mathewhe/aqua_rat huggingface dataset:
Question: For which of the following functions is f(w) = f(−w) for all values of w ?
(A) f(x) = x^3 + 3
(B) f(x) = −x
(C) f(x) = 2x + 3
(D) f(w) = −w^2 + 2
(E) f(x) = 5x − 4
Rationale: f(w) = f(−w)
The above is a property of an even function .
f(w) = f^(n)
f(w) = f(−w) will hold when n is an even integer .
The only case when w is even is option D
Answer D
Answer: (D) f(w) = −w^2 + 2
Question: Given that a is the average (arithmetic mean) of the first eight positive multiples of six and b is the median of the first twelve positive multiples of six, what is the ratio of a to b?
(A) 3:4
(B) 10:13
(C) 5:6
(D) 9:13
(E) 4:3
Rationale: The first nine positive multiples of six are {6, 12, 18, 24,30, 36, 42, 48}
The first twelve positive multiples of six are {6, 12, 18, 24, 30,36,42, 48, 54, 60, 66, 72}
Both sets are evenly spaced, thus their median=mean:
a=(24+30)/2=27 and b=(36+42)/2=39 --> a/b=27/39=9/13.
Answer: D.
Answer: (D) 9:13
Question: Grace packed 5 pairs of shoes, 3 pairs of pants, 8 shirts, and 3 jackets for her business trip. If an outfit consists of one of each item of clothing except shirts, of which she will wear 2, how many different outfits C can does Grace have available during her trip?
(A)  2,520
(B)  1,260
(C)  620
(D)  360
(E)  120
Rationale: The idea is to multiply the number of possibilities for each item of clothing with the different items. For the shirts you essentially choose 2 out of 8 so you should use the combination forumla (don't know how to use math symbols here).
This gives you C=5 x 3 x 28 x 3 = 1'260. Hence, solution B is correct.
Answer: (B)  1,260
Question: Line D passes through point (-2,5), and the product of its x-intercept and y-intercept is positive. Which of the following points could be on line D?
(A) (5,10)
(B) (-3,2)
(C) (-1,7)
(D) (-1,2)
(E) (-3,1)
Rationale: The slope of the line is -ve, the only point that makes the slope -ve is D.
(5 - 2)/(-2 + 1) = 3/-1
Answer - D
Answer: (D) (-1,2)
Question: Find the average (arithmetic mean) of x and y if the average of x, y, and 5 is 20 more than the average of x, y, 5, and 15.
(A) 110
(B) 120
(C) 130
(D) 140
(E) 150
Rationale: consider the statement 50 is 20 more than 30: 50 = 30+20
similarly
the average of x, y, and 5 = (the average of x, y, 5, and 15) + 20
(x+y+5)/3 = (x+y+5+15)/4 + 20
(x+y+5)/3 = (x+y+20)/4 + 20
(x+y+5)/3 = (x+y+20)/4 + 80/4
(x+y+5)/3 = (x+y+20+80)/4
(x+y+5)/3 = (x+y+100)/4
cross multiply
4(x+y+5) = 3(x+y+100)
4x+4y+20 = 3x+3y+300
4x-3x +4y-3y = 300 - 20
x + y = 280
so
(x+y)/2 = 280/2
(x+y)/2 = 140
i.e the average of x and y is 140
D
Answer: (D) 140
Question: The number 97215*6 is completely divisible by 11. What is the smallest whole number in place of * ?
(A) 3
(B) 4
(C) 1
(D) 2
(E) 11
Rationale: From the above given "Divisibility by 11 rule", it is clear that
if 97215*6 is divisible by 11, then (9 + 2 + 5 + 6) - (7 + 1 + *) is divisible by 11
=> 22 - (8 + *) is divisible by 11
=> (14 - *) is divisible by 11
The smallest whole number which can be substituted in the place of * to satisfy the
above equation is 3 such that 14 - 3 = 11 and 11 is divisible by 11.
Answer is A
Answer: (A) 3
Question: A gambler has won 40% of his 30 poker games for the week so far. If, all of a sudden, his luck changes and he begins winning 70% of the time, how many more games must he play to end up winning 60% of all his games for the week?
