mathewhe/aqua_rat huggingface dataset:
Question: For one toss of a certain coin, the probability that the outcome is heads is 0.9. If this coin is tossed 5 times, which of the following is the probability that the outcome will be heads at least 4 times?
(A) (0.9)^5
(B) 2(0.9)^4
(C) 3(0.9)^4
(D) 4(0.9)^4(0.1) + (0.9)^5
(E) 5(0.9)^4(0.1) + (0.9)^5
Rationale: P(5 heads) = (0.9)^5
There are 5 ways to get 4 heads: HHHHT, HHHTH, HHTHH, HTHHH, THHHH
P(4 heads) = 5*(0.9)^4(0.1)
The answer is E.
Answer: (E) 5(0.9)^4(0.1) + (0.9)^5
Question: Working simultaneously at their respective constant rates, Machines A and B produce 800 nails in x hours. Working alone at its constant rate, Machine A produces 800 nails in w hours. In terms of x and w, how many hours does it take Machine B, working alone at its constant rate, to produce 800 nails?
(A) x/(x+y)
(B) y/(x+y)
(C) xy/(x+y)
(D) xy/(x-y)
(E) xw/(w-x)
Rationale: Pick some smart numbers for x and w.
Say x=1 hour and w=2 hours (notice that w must be greater than x, since the time for machine A to do the job, which is w hours, must be more than the time for machines A and B working together to do the same job, which is x hours).
In this case, the time needed for machine B to do the job must also be 2 hours: 1/2+1/2=1.
Now, plug x=1 and w=2 in the options to see which one yields 2. Only option E fits.
Answer: E.
Answer: (E) xw/(w-x)
Question: Jim and John are workers in a department that has a total of 8 employees. Their boss decides that two workers from the department will be picked at random to participate in a company interview. What is the probability that both Jim and John are chosen?
(A) 1/25
(B) 1/14
(C) 1/28
(D) 1/7
(E) 2/19
Rationale: Probability = 2c2/8c2
= 1/28
Answer C
Answer: (C) 1/28
Question: If x>y>0, which of the following must be true:
I. |x|>y
II. x^4 > y^4
III. x^2>y^2
(A) I only
(B) II only
(C) III only
(D) II and III
(E) I, II and III
Rationale: Assuming x and y to be integers
X=3,Y=2
X^2=3^2=9
Y^2=2^2=4
So I is true
Now lets look at option III because if option 3 is true E is the answer or else A
As per question X>Y>0 Hence |X| >Y
So OA=D
Answer: (D) II and III
Question: There are two examinations rooms A and B. If 10 students are sent from A to B, then the number of students in each room is the same. If 20 candidates are sent from B to A, then the number of students in A is double the number of students in B. The number of students in room A is
(A) 20
(B) 80
(C) 100
(D) 200
(E) 180
Rationale: Let the number of students in rooms A and B be x and y respectively.
Then, x - 10 = y + 10 x - y = 20 .... (i)
and x + 20 = 2(y - 20) x - 2y = -60 .... (ii)
Solving (i) and (ii) we get: x = 100 , y = 80.
The required answer A = 100.
Correct answer is 100
Answer: (C) 100
Question: A can do a piece of work in 24 days and B can do it in 15 days and C can do it 20 days. They started the work together and A leaves after 2 days and B leaves after 4 days from the beginning. How long will work lost?
(A) 10
(B) 12
(C) 13
(D) 11
(E) 15
Rationale: 2/24 + 4/15 + x/20 = 1
x = 13 Answer: C
Answer: (C) 13
Question: Anup was asked to find the value of 7/12 of a sum of money W. Instead of multiplying the same by 7/12,he divided it by 7/12 and his answer exceeded the correct answer by 95. The correct answer is:
(A)  48
(B)  89
(C)  84
(D)  69
(E)  49
Rationale: W=12/7*x-7/12*x=95 --> x=84 --> 7/12*x=49.
So if bythe correct answerquestion means 7/12 of the amount then the answer should be E.
