mathewhe/aqua_rat huggingface dataset:
Question: What profit percent is made by selling an article at a certain price, if by selling at 2/3rd of that price, there would be a loss of 20%?
(A) 20%
(B) 25%
(C) 70%
(D) 28%
(E) 30%
Rationale: SP2 = 2/3 SP1
CP = 100
SP2 = 80
2/3 SP1 = 80
SP1 = 120
100 --- 20 => 20%
Answer:A
Answer: (A) 20%
Question: A train 110 meters long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 5
Rationale: Speed of train relative to man = (60 + 6) km/hr = 66 km/hr
[66 * 5/18] m/sec = [55/3] m/sec.
Time taken to pass the man = [110 * 3/55] sec = 6 sec
Answer: B
Answer: (B) 6
Question: The ratio of Ajay’s and Balu’s ages is 4: 5. If the difference between the present age of Balu and the age of Ajay 5 years hence is 3 years, then what is the total of present ages of Ajay and Balu?
(A) 68 years
(B) 72 years
(C) 76 years
(D) 64 years
(E) 74 years
Rationale: Let us consider Ajay as A and Balu as B.
Given A/B = 4/5
And B - (A + 5) = 3
B - A = 8
B = 8 + A
Now, A/(8 + A) = 4/5
A = 32 years
Therefore B = 40 years.
A + B = 72 years
ANSWER:B
Answer: (B) 72 years
Question: If a and b are each greater than x and y, which of the following must be true?
I. ab < xy
II.a + b > x + y
III. |a| + |b| > |x| + |y|
(A) I only
(B) II only
(C) I and II
(D) I and III
(E) I, II and III
Rationale: I. a + b > x + y. Since a and b are each greater than x and y, then the sum of a and b will also be greater than the sum of x and y.
II. ab > xy. Not necessarily true, consider a = b = 0 and x = y = -1 --> ab = 0 < 1 = xy.
III. |a| + |b| > |x| + |y|. Not necessarily true, consider a = b = 0 and x = y = -1 --> |a| + |b| = 0 < 2 = |x| + |y|.
Answer: B.
Answer: (B) II only
Question: How many even integers n, such that 20<=n<=240 are of the form 3k+4, where k is any natural number?
(A) 31
(B) 33
(C) 35
(D) 37
(E) 39
Rationale: The first number is 22 = 16+6(1).
We can continue adding 6 to make a list: 22, 28, 34,...
The last number is 238 = 16+6(37)
There are 37 numbers in the list.
The answer is D.
Answer: (D) 37
Question: In a certain pond, 50 fish were caught, tagged, and returned to the pond. A few days later, 50 fish were caught again, of which 4 were found to have been tagged. If the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond, what is the approximate number of fish in the pond?
(A)  400
(B)  625
(C)  1,250
(D)  2,500
(E)  10,000
Rationale: total fish = x
percentage of second catch = (4/50)*100 = 8%
so, x * 8% = 50
x = 625 ans. B
Answer: (B)  625
Question: The probability that A speaks truth is 3/5 and that of B speaking truth is 3/7. What is the probability that they agree in stating the same fact?
(A) 17/35
(B) 17/39
(C) 17/36
(D) 17/33
(E) 17/32
Rationale: If both agree stating the same fact, either both of them speak truth of both speak false.
Probability = 3/5 * 3/7 + 2/5 * 4/7
= 9/35 + 8/35 = 17/35
Answer: A
Answer: (A) 17/35
Question: Two trains 125 meters and 165 meters in length respectively are running in opposite directions, one at the rate of 80 km and the other at the rate of 65 kmph. In what time will they be completely clear of each other from the moment they meet?
(A) 7.16
(B) 7.16
(C) 7.12
(D) 7.15
(E) 7.2
Rationale: T = (125 + 165)/ (80 + 65) * 18/5
T = 7.2
Answer: E
Answer: (E) 7.2
Question: If Rs. 510 be divided among A, B, C in such a way that A gets 2/3 of what B gets and B gets 1/4 of what C gets, then their shares are respectively:
(A) Rs. 60, Rs. 90, Rs. 389
(B) Rs. 60, Rs. 90, Rs. 360
(C) Rs. 60, Rs. 90, Rs. 368
(D) Rs. 60, Rs. 90, Rs. 329
(E) Rs. 60, Rs. 30, Rs. 329
Rationale: (A = 2/3 B and B = 1/4 C) = A/B = 2/3 and B/C = 1/4
A:B = 2:3 and B:C = 1:4 = 3:12
A:B:C = 2:3:12
A;s share = 510 * 2/17 = Rs. 60
B's share = 510 * 3/17 = Rs. 90
C's share = 510 * 12/17 = Rs. 360.