(A) 36
(B) 42
(C) 48
(D) 54
(E) 60
Rationale: Let x be the number of additional games the gambler needs to play.
0.4(30) + 0.7x = 0.6(x+30)
0.1x = 6
x = 60
The answer is E.
Answer: (E) 60
Question: If 8^z is a factor of 256!, which of the following could be the value of z?
(A) 32
(B) 42
(C) 30
(D) 52
(E) 36
Rationale: 8^z is a factor of 256!, what values can z take.
Powers of 8 in 256! = [256/8] + [256/64] , where [x] is the integral part of x
Powers of 8 in 256! = 32 + 4 = 36
Hence the maximum value of 8^z in 256! = 8^36
Correct Option: E
Answer: (E) 36
Question: The sale price at which a store sells an article is 25% more than its cost price. If the sale price is an integer, which of the following cannot be the cost price?
(A) $20
(B) $37
(C) $48
(D) $60
(E) $84
Rationale: Sale Price = (5/4)*(Cost Price)
If the sale price is an integer, then the cost price must be divisible by 4.
The answer is B.
Answer: (B) $37
Question: A father said his son , " I was as old as you are at present at the time of your birth. " If the father age is 62 now, the son age 5 years back was
(A) 14
(B) 17
(C) 11
(D) 19
(E) 26
Rationale: Let the son's present age be x years .Then, (62 - x) = x x= 31.
Son's age 5 years back = (31 - 5) = 26 years
Answer: E
Answer: (E) 26
Question: In how many ways can a committee consisting of three men and four women be formed from a group of six men and seven women?
(A) ⁶C₄ ⁷C₃
(B) ⁶C₃ ⁷C₅
(C) ⁶C₃⁷C₄
(D) ⁷C₅ ⁶C₄
(E) ⁶C₃ ⁷C₃
Rationale: The group contain six men and seven women
Three men can be selected from six men in ⁶C₃ ways.
Four women can be selected from seven women in ⁷C₄ ways.
Total number of ways = (⁷C₄)(⁶C₃).
ANSWER:C
Answer: (C) ⁶C₃⁷C₄
Question: There are 5 physics books and 1 chemistry book on shelf P and 4 physics books on shelf Q. One book is moved from shelf P to shelf Q. A student picks up a book from shelf Q. What is the probability that the chemistry book is taken by the student?
(A) 1/40
(B) 1/35
(C) 1/30
(D) 1/25
(E) 1/20
Rationale: P(a chemistry book is moved to shelf Q) = 1/6
P(a chemistry book is then chosen from shelf Q) = 1/5
P(the student takes a chemistry book) = 1/6 * 1/5 = 1/30
The answer is C.
Answer: (C) 1/30
Question: A man gets a simple interest of Rs.600 on a certain principal at the rate of 5% p.a in two years. Find the compound interest the man will get on twice the principal in two years at the same rate?
(A) s.1000
(B) s.1056
(C) s.1150
(D) s.1230
(E) s.1256
Rationale: Let the principal be Rs.P
S.I at 5% p.a in 2 years on Rs.P = Rs.600
(P)(2)(5)/100 = 600
P = 6000
C.I on Rs.2P i.e., Rs.12000 at 5% p.a in two years
=12000{ [1 + 5/100]^2 - 1}
= 12000(41/ 400)
= Rs.1230
Answer:D
Answer: (D) s.1230
Question: A rower can row upstream at 20 kph and downstream at 34 kph. What is the speed of the rower in still water?
(A) 26
(B) 27
(C) 28
(D) 29
(E) 30
Rationale: Let V be the rower's speed in still water.
Let S be the speed of the current in the stream
V-S = 20
V+S = 34
When we add the two equations, we get: 2V = 54
Then V = 27 kph.
The answer is B.
Answer: (B) 27
Question: The diagonals of a rhombus are 15 cm and 20 cm. Find its area?
(A) 277
(B) 266
(C) 150
(D) 288
(E) 212
Rationale: 1/2 * 15 * 20 = 150
Answer: C
Answer: (C) 150
Question: 8+88+888+.....+8888........8888. There are 21 “8” digits in the last term of the series.
