mathewhe/aqua_rat huggingface dataset:
Question: It is known that no more than 6 children will be attending a party. What is the smallest number of cookies that must be brought to the party so that each child receives the same number of cookies?
(A) 35
(B) 105
(C) 60
(D) 210
(E) 420
Rationale: The question states that there are no more than 6 children in the party. Thus, the possibility is that there could be 1, 2, 3, 4, 5 or 6 children.
If you assume answer as 35 and there are 3 children, you may not distribute be able to distribute cookies equally.
similarly if there were 105 cookies, and 2 children, cookies cannot be distributed equally.
or if there were 210 cookies, and 4 children, cookies cannot be distributed equally.
Thus, the question asks for a number of cookies which can be distributed to any number of children (from 1 to 6).
And therefore the smallest number of cookies would be lcm of (1, 2, 3, 4, 5, 6), i.e., 60.
Answer (C)
Answer: (C) 60
Question: If the tens digit x and the units digit y of a positive integer n are reversed, the resulting integer is 18 more than n. What is y in terms of x ?
(A) x+2
(B) x-2
(C) x+5
(D) x+6
(E) x+3
Rationale: Original Digits=xy i.e. Number=10x+y
After reversing the digits:
Digits=yx i.e. Number=10y+x
10y+x is 18 more than 10x+y
10x+y+18=10y+x
10x-x+18=10y-y
9x+18=9y
x+2=y
OR
y=x+2
Answer : A
Answer: (A) x+2
Question: As a treat for her two crying children, a mother runs to the freezer in which she has two cherry ice pops, three orange ice pops, and four lemon-lime ice pops. If she chooses two at random to bring outside to the children, but realizes as she runs out the door that she cannot bring them different flavors without one invariably being jealous of the other and getting even more upset, what is the probability that she has to return to the freezer to make sure that they each receive the same flavor?
(A) 1/9
(B) 1/6
(C) 5/18
(D) 13/18
(E) 5/6
Rationale: Probability of not getting the same flavor ->
Favorable -> Cherry - orange [ 2C1 * 3C1 [or simply 2*3 ] or Cherry - lemon [ 2*4] or orange - lemon [3*4]
Prob = (2*3 + 2*4 + 3*4 ) / 9C2 = 26/36 = 13/18
Answer -> D
Answer: (D) 13/18
Question: In a class, 30% of the students offered English, 20% offered Hindi and 10% offered both. If a student is selected at random, what is the probability that he has offered English and Hindi?
(A) 2/10
(B) 1/10
(C) 3/10
(D) 2/5
(E) 3/5
Rationale: P(E)=30/100,
P(H)=20/100
P(E and H)=10/100
P(E or H)=3/10+2/10-1/10
=2/5
ANSWER D 2/5
Answer: (D) 2/5
Question: The length of a rectangular field is 7/5 its width. If the perimeter of the field is 336 meters, what is the width of the field?
(A) 50
(B) 60
(C) 70
(D) 80
(E) 90
Rationale: Let L be the length and W be the width. L = (7/5)W
Perimeter: 2L + 2W = 336, 2(7/5)W + 2W = 336
Solve the above equation to find: W = 70 m and L = 98 m.
correct answer C)70
Answer: (C) 70
Question: The average of 11 numbers is 10.8. If the average of the first six numbers is 10.5 and that of the last six numbers is 11.4, then the middle number is
(A) 71.5
(B) 11.5
(C) 81.5
(D) 11.5
(E) 12.6
Rationale: Explanation:
Middle numbers = [(10.5 x 6 + 11.4 x 6) - 10.9 x 11] = 12.6.
Answer E
Answer: (E) 12.6
Question: f, b, c, and d are positive integers. If the remainder is 9 when f is divided by b, and the remainder is 5 when c is divided by d, which of the following is NOT a possible value for b + d?
(A)  20
(B)  19
(C)  18
(D)  16
(E)  15
Rationale: When f is divided by b remainder is 9 that means b is greater than or equals to 10, similarly d is greater than or equals to 6.
b + d cannot be 15, hence E is the answer.
Answer: (E)  15
Question: Of the teams competing in the world archery championships, sixty percent are from Europe. Half as many are from the United States and one twentieth are from Africa. What fraction of teams are from neither Europe, the US or Africa.