Answer:B
Answer: (B) Rs. 60, Rs. 90, Rs. 360
Question: A sum of money is put out at compound interest for 2 years at 20%. It would fetch Rs.482 more if the interest were payable half-yearly, then it were pay able yearly. Find the sum.
(A) 2200
(B) 1897
(C) 8799
(D) 2000
(E) 2782
Rationale: P(11/10)4 - P(6/5)2 = 482
P = 2000
Answer: D
Answer: (D) 2000
Question: Find the area of circle whose radius is 70m?
(A) 28866
(B) 23456
(C) 76766
(D) 16866
(E) 15400
Rationale: 22/7 * 70 * 70
= 15400
Answer: E
Answer: (E) 15400
Question: What is the least number which should be added to 2697 so that the sum is exactly divisible by 5, 6, 4, and 3?
(A) 3
(B) 11
(C) 19
(D) 27
(E) 35
Rationale: L.C.M. of 5, 6, 4 and 3 = 60.
When dividing 2697 by 60, the remainder is 57.
The number to be added = 60 - 57 = 3.
The answer is A.
Answer: (A) 3
Question: A can do a piece of work in 15 days and B alone can do it in 10 days. B works at it for 5 days and then leaves. A alone can finish the remaining work in
(A) 5days
(B) 6days
(C) 7.5days
(D) 8.5days
(E) 9days
Rationale: Explanation:
B's 5 days work =
1/10∗5=1/2
Remaining work =1−1/2=1/2
A can finish work =15∗1/2=7.5days
Option C
Answer: (C) 7.5days
Question: If the range of the set of numbers {140, 90, 135, 110, 170, 145, x, 123, 136} is 110, which of the following could be x?
(A) 40
(B) 50
(C) 60
(D) 70
(E) 80
Rationale: The range of the other 8 numbers is 170-90 = 80, so x must be either the smallest number or the largest number in the set.
Then x = 170-110 = 60 or x = 90+110 = 200
The answer is C.
Answer: (C) 60
Question: Due to construction, the speed limit along an 8-mile section of highway is reduced from 55 miles per hour to 35 miles per hour. Approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ?
(A) 5
(B) 8
(C) 10
(D) 15
(E) 24
Rationale: Let t1 is time taken @ 55 mph
t1 = 8/55
Let t2 is time taken @ 35 mph
t2 = 8/35
Difference in time = 8/35 - 8/55 = 8 * 20 / (35 * 55) hr = 160 * 60 / (35 * 55) mins = 4.7 = 5 (approx) mins
ANSWER:A
Answer: (A) 5
Question: A train 300 m long passed a pole in 10 sec. How long will it take to pass a platform 600 m long?
(A) 80
(B) 90
(C) 100
(D) 110
(E) 120
Rationale: Speed = 300/10 = 30 m/sec.
Required time = (300 + 600)/10
= 90 sec.
Answer:B
Answer: (B) 90
Question: If i equals the sum of the even integers from 2 to 200, inclusive, and k equals the sum of the even integers from 20 to 200, inclusive, what is the value of i - k?
