mathewhe/aqua_rat huggingface dataset:
Question: The length of a rectangle is two - fifths of the radius of a circle. The radius of the circle is equal to the side of the square, whose area is 100 sq.units. What is the area (in sq.units) of the rectangle if the rectangle if the breadth is 2 units?
(A) 140 sq.units
(B) 158 sq.units
(C) 8 sq.units
(D) 607 sq.units
(E) 815 sq.units
Rationale: Given that the area of the square = 100 sq.units
=> Side of square = √100= 10 units
The radius of the circle = side of the square = 10 units
Length of the rectangle = 2/5 * 10 = 4 units
Given that breadth = 2 units
Area of the rectangle = lb = 4 * 2 = 8 sq.units
Answer: C
Answer: (C) 8 sq.units
Question: If the wheel is 18 cm then the number of revolutions to cover a distance of 1056 cm is?
(A) 18
(B) 26
(C) 14
(D) 12
(E) 9.3
Rationale: 2 * 22/7 * 18 * x = 1056 => x
= 9.3
Answer: E
Answer: (E) 9.3
Question: Last Sunday a certain store sold copies of Newspaper A for $1.00 each and copies of Newspaper B for $1.25 each, and the store sold no other newspapers that day. If r percent of the store's revenues from newspapers sales was from Newspaper A and if j percent of the newspapers that the store sold were copies of Newspaper A, which of the following expresses r in terms of j?
(A) 100p / (125 - p)
(B) 150p / (250 - p)
(C) 300p / (375 - p)
(D) 400j / (500 - j)
(E) 500p / (625 - p)
Rationale: I have just started with qunats section .. I solved this by making two equations and got the answer ... However it was long way of doing it ...
I got the answer as : 100j /(125 - .25 j)...
Multiply this equation by 4 and you get D as the answer ,...
Answer: (D) 400j / (500 - j)
Question: A boat can move upstream at 14 kmph and downstream at 18 kmph, then the speed of the current is?
(A) 5
(B) 6
(C) 8
(D) 4
(E) 2
Rationale: US = 14
DS = 18
M = (18 - 14)/2 = 2 Answer:E
Answer: (E) 2
Question: The average age of husband, wife and their child 3 years ago was 27 years and that of wife and the child 5 years ago was 20 years. The present age of the husband is:
(A) 35 years
(B) 40 years
(C) 50 years
(D) 60 years
(E) None of these
Rationale: Explanation:
Sum of the present ages of husband, wife and child = (27 x 3 + 3 x 3) years = 90 years.
Sum of the present ages of wife and child = (20 x 2 + 5 x 2) years = 50 years.
Husband's present age = (90 - 50) years = 40 years.
ANSWER IS B
Answer: (B) 40 years
Question: The average of seven numbers is 18. The average of first three numbers is 14 and the average of last three numbers is 19. What is the middle number?
(A) 27
(B) 28
(C) 29
(D) 26
(E) 25
Rationale: Explanation:
The total of seven numbers = 7X18 = 126
The total of first 3 and last 3 numbers is = 3 X 14+3 X 19 = 99
So, the middle number is (126 – 99 ) = 27
Answer: A
Answer: (A) 27
Question: In how many years does a sum of Rs. 5000 yield a simple interest of Rs. 14500 at 15% p.a.?
(A) 19.33 years
(B) 18.33 years
(C) 17.33 years
(D) 16.33 years
(E) 15.33 years
Rationale: T = (100 * 14500)/(15 * 5000) = 19.33 years
ANSWER:A
Answer: (A) 19.33 years
Question: A playstation is available for $39000 cash or $17000 as down payment followed by five equal monthly instalments of $4800 each. The simple rate of interest per annum under the instalment plan would be
(A) 18%
(B) 19%
(C) 21.2%
(D) 21.81%
(E) 22.07%
Rationale: Simple interest SI = (P*R*T)/100
where P is the principal amount
R is the rate of interest
and T is time in years
the way I see it:playstation on down payment of 17,000, customer is not paying any interest. it is the remaining sum which will be paid for 5 months that will bear an interest. Therefore, the principal amount for which interest is being charged is 39,000 - 17,000 = 22,000
For this 22,000 a total sum of 5*4800 = 24,000 was pain. (Time is five months, so T = 5/12, as T is in years.)
thus, SI = 2000 or
2000 = (P*R*T)/100
2000 = (22,000*R*5)/(100*12)
R = (2,000*12*100)/22,000*5
R = 21.81%
Therefore answer is D
Answer: (D) 21.81%
Question: 2+2^2+2^+......+2^9=?