Answer: (E)  49
Question: Abby and Bobby type at constant rates of 80 words per minute and 60 words per minute, respectively. Bobby begins typing before Abby and has typed 600 words when Abby begins typing at 1:30 pm. If they continue typing at their respective rates, at what time will Abby have typed exactly 400 more words than Bobby?
(A) 1:40 PM
(B) 1:50 PM
(C) 2:00 PM
(D) 2:10 PM
(E) 2:20 PM
Rationale: Say time needed for Abby to type 200 more words than Bobby is t. In that time she would type 80t words and Bobby would type 60t words.
Now, total words typed by Bobby would be 600+60t and we want that number to be 200 less than 80t: 600+60t=80t-400 --> t=50.
1:30 PM + 50 minutes = 2:20 PM.
Answer: E.
Answer: (E) 2:20 PM
Question: What is the dividend. divisor 17, the quotient is 9 and the remainder is 5?
(A) 148
(B) 154
(C) 156
(D) 158
(E) 170
Rationale: D = d * Q + R
D = 17 * 9 + 5
D = 153 + 5
D = 158
Answer: (D) 158
Question: In a party there are 5 couples. Out of them 5 people are chosen at random. Find the probability that there are at the least two couples?
(A) 5/21
(B) 5/28
(C) 5/20
(D) 5/22
(E) 5/25
Rationale: Number of ways of (selecting at least two couples among five people selected)
As remaining person can be any one among three couples left.
Required probability
= (10 * 6)/252 = 5/21
Answer: A
Answer: (A) 5/21
Question: Find the value of x. (47% of 1442 - 36% of 1412) + 63 = x?
(A) 1
(B) 2
(C) 3
(D) 5
(E) 7
Rationale: C) 3
Answer: (C) 3
Question: A fair is coin is tossed repeatedly. If head appears on first four tosses then what is the probability of appearance of tail in the fifth toss?
(A) 2/3
(B) 1/2
(C) 1/8
(D) 1/0
(E) 1/6
Rationale: As the given coin is a fair coin, the probability of getting tail on the fifth toss is independent of the out comes in the previous 4 tosses. So probability = 1/2
Answer:B
Answer: (B) 1/2
Question: a is an integer greater than 39 but less than 51, b is an integer greater than 49 but less than 61, what is the range of a/b?
(A) 1/4
(B) 1/3
(C) 3/4
(D) 1
(E) 5/4
Rationale: min value of a/b will be when b is highest and a is lowest ---> a=40 and b=60
So, a/b =2/3
max value of a/b will be when b is lowest and a is highest ---> a=50 and b=50
So, a/b = 1
Range is 1-(2/3) = 1/3.
Answer should be B.
Answer: (B) 1/3
Question: Over a three-week period, the price of an ounce of gold increased by 25% in the first week, decreased by 20% in the following week, and increased by 5% in the third week. If the price of gold was G dollars per ounce at the beginning of the three weeks, what was the price, in terms of G, at the end of the three weeks?
(A) 0.95G
(B) 1G
(C) 1.05G
(D) 1.1G
(E) 1.15G
Rationale: Initial price =G
By end of first week increased by 25% => Price =1.25G
By end of second week decreased by 20% => Price= 1.25*0.8G
By end of third week increased by 5% => Price=1.25*0.8*1.05G
=> Price= 1.05G
ANSWER:C
Answer: (C) 1.05G
Question: A sum of money deposited at C.I. amounts to Rs.2442 in 2 years and to Rs.2926 in 3 years. Find the rate percent?
(A) 11
(B) 20
(C) 28
(D) 24
(E) 82
Rationale: Explanation:
2420 --- 484
100 --- ? => 20%
Answer: Option B
Answer: (B) 20
Question: Three persons invested Rs.9000 in a joint business. The second person invested Rs.1000 more than the first and the third Rs.1000 more than second. After two years, they gained Rs.5400. How much third person will get?