(A) 10
(B) 99
(C) 9
(D) 88
(E) 90
Rationale: Use following formulae for such problems:
Sum of evenly spaced integers = (# of integers)*(mean of integers)
# of integers = [(last - first)/2] + 1
Mean of integers = (last + first)/2
In above problem:
# of integers = [(200 - 2)/2] + 1= 100 and [(200-20)/2]+ 1 = 91
Mean of integers = (200 + 2)/2 = 101 and (200 + 20)/2 = 110
Sum of integers = (100*101) = 10100 and (91*110) = 10010
Thus their difference i - k = 10100 - 10010 = 90
ANSWER:E
Answer: (E) 90
Question: If xy = 6 and x^2 + y^2 = 12, then x/y + y/x =
(A) 2
(B) 3 1/7
(C) 5 1/3
(D) 7
(E) 60
Rationale: We can make simplifying of question and get it in view: (x^2 + y^2) / xy and as we know the meaning of this parts:
x^2 + y^2 = 12
xy = 6
we can calculate the answer 12/6 -> 2 so answer is A
Answer: (A) 2
Question: The length of the longest tape in cm which can be used to measure exactly, the length 7m; 3m 85cm; and 12m 95cm is:
(A) 37
(B) 35
(C) 34
(D) 36
(E) 38
Rationale: The three lengths in cm are 700, 385 & 1295.
HCF of 700, 385 & 1295 is 35.
Hence, the answer is 35 cm.
ANSWER:B
Answer: (B) 35
Question: A boat can move upstream at 32 kmph and downstream at 30 kmph, then the speed of the current is?
(A) 5
(B) 9
(C) 1
(D) 9
(E) 5
Rationale: US = 32
DS = 30
M = (32 - 30)/2 = 1
Answer: C
Answer: (C) 1
Question: Calculate Ronald's average score in an exam if he obtained the following marks 51, 57, 68, 60 and 78 out of 100 in different subjects.
(A) 69.8
(B) 67.8
(C) 62.8
(D) 61.8
(E) 60.8
Rationale: Explanation:
(51+57+68+60+78)/5=62.8
Answer: Option C
Answer: (C) 62.8
Question: How many two-digit whole numbers yield a remainder of 1 when divided by 20 and also yield a remainder of 1 when divided by 5?
(A) None
(B) One
(C) Two
(D) Three
(E) Four
Rationale: The possible number N can be written as follow:
N = Multiple of LCM(20,5) + 1st such number
N = 20x + 1
Possible values = 1, 21, 41, 61,81
Answer : 4 such 2 digit number. E.
Answer: (E) Four
Question: What is the greatest positive integer x such that 2^x is a factor of 8^10?
(A) 5
(B) 9
(C) 10
(D) 20
(E) 30
Rationale: 8^10 = (2^3)^10 = 2^30
ANSWER:E
Answer: (E) 30
Question: If A is 25% greater than B then how much percentage is B smaller than A?
(A) 20%
(B) 30%
(C) 40%
(D) 50%
(E) 60%
Rationale: X = 125
Y = 100
X-Y/X × 100 = 25/125 × 100 = 20 % smaller smaller than X
A)
Answer: (A) 20%
Question: If a = 105 and a^3 = 21 × 25 × 45 × d, what is the value of d?
(A) 35
(B) 42
(C) 45
(D) 49
(E) 54
Rationale: a=105 = 3* 5 *7
a^3 = 21 × 25 × 45 × d
=> a^3 = (7*3) x (5*5) x ( 3^2 * 5) x d
=> a^3 = 3^3 * 5^3 * 7 x d
=>( 3* 5 *7) ^3 = 3^3 * 5^3 * 7 x d
d = 7^2 = 49
Answer D
Answer: (D) 49
Question: A can do a piece of work in 12 days. He worked for 15 days and then B completed the remaining work in 10 days. Both of them together will finish it in?
(A) 12 1/2 days
(B) 12 6/2 days
(C) 12 1/6 days
(D) 17 1/2 days
(E) 12 1/8 days
Rationale: 15/25 + 10/x = 1 => x = 25
1/25 + 1/25 = 2/25
25/2 = 12 1/2 days
Answer:A
Answer: (A) 12 1/2 days
Question: The average weight of 5 students decreases by 4 kg when one of them weighing 92 kg is replaced by a new student. The weight of the student is
(A) 62 kg
(B) 60 kg
(C) 70 kg
(D) 72 kg
(E) None of these
Rationale: Explanation :
Let the weight of student be x kg.
Given, Difference in average weight = 4 kg
=> (92-x)/5 = 4
=> x = 72
Answer : D
Answer: (D) 72 kg
Question: A Shopkeeper divides an ice-cream brick in two halves, then cut one of the halves into several smaller portions of equal size. Each of the smaller portions weights 12 grams. The shopkeeper now has a total of 5 portions. How heavy was the original brick?