Find the last three digits of the sum.
(A) 384
(B) 584
(C) 784
(D) 968
(E) 768
Rationale: 21*8=168 carry 16
20*8=160+16=176 carry 17
19*8=152+17=169
the value is 968
ANSWER:D
Answer: (D) 968
Question: A librarian has 4 identical copies of Hamlet, 3 identical copies of Macbeth, 2 identical copies of Romeo and Juliet, and one copy of Midsummer’s Night Dream. In how many distinct arrangements can these ten books be put in order on a shelf?
(A) 720
(B) 1,512
(C) 2,520
(D) 6,400
(E) 12,600
Rationale: If the ten books were all different, the arrangements would be (10!), a very big number. Because we have repeats of identical copies, not all 10! arrangements will be unique. For a subset of k identical members, those k members could be interchanged in k! orders, and the resulting arrangements would be the same, so we have to divide by k! to remove repetitions. In this example, we need to divide 10! by 4! and 3! and 2!:
10!/4!3!2!=12600
Answer : E
Answer: (E) 12,600
Question: Find 12 ×× 19
(A) 238
(B) 228
(C) 208
(D) 277
(E) 101
Rationale: Mentally imagine this number as (10 + 2 ) ×× 19 = 190 + 38 = 228.
Answer:B
Answer: (B) 228
Question: The average age of a class of 19 students is 20 years. The average increased by 1 when the teacher's age also included. What is the age of the teacher?
(A) 39
(B) 41
(C) 40
(D) 42
(E) 43
Rationale: Total age of all students =19Ã—20
Total age of all students + Age of the teacher =20Ã—21
Age of the teacher
=20Ã—21âˆ’20Ã—19=20(21âˆ’19)=20Ã—2=40
Answer is C.
Answer: (C) 40
Question: The distance between a sports store and a recreation center is approximately 3.34 x 10^5 inches. Which of the following is closest to the distance between the sports store and a recreation center, in kilometers? (1 kilometer is approximately 3.9 x 10^4 inches.)
(A) 9.33
(B) 8.98
(C) 8.56
(D) 9.21
(E) 9.03
Rationale: We know that 1 kilometer = 3.9x10^4 inches. Therefore, we now have a ratio of (1 kilometer/3.9x10^4 inches).
We also know that the distance between the sports store and a recreation center is approximately 3.34x10^5 inches. To convert inches to kilometers, we need to multiply 3.34x10^5 inches by the ratio we just found out.
kilometers = 3.34x10^5 inches x (1 kilometer/3.9x10^4 inches) [note: "inches" cancel out, leaving us with just km]
km = 3.34x10^5/3.9x10^4 km
km = 8.56 km
Therefore, we can see that the closest answer is C.
Answer: (C) 8.56
Question: If 25% of a class averages 80% on a test, 50% of the class averages 65% on the test, and the remainder of the class averages 90% on the test, what is the overall class average?
(A) 60%
(B) 65%
(C) 70%
(D) 75%
(E) 80%
Rationale: This question is a Weighted Average question with a series of dependent variables.
The remaining portion of the class represents 100% - 25% - 50% = 25% of the class
Converting the portions of the class population to decimal weights, we find:
Class Average = 0.25x80 + 0.50x65 + 0.25x90 = 75
The class average is 75%
Final Answer
D) 75%
Answer: (D) 75%
Question: Two numbers x and y are such that the sum of 3% of x and 4% of y is one-third of the sum of 2% of of x and 8% of y. Find the ratio of x : y.
(A) 3:8
(B) 6:7
(C) 4:7
(D) 2:5
(E) None of these
Rationale: Explanation :
Solution: 3% of x+ 4% of y=1/3(2% of x+8% of y)
3x/100 + 4y/100 = 2x/300 + 8y/300
(3x+4y)3 = 2x+8y
7x = 4y
x/y = 4/7
Answer : C
Answer: (C) 4:7
Question: How many five digit numbers can be formed using digits 0,1,2,3,4,5, Which are divisible by 7, without any of the digits repeating?