(A) 1/20
(B) 15/20
(C) 13/15
(D) 17/20
(E) 13/17
Rationale: Assume 100 total people.
60% of 100 = 60 --->Europeans
1/2 of 60 ---> 30 Americans
1/20 of 100 ---> 5 Africans
Now you would add them all up, and minus it by the total (100). 100 - 95= 5. So, 65 people out of 100 are not EU, US or Africans. 5/100 is also equal to 1/20.
So therefore, the answer is A.
Answer: (A) 1/20
Question: The population of a town is 8000. It decreases annually at the rate of 10% p.a. What will be its population after 2 years?
(A) 5100
(B) 5120
(C) 5200
(D) 5400
(E) 6480
Rationale: Formula :
( After =100 denominator
Ago = 100 numerator)
8000 Ã— 90/100 Ã— 90/100= 6480
Answer : E
Answer: (E) 6480
Question: When positive integer N is divided by positive integer J, the remainder is 42. If N/J = 204.07, what is value of J?
(A) 200
(B) 400
(C) 800
(D) 600
(E) 1200
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 = 204.07
Here 204 is the quotient.
Given that Remainder = 42
So, 204.07= 204 + 42/J
So, J = 600
Answer: D
Answer: (D) 600
Question: I bought two books; for Rs.470. 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) 274.17
(B) 280.17
(C) 299.17
(D) 266.17
(E) 279.17
Rationale: x*(85/100) = (470 - x)119/100
x = 274.17
Answer: A
Answer: (A) 274.17
Question: A certain sum is invested at simple interest at 15% p.a. for two years instead of investing at 12% p.a. for the same time period. Therefore the interest received is more by Rs. 420. Find the sum?
(A) s. 5000
(B) s. 7000
(C) s. 14000
(D) s. 17000
(E) s. 27000
Rationale: Let the sum be Rs. x.
(x * 15 * 2)/100 - (x * 12 * 2)/100 = 420
=> 30x/100 - 24x/100 =420
=> 6x/100 = 420
=> x = 7000.
ANSWER:B
Answer: (B) s. 7000
Question: The average of 13 numbers is 58. Average of the first 7 of them is 57 and that of the last 7 is 61. Find the 8th number?
(A) 72
(B) 83
(C) 45
(D) 53
(E) 64
Rationale: Sum of all the 13 numbers = 13 * 58 = 754
Sum of the first 7 of them = 7 * 57 = 399
Sum of the last 7 of them = 7 * 61 = 427
So, the 8th number = 427 + 399 - 754 = 72.
Answer:A
Answer: (A) 72
Question: Two trains of length 100 m and 200 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 18 kmph and 72 kmph. In how much time will the trains cross each other?
(A) 8
(B) 16
(C) 11
(D) 12
(E) 21
Rationale: Relative speed = (18 + 72)* 5/18 = 25 mps.
The time required = d/s = (100 + 100 + 200)/25
= 400/25 =16 sec.
Answer:B
Answer: (B) 16
Question: The population of a bacteria colony doubles every day. If it was started 9 days ago with 2 bacteria and each bacteria lives for 12 days, how large is the colony today?
(A) 512
(B) 768
(C) 1024
(D) 2048
(E) 4096
Rationale: It started 9 days ago. So bacterias keep growing for 9 days+ today= 10 days
2^10= 1024
C is the answer
Answer: (C) 1024
Question: Sum of 3 consecutive even no.'s is 28 more than the 1st no. of the series. Find the middle no.?
(A) 8
(B) 13
(C) 14
(D) 16
(E) 18
Rationale: Let the numbers be x, x+2 and x+4 then
x + x+2 + x+4 = x+28
3x + 6 = x + 28
2x = 22
\inline \therefore x = 11
\inline \therefore Middle number = x + 2 = 11+2 = 13
B
Answer: (B) 13
Question: If |3x+20|=|5x-5|, which of the following could be a value of x?
