mathewhe/aqua_rat huggingface dataset:
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 5000, the number of valid votes that the other candidate got, was:
(A) 1800
(B) 2700
(C) 2900
(D) 2200
(E) 2300
Rationale: A
Number of valid votes = 80% of 5000 = 4000.
Valid votes polled by other candidate = 45% of 4000
= (45/100 x 4000) = 1800.
Answer: (A) 1800
Question: Find the product of the local value and absolute value of 2 in 564823
(A) 40
(B) 60
(C) 80
(D) 100
(E) 18000
Rationale: Explanation:
Place value = Local value
Face value = Absolute value
The place value of 2 in 564823 is 2 x 10 = 20
The face value of 2 in 564823 is nothing but 2.
=> 20 x 2 = 40
Answer: Option A
Answer: (A) 40
Question: If each of 4 subsidiaries of Corporation R has been granted a line of credit of $710,500 and each of the other 3 subsidiaries of Corporation R has been granted a line of credit of $112,000, what is the average (arithmetic mean) line of credit granted to a subsidiary of Corporation R?
(A)  $1,568,000
(B)  $454,000
(C)  $406,000
(D)  $313,600
(E)  $116,000
Rationale: My take is B.
(710500*4 + 112000*3)/7 = 454000
Answer: (B)  $454,000
Question: If x ¤ y = (x + y)^2 - (x - y)^2. Then √11 ¤ √11 =
(A) 44
(B) 5
(C) 10
(D) 15
(E) 20
Rationale: X = √11 and Y also =√11
Applying the function (√11+√11)^2 - (√11-√11)^2 = (2√11)^2 - 0 = 4 x 11 = 44.
Note: Alternative Approach is the entire function is represented as X^2 - Y^2 = (X+Y)(X-Y) which can be simplified as (x+y+x-y)(x+y-(x-y)) = (2x)(2y)=4xy. Substituting x=√11 and y = √11 you get the answer 44.
Answer A
Answer: (A) 44
Question: What is the remainder when 43^92 is divided by 5?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: The units digit of the exponents of 3 cycle in a group of 4: {3, 9, 7, 1}
92 has the form 4k so the units digit of 43^92 is 1.
The remainder when dividing by 5 is 1.
The answer is B.
Answer: (B) 1
Question: A and B start a business, with A investing the total capital of Rs.500000, on the condition that B pays A interest @ 10% per annum on his half of the capital. A is a working partner and receives Rs.15000 per month from the total profit and any profit remaining is equally shared by both of them. At the end of the year, it was found that the income of A is twice that of B. Find the total profit for the year?
(A) A)590280
(B) B)590100
(C) C)591900
(D) D)590000
(E) E)927000
Rationale: Interest received by A from B = 10% of half of Rs.500000 = 10% * 250000 = 25000.
Amount received by A per annum for being a working partner = 15000 * 12 = Rs.180000.
Let 'P' be the part of the remaining profit that A receives as his share. Total income of A = (25000 + 180000 + P)
Total income of B = only his share from the remaining profit = 'P', as A and B share the remaining profit equally.
Income of A = Twice the income of B
(25000 + 180000 + P) = 2(P)
P = 205000
Total profit = 2P + 180000
= 2*205000 + 180000 = 590000
Answer:D
Answer: (D) D)590000
Question: What is the maximum number R of 27 cubic centimetre cubes that can fit in a rectangular box measuring 8 centimetre x 9 centimetre x 12 centimetre ?
(A) 36
(B) 32
(C) 24
(D) 21
(E) 15
Rationale: 27 cubic centimetre cubes gives side = 3cm
so if:
L*W*H is 9*12*8, then max. cube we can have are 3*4*2 = 24
L*W*H is 9*8*12, then max. cube we can have are 3*2*4 = 24
L*W*H is 12*8*9, then max. cube we can have are 4*2*3 = 24
L*W*H is 12*9*8, then max. cube we can have are 4*3*2 = 24
L*W*H is 8*12*9, then max. cube we can have are 2*4*3 = 24
L*W*H is 8*9*12, then max. cube we can have are 2*3*4 = 24
In all cases we get R=24 cubes.
Ans. C
Answer: (C) 24
Question: If x and y are integers such that (x+1)^2 is less than or equal to 49 and (y-1)^2 is less than 64, what is the sum of the maximum possible value of xy and the minimum possible value of xy?