(A) 96grams
(B) 97grams
(C) 98grams
(D) 99grams
(E) 95grams
Rationale: Since there are 5 portions, 4 small portions of equal size and one half of original ice-cream brick.
1 small portion = 12 grams
4 small portion = 4*12 = 48grams
Therefore weight of original ice-cream brick = 48*2 = 96grams
ANSWER:A
Answer: (A) 96grams
Question: HCF of
22×32×52,24×34×53×11
is
(A) 24×34×53
(B) 24×34×53×11
(C) 22×32×52
(D) 2×3×5
(E) None of these
Rationale: Explanation:
As in HCF we will choose the minimum common factors among the given.. So answer will be third
option
Answer: Option C
Answer: (C) 22×32×52
Question: What is the average (arithmetic mean) of all the multiples of ten from 10 to 200 inclusive?
(A) 90
(B) 95
(C) 100
(D) 105
(E) 110
Rationale: 10 and 190 inclusive would mean there are 19 terms.
No need to add up all the terms and further divide by 20 since the terms are evenly spaced in ascending order from 10, 20, 30........200
The middle term is the average which is the tenth term = 110
E is the answer.
Answer: (E) 110
Question: Find the area of circle whose radius is 7m?
(A) 124 sq m
(B) 154 sq m
(C) 145 sq m
(D) 167 sq m
(E) 180 sq m
Rationale: r = 7
Area of Circle =∏r2
= (22/7)(7)(7)
= 154 sq m.Answer: B
Answer: (B) 154 sq m
Question: What is the number of integers from 1 to 1000 (inclusive) that are divisible by neither 11 nor by 34?
(A) 884
(B) 890
(C) 892
(D) 910
(E) 945
Rationale: Normally, I would use the method used by Bunuel. It's the most accurate. But if you are looking for a speedy solution, you can use another method which will sometimes give you an estimate. Looking at the options (most of them are spread out), I wont mind trying it. (Mind you, the method is accurate here since the numbers start from 1.)
In 1000 consecutive numbers, number of multiples of 11 = 1000/11 = 90 (Ignore decimals)
In 1000 consecutive numbers, number of multiples of 35 = 1000/35 = 28
Number of multiples of 11*35 i.e. 385 = 1000/385 = 2
Number of integers from 1 to 1000 that are divisible by neither 11 nor by 35 = 1000 - (90 + 28 - 2) {Using the concept of sets here) = 890
Think: Why did I say the method is approximate in some cases?
Think what happens if the given range is 11 to 1010 both inclusive (again 1000 numbers)
What is the number of multiples in this case?
B
Answer: (B) 890
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 5625 sq.units. What is the area (in sq.units) of the rectangle if the rectangle if the breadth is 10 units?
(A) 140 sq.units
(B) 300 sq.units
(C) 367sq.units
(D) 178sq.units
(E) 176sq.units
Rationale: Given that the area of the square = 5625 sq.units
=> Side of square = √5625 = 75units
The radius of the circle = side of the square = 75 units Length of the rectangle = 2/5 * 75 = 30 units
Given that breadth = 10 units
Area of the rectangle = lb = 30 * 10 = 300 sq.units
Answer:B
Answer: (B) 300 sq.units
Question: What is the probability that a 5 person committee chosen at random from a group consisting of 6 men, 7 women, and 5 children contains exactly 1 woman?
(A) 55/204
(B) 77/832
(C) 11/77
(D) 308/1411
(E) 22/832
Rationale: Total possible selections = 5 out of 18 group members = 18C5
Favorable selections = 1 out of 7 women and 4 out of 11 (= 6 men + 5 children) = 7C1 * 11C4
Thus the required probability = 7C1*11C4 / 18C5 = 55/204. Thus A is the correct answer.
Answer: (A) 55/204
Question: Baker Tom is storing cake boxes in cartons that measure 25 inches by 42 inches by 60 inches. If the measurement of each cake box is 8 inches by 7 inches by 5 inches, then what is the maximum number of cake boxes that can be placed in each carton?