(A) 96
(B) 98
(C) 100
(D) 81
(E) 72
Rationale: 0,1,2,3,4,5
One digit will have to remain out for all 5 digit numbers;
if 0 is out; Leftover digits will be 1,2,3,4,5 = Sum(1,2,3,4,5)=15.Ignore
if 1 is out; Leftover digits will be 0,2,3,4,5 = Sum(0,2,3,4,5)=14. divisible by 7)
if 3 is out; Leftover digits will be 0,1,2,4,5 = Sum(0,1,2,4,5)=12. Ignore
if 4 is out; Leftover digits will be 0,1,2,3,5 = Sum(0,1,2,3,5)=11. Ignore
if 5 is out; Leftover digits will be 0,1,2,3,4 = Sum(0,1,2,3,4)=10. Ignore
Total count of numbers divisible by 7 = 4*4! = 96
A
Answer: (A) 96
Question: 20 people going to one temple. (some time waste data) They want Rs. 20. For men-Rs.3, women-Rs.2, children-50 paisa. How much money spends for men, children and women?
(A) 3,7,10
(B) 4,7,10
(C) 5,7,10
(D) 6,7,10
(E) 7,7,10
Rationale: M=1 => 1*3= 3
W=5 => 5*2= 10
C=14 => 14*.5= 7
1+5+14= 20 & 3+10+7=20
ANSWER:A
Answer: (A) 3,7,10
Question: Number of students in institutes A and B were in the ratio of 7 : 15 respectively in 2012. In 2013, the number of students in institute A increased by 25% and number of students in institutes B increased by 26%, then what was the respective ratio between number of students in institutes A and B?
(A) 25 : 56
(B) 24 : 55
(C) 24 : 53
(D) 25 : 53
(E) 25 ratio 54
Rationale: Solution:
Ratio of students in 2012 in institutes A and B,
= 7 : 15.
Let number of students in institute A in 2012 = 700.
And Number of students in institutes B in 2012 = 1500.
25% increase in the number of students in 2013,
Now, number of students in Institute A,
= 700 + 25% of 700. = 875.
Number of students in B in 2013 as 26% students increased in B,
= 1500 + 26% of 1500 = 1890.
Current Ratio of the students,
= 875 /1890 = 25 : 54.
Answer: Option E
Answer: (E) 25 ratio 54
Question: A land owner needs to fence his semicircular land leaving an opening of length of 3m for access. The radius of the semicircular plot is 7m. How long would be the fence in meters?
(A) 22
(B) 33
(C) 36
(D) 44
(E) 51
Rationale: Perimeter of the semicircle= Ï€xD/2 + D
= Ï€x7 + 14
=22+14 = 36m
Length of the fence= 36-3=33m
Answer: B
Answer: (B) 33
Question: A man has Rs. 560 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?
(A) 45
(B) 60
(C) 75
(D) 105
(E) 120
Rationale: Let number of notes of each denomination be x.
Then x + 5x + 10x = 560
16x = 560
x = 35.
Hence, total number of notes = 3x = 105.
Answer = D
Answer: (D) 105
Question: What is the smallest of six consecutive odd integers whose average (arithmetic mean) is x + 2?
(A) x - 5
(B) x - 3
(C) x - 1
(D) x
(E) x + 1
Rationale: Assume the integers to be
n - 5, n - 3, n- 1, n+1, n + 3, n + 5
AM = 6n/6 = n
Given n = x + 2
Therefore, smallest term = n - 5 = x + 2 - 5 = x - 3
Correct Option: B
Answer: (B) x - 3
Question: The grade point average of one third of the classroom is 60; the grade point average of the rest is 66. What is the grade point average of the whole class?
(A) 55
(B) 56
(C) 64
(D) 65
(E) 66
Rationale: Let n=total students in class
total points for 1/3 class=60n/3=20n
total points for 2/3 class=66*2n/3=44n
total points for whole class=20n+44n=64n
64n total class points/n total students=64 grade point average for total class
Answer : C
Answer: (C) 64
Question: If half of 5 were 3, that would one-third of 10 be
(A) 2
(B) 4
(C) 6
(D) 8
(E) 1
Rationale: Explanation:
Half of 5 is 2.5. But given as 3. So take 1/2 of 5x = 3 ⇒ x = 6/5
Now 1/3 (10x) = 1/3 × 10 × 6/5 = 4.