(A) 15/8
(B) 12
(C) -25/8
(D) 15/2
(E) 25/2
Rationale: 3x + 20 = 5x - 5 or 3x + 20 = -5x + 5
-2x = -25 or 8x = -15
x = 25/2 or x = -15/8
Answer: E
Answer: (E) 25/2
Question: 5^b + 5^b + 5^b + 5^b + 5^b =
(A) 5^(b + 1)
(B) 7^(b + 1)
(C) 7^(7b)
(D) 8^b
(E) 49^B
Rationale: Easy one.
5*5^b = 5^(b+1)
Ans. A
Answer: (A) 5^(b + 1)
Question: The present population of a town is 1000. Population increase rate is 20% p.a. Find the population of town after 2 years?
(A) 1440
(B) 1220
(C) 1400
(D) 1500
(E) 1620
Rationale: P = 1000
R = 20%
Required population of town = P*(1 + R/100)^T
= 1000*(1 + 20/100)^2
= 1000*(6/5)^2
= 1440(approximately)
Answer is A
Answer: (A) 1440
Question: What is the average of first 20 multiples of 7 ?
(A) A)70
(B) B)77
(C) C)79
(D) D)84
(E) E)82
Rationale: Required average = 7(1+2+....+20) / 20
(8/20)X ( (20x21) / 2 ) (because sum of first 21 natural numbers)
= 84
D
Answer: (D) D)84
Question: How many numbers between 200 and 600 are divisible by 4, 5 and 6?
(A) 5
(B) 6
(C) 8
(D) 10
(E) 12
Rationale: Sol.
Every such numbers must be divisible by L.C.M. of 4, 5, 6, i.e. 60.
Such numbers are 240, 300, 360, 420, 480, 540.
Clearly, there are 6 such numbers.
Answer B
Answer: (B) 6
Question: A pair of prime numbers that can be expressed in the form {p, (p + 6)} is deﬁned as a pair of “sexy primes.” A “sexy triplet” is a group of three primes that can be expressed in the form Q{p, (p + 6), (p + 12)}. All of the following prime numbers are the middle term of a sexy triplet EXCEPT
(A)  11
(B)  13
(C)  17
(D)  19
(E)  23
Rationale: definetly a sitter.plug in the values for middle term and calculate.We can see clearly that Q for 19 , 19+6 gives 25 which is not a prime
therefore correct answer D
Answer: (D)  19
Question: A, B and C started a business with capitals of Rs. 8000, Rs. 10000 and Rs. 12000 respectively. At the end of the year, the profit share of B is Rs. 4000. The difference between the profit shares of A and C is?
(A) 621
(B) 276
(C) 236
(D) 1600
(E) 211
Rationale: Explanation:
Ratio of investments of A, B and C is 8000 : 10000 : 12000 = 4 : 5 : 6
And also given that, profit share of B is Rs. 4000
=> 5 parts out of 15 parts is Rs. 4000
Now, required difference is 6 - 4 = 2 parts
Required difference = 2/5 (4000) = Rs. 1600
Answer: D
Answer: (D) 1600
Question: In a nationwide poll, N people were interviewed. If 1/6 of them answered yes to question 1, and of those, 1/4 answered yes to question 2, which of the following expressions represents the number of people interviewed who did NOT answer yes to both questions?
(A) N/10
(B) 9N/10
(C) 2N/3
(D) 23N/24
(E) 29N/30
Rationale: The number of people who answered yes to both questions is (1/4)(1/6)N = N/24
The number of people who did not answer yes to both is 1 - N/24 = 23N/24
The answer is D.
Answer: (D) 23N/24
Question: P, Q, R enter into a partnership. P initially invests 25 lakh & adds another 10 lakhs after one year. Q initially invests 35 lakh & withdrawal 10 lakh after 2 years and R invests Rs 30 Lakhs . In what ratio should the profit be divided at the end of 3 years?
(A) 18:19:19
(B) 18:18:19
(C) 19:19:18
(D) 18:19:19
(E) None
Rationale: Solution: P:Q:R = (25*1+35*2) : (35*2 : 25*1) : (30*3)
= 95 : 95 : 90.
= 19 : 19: 18.
Answer: Option C
Answer: (C) 19:19:18
Question: The area of a square garden is Q square feet and the perimeter is P feet. If Q=P+32, what is the perimeter of the garden in feet?