(A) 2044
(B) 1022
(C) 1056
(D) 1065
(E) None of them
Rationale: This is a G.P. in which a=2, r=2^2/2=2 and n=9
S^n=a(r^n -1)/(r-1)
=2x(2^9-1)/(2-1)
=2x(512-1)=2x511
=1022
Answer is B
Answer: (B) 1022
Question: 40 persons like apple. 7 like orange and mango dislike apple. 10 like mango and apple and dislike orange. 3 like all. How many people like apple?
(A) 47
(B) 46
(C) 54
(D) 58
(E) 62
Rationale: orange+mango-apple=7
mango+apple-orange=10
apple=40
orange+mango+apple=3
40+10+3-7=46 like apple
ANSWER:B
Answer: (B) 46
Question: Andy solves problems 74 to 135 inclusive in a Math exercise. How many problems does he solve?
(A) 53
(B) 62
(C) 51
(D) 50
(E) 49
Rationale: 135-74+1= 62
'B' is the answer
Answer: (B) 62
Question: An woman swims downstream 64 km and upstream 24 km taking 8 hours each time; what is the speed of the current?
(A) 1.6
(B) 1.8
(C) 3.5
(D) 1.5
(E) 2.5
Rationale: 64 --- 8 DS = 8
? ---- 1
24 ---- 8 US = 3
? ---- 1 S = ?
S = (8 - 3)/2 = 2.5
Answer: E
Answer: (E) 2.5
Question: The tax on a commodity is diminished by 20% but its consumption is increased by 10%. Find the decrease percent in the revenue derived from it?
(A) 20%
(B) 19%
(C) 15%
(D) 12%
(E) 24%
Rationale: Answer: Option D
100 * 100 = 10000
80 * 110 = 8800
10000------- 1200
100 ------- ? = 12%
Answer: (D) 12%
Question: The average weight of a group of boys is 30 kg. After a boy of weight 35 kg joins the group, the average weight of the group goes up by 1 kg. Find the number of boys in the group originally ?
(A) 4
(B) 8
(C) 5
(D) 2
(E) 9
Rationale: Let the number off boys in the group originally be x.
Total weight of the boys = 30x
After the boy weighing 35 kg joins the group, total weight of boys = 30x + 35
So 30x + 35 + 31(x + 1) = > x = 4.
Answer: A
Answer: (A) 4
Question: In a 1000 m race, A beats B by 50 m and B beats C by 20 m. In the same race, by how many meters does A beat C?
(A) A)69m
(B) B)829m
(C) C)822m
(D) D)929m
(E) E)132mj
Rationale: By the time A covers 1000 m, B covers (1000 - 50) = 950 m.
By the time B covers 1000 m, C covers (1000 - 20) = 980 m.
So, the ratio of speeds of A and C =
1000/950 * 1000/980 = 1000/931 So, by the time A covers 1000 m, C covers 931 m.
So in 1000 m race A beats C by 1000 - 931 = 69 m.
Answer:A
Answer: (A) A)69m
Question: A horse is tethered to one corner of a rectangular grassy field 36 m by 20 m with a rope 12 m long. Over how much area of the field can it graze?
(A) 154 cm2
(B) 113 m2
(C) 123 m2
(D) 115 m2
(E) None of these
Rationale: Area of the shaded portion
= 1⁄4 × π × (12)2 = 113 m2
Answer B
Answer: (B) 113 m2
Question: If x and y are positive integers and 12x=21y what is the least possible value of xy?
(A)  9
(B)  28
(C)  63
(D)  84
(E)  252
Rationale: 12x=21y
=> x/y = 7/4
=> 4x=7y
4(3)=7(3) => x*y=9
A
Answer: (A)  9
Question: Average of five numbers is 9, and the sum of three of the numbers is 30, what is the average of the other 2 numbers?
