mathewhe/aqua_rat huggingface dataset:
Question: If 9 is a factor of 2k, then which of the following may not be an integer?
(A) 6k/54 + 2k/3
(B) (4k-18)/9
(C) (2k+27)/9
(D) (81-4k^2)/81
(E) (2k-3)/3
Rationale: I got the right answer A after plugging in 18 for k.
While going through Kaplan's explanation, I couldn't understand the part about choice A.
"6k/54 + 2k/3 = 3/6 * 2k/9 + 2k/3.
Since 9 is a factor of 2k, 3 is also factor of 2k. So 2k/3 is an integer, as is 2k/9. But 3/6 = 1/2, so if 2k/9 is not even, the expression 3/6 * 2k/9 will not be even."
But, isn't 2k/9 always even? 9 is a factor of 2k, which means that we could have 2(9), 2(2)(9), 2(3)(9), and so forth. The 9 in the denominator cancels out the 9 in the numerator. So we are left with 2 * something. So 2k/9 is even.A
Answer: (A) 6k/54 + 2k/3
Question: If the selling price of 50 books is equal to the cost price of 40 books, then the loss or gain percent is:
(A) 10
(B) 30
(C) 20
(D) 40
(E) 50
Rationale: C
20%
Let C.P. of each books be $ 1.
Then, C.P. of 50 books= $50;
S.P. of 50 books = $40.
Loss % = 10/50 * 100 = 20%
Answer: (C) 20
Question: At a certain resort, each of the 39 food service employees is trained to work in a minimum of 1 restaurant and a maximum of 3 restaurants. The 3 restaurants are the family buffet, the dining room, and the snack bar. Exactly 19 employees are trained to work in the family buffet, 18 are trained to work in the dining room, and 12 are trained to work in the snack bar. If 2 employees are trained to work in exactly 2 restaurants, how many employees are trained to work in all 3 restaurants?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: 39 = 19 + 18 + 12 - 2 - 2x
2x = 19 + 18 + 12 - 2 - 39
= 45 - 37
= 8
x = 4
C
Answer: (C) 4
Question: The area of a circle of radius 5 is numerically what percent of its circumference?
(A) 200
(B) 225
(C) 240
(D) 250
(E) None
Rationale: Solution
Required % = [ Π x (5)2 / 2Π x 5 x 100]%
‹=›250%.
Answer D
Answer: (D) 250
Question: The length of the bridge, which a train 130 meters long and travelling at 45 km/hr can cross in 30 seconds, is?
(A) 297 m
(B) 178 m
(C) 245 m
(D) 278 m
(E) 297 m
Rationale: Speed = (45 * 5/18) m/sec
= (25/2) m/sec. Time = 30 sec. Let the length of bridge be x meters. Then, (130 + X)/30 = 25/2
==> 2(130 + X) = 750 ==> X
= 245 m.
Answer:C
Answer: (C) 245 m
Question: How many paying stones, each measuring 2 m * 2 m are required to pave a rectangular court yard 30 m long and 18 m board?
(A) 99
(B) 18
(C) 135
(D) 17
(E) 12
Rationale: 30 * 18= 2* 2 * x => x
= 135
Answer: C
Answer: (C) 135
Question: Vijay spends 40% of his monthly income on household items, 20% of his monthly income on buying cloths, 10% of his monthly income on medicines and saves the remaining amount which is Rs. 6000. Find his monthly income.
(A) Rs. 40000
(B) Rs. 20000
(C) Rs. 50000
(D) Rs. 45000
(E) None of these
Rationale: Savings 30% - 6000
Expenditure 70% - 14000
Total - 20000
Answer : B
Answer: (B) Rs. 20000
Question: X and Y invest Rs.21000 and Rs.15000 respectively in a business. At the end of the year, they make a profit of Rs.26400. What is the share of X in the profit?
(A) Rs.14400
(B) Rs.26400
(C) Rs.12000
(D) Rs.12500
(E) Rs.15400
Rationale: Ratio of the investment=21000:15000=7:5
Share of X in the profit=(26400×7)/12=
=15400
ANSWER:E
Answer: (E) Rs.15400
Question: Company KW is being sold, and both Company A and Company B were considering the purchase. The price of Company KW is 30% more than Company A has in assets, and this same price is also 100% more than Company B has in assets. If Companies A and B were to merge and combine their assets, the price of Company KW would be approximately what percent of these combined assets?