Answer: B
Answer: (B) 4
Question: An article is bought for Rs.675 and sold for Rs.900, find the gain percent?
(A) 33 1/7%
(B) 33 2/3%
(C) 33 1/3%
(D) 37 1/3%
(E) 23 1/3%
Rationale: 675 ---- 225
100 ---- ? =>
=33 1/3%
Answer:C
Answer: (C) 33 1/3%
Question: Which of the following has 15^80 as a factor?
(A) 15^60
(B) 30^40
(C) 40^80
(D) 60^60
(E) 90^80
Rationale: Here 15^80 = 3^80 * 5^80 Only Option E has both .
ANSWER:E
Answer: (E) 90^80
Question: Cream costs twice as much as skim milk. A certain brand of milk is 1/3 cream and 2/3 skim milk. What fraction of the cost of this brand is due to the cream?
(A) 1/3
(B) 1/2
(C) 2/5
(D) 3/5
(E) 3/4
Rationale: Let x be the cost of the skim milk in the mixture.
The cost of the cream is (1/2)*x*2 = x.
The total cost is x+x = 2x and the fraction due to the cream is x/2x = 1/2
The answer is B.
Answer: (B) 1/2
Question: The number 110 can be written as the sum of the squares of 3 different positive integers. What is the sum of these 3 integers?
(A) 18
(B) 16
(C) 15
(D) 14
(E) 13
Rationale: 7^2+5^2+6^2=49+25+36 = 110
7+5+6 =18
Hence answer is A
Answer: (A) 18
Question: Given two sets A = {1,1,4,4,5,5} and B = {0,1}, if one number is chosen from each set at random, what is the probability that the sum of both numbers is an even number
(A) 1/4
(B) 1/8
(C) 1/7
(D) 1/2
(E) 3
Rationale: One way to look at it:
The number from set A can be ANYTHING.
The number selected from set B will determine whether the sum is odd or even.
For example, if a 4 is selected from set A, we need a 0 from set B to get an even sum.
If a 5 is selected from set A, we need a 1 from set B to get an even sum.
And so on.
So, P(sum is even) = P(select ANY number from set AANDselect the number from set B that makes the sum even)
= P(select ANY number from set A)xP(select the number from set B that makes the sum even)
= 1x1/2
= 1/2
= D
Answer: (D) 1/2
Question: For 2consecutive yrs, my incomes are in the ratio of 4:7 and expenses in the ratio of 3:5. If my income in the 2nd yr is Rs. 42000 & my expenses in the first yr in Rs.22000, my total savings for the two-year is
(A) s. 8000
(B) s. 9000
(C) s. 9900
(D) s. 9990
(E) s. 10000
Rationale: Sol. Income in first year = * x 42000 = Rs. 24000
Expenses in second year = \ x 21000 = Rs. 35000 Total savings = Total income - Total expenses = (42000 + 24000)- (22000 + 35000)
= 66000 - 57000 = Rs. 9000
B
Answer: (B) s. 9000
Question: If the SI on a certain sum of money is 4/25 of the sum and the rate per cent equals the number yrs, then the rate of interest/annum is?
(A) 4%
(B) 5%
(C) 6%
(D) 7%
(E) 8%
Rationale: Sol Let the prmcipal be Rs. x
Then the simple interest (1)
Let the me ofinterestp 3 be 1%,
than tune m : ryears
max! max
pm
‘X:5
4%
A
Answer: (A) 4%
Question: A boy multiplied 987 by a certain number and obtained 559981 as his answer. If in the answer both 98 are wrong and other digits are correct, then the correct answer would be:
(A) 553681
(B) 555181
(C) 555681
(D) 556581
(E) 555581
Rationale: 987 = 3 x 7 x 47.
So, the required number must be divisible by each one of 3, 7, 47
553681 --> sum of digits = 28, not divisible by 3
555181 sum of digits = 25, not divisible by 3
555681 is divisible by each one of 3, 7, 47.
556581 sum of digits = 30, not divisible by 7
555581 sum of digits = 29, not divisible by 3
so the answer is C.