(A) 2400
(B) 2408
(C) 24028
(D) 24128
(E) 2121
Rationale: First persons investment = x
Second persons investment = x + 1000
Third persons investments = x + 2000
x + x + 1000 + x + 2000 = 9000
3x = 6000
x = 2000
Ratio = 2000 : 3000 : 4000
2:3:4
4/9 * 54000 = 2400
Answer:A
Answer: (A) 2400
Question: On the xy-plane, each point on circle C has coordinates such
that x 0 and y 0. If the center of circle C is the point (3; 4),
what is the maximum possible area of C?
(A)  6
(B)  9
(C)  24
(D)  32
(E)  64
Rationale: I think that theintentof this question is that the circle will have NO CO-ORDINATES that fit the following 2 forms: (0, Y) or (X, 0). In real basic terms, this circle will NEITHER touch (nor cross) the X-axis NOR will it touch (nor cross) the Y-axis.
With a center at (3,8), the longest possible radius would ALMOST touch the X-axis, so the radius would be a little less than 3.
If the radius WAS 3 exactly, then the area would be 9pi, which is approximately 28.26
Since the circle CAN'T touch the X-axis, the area has to be LESS than approximately 28.26
As it's written, none of the answers is clearly the correct one.
B
Answer: (B)  9
Question: Roger can read a book in k minutes. What part of the book can he read in 7 minutes? (k>8)
(A) 8+k
(B) k/8
(C) 7/k
(D) (k+ 8)/k
(E) (k-8) / k
Rationale: Let's sayk = 24
That is, it takes 24 minutes to read the entire book.
So, in 8 minutes, Roger can read1/3of the book
So, we're looking for the answer choice that yields an OUTPUT of1/3whenk = 24
A) 8+24=32ELIMINATE
B) 8/24=1/3KEEP
C)24/8 =3ELIMINATE
D) (24+ 8)/24=32/24 = 4/3ELIMINATE
E) (24-8) /24=16/24 = 2/3ELIMINATE
Answer: C
Answer: (C) 7/k
Question: If n = 2×3×5×7×11×13×16, then which of the following statements must be true?
I. n^2 is divisible by 600
II. n + 19 is divisible by 19
III. (n + 4)/2 is even
(A) I only
(B) II only
(C) III only
(D) I and III
(E) None of the above
Rationale: Statement I: 600 = (2^3)*(3)*(5^2) this is true.
Statement 2 this is NOT true.
Statement 3: (n+4)/2 = n/2 + 2, So this is true.
Hence option (D).
Answer: (D) I and III
Question: The average monthly salary of 20 employees in an organisation is Rs. 1400. If the manager's salary is added, then the average salary increases by Rs. 100. What is the manager's monthly salary ?
(A) 3600
(B) 3890
(C) 88798
(D) 2789
(E) 3500
Rationale: Explanation:
Manager's monthly salary Rs. (1500 * 21 - 1400 * 20) = Rs. 3500.
Answer: E
Answer: (E) 3500
Question: Judges will select 5 finalists from the 8 contestants entered in a singing competition. The judges will then rank the contestants and award prizes to the 3 highest ranked contestants: a blue ribbon for first place, a red ribbon for second place, and a yellow ribbon for third place. How many different arrangements of prize-winners are possible?
(A) 10
(B) 21
(C) 210
(D) 420
(E) 560
Rationale: First Select 5 from 7 contestants and then select top 3 from those 5 =
8C5*5C3 = 56 * 10 = 560
ANS:E
Answer: (E) 560
Question: Let f(x) = 3x2+2x+6. Two distinct lines l1 and l2 exist that are tangent to f(x) and intersect
at the origin. Given that l1 is tangent to f(x) at (x1; f(x1)) and that l2 is tangent to f(x) at
(x2; f(x2)), compute x1x2.
(A) -1
(B) -2
(C) -3
(D) -4
(E) -5
Rationale: At any point (x0, y0) in f(x), the slope of the tangent line is
m = 6x0 + 2
Hence, the equation of the tangent line is given by
(y - y0) = m(x- x0)
y - (3x2
0 + 2x0 + 6) = (6x0 + 2)(x - x0)
y = (6x0 + 2)x - 6x2
0- 2x0 + 3x2
0 + 2x0 + 6
y = (6x0 + 2)x- 3x2
0 + 6
For the tangent line to cross the origin, we must have 3x2
0 - 6 = 0. This equation has two
solutions, the product of which is given by 􀀀6
3 = -2 .
correct answer B
Answer: (B) -2
Question: The salary of a typist was at first raised by 10% and then the same was reduced by 5%. If he presently draws Rs.1045.What was his original salary?
