%
the student play only football=(50-15-15-5)%=15%
the student play only basketball=(60-15-20-5)%=20%
the student play only cricket=(40-15-20-5)%=0%
so sdtudent play games=(0+20+15+15+15+20+5)%=90%
so student does not play games=(100-90)%=10%
as 10%=100 student den 100%=1000 student
there are 1000 student in the college
ANSWER:D
Answer: (D) 1000
Question: A bag contains 3 blue and 5 white marbles. One by one, marbles are drawn out randomly until only two are left in the bag. What is the probability Q that out of the two, one is white and one is blue?
(A) 15/56
(B) 41/56
(C) 13/28
(D) 15/28
(E) 5/14
Rationale: The required probability Q= probability of choosing 6 balls out of the total 8 in such a way that we remove 4 out of 5 white and 2 out of 3 blue balls.
Ways to select 6 out of total 8 = 8C6
Ways to select 4 out of 5 white balls = 5C4
Ways to select 2 out of 3 blue balls = 3C2
Thus the required probability = (5C4*3C2)/8C6 = 15/28.
D is thus the correct answer.
Answer: (D) 15/28
Question: What will come in place of the x in the following Number series? 25, 100, 400, 1600, 6400, X
(A) 64000
(B) 69000
(C) 25600
(D) 75000
(E) 79000
Rationale: (C)
25 x 4 = 100, 100 x 4 = 400, 400 x 4 = 1600, 1600 x 4 = 6400, 6400 x 4 = 25600
Answer: (C) 25600
Question: y = x^2 + bx + 512 cuts the x axis at (h, 0) and (k, 0). If h and k are integers, what is the least value of b?
(A) -512
(B) -257
(C) -256
(D) -513
(E) 128
Rationale: As the curve cuts the x-axis at (h,0) and (k,0). Therefore h,k are the roots of the quadratic equation.
For the quadratic equation is in the form of ax^2+bx+c=0,
The product of the roots =c/a= 512/1=256 and the sum of the roots =-b/a=-b
512 can be expressed as product of two numbers in the following ways:
1 * 512
2 * 256
4 * 128
8 * 64
16 *32
The sum of the roots is maximum when the roots are 1 and 256 and the maximum sum is 1 + 512 = 513.
The least value possible for b is therefore -513.
D
Answer: (D) -513
Question: 75 percent of Andrea's living room floor is covered by a carpet that is 4 feet by 9 feet. What is the area of her living room floor?
(A) 48
(B) 180/7
(C) 50.4
(D) 60
(E) 90
Rationale: 75% of Area of the floor = 4*9 square feet = 36 square feet
i.e. 100% Area of Floor = (36/75)*100 = 48 square feet
Answer: Option A
Answer: (A) 48
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) 120 metres
(B) 110metres
(C) 90 metres
(D) 150 metres
(E) 100 metres
Rationale: Answer: Option D
Speed=(60 * 5/18) m/sec = (50/3) m/sec Length of the train = (Speed x Time) = (50/3 * 9) m = 150 m.
Answer: (D) 150 metres
Question: A person has 12 friends and he wants to invite 8 of them to a birthday party. Find how many times 3 particular friends will always attend the parties.
(A) 126
(B) 95
(C) 130
(D) 155
(E) None
Rationale: Explanation :
No. of times 3 particular friends will attend the party always.
Hence the number of ways of selection is :-
=> n-kCr-k, where n= 12, r=8 and k=3.
=> No. of combinations = 12-3C8-3 .
=> 9C5.
=> 126.
Hence, the number of combinations with 3 particular friends present in each combination (party) is 126.
Answer : A
Answer: (A) 126
Question: 852.68 âˆ’ 4.5 + 108.90 = ? âˆ’ 2132.54
(A) 6078.58
(B) 5225.9
(C) 6258.58
(D) 6078.5
(E) None
Rationale: Option 'D'
Answer: (D) 6078.5
Question: An officer was appointed on maximum daily wages on contract money of Rs. 4956. But on being absent for some days, he was paid Rs. 3894. For how many days was he absent?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: Explanation:
HCF (4956, 3894) = 354
Here 354 are the maximum daily wages.
The officer was appointed on contract money of Rs. 4956 = 354 × 14.
i.e., he was appointed for 14 days.
But he was paid Rs. 3894 = 354 × 11,
i.e., he was present for 11 days.
Hence he was absent for 3 days.
Answer: C
Answer: (C) 3
Question: Pamela bought an electric drill at 85% of the regular price.
She paid $32.89 for the drill. What was the regular price?
(Round to the nearest cent)
(A) $28.69
(B) $18.69
(C) $38.69
(D) $58.69
(E) $48.69
Rationale: we know
85/100=32.89/x
Multiply the opposites:
100 x 32.89 = 3289
Divide by the remaining number:
38.694/3289 .000
85
$38.69
correct answer C
Answer: (C) $38.69
Question: The average (arithmetic mean) of 7 numbers is 7. If 3 is added from each of 5 of the numbers, what is the new average?
(A) 7.3
(B) 5.6
(C) 4.6
(D) 9.1
(E) 8.9
Rationale: Sum of 8 numbers = 7*7=49
If 3 is added from each of five of the numbers , we added 3*5=15 from the total sum
Sum of 7 number after adding 3 from each of five of the numbers =49+15=64
New average =64/7=9.1
Answer (D)
Answer: (D) 9.1
Question: In a basket the number of cherries is 20% of the number of apples. Express the number of apples as a percentage of cherries in the basket?
(A) 2%
(B) 7%
(C) 12%
(D) 5%
(E) 15%
Rationale: The number of cherries is 20% the number of apples.
If apples=10
cherries=2
We are asked for the number of apples as a percentage of cherries
A/C=10/2=5%
Answer is D
Answer: (D) 5%
Question: An analyst will recommend a combination of 4 industrial stocks, 3 transportation stocks, and 4 utility stocks. If the analyst can choose from 5 industrial stocks, 4 transportation stocks, and 5 utility stocks, how many different combinations of 11 stocks are possible?
(A) 12
(B) 19
(C) 60
(D) 100
(E) 720
Rationale: 5C4 * 4C3 * 5C4 = 5*4*5 = 100.
Answer: D
Answer: (D) 100
Question: The simple interest and the true discount on a certain sum for a given time and at a given rate are Rs. 85 and Rs. 70 respectively. The sum is:
(A) 1360
(B) 1450
(C) 1600
(D) 1800
(E) None
Rationale: Sol.
Sum = S.I. * T.D. / (S.I)-(T.D.) = 85 * 70 / (85 - 70) = Rs.396.7.
Answer E
Answer: (E) None
Question: The average age of 18 persons in a office is 15 years. Out of these, the average age of 5 of them is 14 years and that of the other 9 persons is 16 years. The age of the 15th person is?
(A) 9
(B) 31
(C) 56
(D) 72
(E) 90
Rationale: Age of the 15th student = 18*15 - (14*5+16*9) = 270-214 = 56 years
Answer is C
Answer: (C) 56