(A) 17
(B) 15.5
(C) 8.5
(D) 7.5
(E) 3.5
Rationale: Let the five numbers be a, b, c, d, e. Then their average is (a+b+c+d+e)/5=9a+b+c=30(30+d+e)/5=930+d+e=45d+e=15average=15/2=7.5Ans D
Answer: (D) 7.5
Question: In a survey of 340 employees, 104 of them are uninsured, 54 work part time, and 12.5 percent of employees who are uninsured work part time. If a person is to be randomly selected from those surveyed, what is the probability that the person will neither work part time nor be uninsured?
(A) 7/12
(B) 8/41
(C) 39/68
(D) 1/8
(E) 41/91
Rationale: ---------UI----------------NUI-------Total
PT----(12.5/100)*104 = 13----------- --54
NPT---104-13-------------- x--------286
Total--104----------------------------340
we have to find not part time and not uninsured . in other words not part time and insured = x/340 = (286-104+13)/340
= 39/68
Answer is C.
Answer: (C) 39/68
Question: From a pack of cards two cards are drawn one after the other, with replacement. The probability that the first is a red card and the second is a king is?
(A) 1/26
(B) 1/25
(C) 1/87
(D) 1/17
(E) 1/12
Rationale: Let E1 be the event of drawing a red card.
Let E2 be the event of drawing a king .
P(E1 ∩ E2) = P(E1) . P(E2)
(As E1 and E2 are independent)
= 1/2 * 1/13 = 1/26
Answer:A
Answer: (A) 1/26
Question: A table is bought for Rs.600/- and sold at a loss of 8% find its selling price
(A) s.500/-
(B) s.552/-
(C) s.540/-
(D) s.600/-
(E) s.700/-
Rationale: 100 % ------> 600 (100 * 6 = 600)
92 % ------> 552 (92 * 6 = 552)
Selling price = Rs.552/-
B
Answer: (B) s.552/-
Question: 19 men take 21 days of 8 hours each to do a piece of work. How many days of 6 hours each would 21 women take to do the same. If 3 women do as much work as 2 men?
(A) 32
(B) 87
(C) 38
(D) 99
(E) 77
Rationale: 3W = 2M
19M ------ 21 * 8 hours
21 W ------ x * 6 hours
14 M ------ x * 6
19 * 21 * 8 = 14 * x * 6
x = 38
Answer: C
Answer: (C) 38
Question: If 40 honey bees make 40 grams of honey in 40 days, then 1 honey bee will make 1 gram of honey in how many days?
(A) 1
(B) 3.5
(C) 40
(D) 49
(E) 30
Rationale: Explanation :
Let the required number days be x.
Less honey bees, More days (Indirect Proportion)
Less honey, Less days (Direct Proportion)
Honey bees 1 : 40 :: 40 : x
Honey 40 : 1
=> 1 x 40 x x = 40 x 1 x 40
=> x = 40.
Answer : C
Answer: (C) 40
Question: Two trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 16 hours respectively. The ratio of their speeds is?
(A) 4:6
(B) 4:3
(C) 4:9
(D) 4:4
(E) 4:2
Rationale: Let us name the trains A and B.
Then, (A's speed) : (B's speed)
= √b : √a = √16 : √9 = 4:3.Answer: B
Answer: (B) 4:3
Question: If s is the product of the integers from 50 to 60 inclusive, and if t is the product of the integers from 50 to 61 inclusive, what is 1/s + 1/t in terms of t?
(A) 32/t
(B) 42/t
(C) 52/t
(D) 62/t
(E) 72/t
Rationale: Similarly in the actual problem
s =t/61. 1/s = 1/(t/61) or 1/s = 61/t
1/s + 1/t = 61/t + 1/t = 62/t
D
Answer: (D) 62/t
Question: By selling 20 pencils for a rupee a man loses 35%. How many for a rupee should he sell in order to gain 30%?
(A) 8
(B) 9
(C) 6
(D) 14
(E) 10
Rationale: 65% --- 20130% --- ?65/130 * 20 = 10Answer: E
Answer: (E) 10
Question: A man can row a boat at 20 kmph in still water. If the speed of the stream is 6 kmph, what is the time taken to row a distance of 60 km downstream?
(A) 30/83 hours
(B) 80/13 hours
(C) 30/13 hours
(D) 30/19 hours
(E) 32/13 hours
Rationale: Speed downstream = 20 + 6 = 26 kmph.