(A) 2888
(B) 1266
(C) 1000
(D) 2779
(E) 2661
Rationale: X * (110/100) * (95/100) = 1045
X * (11/10) * (1/100) = 11
X = 1000
Answer: C
Answer: (C) 1000
Question: A certain taxi company charges $3.50 for the first 1/5 of a mile plus $0.40 for each additional 1/5 of a mile. What would this company charge for a taxi ride that was 8 miles long?
(A) 15.6
(B) 16.0
(C) 17.5
(D) 18.7
(E) 19.1
Rationale: A certain taxi company charges $3.50 for the first 1/5 of a mile plus $0.40 for each additional 1/5 of a mile. What would this company charge for a taxi ride that was 8 miles long?
A. 15.60
B. 16.00
C. 17.50
D. 18.70
E. 19.10
1/5 miles = 0.2 miles.
The cost of 8 miles long ride would be $3.50 for the first 0.2 miles plus (8-0.2)/0.2*0.4 = $3.5 + $15.6 = $18.7.
Answer: E.
Answer: (E) 19.1
Question: B alone can do piece of work in 10 days. A alone can do it in 15 days. If the total wages for the work is Rs 5000, how much should B be paid if they work together for the entire duration of the work?
(A) 267
(B) 7
(C) 76
(D) 8
(E) 82
Rationale: Answer:A
Answer: (A) 267
Question: Find the value of y from the given equation. 9^y = 3^12, what is y?
(A) 3
(B) 5
(C) 7
(D) 8
(E) 6
Rationale: 3^2y = 3^12
2y=12, therefore y=6
E
Answer: (E) 6
Question: If x and y are both odd prime numbers and x < y, how many distinct positive integer T factors does 2xy have?
(A) 3
(B) 4
(C) 6
(D) 8
(E) 12
Rationale: Since 2xy prime T factors are x^1*y^1*2^1, its total number or factors must be (1+1)(1+1)(1+1)=2^3=8. Thus, I think D would be the correct answer.
Answer: (D) 8
Question: If each of 4 subsidiaries of Corporation R has been granted a line of credit of $464,800 and each of the other 3 subsidiaries of Corporation R has been granted a line of credit of $112,000, what is the average (arithmetic mean) line of credit granted to a subsidiary of Corporation R?
(A)  $1,568,000
(B)  $448,000
(C)  $406,000
(D)  $313,600
(E)  $116,000
Rationale: My take is D.
(464800*4 + 112000*3)/7 = 313600
Answer: (D)  $313,600
Question: A bag contains 40 black balls and 40 white balls. One ball is drawn at random. What is the probability that the ball drawn is white?
(A) 2/5
(B) 5/7
(C) 1/2
(D) 1/4
(E) 1/3
Rationale: Total number of balls = 40+40 = 80
no. of white balls = 40
probability of drawing a white ball = 40/80 = 1/2
Answer is C
Answer: (C) 1/2
Question: At 9:00 a.m., Tom begins traveling on a certain bike path from Riverdale at a constant rate of 10 mph. If, at 2:00 p.m., Jim begins traveling from Riverdale on the same path at a constant rate of 20 mph, at what time will he catch up to Peter?
(A) 4:00 p.m.
(B) 5:00 p.m.
(C) 6:00 p.m.
(D) 7:00 p.m.
(E) 8:00 p.m.
Rationale: My ans: D
By the time Jim starts, Tom has already covered = 5 hr * 10 mph = 50 miles
Relative speed = 20- 10 = 10mph
To catch up, Jim needs to cover 50 miles which can be covered in = 50/10= 5 hours
If Jim leaves at 2 pm, he will catch Tom at 7 pm.
Answer: D
Answer: (D) 7:00 p.m.
