mathewhe/aqua_rat huggingface dataset:
Question: What is the smallest number which, when increased by 5, is divisible by 7, 8, and 24?
(A) 148
(B) 153
(C) 158
(D) 163
(E) 168
Rationale: LCM(7,8,24)=24x7=168
So the least divisible number is 168, and the number we are looking for is 168-5=163.
The answer is D.
Answer: (D) 163
Question: Ravi and Kavi start a business by investing â‚¹ 5000 and â‚¹ 72000, respectively. Find the ratio of their profits at the end of year.
(A) 2 : 72
(B) 5 : 72
(C) 7 : 72
(D) 1 : 72
(E) 3 : 72
Rationale: Ratio of profit = Ratio of investments
= 5000 : 72000 = 5 : 72
Answer : B
Answer: (B) 5 : 72
Question: The average age of a group of 10 students was 20. The average age increased by 2 years when two new students joined the group. What is the average age of the two new students who joined the group?
(A) 22 years
(B) 30 years
(C) 32 years
(D) 44 years
(E) None of these
Rationale: The total age of 10 students with average 20 = 200
The total age of 12 students with average 22 = 264
The total age of 2 new students = 64
Their average =32
ANSWER:C
Answer: (C) 32 years
Question: If x 2 – y 2 = 101, find the value of x 2 + y 2 ,
given that x and y are natural numbers.
(A) 5100
(B) 5101
(C) 5102
(D) 5103
(E) 5104
Rationale: x^2 – y^2 = 101
=> (x+y)*(x-y) = 101*1
x+y = 101
x-y = 1
so, x = 51, y = 50
(x^2 + y^2) = 51^2 + 50^2 = 5101
ANSWER:B
Answer: (B) 5101
Question: Virginia, Adrienne, and Dennis have taught history for a combined total of 93 years. If Virginia has taught for 9 more years than Adrienne and for 9 fewer years than Dennis, for how many years has Dennis taught?
(A)  23
(B)  32
(C)  40
(D)  41
(E)  44
Rationale: Let number of years taught by Virginia = V
number of years taught by Adrienne = A
number of years taught by Dennis = D
V+A+D = 96
V= A+9
=>A = V-9
V= D-9
=> A = (D-9)-9 = D-18
D-9 + D-18 + D = 93
=> 3D = 93 + 27 = 120
=> D = 40
Answer C
Answer: (C)  40
Question: How many ODD integers n, where 100 <= n <= 200, are divisible neither by seven nor by nine?
(A) 37
(B) 38
(C) 39
(D) 40
(E) 46
Rationale: Total Integers from 100 to 200 inclusive = 101 (51 even and 50 odd)
Total Odd Integers from 100 to 200 = 50
Total No. that are multiple of 7 from 1-200 = 200/7 = 28 (i.e. 14 even and 14 odd)
Total No. that are multiple of 7 from 1-100 = 100/7 = 14 (i.e. 7 even and 7 odd)
Total No. that are ODD multiple of 7 from 100-200 = 14-7 = 7
Total No. that are multiple of 9 from 1-200 = 200/9 = 22 (i.e. 11 even and 11 odd)
Total No. that are multiple of 9 from 1-100 = 100/9 = 11 (i.e. 5 even and 6 odd)
Total No. that are ODD multiple of 9 from 100-200 = 11-6 = 5
Total No. that are odd multiple of 7 and 9 will be multiple of 63 and count of such numbers from 100-200 = 1
So Total No. that are odd multiple of 7 and/or 9 from 100-200 = 7+5-1 = 11
So Total No. that are NOT odd multiple of 7 and/or 9 from 100-200 = 50-11 = 39
Answer: Option C
Answer: (C) 39
Question: Find the lowest common multiple of 15, 25 and 35.
(A) 360
(B) 420
(C) 510
(D) 525
(E) 280
Rationale: LCM=3*5*5*7=525.
Answer is D
Answer: (D) 525
Question: In a class there are 20 boys and 25 girls. In how many ways can a boy and a girl be selected?