Time required to cover 60 km downstream
= d/s = 60/26
= 30/13 hours.
Answer:C
Answer: (C) 30/13 hours
Question: If the cost price of 50 articles is equal to the selling price of 40 articles, then the gain or loss percent is?
(A) 33
(B) 21
(C) 92
(D) 12
(E) 25
Rationale: Explanation:
Given that, cost price of 50 article is equal to selling price of 40 articles.
Let cost price of one article = Rs. 1
Selling price of 40 articles = Rs. 50
But Cost price of 40 articles = Rs. 40
Therefore, the trader made profit.\Percentage of profit = 10/40 * 100 = 25%
Answer:E
Answer: (E) 25
Question: The length of rectangle is thrice its breadth and its perimeter is 96 m, find the area of the rectangle?
(A) 432
(B) 456
(C) 546
(D) 258
(E) 277
Rationale: 2(3x + x)
= 96
l = 36
b = 12
lb = 36 * 12
= 432
Answer: A
Answer: (A) 432
Question: I bought two books; for Rs.360. I sold one at a loss of 15% and other at a gain of 19% and then I found each book was sold at the same price. Find the cost of the book sold at a loss?
(A) 197
(B) 210
(C) 189
(D) 278
(E) 268
Rationale: x*(85/100)
= (360 - x)119/100
x = 210
Answer: B
Answer: (B) 210
Question: 10 books are placed at random in a shelf. The probability that a pair of books will always be together is?
(A) 1/0
(B) 1/3
(C) 1/5
(D) 1/2
(E) 1/1
Rationale: 10 books can be rearranged in 10! ways consider the two books taken as a pair then number of favourable ways of getting these two books together is 9! 2!
Required probability = 1/5
Answer: C
Answer: (C) 1/5
Question: Two students appeared at an examination. One of them secured 9 marks more than the other and his marks was 56% of the sum of their marks. The marks obtained by them are:
(A) 39,30
(B) 41,32
(C) 42,33
(D) 43,34
(E) 35,36
Rationale: Let their marks be (x + 9) and x.
then x+9 = 56/100(x+9+x)
3x=99
x=33
their marks 42 and 33
ANSWER C
Answer: (C) 42,33
Question: Difference between the length &breadth of a rectangle is 23 m. If its perimeter is 206 m, then its area is?? We have: (l - b) = 23 and 2(l + b) = 206 or (l + b) = 103?
(A) 2400 m^2
(B) 2420 m^2
(C) 2520 m^2
(D) 2640 m^2
(E) 2750 m^2
Rationale: Solving the two equations, we get: l = 63 and b = 40.
Area = (l x b) = (63 x 40) m2 = 2520 m^2
C
Answer: (C) 2520 m^2
Question: What is the ratio between perimeters of two squares one having 3 times the diagonal then the other?
(A) 3:6
(B) 3:4
(C) 3:2
(D) 3:1
(E) 3:7
Rationale: d = 3d d = d
a√2 = 3d a√2 = d
a = 3d/√2 a = d/√2
=> 3:1
Answer: D
Answer: (D) 3:1
Question: If x is an integer, then x(x - 1)(x - n) must be evenly divisible by three when n is any of the following values EXCEPT
(A) -4
(B) -2
(C) -1
(D) 2
(E) 5
Rationale: here's another approach
x(x - 1)(x - n)
all three are consecutive, so the product MUST be a multiple of 3
we don't know the value of n just yet ... so let's extend the series ... the extension itself reveals the answers
..(x-5)..(x-2)(x-1)x(x+1)..(x+4)..
we can see the possible values of n too from the series
n = 2 OR 2+3n [25]
n = -1 OR -1+3n [-1-4]
B i.e. -2 does not fit in any value of n
so B it is
Answer: (B) -2
Question: The parameter of a square is equal to the perimeter of a rectangle of length 7.5cm and breadth 6.5 cm. Find the circumference of a semicircle whose diameter is equal to the side of the square. (Round off your answer to two decimal places)?
(A) 10.2
(B) 10.27
(C) 10.23
(D) 10.21
(E) 10.25
Rationale: Let the side of the square be a cm.