(A) 66%
(B) 79%
(C) 86%
(D) 116%
(E) 150%
Rationale: Let the price of Company A's assets be 100
Price of assets of KW is 30% more than company A's assets which is 130
Price of assets of KW is 100% more than company B's assets which means price of Company B's assets is half the price of KW = 65
A+B = 165
KW = 130
KW/(A+B)*100 = 130/165*100 = 78.78% or 79%
B
Answer: (B) 79%
Question: Find the distance covered by a man walking for 72min at a speed of 10km/hr?
(A) 12 km
(B) 3km
(C) 4km
(D) 5km
(E) 6km
Rationale: Distance = 10*72/60 = 12 km
Answer is A
Answer: (A) 12 km
Question: The sum of the heights of two high-rises is x feet. If the first high rise is 37 feet taller than the second, how tall will the second high rise be?
(A) (x- 37)
(B) 2x−(37+z)
(C) (x−37)/2 + z
(D) x/2 - 37 + z
(E) (2x−37)/z
Rationale: I will note h1 the height of high-rise 1 and h2 the height of high-rise 2. SO:
h1 + h2 = x
and h1 = h2 + 37 =>
h2 + h2 + 37 = x => 2h2 = x-37 =? h2 = (x-37)
CORRECT ANSWER A
Answer: (A) (x- 37)
Question: If (a-5)(y+2) = 0 which of the following must be true?
(A)  a = y
(B)  a > y
(C)  a < y
(D)  ay = -10
(E)  None of the above
Rationale: From (a-5)(y+2) = 0 it follows that either a=5 or y=-2.
(A) a = y --> not necessarily true. Consider a=5 and y=0.
(B) a > y --> not necessarily true. Consider a=5 and y=10.
(C) a < y --> not necessarily true. Consider a=5 and y=0.
(D) ay = -10 --> not necessarily true. Consider a=5 and y=0.
Thus, none of the statements must be true.
Answer: E.
Answer: (E)  None of the above
Question: There are two decks of 10 cards each. The cards in each deck are labeled with integers from 10 to 20 inclusive. If we pick a card from each deck at random, what is the probability that the product of the numbers on the picked cards is a multiple of 6?
(A) 0.23
(B) 0.36
(C) 0.4
(D) 0.42
(E) 0.46
Rationale: If 6 is a multiple, we need 2 and 3 as a factor of the number. If we factor the numbers 11 through 20 we have:
11 = 11
12 = 2*2*3
13 = 13
14 = 7*2
15 = 5*3
16 = 2*2*2
17 = 17
18 = 3*2*3
19 = 19
20 = 5*2*2
Combos that have a 2 and a 3 as factors (first + second card):
12 + anything - 19 of these possibilities (we count 12 + 12 only once)
14 + 15 - 2 of these possibilities
15 + 16 - 2 of these possibilities
15 + 20 - 2 of these possibilities
18 + anything (except 12, since that is counted in our first option) - 17 of these possibilities
Total possibilities that will be a multiple of 6: 42
Total possibilites: 10*10=100
Probability = 42/100 = 0.40
Answer:C
Answer: (C) 0.4
Question: What is the difference between the C.I. on Rs. 6000 for 1 1/2 years at 4% per annum compounded yearly and half-yearly?
(A) s.2.04
(B) s.2.08
(C) s.2.02
(D) s.2.83
(E) s.2.45
Rationale: C.I. when interest is compounded yearly
= [6000 * (1 + 4/100) * (1 + (1/2 * 4)/100]
= 6000 * 26/25 * 51/50 = Rs. 6364.8
C.I. when interest is compounded half-yearly
= [6000 * (1 + 2/100)2]
= (6000 * 51/50 * 51/50 * 51/50)
= Rs. 6367.25 Difference
= (6367.25 - 6364.8)
= Rs.2.45.
Answer: E
Answer: (E) s.2.45
Question: Cistern may be filled by a tap in 4 hours while it can be emptied by another tap in 9 hours. If both the taps are opened simultaneously, then after how much time cistern will get filled ?