Question: If a jury of 12 people is to be selected randomly from a pool of 15 potential jurors, and the jury pool consists of 2/3 men and 1/3 women, what is the probability that the jury will comprise at least 2/3 men?
(A) 24/91
(B) 45/91
(C) 2/3
(D) 67/91
(E) 84/91
Rationale: We have a pool of 10 men and 5 women
We need a jury of 12 people
What is the probability that the jury will comprise at least 2/3 men?
2/3 of a jury of 12 = 8 men. There will always be at least 8 men on the jury unless all 5 women are selected, in that case there will be 7 men and 5 women.
15C12 = 455 ways to select a jury of 12 from a pool of 15
5C5 = 1 way to select all 5 women
10C7 = 120 ways to select 7 men from a pool of 10
1*120 = 120 ways to select a jury with fewer than 8 men
(455-120)/455 = 335/455 = 67/91
Answer D
Answer: (D) 67/91
Question: A company has two types of machines, type R and type S. Operating at a constant rate, a machine of type R does a certain job in 36 hrs and a machine of type S does the same job in 18 hours. If the company used the same number of each type of machine to do the job in 1 hours, how many machines of type R were used?
(A) 3
(B) 4
(C) 6
(D) 9
(E) 12
Rationale: Rate of machine R =1/36
Rate of machine S =1/18
since same no of machines used for R and S to do the same work in 1 hrs
So collective rate needed to finish the work in 1 hrs= 1/1
Let the no of machine be x
So, x/36 +x/18 =1/1
x3/36=1/1
x=12
So no of machine R is 12
Answer E
Answer: (E) 12
Question: A company produces 60000 bottles of water everyday. If a case can hold 5 bottles of water .How many cases are required by the company to hold its one day production
(A) 12000
(B) 4500
(C) 5000
(D) 8000
(E) 9000
Rationale: Number of bottles that can be held in a case = 5
Number of cases required to hold 60000 bottles = 60000/5=12000 cases.
So the answer is A =12000
Answer: (A) 12000
Question: What is the average (arithmetic mean) of all the multiples of ten from 10 to 160 inclusive?
(A) 90
(B) 95
(C) 70
(D) 105
(E) 110
Rationale: 10 and 190 inclusive would mean there are 15 terms.
No need to add up all the terms and further divide by 15 since the terms are evenly spaced in ascending order from 10, 20, 30........160
The middle term is the average which is the tenth term = 70
C is the answer.
Answer: (C) 70
Question: Vijay's salary is Rs. 21,600 per month. In the first month of the year, he spends 30% of his income on clothing, 20% of the remaining on entertainment and some percentage of the remaining on food. He saves of the amount he spends. Find the percentage of spending on food as a percentage of saving.
(A) 180%
(B) 124%
(C) 160%
(D) 154%
(E) 140%
Rationale: Let monthly income be = x on clothing =.3x on entertainment = .2(.7x) =.14x on food = (.16x)k saving =( .3x .14x .16xk)*13 solving we get k =.31.16 putting the value and we get ...... on the food =.31x ,and saving =.25x %on food / %on saving = .06x/.25x =24%
correct answer - B
Answer: (B) 124%
Question: The compound interest on Rs. 30,000 at 7% per annum is Rs. 4347. The period(in years) is?
(A) 2 years
(B) 6 years
(C) 7 years
(D) 9 years
(E) 4 years
Rationale: Amount = (30000 + 4347) = Rs. 34347
Let the time be n years. Then,
30000(1 + 7/100)n = 34347
= (107/100)n = 34347/30000 = (107/100)2
n = 2 years.
Answer: A:
Answer: (A) 2 years
Question: 5% people of a village in Sri Lanka died by bombardment, 15% of the remainder left the village on account of fear. If now the population is reduced to 3553, how much was it in the beginning?
(A) 3238
(B) 2667
(C) 4400
(D) 2977
(E) 2712
Rationale: X * (95/100) * (85/100) = 3553
X = 4400
Answer: C
Answer: (C) 4400
Question: A started a business with an investment of Rs. 70000 and after 6 months B joined him investing Rs. 120000. If the profit at the end of a year is Rs. 52000, then the share of B is?