Parameter of the rectangle = 2(7.5+ 5.5) = 26 cm Parameter of the square = 26 cm
i.e. 4a = 26
a = 6.5
Diameter of the semicircle = 6.5 cm
Circimference of the semicircle
= 1/2(âˆ)(6.5)
= 1/2(22/7)(6.5) = 143/14 = 10.21 cm to two decimal places
Answer: D
Answer: (D) 10.21
Question: A group of 7 fishermen chartered a boat for a day to fish for flounder. The boat costs x dollars per day to rent. If the group can find 3 more fishermen on the docks who are willing to come aboard and share the rental costs, how much less will the rental cost be per person in terms of x?
(A) x/70
(B) x/35
(C) 3x/70
(D) 3x/10
(E) 3x/7
Rationale: cost of boat per day = x
cost per person =x/7
if three more persons afre there, cost =x/10
difference = x/7-x/10
=3x/70
ANSWER:C
Answer: (C) 3x/70
Question: A bag contains 7 green and 8 white balls. If two balls are drawn simultaneously, the probability that both are of the same colour is ?
(A) 7/19
(B) 7/14
(C) 7/98
(D) 7/18
(E) 7/15
Rationale: Drawing two balls of same color from seven green balls can be done in ⁷C₂ ways.
Similarly from eight white balls two can be drawn in ⁸C₂ ways.
P = ⁷C₂/¹⁵C₂ + ⁸C₂/¹⁵C₂
= 7/15
Answer: E
Answer: (E) 7/15
Question: At what rate percent on simple interest will Rs.1750 amount to Rs.2000 in 4 years?
(A) 4 %
(B) 3.57 %
(C) 2 6/7 %
(D) 5 %
(E) 6 %
Rationale: Explanation:
250 = (1750x4xR)/100
R = 3.57 %
Answer: Option B
Answer: (B) 3.57 %
Question: The largest 4 digit number exactly divisible by 55 is?
(A) 9935
(B) 9939
(C) 9944
(D) 9955
(E) 9960
Rationale: Largest 4-digit number = 9999
55) 9999 (181
9955
Answer : D
Answer: (D) 9955
Question: x is the product of each integer from 1 to 50, inclusive and y=100^k, where k is an integer . What is the greatest value of k for which y is a factor of x?
(A) 0
(B) 5
(C) 6
(D) 10
(E) 12
Rationale: x = 1*2*3*4*5*......*49*50 = 50!
y = 100^k
100 = 10^2 = 2^2 * 5^2
On prime factorization of x, power of 5 will always be greater than power of 2
CONCEPT: In every Factorial value (x!), On prime factorization, the power of Bigger Prime number > the power of Smaller Prime number
Also, Power of any Prime Number in any factorial can be calculated by following understanding
Power of prime x in n! = [n/x] + [n/x^2] + [n/x^3] + [n/x^4] + ... and so on
Where,
[x] = Greatest Integer less than or equal to x and the explanation of terms is as follows
[n/x] = No. of Integers that are multiple of x from 1 to n
[n/x^2] = No. of Integers that are multiple of x^2 from 1 to n whose first power has been counted in previous step and second is being counted at this step
[n/x^3] = No. of Integers that are multiple of x^3 from 1 to n whose first two powers have been counted in previous two step and third power is counted at this step
And so on.....
Where [n/x] is greatest Integer value of (n/x) less than or equal to (n/x)
i.e. [100/3] = [33.33] = 33
i.e. [100/9] = [11.11] = 11 etc.
Power of 5 in x = [50/5] + [50/5^2] + [50/5^3]... = 10 + 2 + 0 = 12
Power of 2 in x = [50/2] + [50/2^2] + [50/2^3]... = 25 + 12 + 6 + 3 + 1 = 47
i.e. x = 50! = 2^47 * 5^12 * ... = 10^12 * ... = 100^6 * ...
i.e. x is divisible by a 6th power of 100 at the most
i.e. y = 100^k = 100^6
i.e. k = 6
Answer: option C
Answer: (C) 6
Question: The least number which should be added to 3218 so that the sum is exactly divisible by 5, 6, 4 and 3 is?
(A) 10
(B) 20
(C) 30
(D) 40
(E) 50
Rationale: L.C.M. of 5, 6, 4 and 3 = 60.