(A) 32
(B) 36
(C) 40
(D) 44
(E) 48
Rationale: Let x be the length of one side of the square garden.
x^2 = 4x + 32
x^2 - 4x - 32 = 0
(x-8)(x+4) = 0
x = 8, -4
P = 4(8) = 32
The answer is A.
Answer: (A) 32
Question: Of the science books in a certain supply room, 50 are on botany, 65 are on zoology, 90 are on physics. 50 are on geology, and 110 are on chemistry. If science books are removed randomly from the supply room, how many must be removed to ensure that 80 of the books removed are on the same science?
(A) 81
(B) 159
(C) 166
(D) 285
(E) 324
Rationale: We can remove 80 books only from physics or from chemistry. Worst case scenario would be if we remove all books on botany, zoology, geology, 79 books on physics and 79 books on chemistry.
We would have 50(botany)+65(zoology)+50(geology)+79(physics)+79(chemistry)=323 books and still won't have 80 books from the same science. As after this, only books on physics and chemistry will be left then any next book would become the 80th book either on physics or on chemistry.
Answer: E.
Answer: (E) 324
Question: A rectangular field has to be fenced on three sides leaving a side of
20
20 feet uncovered. If the area of the field is
680
680 sq. feet, how many feet of fencing will be required?
(A) 95
(B) 92
(C) 88
(D) 82
(E) 80
Rationale: Area of the field=680 sq. feet.
Length of the adjacent sides are 20 feet and 680/20=34feet.
Required length of the fencing=20+34+34=88 feet
ANSWER:C
Answer: (C) 88
Question: Let f(x) = x^2 + bx + c. If f(1) = 0 and f(-5) = 0, then f(x) crosses the y-axis at what y-coordinate?
(A) -5
(B) -1
(C) 0
(D) 1
(E) 5
Rationale: When x = 1 and when x = -5, the expression f(x) = x² + bx + c equals 0.
Then f(x) = (x-1)(x+5)
f(0) = -5
The answer is A.
Answer: (A) -5
Question: If it is a possible to make a meaningful word from the first, the fourth, the seventh and the ninth letters of the word PESTICIDE, then last letter of the word is your answer. If more than one such word can be formed give 'M' as your answer and if no such word can be formed give 'X' as your answer.
(A) E
(B) T
(C) P
(D) M
(E) X
Rationale: If we observe from the given word 1st=p,4th=T,7th=I,9th=E
by the combination and arrangement we cant make a word
So the answer is X
ANSWER:E
Answer: (E) X
Question: If the time is currently 1:30pm, what time will it be in exactly 649 hours?
(A) 12:30am
(B) 1:30am
(C) 12:30pm
(D) 2:30pm
(E) 10:30pm
Rationale: Every 24 hours will bring us to the same 1:30pm. 648 is divisible by 24 (27*24=648), so if it were 648 hours we would have 1:30pm, but since it's 648 hours then it will be 1 hour more, so 2:30pm.
Answer: D.
Answer: (D) 2:30pm
Question: Replace the ? mark with an appropriate approximate value in the following equation’?
7 1/2 of 265.6+15% of 2564= ? - 620.5
(A) 2297.1
(B) 2997.1
(C) 2557.1
(D) 2937.1
(E) 2992.1
Rationale: 7 1/2 of 265.6+15% of 2564= ? - 620.5
15/2 of 265.6+15% of 2564= ? - 620.5
1992+384.6= ? - 620.5
1992+384.6 +620.5= ?
≈ 2997.1
Answer B
Answer: (B) 2997.1
Question: How many numbers from 2 to 11 are exactly divisible by 2?
(A) A)2
(B) B)3
(C) C)5
(D) D)7
(E) E)8
Rationale: 2/2 = 1 and11/2 = 5
5 - 1 = 4
4 + 1 = 5 Numbers.
Answer : C
Answer: (C) C)5
Question: What two-digit number is less than the sum of the square of its digits by 12 and exceeds their doubled product by 5?
(A)  95
(B)  99
(C)  26
(D)  73
(E)  None of the Above
Rationale: Let the digits be x and y. The number would be 10x + y.