Answer: (C) 555681
Question: One side of a rectangular field is 15m and one of its diagonal is 17m. Find the area of field?
(A) 120 sq. m
(B) 140 sq. m
(C) 125 sq. m
(D) 130 sq. m
(E) 110 sq. m
Rationale: Other side = [(17 x 17) - (15 x 15)] = (289 - 225) = 8m
Area = 15 x 8 =120 sq. m
ANSWER:A
Answer: (A) 120 sq. m
Question: Sandy gets 3 marks for each correct sum and loses 2 marks for each incorrect sum. Sandy attempts 30 sums and obtains 60 marks. How many sums did Sandy get correct?
(A) 18
(B) 20
(C) 22
(D) 24
(E) 26
Rationale: Let x be the correct sums and (30-x) be the incorrect sums.
3x - 2(30-x) = 60
5x = 120
x = 24
The answer is D.
Answer: (D) 24
Question: The distance between two planets is 4 × 10^6 light years. What is the distance between the two planets, in parsecs? (1 parsec = 3.26 light years)
(A)  9.3 × 10^5
(B)  9.9 × 10^6
(C)  9.3 × 10^7
(D)  9.9 × 10^7
(E)  1.2 × 10^6
Rationale: 4*10^6 light years = 4*10^6/3.26 parsecs.
4/3.26 is a little bit less than 1, something like 0.9, thus 4*10^6/3.26 = ~1.2*10^6.
Answer: E.
Answer: (E)  1.2 × 10^6
Question: Train A leaves the station traveling at 30 miles per hour. Two hours later train В leaves the same station traveling in the same direction at 45 miles per hour. How many miles from the station was train A overtaken by train B?
(A) 100
(B) 120
(C) 140
(D) 160
(E) 180
Rationale: After two hours, Train A is ahead by 60 miles.
Train B can catch up at a rate of 15 miles per hour.
The time to catch up is 60/15 = 4 hours.
In 4 hours, train A travels another 30*4 = 120 miles for a total of 180 miles.
The answer is E.
Answer: (E) 180
Question: The dimensions of an open box are 52, 40 and 29 cms. Its thickness is 2 cms. If 1 cm3 of metal used in the box weighs 0.5 gms, the weight of the box is?
(A) 6.892 kg
(B) 9.832 kg
(C) 6.830 kg
(D) 6.832 kg
(E) 6.862 kg
Rationale: Explanation:
52 * 40 * 29 = 60320
48 * 36 * 27 = 46650
------------
13664
13664 * 1/2 = 6832 => 6.832 kg
Answer: Option D
Answer: (D) 6.832 kg
Question: How many liters of water must be evaporated from 50 liters of a 4 percent sugar solution to get a 5 percent sugar solution?
(A) 4
(B) 6
(C) 8
(D) 10
(E) 12
Rationale: Let x be the amount that needs to be evaporated.
0.04(50) = 0.05(50-x)
0.05x = 2.5 - 2
x = 0.5/0.05 = 10 liters
The answer is D.
Answer: (D) 10
Question: An urn contains 4 white 6 black and 8 red balls . If 3 balls are drawn one by one without replacement, find the probability of getting all white balls.
(A) 1/209
(B) 1/204
(C) 1/207
(D) 1/202
(E) 1/201
Rationale: Explanation:
Let A, B, C be the events of getting a white ball in first, second and third draw respectively, then
Required probability =
=
Now, P(A) = Probability of drawing a white ball in first draw = 4/18 = 2/9
When a white ball is drawn in the first draw there are 17 balls left in the urn, out of which 3 are white
Since the ball drawn is not replaced, therefore after drawing a white ball in the second draw there are 16 balls left in the urn, out of which 2 are white.
Hence the required probability
Answer: B) 1/204
Answer: (B) 1/204
Question: The difference between the compound interest compounded annually and simple interest for 2 years at 20% per annum is Rs.144. Find the principal?
(A) 3629
(B) 3608
(C) rs.3600
(D) 3613
(E) 6192
Rationale: P = 144( 100 / 5)2 => P
= 3600
Answer:C
Answer: (C) rs.3600
Question: An error 2% in excess is made while measuring the side of a square. The percentage of error in the calculated area of the square is?