(A)  -16
(B)  -14
(C)  0
(D)  14
(E)  16
Rationale: (x+1)^2 <= 49
x <= 6
x >= -8
(y-1)^2 < 64
y < 9
y > -7
Max possible value of xy is -8 × -6 = 48
minimum possible value of xy is -8 × 8 = -64
-64 + 48 = -16
Answer : A
Answer: (A)  -16
Question: A cistern normally takes 6 hours to be filled by a tap but because of a leak, 2 hours more. In how many hours will the leak empty a full cistern ?
(A) 20 hours
(B) 24 hours
(C) 26 hours
(D) 18 hours
(E) None of these
Rationale: ∵ cistern fill in 6 hours.
∴ in 1 hour, filled part = 1⁄6th
Now, due to leakage, filled part in 1 hour = 1⁄8th
Part of the cistern emptied, due to leakage in 1 hour
= 1⁄6 - 1⁄8 = 1⁄24th
∴ The leakage will empty the full cistern in 24 hrs.
Answer B
Answer: (B) 24 hours
Question: If the two hands in a clock are 24 minutes divisions apart,then the angle between them is
(A) 3Â°
(B) 18Â°
(C) 24Â°
(D) 60Â°
(E) None of these
Rationale: In a clock, each minute makes 6Â°
âˆ´ 24 minutes will make 6 Ã— 24 = 144Â°
Answer E
Answer: (E) None of these
Question: A train passes a station platform in 24 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
(A) 123
(B) 60
(C) 240
(D) 157
(E) 198
Rationale: Speed = [54 * 5/18] m/sec = 15 m/sec.
Length of the train = (15 * 20) m = 300 m.
Let the length of the platform be x meters.
Then, (x + 300) / 24 = 15
x + 300 = 360
x = 60 m.
Answer: B
Answer: (B) 60
Question: Michael, Steve and Tyler shared a box of cookies. Michael ate 1/8 of the cookies, Steve ate one half and Tyler ate 150 more cookies than Michael. If no cookies remain in the box, how many cookies were in the box?
(A) 1200.
(B) 800.
(C) 600
(D) 550
(E) 400
Rationale: Let no of cookies that Michael, Steve and Tyler ate are M, S, T
M+S+T = Total no of cookies (Let it be C)----------------(1)
Then : M=C/8, S=C\2, T= C/8 +150
Putting the Values in (1)
We get C as 600.. hence the answer : C
Answer: (C) 600
Question: Two trains are moving in the same direction at 72 kmph and 36 kmph. The faster train crosses a man in the slower train in 27 seconds. Find the length of the faster train?
(A) 270
(B) 2877
(C) 187
(D) 1776
(E) 191
Rationale: Relative speed = (72 - 36) * 5/18 = 2 * 5 = 10 mps.
Distance covered in 27 sec = 27 * 10 = 270 m.
The length of the faster train = 270 m.
Answer:A
Answer: (A) 270
Question: A 20% product produces 50%. The market value of the product is:
(A) Rs. 40
(B) Rs. 60
(C) Rs. 45
(D) Rs. 80
(E) Rs. 70
Rationale: Let the face value of the product is Rs.100
It produces Rs.20
Market value of the stock=(20/50)*100=Rs.40
ANSWER:A
Answer: (A) Rs. 40
Question: A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 58 years now, the son's age five years back was:
(A) 14
(B) 17
(C) 19
(D) 22
(E) 24
Rationale: Let the son's present age be x years. Then, (58 - x) = x
2x = 58.
x = 29.
Son's age 5 years back (29 - 5) = 24 years.
answer :E
Answer: (E) 24
Question: Machine R can produce x units in 3/4 of the time it takes machine N to produce x units. Machine N can produce x units in 2/3 the time it takes machine O to produce x units. If all three machines are working simultaneously, what fraction of the total output is produced by machine N?
(A)  1/2
(B)  1/3
(C)  4/13
(D)  8/29
(E)  6/33
Rationale: Let the following be true:
R makes x in time t
Then the following follows:
N makes x in 4t/3
O makes x in 3/2(4t/3) = 2t
M:N:O = 1:4/3:2=3:4:6
So N=4/(3+4+6)=4/13=C
Answer: (C)  4/13
Question: If abc < 0 and bc > 0, which of the following must be positive?