(A) 8 hrs
(B) 8.5 hrs
(C) 7 hrs
(D) 7.2 hrs
(E) 9 hrs
Rationale: filled in 1 hr = 1/4
empties in 1 hr = 1/9
net filled in 1 hr = 1/4-1/9
==>filled in 36/5 ==> 7.2 hrs
ANSWER D
Answer: (D) 7.2 hrs
Question: A feed store sells two varieties of birdseed: Brand A, which is 40% millet and 60% sunflower, and Brand B, which is 65% millet and 35% safflower. If a customer purchases a mix of the two types of birdseed that is 50% millet, what percent of the mix is Brand A?
(A) 40%
(B) 45%
(C) 50 %
(D) 60 %
(E) 55 %
Rationale: Another method to solve this question using equations:
1 kg of Brand A will have 400g millet and 600g sunflower.
1 kg of Brand B will gave 650g millet and 350g sunflower.
Suppose,x kg of Brand A and y kg of Brand B are in the mixture.
Then total weight of millet = 400x+650 y g
Total weight of mixture = 1000x + 1000 y g
Given that millet is 500% hence
(400x+650y)/(1000x + 1000y) = 1/2
or, 800x + 1300 y = 1000x+1000y
or 300y=200x
or, x/y = 3/2
% of Brand A = (3/(3+2))*100 =60%
Hence answer is D
Answer: (D) 60 %
Question: A man is 24 years older than his son. In two years, his age will be twice the age of his son. What is the present age of his son?
(A) 23 years
(B) 22 years
(C) 21 years
(D) 20 years
(E) 19 years
Rationale: Let present age of the son =x years
Then, present age the man =(x+24) years
Given that, in 2 years, man's age will be twice the age of his son
⇒(x+24)+2=2(x+2)
⇒x=22
ANSWER:B
Answer: (B) 22 years
Question: Excluding stoppages, the speed of a train is 45 kmph and including stoppages it is 32 kmph. Of how many minutes does the train stop per hour?
(A) 17
(B) 83
(C) 12
(D) 83
(E) 28
Rationale: Explanation:
T = 13/45 * 60 = 17
Answer: Option A
Answer: (A) 17
Question: If 9/(1 + 4/x) = 1, then x =
(A) 3
(B) 1/2
(C) 1/3
(D) -1/3
(E) -3
Rationale: The expression 9/(1 + 4/x) = 1should have been equal to something .
If 9/(1 + 4/x) = 1 = 1
=> 9x/(x + 4) = 1
=> 9x = x + 4
=>8x = 4
=>x = 1/2
Correct Option : B
Answer: (B) 1/2
Question: A rectangular lawn of dimensions 80 m * 60 m has two roads each 10 m wide running in the middle of the lawn, one parallel to the length and the other parallel to the breadth. What is the cost of traveling the two roads at Rs.3 per sq m?
(A) Rs.3600
(B) Rs.3700
(C) Rs.3800
(D) Rs.3900
(E) Rs.4900
Rationale: Area = (l + b – d) d
(80 + 60 – 10)10 => 1300 m2
1300 * 3 = Rs.3900
ANSWER:D
Answer: (D) Rs.3900
Question: In how many different ways can the letters of the word JUDGE be arranged so that the vowels always come together?
(A) 36
(B) 48
(C) 52
(D) 30
(E) 24
Rationale: Required number = 4!2! = 48
Answer is B
Answer: (B) 48
Question: What number comes next in this Number series.
4 4 6 9 7 8 8 ?
*Hint: check calende
(A) 1
(B) 3
(C) 6
(D) 7
(E) 8
Rationale: A
7 (the number of letters in the month January)
June : 4 letters
July : 4 letters
August: 6 letters
September : 9 letters
October : 7 letters
November : 8 letters
December : 8 letters
Answer: (D) 7
Question: If the price of petrol increases by 32, by how much must a user cut down his consumption so that his expenditure on petrol remains constant?
(A) 25%
(B) 20%
(C) 24.2%
(D) 33.33%
(E) None of these
Rationale: Explanation :
let us assume before increase the petrol will be Rs. 100.
After increase it will be Rs (100+32) i.e 132.
Now, his consumption should be reduced to :-
=(132−100)/132 ∗ 100.