(A) 4%
(B) 4.04%
(C) 4.14%
(D) 5%
(E) 5.13%
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: Two equally sized jugs full of water are each emptied into two separate unequally sized empty jugs, X and Y. Now, jug X is 1/3 full, while jug Y is 2/3 full. If water is poured from jug X into jug Y until jug Y is filled, what fraction of jug X then contains water?
(A) 0
(B) 1/15
(C) 2/15
(D) 1/6
(E) 2/10
Rationale: Suppose the water in each jug is L liters
CX x (1/3) = L
CX = 3L liters
CX is capacity of X
CY x (2/3) = L
CY = 3L/2 liters
CY is capacity of Y
Now, Y is 3L/2 - L empty = L/2 empty
So, we can put only L/2 water in jug Y from Jug X
Jug X's remaining water = L - L/2 = L/2
Fraction of X which contains water = water / CX
= (L/2)/ 3L
= 1/6
Answer will be D
Answer: (D) 1/6
Question: How many integers n greater than and less than 100 are there such that,if the digits of n are reversed, the resulting integer is n+9 ?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
Rationale: (10x+y)=(10y+x)+9
=> 9x-9y=9
=> x-y=1
and only 8 numbers satisfy this condition and the numbers are 21,32,43,54,65,76,87,98
ANSWER:D
Answer: (D) 8
Question: An accurate clock shows 8 o’clock in the morning. Through how many degrees will the hour hand rotate when the clock shows 12 o’clock in the afternoon?
(A) 120°
(B) 90°
(C) 180°
(D) 320°
(E) None of these
Rationale: Sol.
Angle traced by the hour hand in 4 hours = [360/12 * 4]° = 120°
Answer A
Answer: (A) 120°
Question: Which of the following could be the value of x, if |3x – 9| = 0?
(A) –3
(B) 1/9
(C) 1/3
(D) -1/3
(E) 3
Rationale: |3x – 9| = 0
=> 3x - 9 = 0
or -(3x - 9) = 0
=> 3x = 9 or -3x = -9
=> x = 3 or x = 3
Answer E
Answer: (E) 3
Question: I. a^2 - 9a + 20 = 0,
II. 2b^2 - 5b - 12 = 0 to solve both the equations to find the values of a and b?
(A) If a < b
(B) If a ≤ b
(C) If the relationship between a and b cannot be established
(D) If a > b
(E) If a ≥ b
Rationale: I. (a - 5)(a - 4) = 0
=> a = 5, 4
II. (2b + 3)(b - 4) = 0
=> b = 4, -3/2 => a ≥ b
Option E
Answer: (E) If a ≥ b
Question: How many ways are there to select a subcommittee of 11 members from among a committee of 17?
(A) 12376
(B) 19448
(C) 28791
(D) 27711
(E) 12111
Rationale: Explanation:
Since it does not matter what order the committee members are chosen in, the combination formula is used.
Committees are always a combination unless the problem states that someone like a president has higher hierarchy over another person. If the committee is ordered, then it is a permutation.
C(17,11)= 12,376
Answer: A
Answer: (A) 12376
Question: What least number should be added to 1053, so that the sum is completely divisible by 23
(A) A)4
(B) B)1
(C) C)2
(D) D)3
(E) E)5
Rationale: Explanation:
(1053 / 23) gives remainder 18
18 + 5 = 23, So we need to add 5
Answer: Option E
Answer: (E) E)5
Question: The sum of three consecutive even numbers is 93. Find the middle number of the three?
(A) 14
(B) 35
(C) 39
(D) 31
(E) 12
Rationale: Middle value =93/3
=31
Ans D
Answer: (D) 31
Question: A boy has 9 trousers and 15 shirts. In how many different ways can he select a trouser and a shirt?
(A) 100
(B) 140
(C) 104
(D) 135
(E) 125
Rationale: The boy can select one trouser in nine ways.
The boy can select one shirt in 12 ways.
The number of ways in which he can select one trouser and one shirt is 9 * 15 = 135 ways.
D
Answer: (D) 135