We are given that 2xy + 5 = 10x +y = x^2 y^2 -12
Thus 2xy +5 = x^2 + y^2 - 12
x^2 + y^2 -2xy = 16
(x-y)^2 = 16
(x-y) = 4 or -4
Substituting the values of (x-y) in the equation 2xy +5 = 10x + y
x comes out to be 1 or 9... thus the two numbers can be 15 or 99
Thus the answer is B
Answer: (B)  99
Question: Susan weighs 20 pounds more than Anna does, and together they weigh a total of 160 pounds. Which of the following represents Anna’s weight in pounds?
(A) 55
(B) 50
(C) 70
(D) 65
(E) 63
Rationale: Total weight = 160
Anna's weight = 160-20 /2 = 70
Answer : C
Answer: (C) 70
Question: Daniel went to a shop and bought things worth Rs. 25, out of which 30 Paise went on sales tax on taxable purchases. If the tax rate was 10%, then what was the cost of the tax free items?
(A) A)19.7
(B) B)20
(C) C)21.3
(D) D)21.7
(E) E)22
Rationale: Total cost of the items he purchased = Rs.25
Given that out of this Rs.25, 30 Paise is given as tax
=> Total tax incurred = 30 Paise = Rs.30/100
Let the cost of the tax free items = x
Given that tax rate = 10%
∴ (25−30/100−x)10/100 = 30/100
⇒ 10(25 −0.3 −x) = 30
⇒ (25 − 0.3 − x) = 3
⇒ x = 25 − 0.3 − 3
= 21.7
D
Answer: (D) D)21.7
Question: A reduction of 25% in the price of oil enables a house wife to obtain 5kgs more for Rs.800, what is the reduced price for kg?
(A) 22
(B) 80
(C) 40
(D) 77
(E) 12
Rationale: 800*(25/100) = 200 ---- 5
? ---- 1 => Rs.40
Answer: C
Answer: (C) 40
Question: A truck traveled 200 km in 2 hours. Calculate the speed
(A) 85 kmh
(B) 140 kmh
(C) 70 kmh
(D) 20 kmh
(E) 100 kmh
Rationale: Speed= Distance/Time
200/2=100
Answer: E
Answer: (E) 100 kmh
Question: In a class, the average age of 25 boys is 10 years and the average of 18 girls is 10 years. what is the average age of the whole class?
(A) 10 Years
(B) 12.6 Years
(C) 13 Years
(D) 13.5 Years
(E) 14 Years
Rationale: Total age of 43 students
(25X 10+18 X 10) = 430
Average = 430/43 = 10 Years
A)
Answer: (A) 10 Years
Question: Event E is defined to be rolling an even number on a 6-sided die and Event F is defined to be rolling a 1, 2 or 3. Calculate the probability of rolling a die such that events E and F occur simultaneously on a single roll of the die.
(A) 1/2
(B) 1/6
(C) 0
(D) 5/6
(E) 1
Rationale: Determine if E and F are independent.
P(E|F) = the probability of event E occurring given that event F has already occurred
P(E|F) ≠ P(E) as P(E) is changed if it is given that F occurs.
Consequently, P(E∩F) ≠ P(E)P(F) since the events are not independent. As a result, P(E∩F) ≠ 1/4 = P(E)P(F)
We must use the more complex formula for finding the intersection of E and F:
P(E∩F) = P(F)P(E|F)
P(F) = the probability of event F occurring
The probability of rolling a 1, 2, or 3 is 3/6 = 1/2
P(E|F) = the probability of event E occurring given that event F has already occurred
If event F already occurred, we are limited to the numbers 1, 2, or 3. Within this range of 3 possible numbers, only one number--namely, 2--is an even number. Therefore, P(E|F) = 1/3
P(E∩F) = P(F)P(E|F) = (1/2) * (1/3) = 1/6
Answer B
Answer: (B) 1/6
Question: How many words can be formed by using all letters of the word “FAR”
(A) 12
(B) 24
(C) 8
(D) 6
(E) 140
Rationale: The word FAR contains 3 different letters.
Required number of words = 3p3 = 3! = (3x2x1) = 6.
Answer D.
Answer: (D) 6
Question: In a class, except 18 all are above 50 years.15 are below 50 years of age. How many people are there
(A) 30
(B) 33
(C) 36
(D) can not be determined.