(A)  xy
(B)  ac
(C)  (a^2)bc
(D)  a(b^2)c
(E)  xy(z^2)
Rationale: Given that bc is positive and abc is negative, you can say that a MUST be negative. As for b and c either they are both positive or both negative.
Option (C) has a^2 which is positive and bc which is positive. So (C) must be positive.
Answer: (C)  (a^2)bc
Question: What is the cost of leveling the field in the form of parallelogram at the rate of Rs.50/10 sq.metre, whose base & perpendicular distance from the other side being 54m & 24m respectively?
(A) Rs. 6000
(B) Rs. 6250
(C) Rs. 6400
(D) Rs. 6480
(E) Rs. 7000
Rationale: Area of the parallelogram = Length of the base * Perpendicular height
= 54 * 24 = 1296 m.
Total cost of levelling = Rs. 6480
D
Answer: (D) Rs. 6480
Question: Sreenivas sells a table to Shiva at 10% profit and Shiva sells it to Mahesh at 10% loss. At what price did Sreenivas purchase the table if Mahesh paid Rs. 2970?
(A) 3000
(B) 2669
(C) 2200
(D) 2766
(E) 2998
Rationale: Let the cost price of table for Sreenivas be Rs. x and given that, cost price of table for Mahesh = Rs. 2970.
=> (90%) of (110%) of x = Rs. 2970.
=> (90/100)(110/100)x = 2970
=> x = (2970 * 100)/(9 * 11)
=> x = Rs. 3000
Answer: A
Answer: (A) 3000
Question: The public library has exactly 2 floors. It has 1/4 as many shelves on its 2nd floor as it does on its 1st. If the second floor has 5/6 as many books per shelf as the first floor, what fraction of the library's books are on the first floor?
(A) 1/4
(B) 5/14
(C) 5/9
(D) 24/29
(E) 5/6
Rationale: Let x be the no of shelves and y be the no of books per shelf on first floor.
Now no of shelves on 2nd floor = (1/4)*x
no of books per shelf on 2nd floor = (5/6) * y
So total no books on first floor = xy and total no of books on 2nd floor = (1/4)*x*(5/6)*y = (5/24)*xy
fraction of library books on first floor = (xy)/(xy + (5/24)*xy)
=1 / (1+(5/24))
=24/29
So D
Answer: (D) 24/29
Question: The population of a town increased from 1,75,000 to 2,80,000 in a decade. The average percent increase of population per year is
(A) 4.37%
(B) 5%
(C) 6%
(D) 8.75%
(E) None
Rationale: Solution
Increase in 10 years	= (280000 - 175000)
= 105000.
Increase%	= (105000/175000Ã—100)%
= 60%.
Required average	= (60/10)%
= 6%.
Answer C
Answer: (C) 6%
Question: At a certain conference, 150 students spoke one or more of the following languages: Spanish, English, and French. If 41 students spoke Spanish, 90 spoke English, 65 spoke French, and 32 spoke only 2 languages, how many students spoke three different languages?
(A) 7
(B) 9
(C) 12
(D) 15
(E) 18
Rationale: 150=41+90+65-32-2x
x=7
A. 7
Answer: (A) 7
Question: If a rectangular room measures 9 meters by 5 meters by 4 meters, what is the volume of the room in cubic centimeters? (1 meter=100 centimeters)
(A) 24,000
(B) 240,000
(C) 18,000,000
(D) 24,000,000
(E) 240,000,000
Rationale: C. 180,000,000
9*100*5*100*4*100 = 180,000,000
Answer: (C) 18,000,000
Question: On dividing 109 by a number, the quotient is 9 and the remainder is 1. Find the divisor.
(A) 8
(B) 12
(C) 16
(D) 18
(E) 22
Rationale: d = (D-R)/Q
= (109 - 1)/9
= 108/9 = 12
B)
Answer: (B) 12
Question: What is the product of all the prime factors of 26?
(A) 24
(B) 25
(C) 22
(D) 26
(E) 21
Rationale: 26 , factors are 2,13,1. Now again prime Numbers are Only Two i.e 2 and 13 , this time we would have 2*13=26
Answer : D
Answer: (D) 26
Question: In a game of billiards, A can give B 20 points in 60 and he can give C 30 points in 60. How many points can B give C in a game of 150?