(A) 330
(B) 300
(C) 252
(D) 225
(E) 210
Rationale: Baker Tom is storing cake boxes in cartons The dimensions of the carton are 25x 42x 60and those of each cake box are 8x 7x 5.
To maximize number of boxes try and fit maximum into the base of the box. If you take the base as 25x 42and fit 5 x 6 boxes of 5x 7, then the total number of boxes is 5 x 6 x integer(60/8) = 5 x 6 x 7 = 210.
Alternatively you could try taking the base as 60x 42and fit 12 x 6 boxes of 5x 7, then the total number of boxes is 12 x 6 x integer(25/8) = 12 x 6 x 3 = 216. But since that is not an answer option, I go with (E) 210.
Answer: (E) 210
Question: A man buys a cycle for Rs. 1400 and sells it at a loss of 15%. What is the selling price of the cycle?
(A) Rs. 1090
(B) Rs. 1160
(C) Rs. 1190
(D) Rs. 1202
(E) Rs. 1502
Rationale: S.P. = 85% of Rs. 1400 = Rs. 85/100	x 1400 = Rs. 1190
Answer: Option C
Answer: (C) Rs. 1190
Question: The original price of a camera was displayed as a whole dollar amount. After adding sales tax of 5 percent, the final price was also a whole dollar amount. Which of the following could be the final price of the camera?
(A) $107
(B) $109
(C) $106
(D) $111
(E) $105
Rationale: Final price = (1+5/100) * Original Price
= 1.05 * Original Price
From options given only 105 is divisible by 1.05 as it is stated OP is whole dollar amount.
Hence E
Answer: (E) $105
Question: Three candidates contested an election and received 936, 7636 and 19628 votes respectively. What percentage of the total votes did the winning candidate got
(A) 55%
(B) 56%
(C) 57%
(D) 58%
(E) 69.6%
Rationale: Explanation:
Total number of votes polled = (936 + 7636 + 19628) = 28200
So, Required percentage = 19628/28200 * 100 = 69.6%
Answer: Option E
Answer: (E) 69.6%
Question: Company A has 13 employees, 8 of whom belong to the union. If 5 people work any one shift, and the union contract specifies that at least 5 union members work each shift, then how many different combinations of employees might work any given shift?
(A) 56
(B) 231
(C) 336
(D) 350
(E) 406
Rationale: Looks easy: -- 8C5*5C1 + 8C5 -- 336 (C).
Answer: (C) 336
Question: P can do piece of work in 30 days while Q alone can do it in 40 days. In how many days can P and Q working together do it?
(A) 17 1/7
(B) 18 1/7
(C) 20 1/7
(D) 22 1/7
(E) 24 2/7
Rationale: P DAYS WORK = 1/30
Q ONE DAY WORK = 1/40
(P+Q) ONE DAY = 1/30 + 1/40 = 7/120
A AND B FINISH WORK = 17 1/7 DAYS
ANSWER A
Answer: (A) 17 1/7
Question: If 1535/1038 = a +1/[b+1/{c+(d+1/e)}]. Find a*b*c*d*e?
(A) 165/2
(B) 175/2
(C) 178/3
(D) 187 by 2
(E) 197/2
Rationale: by expanding 1535/1038 make form like a+1/[b+1/{c+(d+1/e)}
=1+(497/1038) now a=1
=1+{1/(1038/497)}
=1+{1/(2+42/497)}
=1+{1/ (2+1/(497/42)} now b= 2 similarly expand
c=11 d= 1 e=34/8
finally a*b *b*c*d*e
1*2*11*1*34/8
187/2
ANSWER:D
Answer: (D) 187 by 2
Question: In how many different number of ways 4 boys and 1 girls can sit on a bench?
(A) 120
(B) 730
(C) 740
(D) 750
(E) 800
Rationale: npn = n!