(E) none of these.
Rationale: As per given statements,
15 are below 50 years of age.
except 18 all are above 50 years. means 3 are of 50 years of age.
there is no information about no of students above 50 years of age.
so total no can not be determined. ANSWER:D
Answer: (D) can not be determined.
Question: The MegaTek Corporation is displaying its distribution of employees by department in a circle graph. The size of each sector of the graph representing a department is proportional to the percentage of total employees in that department. If the section of the circle graph representing the manufacturing department takes up 144° of the circle, what percentage of MegaTek employees are in manufacturing?
(A) 20%
(B) 25%
(C) 30%
(D) 40%
(E) 72%
Rationale: ANSWER: D 144° divided by 360° equals 0.4, therefore the sector is equal to 40% of the total
Answer: (D) 40%
Question: Each of the integers from 0 to 9, inclusive, is written on a separate slip of blank paper and the ten slips are dropped into hat. If the slips are then drawn one at a time without replacement, how many must be drawn to ensure that the numbers on two of the slips drawn will have a sum of 9?
(A) 2
(B) 3
(C) 1
(D) 6
(E) 4
Rationale: You should consider the worst case scenario: if you pick numbers 0, 1, 2, 3 and 4 then no two numbers out of these 5 add up to 9.
Now, the next, 6th number whatever it'll be (5,6,7,8 or 9) will guarantee that two number WILL add up to 9. So, 6 slips must be drawn to ensure that the numbers on two of the slips drawn will have a sum of 9
Answer: D
Answer: (D) 6
Question: Out of 9 persons, 8 persons spent Rs. 30 each for their meals. The ninth one spent Rs. 20 more than the average expenditure of all the nine. The total money spent by all of them was
(A) Rs. 292.50
(B) Rs. 292.77
(C) Rs. 292.21
(D) Rs. 292.19
(E) Rs. 292.11
Rationale: Explanation:
Let the average expenditure be Rs. x Then,
Total money spent = 9x = Rs. (9 x 32.5O) = Rs 292. 50
Answer: A
Answer: (A) Rs. 292.50
Question: If a - b = 3 and a(power 2) + b(power 2) = 27, find the value of ab.
(A) 5
(B) 9
(C) 4
(D) 10
(E) 3
Rationale: 2ab = (a(power 2) + b(power 2) - (a - b)(power 2)
= 27 - 9 = 18
ab = 9.
Answer is B.
Answer: (B) 9
Question: Ron begins reading a book at 4: 30 p.m. and reads at a steady pace of 30 pages per hour. Michelle begins reading a copy of the same book at 7: 30 p.m. If Michelle started 5 pages behind the page that Ron started on and reads at an average pace of 50 pages per hour, at what time would Ron and Michelle be reading the same page?
(A) 7: 00 p.m.
(B) 7: 30 p.m.
(C) 7: 45 p.m.
(D) 10: 00 p.m.
(E) 10: 30 p.m.
Rationale: M gains 50-30=20 pages per hour on R
at 7:30pm R has read 45 pages and M is 45+5=50 pages behind him
time=50/20=2.5 hours
they are on the same page at 10:00pm
D
Answer: (D) 10: 00 p.m.
Question: A dice is numbered from 1 to 6 in different ways.
If 1 is adjacent to 2, 4 and 6, then which of the following statements is necessarily true?
(A) 3 is adjacent to 8
(B) 3 is adjacent to 2
(C) 3 is adjacent to 5
(D) 3 is adjacent to 1
(E) 6 is adjacent to 8
Rationale: Explanation:
If 1 is adjacent to 2, 4 and 6 then either 3 or 5 lies opposite to 1. So, the numbers 3 and 5 cannot lie opposite to each other. Hence, 3 is adjacent to 5 (necessarily).
Answer: C
Answer: (C) 3 is adjacent to 5
Question: If y is the smallest positive integer such that 1,260 multiplied by y is the square of an integer, then y must be
(A) 23
(B) 51
(C) 38
(D) 35
(E) 37
Rationale: 1260= 2*2*3*3*7*5, so we need one 7 and one 5 to make it a square of a number. so 7*5= 35
Ans: D
Answer: (D) 35
Question: If 5400 mn = k^4, where m, n, and k are positive integers, what is the least possible value of m + n?