(A) 15
(B) 75
(C) 25
(D) 18
(E) 12
Rationale: A scores 60 while B score 40 and C scores 30.
The number of points that C scores when B scores 100 = (100 * 30)/40 = 25 * 3 = 75.
In a game of 100 points, B gives (150 - 75) = 75 points to C.
Answer:B
Answer: (B) 75
Question: In the coordinate plane, a circle centered on point (3, -4) passes through point (1, 1). What is the area of the circle?
(A) 29π
(B) 18π
(C) 25π
(D) 37π
(E) 41π
Rationale: r^2=(3-1)^2+(-4-1)^2=4+25=29
Area of circle=πr^2=29π
Answer : A
Answer: (A) 29π
Question: The average of 10 numbers is calculated as 20. It is discovered later on that while calculating the average, one number namely 36 was wrongly read as 26. The correct average is?
(A) 12
(B) 26
(C) 16
(D) 97
(E) 20
Rationale: 10 * 20 + 36 – 26
= 200/10
= 20
Answer: E
Answer: (E) 20
Question: The spherical ball of lead 3 cm in diameter is melted and recast into 3 spherical balls. The diameters of two of these are 1 ½ cm and 2 cm respectively. The diameter of third ball is?
(A) 2.66 cm
(B) 2.5 cm
(C) 3 cm
(D) 3.5 cm
(E) 4 cm
Rationale: 4/3 π * 3 * 3 * 3 = 4/3 π[(3/2)3 + 23 + r3]
r = 1.25
d = 2.5
ANSWER:B
Answer: (B) 2.5 cm
Question: A batsman in his 12th innings makes a score of 80 and thereby increases his average by 2 runs. What is his average after the 12th innings if he had never been ‘not out’?
(A) 42
(B) 43
(C) 44
(D) 45
(E) 58
Rationale: Let ‘x’ be the average score after 12 th innings
⇒ 12x = 11 × (x – 2) + 80
∴ x = 58
Answer E
Answer: (E) 58
Question: Find (7x + 6y ) / (x-2y) if x/2y = 3/2 ?
(A) 24
(B) 25
(C) 26
(D) 27
(E) 29
Rationale: x/2y=3/2
=>x=6y/2=3y
=>(7x+6y)/(x-2y)=((7*(3y))+6y)/(3y-2y)
=>27y/y=27
ANSWER:D
Answer: (D) 27
Question: Two varieties of wheat - A and B costing Rs. 9 per kg and Rs. 15 per kg were mixed in the ratio 3 : 7. If 5 kg of the mixture is sold at 25% profit, find the profit made?
(A) Rs. 13.50
(B) Rs. 16.54
(C) Rs. 16.80
(D) Rs. 16.50
(E) Rs. 16.00
Rationale: Explanation:
Let the quantities of A and B mixed be 3x kg and 7x kg.
Cost of 3x kg of A = 9(3x) = Rs. 27x
Cost of 7x kg of B = 15(7x) = Rs. 105x
Cost of 10x kg of the mixture = 27x + 105x = Rs. 132x
Cost of 5 kg of the mixture = 132x/10x (5) = Rs. 66
Profit made in selling 5 kg of the mixture = 25/100 (cost of 5 kg of the mixture) = 25/100 * 66 = Rs. 16.50
Answer: Option D
Answer: (D) Rs. 16.50
Question: An error 2% in excess is made while measuring the side ofa square. The % of error in the calculated area of the square is?
(A) 4.01%
(B) 4.04%
(C) 4.16%
(D) 5.12%
(E) 5.16%
Rationale: 100 cm is read as 102 cm.
A1 = (100 x 100) cm2 and A2 (102 x 102) cm2.
(A2 - A1) = [(102)2 - (100)2]
= (102 + 100) x (102 - 100)
= 404 cm2.
Percentage error = 404 x 100 % = 4.04%
100 x 100
B
Answer: (B) 4.04%
Question: A team won 40 percent of its first 30 games in a particular season, and 80 percent of its remaining games. If the team won a total of 70 percent of its games that season, what was the total number of games that the team played?