(A) 24029
(B) 24000
(C) 24028
(D) 24014
(E) 24012
Rationale: Ratio of investments of A and B is (70000 * 12) : (120000 * 6) = 7 : 6
Total profit = Rs. 52000
Share of B = 6/13 (52000) = Rs. 24000
Answer:B
Answer: (B) 24000
Question: A cistern has a leak which empty it in 8 hrs, A tap is turned on which admits 6 liters a minute into the cistern, and it is now emptied in 12 hours, How many liters does the cistern hold ?
(A) 8640
(B) 8740
(C) 8840
(D) 8540
(E) 8940
Rationale: Inflow of water in 12hrs with rate 6 lit/min= 6*60*12= 4320
But, the same volume is emptied in 12 hrs, so the total capacity = total inflow + total outflow= 4320+4320= 8640
ANSWER:A
Answer: (A) 8640
Question: In a contest, a bowl contains 20 keys, only one of which will open a treasure chest. If a contestant selects the key that opens the treasure chest, she wins the contents of that chest. If Anna is allowed to draw two keys, simultaneously and at random, from the bowl as the first contestant, what is the probability that she wins the prize?
(A) 2/39
(B) 3/40
(C) 1/40
(D) 1/20
(E) 1/10
Rationale: P(not winning) = 19/20*18/19 = 9/10
P(winning) = 1 - 9/10 = 1/10
The answer is E.
Answer: (E) 1/10
Question: 60% of a number is added to 180, the result is the same number. Find the number?
(A) 300
(B) 277
(C) 266
(D) 99
(E) 450
Rationale: :
(60/100) * X + 180 = X
2X = 900
X = 450
Answer: E
Answer: (E) 450
Question: Kanul spent $5000 in buying raw materials, $200 in buying machinery and 30% of the total amount he had as cash with him. What was the total amount?
(A) $7456.00
(B) $7500.55
(C) $7428.57
(D) $7852.56
(E) $7864.00
Rationale: Let the total amount be x
then, (100-20)% of x = 5000+200
70% of x = 5200
70x/100 = 5200
x = $52000/7
x = $7428.57
Answer is C
Answer: (C) $7428.57
Question: There are n cities. What is the number of airlines that connected 2 different cities (airline from city A to city B is different with airline from city B to city A)?
(A) n(n-1)
(B) n(n+1)
(C) n(n-1)/2
(D) n(n+1)/2
(E) n2
Rationale: the Q basically asks to choose two cities out of n and since the DIRECTION is important, we are looking at Permutations or combinations with Order..
nP2=nC2∗2!=n(n−1)2∗2=n(n−1)
ANSWER:A
Answer: (A) n(n-1)
Question: A certain manufacturer of cake, muffin, and bread mixes has 100 buyers, of whom 50 purchases cake mix, 40 purchase muffin mix, and 16 purchase both cake mix and muffin mix. If a buyer is to be selected at random from the 100 buyers, what is the probability that the buyer selected will be one who purchases neither cake mix nor muffin mix?
(A) 1/10
(B) 13/50
(C) 1/2
(D) 7/10
(E) 9/10
Rationale: C+M+B-CM-MB-CB-2CMB = 100
C - cake buyers, M - muffin and B - Bread buyers. CM,MB,CB and CMB are intersecting regions.
the question asks for people who have bought only bread mixes = B-CB-MB-2CMB has to be found out.
50 + 40 + B-CB-MB-16-2CMB = 100
B-CB-MB-2CMB =26
hence the probability = 26/100 = 13/50.
B
Answer: (B) 13/50
Question: A jeep takes 8 hours to cover a distance of 280 Km. how much should the speed in Kmph be maintained to cover the same direction in 3/2th of the previous time?
(A) 28 Kmph
(B) 52 Kmph
(C) 20 Kmph
(D) 23 Kmph
(E) 65 Kmph
Rationale: Time = 8
Distance = 280
3/2 of 8 hours = 8 * 3/2 = 12 Hours
Required speed = 280/12= 23 Kmph
D)
Answer: (D) 23 Kmph
Question: If Scott has earned x dollars by working 3 days a week at a constant daily rate for w weeks, which of the following represents his daily wage?