5p5 = 5 × 4 × 3 × 2 × 1 = 120
A
Answer: (A) 120
Question: An automobile financier claims to be lending money at simple interest, but he includes the interest every six months for calculating the principal. If he is charging an interest of 10%, the effective rate of interest becomes:
(A) 10%
(B) 10.25%
(C) 10.5%
(D) 11 %
(E) None of these
Rationale: Let the sum be Rs. 100. Then,
S.I. for first 6 months = Rs.((100 x 10 x 1)/(100 x 2))	= Rs. 5
S.I. for last 6 months = Rs.((105 x 10 x 1)/	(100 x 2))= Rs. 5.25
So, amount at the end of 1 year = Rs. (100 + 5 + 5.25) = Rs. 110.25
Effective rate = (110.25 - 100) = 10.25%
Answer : B
Answer: (B) 10.25%
Question: In a given community, it is estimated that the overall population of white dogs is 50% more than the number of white male dogs. The total population of female dogs is 7 times the number of white female dogs. If the number of male and female dogs in the community is equal, what percentage of male dogs are white?
(A) 28.6
(B) 25.5
(C) 56.1
(D) 15.1
(E) 30.1
Rationale: Since we are dealing in percentage let us pick 100 as the number of white male dogs.
That means that the total number of white dogs is= 150 (50% more),
therefore the number of white female dogs is 50.
The total number of female dogs is 7x the number of white female dogs= 7*50=350 female dogs.
population of male dogs is equal with the population of the female dogs = 350
Therefore percentage of white male dogs = 100/350*100=28.6
Correct option is A
Answer: (A) 28.6
Question: in how many ways seven letters between A & B be arranged from alphabets so that repetition is not allowed?
(A) 24P7 * 2!
(B) 24P7 * 3!
(C) 24P7 * 4!
(D) 24P7 * 5!
(E) 24P7 * 6!
Rationale: 7 letters between A & B &,A,B has a fixed position
so,
24P7 * 2!
ANSWER:A
Answer: (A) 24P7 * 2!
Question: When positive integer N is divided by positive integer J, the remainder is 28. If N/J = 142.07, what is value of J?
(A) 300
(B) 375
(C) 400
(D) 460
(E) 500
Rationale: When a number is divided by another number, we can represent it as : Dividend = Quotient * Divisor + Remainder
So, Dividend/Divisor = Quotient + Remainder/Divisor
Given that N/J = 142.07
Here 142 is the quotient.
Given that Remainder = 28
So, 142.07= 142 + 28/J
So, J = 400
Answer- C
Answer: (C) 400
Question: What is the remainder when 7^498 is divided by 5 ?
(A) 4
(B) 3
(C) 2
(D) 1
(E) 0
Rationale: 7^0 = 1
7^1 = 7
7^2 = 49
7^3 = 343
7^4 = ...1
7^5 = ....7
7^6 = ......9
and so on in a recurring pattern of 1,7,9,3,1,7,9,3....
498/4 = 124 (with a remainder 2) so the last number is a 9.
so when 7^498 is divided by 5 the remainder is 4, ANS = A
Answer: (A) 4
Question: A 20 litre mixture of milk and water contains milk and water in the ratio 3 : 2. 10 litres of the mixture is removed and replaced with pure milk and the operation is repeated once more. At the end of the two removal and replacement, what is the ratio of milk and water in the resultant mixture?
(A) 17 : 3
(B) 9 : 1
(C) 3 : 17
(D) 5 : 3
(E) 11: 2
Rationale: rom the beginning;
Initially milk to water is 12l : 8l
remove half 6 - 4
add 10l milk 16 - 4
remove half 8 - 2
add 10l milk 18 - 2
18:2 = 9:1
ANSWER:B
Answer: (B) 9 : 1
Question: We are required to form different words with the help of letters of the word INTEGER. Let m1 be the number of words in which I and N are never together and m2 be the number of words which begin with I and end with R, then what is the value if m1/m2?
(A) 18
(B) 24
(C) 30
(D) 36
(E) 40
Rationale: Total possible combination without any restriction:- 7!/2! (E is mentioned two times in the word INTEGER, hence we are dividing by 2!)
Total Possible combination when letter 'I' and 'N' are together- 6!*2/2! (Think of I and N as one, hence total letters are 6, but I and N can be written in two ways- IN and NI- that is why we multiplied 6!*2)
Total possible combination when letter 'I' and 'N' are not together, i.e. m1= 7!/2! - 6!*2/2!= 6!*5/2
Now fix 'I' and 'R', then total possible combination, i.e m2, are= 5!/2!
m1/m2= 6!*5/2/5!/2= 30
Answer is 'C'
Answer: (C) 30
Question: In a group of 130 people, 90 have an age of more 30 years, and the others have an age of less than 20 years. If a person is selected at random from this group, what is the probability the person's age is less than 20?