(A) 60
(B) 90
(C) 120
(D) 150
(E) 180
Rationale: 70% is 30%-points above 40% and 10%-points below 80%.
Thus the ratio of "the first 30 games" to "remaining games" is 1:3.
So the team played a total of 30+90 = 120 games.
The answer is C.
Answer: (C) 120
Question: A specialized type of sand consists of 40% mineral X by volume and 60% mineral Y by volume. If mineral X weighs 2.5 grams per cubic centimeter and mineral Y weighs 4 grams per cubic centimeter, how many grams does a cubic meter of specialized sand combination weigh? (1 meter = 100 centimeters)
(A) 3,400,000
(B) 2,800,000
(C) 55,000
(D) 28,000
(E) 280
Rationale: Let the volume be 1 m^3 = 1m * 1m * 1m = 100cm * 100cm * 100cm = 1,000,000 cm^3
By volume
40% is X = 400,000 cm^3
60% is Y = 600,000 cm^3
By weight,
In 1 cm^3, X is 2.5 gms
In 400,000 cm^3 , X = 2.5 * 400,000 = 1,000,000 grams
In 1 cm^3, Y is 4 gms
In 600,000 cm^3, Y = 4 * 600,000 = 2,400,000 gms
Total gms in 1 m^3 = 1,000,000 + 2,400,000 = 3,400,000
ANSWER:A
Answer: (A) 3,400,000
Question: A man purchased 3 blankets @ Rs.100 each, 5 blankets @ Rs.150 each and two blankets at a certain rate which is now slipped off from his memory. But he remembers that the average price of the blankets was Rs.150. Find the unknown rate of two blankets?
(A) 450
(B) 992
(C) 276
(D) 187
(E) 161
Rationale: 10 * 150 = 1500
3 * 100 + 5 * 150 = 1050
1500 – 1050 = 450
Answer: A
Answer: (A) 450
Question: For which of the following functions f(x), is it always true that f(a/b) = f(b/a)?
(A) f(x) = 1/x
(B) f(x) = x^2
(C) f(x) =1/(x/2)
(D) f(x) = x+1
(E) None of the above
Rationale: Consider a/b = 2 and b/a = 0.5
A) f(2)=1/2
f(0.5)=2
NO
B) f(2) = 2^2 = 4
f(0.5)= 0.5^2 = 0.25
NO
C) f(2)= 1/(2/2) =1
f(0.5) = 1/(0.5/2) = 4
NO
D) f(2)=2+1=3
f(0.5) = 0.5+1=1.5
NO
Answer is E
Answer: (E) None of the above
Question: If x is Negative integer ,y is positive integer, and 7x+3y=14 , which of the following could be the value of x ?
(A) -1
(B) -5
(C) -2
(D) -3
(E) -4
Rationale: Use answer options to solve this problem -
x is negative integer (-1,-2,-3......)
put x=-1
7x+3y=14
7(-1)+3y=14
-7+3y=14
3y=14+7
3y=21
y=7
Answer will be (A)
Answer: (A) -1
Question: The length of a rectangular plot is 10 meters more than its width. If the cost of fencing the plot at $15.50 per meter is $930, what is the length of the plot in meters?
(A) 23
(B) 20
(C) 28
(D) 11
(E) 19
Rationale: perimeter = 2L + 2W = 2L + 2(L-10) = 4L - 20
cost of fencing = (4L - 20) * 15.50 = 62L - 310 = 930
62L = 1240
L = 20 meters
The answer is B.
Answer: (B) 20
Question: If the area of a circle is 25pi square feet, find its circumference.
(A) 10 pi feet
(B) 28 pi feet
(C) 38 pi feet
(D) 48 pi feet
(E) 58 pi feet
Rationale: The area is given by pi *r* r. Hence
pi * r *r = 25 pi
r * r = 25 ; hence r = 25 feet
The circumference is given by
2 * pi * r = 2 * pi * 5 = 10 pi feet
correct answer A
Answer: (A) 10 pi feet
Question: What is the dividend. divisor 17, the quotient is 8 and the remainder is 5
(A) A)145
(B) B)141
(C) C)150
(D) D)153
(E) E)158
Rationale: D = d * Q + R
D = 17 * 8 + 5
D = 136 + 5
D = 141
Answer : B
Answer: (B) B)141
Question: How many two-digit integers exist such that all their digits are odd?