Hence, the consumption should be reduced to 24.2%.
Answer : C
Answer: (C) 24.2%
Question: In a can, there is a mixture of milk and water in the ratio 5:3. If the can is filled with an additional 8 liters of milk, the can would be full and the ratio of milk and water would become 2:1. Find the capacity of the can?
(A) 56
(B) 60
(C) 64
(D) 68
(E) 72
Rationale: Let C be the capacity of the can.
(5/8)*(C-8)+8=(2/3)*C
15C-120+192=16C
C=72
The answer is E.
Answer: (E) 72
Question: Running at the same constant rate,6 identical machines can produce a total of 270 bottles per minute.At this rate,how many bottles could 16 such machines produce in 4 minutes ?
(A) 2880
(B) 1800
(C) 2700
(D) 10800
(E) None of these
Rationale: Solution
Let the required number of bottles be x.
More machines,More bottles (Direct Proportion)
More minutes,More bottles (Direct Proportion)
âˆ´ 6 Ã— 1 Ã— x = 16 Ã— 4 Ã— 270 â‡” x = 16x4x270/6= 2880 . Answer A
Answer: (A) 2880
Question: If x^2 = y^3 , where x and y are non negative and non zero integers, what is the greatest possible value of x * y from options below?
(A) 343
(B) 625
(C) 243
(D) 921
(E) 741
Rationale: C. x=27, y=9
27^2=729
9^3=729
x * y = 27 * 9 = 243
My answer is (C) 243
Answer: (C) 243
Question: The ratio between the speeds of two trains is 7: 9. If the second train runs 540 kms in 3 hours, then the speed of the first train is ?
(A) 140 km/hr
(B) 130 km/hr
(C) 110 km/hr
(D) 120 km/hr
(E) None of these
Rationale: Explanation:
Let the speeds of two trains be 7X and 9X km/hr.
9/X=540/3=>X=20Km/hr
So speed of first train is 20*7 = 140 km/hr
Option A
Answer: (A) 140 km/hr
Question: Vehicle X is 22 miles ahead of Vehicle Y, which is traveling the same direction along the same route as Vehicle X. If Vehicle X is traveling at an average speed of 36 miles per hour and Vehicle Y is traveling at an average speed of 45 miles per hour, how long will it take Vehicle Y to overtake and drive 23 miles ahead of Vehicle X?
(A) 5 hours
(B) 7 hours 20 minutes
(C) 4 hours
(D) 3 hours 45 minutes
(E) 2 hours 30 minutes
Rationale: Relative speed = 45-36 = 9 miles per hour
Dist required = 22+23 = 45 miles
Time taken to overtake = 45/9 = 5 hours. A is the answer.
Answer: (A) 5 hours
Question: If the personal income tax rate is lowered from 38% to 30%, what is the differential savings for a tax payer having an annual income before tax to the tune of $36500?
(A) $1825
(B) $5000
(C) $3150
(D) $7000
(E) $10000
Rationale: Saving = (38-33)% of 36500 = 1825.
Answer:A
Answer: (A) $1825
Question: Currently guavas cost 30 cents/pound. Due to a disease affecting the guava trees it is expected that next month guavas will cost 50% more than they do currently. How much are guavas expected to cost next month?
(A) 50 cents /pound
(B) 45 cents /pound
(C) 55 cents /pound
(D) 60 cents /pound
(E) 65 cents /pound
Rationale: If a new cost is p percent greater than the old cost, then (new cost) = (old cost) + (p/100)(old cost).
In this case, (new cost) = 30 cents/pound + (50/100)(30 cents/pound)
= 30 cents/pound + 15 cents/pound
= 45 cents /pound
Answer : B
Answer: (B) 45 cents /pound
Question: There are 10 children in a company's day-care center, and a pair of children is to be selected to play a game. At most, how many different pairs are possible?