On dividing 3220 by 60, the remainder is 40.
Number to be added = (60 - 40) = 20
B)
Answer: (B) 20
Question: A professional athlete was offered a three-year contract to play with Team K that provided for an annual salary of $100,000 in the first year, an increase in annual salary of 20% over the previous year for the next two years, and a bonus of $50,000 on signing. Team L offered a three-year contract providing for an annual salary of $120,000 in the first year, an increase in annual salary of 10% over the previous year for the next two years, and no signing bonus. If he accepts the offer of Team L and fulfills the three-year contract terms, the athlete will receive how much more money by choosing Team L over Team K ?
(A) $16,800
(B) $50,000
(C) $82,500
(D) $92,000
(E) $100,000
Rationale: Team K's contract = $100,000 + $100,000*1.2 + $100,000*1.2*1.2 + $50,000 = $414,000
Team L's contract = $120,000 + $120,000*1.1 + $120,000*1.1*1.1 = $397,200
The difference = $16,800.
Answer: A.
Answer: (A) $16,800
Question: 385, 462, 572, 396, 424, 671, 264
(A) 385
(B) 424
(C) 671
(D) 264
(E) None of these
Rationale: Solution
In each number except 424,the middle digit is the sum of the other two. Answer B
Answer: (B) 424
Question: Three coworkers P , H , R meet for Dinner. P had 5 sandwiches, H had 3 and R had none. Both PH share their sandwiches with R such that each one got the same amount. If R paid $ 8 to PH, how much of $ 8 should P get? Assume both sandwiches and Dollars can be split.
(A) a) 5$
(B) b) 3 $
(C) c) 7 $
(D) d) 4 $
(E) e) 5.5 $
Rationale: we got total 8 sandwiches ....we are dividing equally in 3 people.
per person: 8/3
initially
p:8
H:3
r:0
now since r ate 8/3 so he is paying 8 dollars for 8/3 sandwiches.
now p also ate 8/3 of his 5 sandwiches = so he gave 5-8/3 to r ==>7/3 to r
ok we have 8 dollars for 8/3 sandwich
therefore for 7/3 sandwich we will get 7 dollars.
hence p should get 7 dollars.
hence C
Answer: (C) c) 7 $
Question: A paint store mixes 3/4 pint of red paint and 2/3 pint of white paint to make a new paint color called Perfect Pink. How many pints of red paint would be needed to make 30 pints of Perfect Pink paint?
(A) 9
(B) 16
(C) 15
(D) 25 1/3
(E) 28 1/2
Rationale: 3/4 pint is required to make 3/4 + 2/3 = 17/12 pint of perfect pink
so 17/12 pint requires 3/4 pint of red..
1 pint will require 3/4 * 12/17=9/17..
30 pints will require 9/17 * 30= 15 pints..
C
Answer: (C) 15
Question: Awordis defined as a sequence of Four dots arranged in a row. Each dot is colored either yellow or blue. How many distinct words can be formed?
(A) 13
(B) 15
(C) 16
(D) 18
(E) 19
Rationale: Each dot can be either yellow or blue, so 2 options for each dot: 2*2*2*2 = 16.
Answer: C
Answer: (C) 16
Question: Find the total no. of distinct bike no.'s that can be formedusing 2 letters followed by 2 no.'s. How manyletters need to be distinct?
(A) 45789
(B) 49653
(C) 57900
(D) 65000
(E) 70046
Rationale: Out of 26 alphabets two distinct letters can be chosen in \inline {\color{Black}26P_2{}} ways. Coming to numbers part, there are 10 ways.(any number from 0 to 9 can be chosen) to choose the first digit and similarly another 10ways to choose the second digit. Hence there are totally 10X10 = 100 ways.
Combined with letters there are \inline {\color{Black}6P_2{}} X 100 ways = 65000 ways to choose vehicle numbers.
D
Answer: (D) 65000
Question: During a special promotion, a certain filling station is offering a 10 percent discount on gas purchased after the first 5 gallons. If Kim purchased 20 gallons of gas, and Isabella purchased 25 gallons of gas, then Isabella‟s total per-gallon discount is what percent of Kim‟s total per-gallon discount?