(A) 0.31
(B) 0.55
(C) 0.65
(D) 0.75
(E) 0.85
Rationale: Number of people whose age is less than 20 is given by
130 - 90 = 40
Probability P that a person selected at random from the group is less than 20 is given by
40 / 130 = 0.31
correct answer A
Answer: (A) 0.31
Question: A train crosses a bridge of length 200 m in 10 seconds and a lamp post on the bridge in 5 seconds. What is the length of the train in metres?
(A) 375 m
(B) 750 m
(C) 200 m
(D) 800 m
(E) 300 m
Rationale: Let Length of Train = L
Case-1: Distance = 200+L (While crossing the bridge)
Time = 10 Seconds
i.e. Speed = Distance / Time = (200+L)/10
Case-2: Distance = L (While passing the lamp post)
Time = 5 Seconds
i.e. Speed = Distance / Time = (L)/5
But Since speed has to be same in both cases so
(200+L)/10 = (L)/5
i.e. 2L = L + 200
i.e. L = 200
Answer: option C
Answer: (C) 200 m
Question: 50% of the apartments in a certain building have windows and hardwood floors. 25% of the apartments without windows have hardwood floors. If 40% of the apartments do not have hardwood floors, what Q percent of the apartments with windows have hardwood floors?
(A) 10
(B) 16 2/3
(C) 40
(D) 50
(E) 83 1/3
Rationale: yup you need to construct a matrix
X********| Windows'|No Windows'''| total
hardFl****'|50*****''|10*********'|60
Not hardFl*|10******|30*********'|40
Total*****|60******'|40*********'|100
so Q percent of the apartments with windows have hardwood floors = 50/60 *100
= 83 1/3
so E is the answer.[/u]
Answer: (E) 83 1/3
Question: 36 men can complete a piece of work in 18 days. In how many days will 27 men complete the same work?
(A) 16
(B) 18
(C) 24
(D) 22
(E) 26
Rationale: C
24
Let the required number of days be x.
Less men, More days (Indirect Proportion)
27 : 36 :: 18 : x <-> 27 x x = 36 x 18
x = (36 x 18)/27
x = 24
Answer: (C) 24
Question: How many integerskgreater than 100 and less than 900 are there such that if the hundreds and the units digits ofkare reversed, the resulting integer is k+99?
(A) 50
(B) 60
(C) 70
(D) 80
(E) 90
Rationale: Numbers will be like 102 => 201 = 102 + 99
203 => 302 = 103 + 99
so the hundereth digit and units digit are consecutive where unit digit is bigger than hundred digit.
There will be seven pairs of such numbers
for every pair there will 10 numbers like for 12 => 102, 112,132,142,152, 162,172,182,192.
Total = 7 *10 = 70 hence C.
Answer: (C) 70
Question: If B + L < B - L < L - B, which of the following is correct?
(A) L < B < 0.
(B) B < L < 0.
(C) B < 0 < L.
(D) 0 < B < A.
(E) B > A > 0.
Rationale: Check first inequality
B + L < B - L
L<-L
L is -ve
Check another equality
B - L < L - B
-2L<-2B
L>B
Combining both 0>L>B
Option B fits only
Ans B
Answer: (B) B < L < 0.
Question: 30 pens and 75 pencils were purchased for 510. If the average price of a pencil was 2.00, find the average price of a pen.
(A) 10
(B) 11
(C) 12
(D) 13
(E) 14
Rationale: Since average price of a pencil = 2
∴ Price of 75 pencils = 150
∴ Price of 30 pens = (510 – 150) = 360
∴ Average price of a pen = 360⁄60 = 12
Answer C
Answer: (C) 12
Question: The product of two numbers is 1320 and their H.C.F is 6.The L.C.M of the numbers is
(A) 220
(B) 1314
(C) 1326
(D) 7920
(E) None
Rationale: Solution
L.C.M	= product of numbers / H.C.F
‹=› 1320 / 6
‹=›220.
Answer A
Answer: (A) 220