(A) 80
(B) 25
(C) 120
(D) 125
(E) 135
Rationale: so last digit can be filled in 5 ways- 1,3,5,7,9
there are 5 possibilities. The answer is 5∗5=25
The correct answer is B
Answer: (B) 25
Question: The true discount on Rs.1600 due to after a certain of 5% per annum is Rs.160. The time after which it is due is
(A) 27months
(B) 23months
(C) 20months
(D) 12months
(E) None of these
Rationale: Explanation:
P.W. = Rs. (1600 - 160) = Rs. 1440
∴ S.I. on Rs.1440 at 5% is Rs. 160.
∴ Time = [100 × 160/1440 × 5] = 20/9 years = [20/9 × 12] months = 27 months.
Answer: A
Answer: (A) 27months
Question: A shopkeeper sold sarees at Rs. 266 each after giving 5% discout on labelled price. Had he not given the discount, he would have earned a profit of 12% on the cost price. What was the cost price of each saree?
(A) 240
(B) 250
(C) 260
(D) 270
(E) None
Rationale: Sol.
S.P. of 1 saree = Rs.266. Let the labelled price of each saree be Rs. x.
Then, 95/100x = 266 ⇒ x = Rs. [266*100]/95 = Rs. 280.
New, S.P. = Rs. 280, Profit = 12%.
∴ C.P. of 1 saree = Rs. [100/112 * 280] = Rs. 250.
Answer B
Answer: (B) 250
Question: Pipes A and B can fill a tank in 6 and 3 hours respectively. Pipe C can empty it in 12 hours. If all the three pipes are opened together, then the tank will be filled in:
(A) 2 2/5 hours.
(B) 3 2/5 hours.
(C) 1 1/5 hours.
(D) 4 2/5 hours.
(E) 2 1/5 hours.
Rationale: Explanation:
Pipes A and B can fill the tank in 5 and 6 hours respectively. Therefore,
part filled by pipe A in 1 hour =1/6
part filled by pipe B in 1 hour = 1/3
Pipe C can empty the tank in 11 hours. Therefore,
part emptied by pipe C in 1 hour =1/12
Net part filled by Pipes A,B,C together in 1 hour
=1/6+1/3-1/12=5/12
i.e., the tank can be filled in 12//5=2 2/5 hours.
Answer: Option A
Answer: (A) 2 2/5 hours.
Question: Of the 13 employees in a certain department, 1 has an annual salary of 38,000, 2 have an annual salary of 45,900 each, 2 have an annual salary of 42,500 each, 3 have an annual salary of 40,000 each and 5 have an annual salary of 48,500 each. What is the median annual salary for the 13 employees?
(A) 38,000
(B) 40,000
(C) 42,500
(D) 45,900
(E) 48,500
Rationale: Median is just the value in the middle when you arrange all values in the ascending order
In this question, the 7th value would be the median (Since there are 13 employees)
38, 40, 40, 40, 42.5, 42.5,45.9
So, answer is D.
Answer: (D) 45,900
Question: Observe the dots on a dice (one to six dots) in the following figures. How many dots are contained on the face opposite to that containing four dots?
(A) 2
(B) 6
(C) 7
(D) 8
(E) 9
Rationale: Explanation:
We shall assume the dice in fig. (ii) to be rotated so that the 5 dots appear at the same position as in fig. (i) i.e. on RHS face (i.e. on face II as per activity 1) and 1 dot appears at the same position as in fig; (i) i.e. on Front face (i.e. on face I). Then, from the, two figures, 2 dots appear on the top face (i.e. on face V) and 4 dots appear on the Bottom face (i.e. on face VI).
Since, these two faces are opposite to each other, therefore, two dots are contained on the face opposite to that containing four dots.
Answer: A) 2
Answer: (A) 2
Question: 11234783131 find the next three numbers
(A) 145
(B) 178
(C) 176
(D) 181
(E) 191
Rationale: we can write in this way
23 - 11 = 12 = 12*1
47-23 = 24 = 12*2
83-47 = 36 = 12*3
131 - 83 = 48 =12*4
x-131 = 60 = 12*5, x is the unknown
=>x= 131+60 = 191
so the answer is 191
ANSWER:E
Answer: (E) 191
Question: When the integer n is divided by 17, the quotient is x and the remainder is 5. When n is divided by 23, the quotient is y and the remainder is 16. Which of the following is true?