(A) 80%
(B) 107%
(C) 116.7%
(D) 120%
(E) 140%
Rationale: Kim purchased 20 gallons of gas. She paid for 5 + 0.9*15 = 18.5 gallons, so the overall discount she got was 1.5/20 = 7.5%.
Isabella purchased 25 gallons of gas. She paid for 5 + 0.9*20 = 23 gallons, so the overall discount she got was .5/25 = 8%.
8 is 8/7.5*100 = 107% of 7.5.
Answer: B.
Answer: (B) 107%
Question: One-third of Rahul’s savings in National Savings Certificate is equal to one-half of his savings in Public Provident Fund. If he has Rs. 2,50,000 as total savings, how much has he saved in Public Provident Fund ?
(A) Rs. 30,000
(B) Rs. 50,000
(C) Rs. 60,000
(D) Rs. 100,000
(E) None
Rationale: EXPLANATION
Let savings in N.S.C and P.P.F. be Rs. x and Rs. (250000 – x) respectively. Then,
1/3x=1/2(250000-x)
=> x/3 + x/2 = 125000
=> 5x/6 = 125000
=> x= 125000 x 6 /5= 150000
Savings in Public Provident Fund = Rs. (250000 – 150000) = Rs. 100000
Answer D
Answer: (D) Rs. 100,000
Question: A shopkeeper sold an article at $1050 and gained a 20% profit. What was the cost price?
(A) $835
(B) $845
(C) $855
(D) $865
(E) $875
Rationale: Let x be the cost price.
1.2x = 1050
x = 1050/1.2 = 875
The answer is E.
Answer: (E) $875
Question: In how many different number of ways 6 men and 2 women can sit on a shopa which can accommodate persons?
(A) 200
(B) 1680
(C) 240
(D) 250
(E) 260
Rationale: 8p4 = 8 X 7 Ã— 6 Ã— 5 = 1680
B
Answer: (B) 1680
Question: One-third of Rahul's savings in National Savings Certificate is equal to one-half of his savings in Public Provident Fund. If he has Rs. 1,50,000 as total savings, how much has he saved in Public Provident Fund ?
(A) 90000
(B) 85000
(C) 50000
(D) 75000
(E) 60000
Rationale: Let savings in N.S.C and P.P.F. be Rs. x and Rs. (150000 - x) respectively. Then,
=1/3 x = 1/2 (150000 - x)
=x/3 + x/2 = 75000
=5x/6 = 75000
=x = 75000 x 6 /5	= 90000
Savings in Public Provident Fund = Rs. (150000 - 90000) = Rs. 60000
Answer is E.
Answer: (E) 60000
Question: 5 cats can catch 5 mice in 5 minutes. How many cats does it take to catch 100 mice in 100 minutes?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: let x be no. of cat
5 cat catch 5 mice in 5 min
5 cat catch 1 mice in (5/5=1 min)
1 cat catch 1 mice in 1*5=5 min
1 cat catch 100 mice in 5*100 min
x cat catch 100 mice in (5*100)/x min
A/Q (5*100)/x = 100
=> 5*100=x*100
=> x=5
ANSWER:E
Answer: (E) 5
Question: Arjun started a business with Rs. 20,000 and is joined afterwards by Anoop with Rs.80, 000. After how many months did Anoop join if the profits at the end of the year are divided equally?
(A) 3
(B) 9
(C) 5
(D) 6
(E) 7
Rationale: Suppose Anoop joined after 3 months.
Then, 20000 * 12 = 80000 * (12 – x)
=> x = 9.
ANSWER:B
Answer: (B) 9
Question: If n ≠ 0, which of the following could be less than n?
I. 2n
II. n^2
III. 2 - n
(A) I only
(B) II only
(C) I and II only
(D) I and III only
(E) None
Rationale: n ≠ 0 => n = negative or n = positive
if n = negative:
2n < n (n = -1 then 2n = -2 => -2 < -1)
n^2 > n (n =-1 then n^2 = 1 => n^2 > n)
2 - n > n (n = -1 then 2--1 = 2+1=3 => 2-n > n)
but if n = positive:
n^2 > n (n = 2 then n^2 = 4 => n^2 > n) => II
2 - n < n(n =2 then 2-2 = 0)
=>answer is D
Answer: (D) I and III only