(A) 11
(B) 18
(C) 20
(D) 25
(E) 33
Rationale: k^4=5400∗mn
k^4=3^3.2^3.5^2.mn
In order to make RHS a perfect power of 4, we require it to be multiplied by 3, 2 & 5^2
mn=3.2.5^2
mn = 150 = 10 * 15 (Least possible)
Answer = 10 + 15 = 25
ANSWER:D
Answer: (D) 25
Question: If x is divisible by 6, 7, and 11, which of the following must be the least multiple of x?
(A) 264
(B) 154
(C) 66
(D) 77
(E) 462
Rationale: If x is divisible by 6, 7, and 11, then x must be a multiple of 6, 7, and 11.
Hence,the least multiple of x will be 6*7*11=462.
ANSWER:E
Answer: (E) 462
Question: 20 men or 25 women can finish a work in 25 days. How many days 38 men and 15 women will take to finish this job?
(A) 12days
(B) 10days
(C) 5days
(D) 6days
(E) 15days
Rationale: 20 men = 25 women
Therefore, 1 women = 20/25 men = 4/5 men
15 women = 4/5 *15 men = 12 men
i.e. 38 men + 15 women = 38 men + 12 men = 50men
1 work done by men = 20*25
20 *25 = 50 * ?
number of days = 20 *25/50 = 10days.
B
Answer: (B) 10days
Question: What is the leastvalue of x. So that 23x57 is divisible by 3?
(A) 2
(B) 5
(C) 1
(D) 6
(E) 7
Rationale: The sum of the digits of the number is divisible by 3, then the number is divisible by3.
2 + 3 + x + 5 + 7 = 17 + x
Least value of x may be 1
Therefore 17 + 1 = 18 is divisible by 3.
C
Answer: (C) 1
Question: Which of the following is equivalent to the pair of inequalities x + 4 > 10 and x - 2 <= 5 ?
(A)  2 < x < 16
(B)  2 <= x < 4
(C) (D) 6 < x <= 7
(D) (C) 2 < x <= 8
(E)  4 <= x <= 16
Rationale: Solution:
Let’s isolate x in both inequalities, starting with x + 4 > 10.
x + 4 > 10
x > 6
Next we isolate x in the inequality x – 2 5.
x – 2 <= 5
x <= 7
Bringing these two inequalities together we know:
6 < x <= 7
The answer is C.
Answer: (C) (D) 6 < x <= 7
Question: If log3(2), log3(2x - 5), log3(2x - 7/2) are in arithmetic progression, then the value of x is equal to
(A) 5
(B) 4
(C) 2
(D) 3
(E) 1
Rationale: Explanation :
Using log a – log b = log(a/b) ,
=> 2/(y-5) = (y-5) / (y-3.5), where y = 2x.
Solving we get, y= 4 or 8 i.e x = 2 or 3.
It can't be 2 as log of negative number is not deifned.
Answer : D
Answer: (D) 3
Question: The cross-section of a lake is a trapezium in shape. If the lake is 20m wide at the top and 5m wide at the bottom and the area of cross-section is 600 sq m, the depth of lake is?
(A) 48 m
(B) 68 m
(C) 46 m
(D) 84 m
(E) 97 m
Rationale: 1/2 * d (20+5) = 600
d = 48
ANSWER:A
Answer: (A) 48 m
Question: ELFA, GLHA, ILJA, _____, MLNA
(A) IOH
(B) HTY
(C) YOU
(D) FLQ
(E) KLLA
Rationale: The second and forth letters in the series, L and A, are static. The first and third letters consist of an alphabetical order beginning with the letter E.
ANSWER:E
Answer: (E) KLLA
Question: Two boys starts from the same place walking at the rate of 5 kmph and 5.5 kmph respectively in the same direction. What time will they take to be 8.5 km apart?
(A) 17 hr
(B) 14 hr
(C) 12 hr
(D) 19hr
(E) 23 hr
Rationale: Relative speed = 5.5 - 5 = 0.5 kmph (because they walk in the same direction)
distance = 8.5 km
time = distance/speed=8.5/0.5=17 hr
Answer is A
Answer: (A) 17 hr