(A)  23x + 17y =19
(B)  17x –23y = 11
(C)  17x +23y =19
(D)  14x + 5y = 6
(E)  5x – 14y = -6
Rationale: From the problem it follows:
n=17x+5
n=23y+16
So, 17x+5=23y+16
17x-23y=11
The answer is B
Answer: (B)  17x –23y = 11
Question: 1, 8, 27, 64, 125, ?
(A) 216
(B) 205
(C) 200
(D) 250
(E) 180
Rationale: The sequence is a series of cubes, 1, 8, 27, 64, 125, 216....
Answer : A.
Answer: (A) 216
Question: The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 8 minutes, then the area of the park (in sq. m) is:
(A) 152600m2
(B) 153500m2
(C) 153600m2
(D) 153800m2
(E) None of these
Rationale: Explanation:
Question seems to be typical, but trust me it is too easy to solve, before solving this, lets analyse how we can solve this.
We are having speed and time so we can calculate the distance or perimeter in this question.
Then by applying the formula of perimeter of rectangle we can get value of length and breadth, So finally can get the area. Lets solve it:
Perimeter = Distance travelled in 8 minutes,
=> Perimeter = 12000/60 * 8 = 1600 meter. [because Distance = Speed * Time]
As per question length is 3x and width is 2x
We know perimeter of rectangle is 2(L+B)
So, 2(3x+2x) = 1600
=> x = 160
So Length = 160*3 = 480 meter
and Width = 160*2 = 320 meter
Finally, Area = length * breadth
= 480 * 320 = 153600
Answer: Option C
Answer: (C) 153600m2
Question: A forest consists of 4 elms, 6 red woods, and 5 birches In how many ways can 2 elms, 2 red woods and 2 birches be selected from the given group?
(A) 987 ways
(B) 346 ways
(C) 5400 ways
(D) 157 ways
(E) 134 ways
Rationale: The number of ways of selecting two elms, two red woods and two birches is:
= ⁴C₂ * ⁶C₂ * ⁵C₂
= (4 * 3 * 2)/(2 * 1) * (6 * 5)/(2 * 1) * (5 * 4 * 3)/(2 * 1)
= 12 * 15 * 30
= 5400 ways.
Answer: C
Answer: (C) 5400 ways
Question: A committee of 6 is chosen from 8 men and 5 women so as to contain at least 2 men and 3 women. How many different committees could be formed?
(A) 635
(B) 700
(C) 1404
(D) 2620
(E) 3510
Rationale: The only cases possible are :
1. 2 men and 4 women : 8C2 * 5C4 = 140
2. 3 men and 3 women: 8C3*5C3 = 560
Rest of the cases will either have 1 or 0 men (not allowed) or will have 1 or 2 or 0 women (not allowed)
Total possible combinations = 140+560 = 700. Thus B is the correct answer.
Answer: (B) 700
Question: A box contains 100 balls, numbered from 1 to 100. If 3 balls are selected at random and with replacement from the box. If the 3 numbers on the balls selected contain two odd and one even. What is the probability J that the first ball picked up is odd numbered?
(A) 	0
(B) 	1/3
(C) 	1/2
(D) 	2/3
(E) 	1
Rationale: Answer-D
Selecting the balls either Even or Odd is having probability 50/100=1/2
We have already selected 3 balls with 2 odd numbers and 1 even number.
So we have 3 combinations OOE, OEO, EOO. We have 3 outcomes and 2 are favourable as in 2 cases 1st number is odd. So probability J is 2/3.D
Answer: (D) 	2/3
Question: A can run 22.5 m while B runs 25 m. In a kilometre race B beats A by:
(A) 100
(B) 378
(C) 777
(D) 299
(E) 277
Rationale: Explanation:
When B runs 25 m, A runs \inline \fn_jvn {\color{Black} \frac{45}{2}} m
When B runs 1000 m, A runs \inline \fn_jvn {\color{Black} \left ( \frac{45}{2}\times \frac{1}{25}\times 1000 \right )}m = 900 m.
\inline \fn_jvn {\color{Black} \therefore }B beats A by 100 m.
Answer: A) 100 m
Answer: (A) 100