(A) 100
(B) 90
(C) 50
(D) 45 different pairs
(E) 25
Rationale: 1. first child out of 0 - 10 possibilities
2. second child out of 9 - 9 possibilities. the total number of pairs = 9*10=90
3. exclude xy yx cases: 90/2=45
Second way
N=10C2=10!/(8!2!) =10*9/2=45
ANS:D
Answer: (D) 45 different pairs
Question: 8.008/4.004
(A) 2
(B) 0.02
(C) 0.2
(D) 20
(E) 2
Rationale: Answer is 2, move the decimal forward three places for both numerator and denominator or just multiply both by a thousand. The result is 8008/4004= 2
Answer A
Answer: (A) 2
Question: If the sides of a cube are in the ratio 4:3. What is the ratio of their diagonals?
(A) 4:3
(B) 4:0
(C) 4:5
(D) 4:7
(E) 4:2
Rationale: Explanation:
a1:a2 = 4:3
d1:d2 = 4:3
Answer: Option A
Answer: (A) 4:3
Question: A rectangular garden is to be twice as long as it is wide. If 150 yards of fencing, including the gate, will completely enclose the garden, what will be the length of the garden, in yards?
(A) 40
(B) 50
(C) 60
(D) 70
(E) 80
Rationale: ALTERNATE APPROACH
Backsolving ( Using answer options to reach the correct answer ) can work wonders here if one is fast in calculations.
Given Perimeter is 150
So, 2 ( L + B ) = 150
Or, L + B = 75
Now use the answer options ( Given Length ; Breath will be half the length)
(A) 40
L = 40 ; B = 20
L + b = 60
(B) 50
L = 50 ; B = 25
L + b = 75
(C) 60
L = 60; B = 30
L + b = 90
(D) 70
L = 70; B = 35
L + b = 105
(E) 80
L = 80; B = 40
L + b = 120
Thus you see no, need of any calculations, U can reach the correct option only by checking options ; correct answer will be (B)
Answer: (B) 50
Question: Find the roots of quadratic equation: 3x2 - 7x - 6 = 0?
(A) -6, 3
(B) 3, -2/3
(C) -5, 2
(D) -9, 2
(E) None of these
Rationale: 3x2 - 9x + 2x - 6 = 0
3x(x - 3) + 2(x - 3) = 0
(x - 3)(3x + 2) = 0 => x = 3, -2/3
ANSWER:B
Answer: (B) 3, -2/3
Question: While purchasing one item costing Rs. 400, I had to pay the sales tax at 7% and on another costing Rs. 6400, the sales tax was 9%. What percent of the sales tax I had to pay, taking the two items together on an average ?
(A) 8 + 15/17
(B) 8 + 15/18
(C) 8 + 15/12
(D) 8 + 15/11
(E) 8 + 15/110
Rationale: Explanation:
Total sales tax paid = 7% of Rs, 400 + 9% of Rs. 6400
== Rs. (28 + 576) = Rs. 604.
Total cost of the items = Rs. (400 + 6400) = Rs. 6800.
Required percentage =% =%.
Answer: A) 8 + 15/17
Answer: (A) 8 + 15/17
Question: In a ground there are men and dogs. In all, there are 20 heads and 72 feet. How many men and how many horses are in the ground?
(A) 8 men and 14 dogs.
(B) 7 men and 14 dogs.
(C) 6 men and 14 digs.
(D) 5 men and 14 dogs.
(E) 4 men and 14 dogs.
Rationale: 6 men and 14 dogs.
Let M = men and D = dogs. We can come up with 2 equations.
M + D = 20
2M + 4D= 72
Solving the 2 equations will give 6 men and 14 dogs.
Answer C
Answer: (C) 6 men and 14 digs.
Question: A walks around a circular field at the rate of one round per hour while B runs around it at the rate of six rounds per hour. They start at same point at 8:30 am. They shall first cross each other at ?
(A) 7:15 am
(B) 7:30 am
(C) 8: 42 am
(D) 7:50 am
(E) 7:60 am
Rationale: Explanation:
Relative speed between two = 6-1 = 5 round per hour
They will cross when one round will complete with relative speed,
which is 1/5 hour = 12 mins.
So 8:30 + 12 mins = 8:42
Option C
Answer: (C) 8: 42 am
Question: A 28 cm long wire is to be cut into two pieces so that one piece will be 2/5th of the other, how many centimeters will the shorter piece be?