(A) 3xw
(B) 3w/x
(C) w/(3x)
(D) xw/3
(E) x/(3w)
Rationale: In 1 week -- Scott works 3 days
In 'w' weeks---Scott works 3w days
3w day's wage -- x $
1 day's wage --- x/3w $
Answer : E
Answer: (E) x/(3w)
Question: If k is an integer and 0.00010101 x 10^k is greater than 10, what is the least possible value of k?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: 0.00010101 * 10^k > 10
We need to move the decimal point to the right 5 places to get 10.101
This is equivalent to multiplying by 10^5.
The answer is C.
Answer: (C) 5
Question: The number of positive integers n in the range 12 ≤ n ≤ 40 such that the product
(n − 1)(n − 2)...3.2.1 is not divisible by n is
(A) 5
(B) 7
(C) 13
(D) 14
(E) 16
Rationale: Explanation :
(n-1)! is always divisible by n unless and untill n is a prime number
e.g.(5-1)!=4! which is not divisible by 5 bcuz 5 is a prime number
Therefore, find all prime numbers in the range of 12 to 40 i.e
13, 17, 19, 23, 29, 31 and 37
Hence, the number of positive integers n is 7.
Answer : B
Answer: (B) 7
Question: The ratio between the present ages of P and Q is 5:7 respectively. If the difference between Q's present age and P's age after 6 years is 2. What is the total of P's and Q's present ages?
(A) 48 years
(B) 52 years
(C) 56 years
(D) Cannot be determined
(E) None of these
Rationale: Let the present ages of P and Q be 5x and 7x years respectively.
Then, 7x - (5x + 6) = 2
2x = 8 => x = 4
Required sum = 5x + 7x = 12x = 48 years.
ANSWER:A
Answer: (A) 48 years
Question: If n = 7p, where p is a prime number greater than 2, how many different positiveevendivisors does n have, including n ?
(A)  Two
(B)  Three
(C)  Four
(D)  Six
(E)  Eight
Rationale: This is an interesting question because we are immediately given the option to insert any prime number we wish for p. Since this is a problem-solving question, and there can only be one correct answer, we can select any value for p, as long as it is a prime number greater than 2. We always want to work with small numbers, so we should select 3 for p. Thus, we have:
n = 4 x 3
n = 12
Next we have to determine all the factors, or divisors, of P. Remember the term factor is synonymous with the term divisor.
1, 12, 6, 2, 4, 3
From this we see that we have 4 even divisors: 12, 6, 2, and 4.
If you are concerned that trying just one value of p might not substantiate the answer, try another value for p. Let’s say p = 5, so
n = 4 x 5
n = 20
The divisors of 20 are: 1, 20, 2, 10, 4, 5. Of these, 4 are even: 20, 2, 10 and 4. As we can see, again we have 4 even divisors.
No matter what the value of p, as long as it is a prime number greater than 2, n will always have 4 even divisors.
The answer is E
Answer: (E)  Eight
Question: What will be the percentage increase in the area of the cube's surface if each of the cube's edges grows by 60%?
(A) 150%
(B) 160%
(C) 156%
(D) 158%
(E) 162%
Rationale: The question is very easy. My logic is the following:
A surface = 6*a^2
After 60% increase A surface = 6* ((1.6a)^2) = 6*2.56*a^2
The increase in the surface area = (6*2.56*a^2 - 6*a^2)/6*a^2 = (6*a^2(2.56-1))/(6*a^2) = 2.56-1=1.56 = 156%
Answer :C
Answer: (C) 156%
Question: Usha took a loan of Rs. 1500 with simple interest for as many years as the rate of interest. If she paid Rs. 375 as interest at the end of the loan period, what was the rate of interest?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
Rationale: Let rate = R% and time = R years.
Then, (1500 * R * R) / 100 = 375
15R2 = 375
R2 = 25 => R = 5
Answer:B
Answer: (B) 5