(A) 12
(B) 8
(C) 88
(D) 77
(E) 14
Rationale: 1: 2/5 = 5: 2
2/7 * 28 = 8
Answer: B
Answer: (B) 8
Question: Speed of a boat in standing water is 9 kmph and the speed of the stream is 1. 5 kmph. A man rows to a place at a distance of 105 km and comes back to the starting point. The total time taken by him is
(A) 16 hours
(B) 18 hours
(C) 20 hours
(D) 24 hours
(E) None
Rationale: Solution
Speed upsteram	= 7.5 kmph.
Speed downsteram	= 10.5 kmph.
Total time taken	=[10.5/7.5 + 105/10.5]hours
= 24 hours.
Answer D
Answer: (D) 24 hours
Question: If m = ||n – 3| – 2|, for how many values of n is m = 6?
(A) 1
(B) 3
(C) 4
(D) 5
(E) 2
Rationale: m = ||n – 3| – 2| can be 4 only and only when n-3= +/-8. so there are 2 values of n
Answer : E
Answer: (E) 2
Question: Pascal has 96 miles remaining to complete his cycling trip. If he reduced his current speed by 4 miles per hour, the remainder of the trip would take him 16 hours longer than it would if he increased his speed by 50%. What is his current speed W ?
(A)  6
(B)  8
(C)  10
(D)  12
(E)  16
Rationale: Let the current speed be x miles per hour.
Time taken if speed is 50% faster (i.e. 3x/2 = 1.5x) = 96/1.5x
Time taken if speed is reduced by 4 miles/hr (i.e. (x-4)) = 96/(x-4)
As per question, 96/(x-4) - 96/1.5x = 16
Solving this W we get x = 8.
B.
Answer: (B)  8
Question: A merchant has 100 lbs of sugar, part of which he sells at 7% profit and the rest at 15% profit. He gains 10 % on the whole. Find how much is sold at 7% profit?
(A) 70 lbs
(B) 40 lbs
(C) 30 lbs
(D) 50 lbs
(E) 63 lbs
Rationale: These types ofweighted averagequestions can be solved in a variety of ways, so you can choose whichever method you find easiest/fastest. Here's another variation on the Weighted Average Formula:
A = # of pounds sold at 7% profit
B = # of pounds sold at 15% profit
A+B = 100 pounds
(.07A + .15B)/(A+B) = .10
.07A + .15B = .1A + .1B
.05B = .03A
5B = 3A
5/3 = A/B
So, for every 5 pounds of A, we have 3 pounds of B.
With 100 pounds total, we have 63 pounds of A and 37 pounds of B.
option E
Answer: (E) 63 lbs
Question: The difference between two integers is 5. Their product is 500. Find the numbers.
(A) 15, 20
(B) 20, 25
(C) 30, 25
(D) 21, 26
(E) 25, 27
Rationale: Explanation:
Let the integers be x and (x + 5). Then,
x(x + 5) = 500
x2 + 5x - 500 = 0
(x + 25)(x - 20) = 0
x = 20
So, the numbers are 20 and 25.
ANSWER IS B
Answer: (B) 20, 25
Question: The sum of the first 60 positive even integers is 3,750. What is the sum of the odd integers from 101 to 200, inclusive?
(A)  4,700
(B)  7,500
(C)  10,500
(D)  15,000
(E)  19,600
Rationale: 101+103+.......199
If we remove 100 from each of these it will be sum of 1st 100 odd numbers.
so 101+103+.......199 = 60 * 100 + (1+3+5+7+......)
sum of 1st 100 natural numbers = (100 * 101) / 2 = 5050
Sum of 1st 60 positive even integers = 3750
sum of 1st 100 odd numbers = 5050 - 3750 = 1300
so 101+103+.......199 = 60 * 100 + (1+3+5+7+......) = 6000 + 1300 =4700
A is the answer.
Answer: (A)  4,700
Question: Source: Knewton
A cyclist's speed varies, depending on the terrain, between 6.0 miles per hour and 12.0 miles per hour, inclusive. What is the maximum distance, in miles, that the cyclist could travel in 7 hours?
(A)  42
(B)  84
(C)  70
(D)  98
(E)  140
Rationale: We are told that:generallya cyclist's speed varies, depending on the terrain, between 6.0 miles per hour and 12.0 miles per hour, inclusive. Is it possible the cyclist to travel with maximum speed for some time? Why not, if there is right terrain for that. So, if there is long enough terrain for the maximum speed of 12 mph then the maximum distance, in miles, that the cyclist could travel in 7 hours would be 7*12=84 miles.
Answer: B.
Answer: (B)  84
Question: If x ≠ 0 and x^3 - (2- x^3)/x^3 = y/x^2, then y =
(A) -2-x
(B) -2+x
(C) -(x+2)
(D) -2/x
(E) 1/x
Rationale: x^3 - (2- x^3)/x^3 = y/x^2
-2/x^3 = y/x^2
y = -2/x
Answer : D
Answer: (D) -2/x
Question: Three friends are planning to attend a concert. If another friend also goes with them, they will get a group discount on their tickets. If the new total price of the tickets with the group discount is the same as the original total price of the tickets without the group discount, how much is the discount?
(A) 5%
(B) 10%
(C) 20%
(D) 25%
(E) 33%
Rationale: Let x be the original price of one ticket.
The total original cost is 3x.
The new cost is 4y, where y is the discounted price of one ticket.
3x = 4y
y = 3x/4 =0.75x which is a discount of 25%.
The answer is D.
Answer: (D) 25%
Question: A can do a piece of work in 15 days. A does the work for 5 days only and leaves the job. B does the remaining work in 10 days.In how many days B alone can do the work?
(A) 5days
(B) 15 days
(C) 12 days
(D) 9 days
(E) 10 days
Rationale: Explanation:
A’s 5 day work = 5*1/15=1/3
Remaining work = 1-1/3=2/3
B completes 2/3 work in 6 days
B alone can do in x days
2/3*x=10
X=15 days
Answer: Option B
Answer: (B) 15 days
Question: If the sum of 5 consecutive integers is y, which of the following must be true?
I. y is an even number
II. y is an odd number
III. y is a multiple of 5
(A)  I only
(B)  II only
(C)  III and II only
(D)  I and III
(E)  III only
Rationale: I. If you start off with an even number, the sum (y) is even, and if you start off with an odd number the sum (x) is odd. Therefore this is not always true.
II. Same as above. This need not be always true.
III. Say, the first number is p. Then the sum of the five numbers = p + (p+1) + (p+2)...... + (p+4)
= 5p + 10 = 5 (p+2) => divisible by 5. There this must be true in all cases.
Therefore E is the answer.
Answer: (E)  III only
Question: A company consists of 5 senior and 3 junior staff officers. If a committee is created with 1 senior and 2 junior staff officers, in how many ways can the committee be formed?
(A)  15
(B)  30
(C)  45
(D)  80
(E)  200
Rationale: Choose 1 senior from 5 senior and choose 2 junior from 3 junior:
5C1 * 3C2 = 5 * 3 = 15
Ans: A
Answer: (A)  15
Question: The average of first ten prime numbers which are odd is?
(A) 15.9
(B) 15.5
(C) 15.2
(D) 15.8
(E) 13.2
Rationale: Sum of first 10 prime no. which are odd = 158
Average = 158/10 = 15.8
Answer: D
Answer: (D) 15.8
Question: Nitin 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 eleven years is Rs. 10200, how much money did he borrow?
(A) 10000
(B) 80288
(C) 2668
(D) 2600
(E) 2781
Rationale: Let the sum be Rs. x. Then,
[(x * 6 * 3)/100] + [(x * 9 * 5)/100] + [(x * 13 * 3)/100] = 10200
18x + 45x + 39x = (10200 * 100)
102x = 1020000 => x = 10000.
Answer:A
Answer: (A) 10000
Question: By how much is three-fifth of 600 greater than four- seventh of 210 ?
(A) 320
(B) 240
(C) 420
(D) None of these
(E) Cannot be determined
Rationale: Solution
3/5 of 600 - 4/7 of 210 = 240.
Answer B
Answer: (B) 240
Question: If we have 8 people in a meeting, in how many ways they can sit around a table?
(A) 10*9!
(B) 9*8!
(C) 8*7!
(D) 7*6!
(E) 6*5!
Rationale: If there are "n" people sitting around a table, there are "(n-1)!" possible arrangements:
Here, n=8
(n-1)!=7!=7*6!
Ans:"D"
Answer: (D) 7*6!