(A) 288
(B) 500
(C) 277
(D) 266
(E) 255
Rationale: We can select one boy from 20 boys in 20 ways.
We select one girl from 25 girls in 25 ways
We select a boy and girl in 20 * 25 ways i.e.,
= 500 ways.
Answer: B
Answer: (B) 500
Question: If two numbers are in the ratio 2:3. If10 is added to both of the numbers then the ratio becomes 5:6 then find the largest number?
(A) 20
(B) 40
(C) 20/3
(D) 30
(E) 10
Rationale: 2:3
2x + 10 : 3x + 10 = 5 : 6
6[2x + 10] = 5[3x + 10]
12x + 60 = 15x + 50
15x -12x = 60 - 50
3x = 10, then X=10/3
Then the first number is = 2
3x = 10
Option E
Answer: (E) 10
Question: The average of runs of a cricket player of 10 innings was 35. How many runs must he make in his next innings so as to increase his average of runs by 4 ?
(A) 76
(B) 79
(C) 85
(D) 87
(E) 89
Rationale: Explanation:
Average = total runs / no.of innings = 35
So, total = Average x no.of innings = 35 x 10 = 350.
Now increase in avg = 4runs. So, new avg = 35+4 = 39runs
Total runs = new avg x new no. of innings = 39 x 11 = 429
Runs made in the 11th inning = 429 - 350 = 79 Answer: B
Answer: (B) 79
Question: 3 years ago the average age of a family of 5 members was 17 years. With the birth of a new baby, the average age of six members remains the same even today. Find the age of the new baby.
(A) 1 year
(B) 2 years
(C) 1 1⁄2 years
(D) cannot be determined
(E) None of the above
Rationale: Sum of present ages of the six members
= (17 × 6) years = 102 years.
Sum of present ages of the 5 members (excluding baby)
= 5 × (17 + 3) years = 100 years.
∴ Age of the baby = 102 – 100 = 2 years
Answer B
Answer: (B) 2 years
Question: A boat covers a distance of 30 kms in 2 ½ hours running down streams. While returning, it covers the same distance in 3 ¾ hours. What is the speed of the boat in kmph?
(A) 12
(B) 8
(C) 14
(D) 10
(E) 15
Rationale: b+s=30*2/5
b-s=30*4/15
solving ths we get value of b
b=10
ANSWER:D
Answer: (D) 10
Question: A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
(A) 245
(B) 248
(C) 240
(D) 246
(E) 214
Rationale: Speed = [54 * 5/18] m/sec = 15 m/sec.
Length of the train = (15 * 20) m = 300 m.
Let the length of the platform be x meters.
Then, x + 300 / 36 = 15
x + 300 = 540
x = 240 m.
Answer: Option C
Answer: (C) 240
Question: If (4y)/(x/z - 10) = 2y then which of the following is true?
(A) x = -12z
(B) -12x = z
(C) x = -z
(D) x = 6z
(E) x = 12z
Rationale: (4y)/(x/z - 10) = 2y
=> 2z/(x - 10z) = 1
=> 2z = x - 10z
=> x = 12z
Hence Ans is E
Answer: (E) x = 12z
Question: A sum was put at simple interest at certain rate for 3 years. Had it been put at 1% higher rate it would have fetched Rs. 63 more. The sum is: A. Rs. 2,400 B. Rs. 2,100 C. Rs. 2,200 D.Rs. 2,480
(A) 2000
(B) 2100
(C) 2200
(D) 2300
(E) 2400
Rationale: 1 percent for 3 years= 63
1 percent for 1 year = 21
=> 100 percent = 2100
ANSWER:B
Answer: (B) 2100
Question: At present, the ratio between the ages of Arun and Deepak is 4:3. After 4 years, Arun's age will be 32 years. What is the age of Deepak at present?
(A) 16
(B) 17
(C) 22
(D) 19
(E) 21
Rationale: Let the present ages of Arun and Deepak be 4x and 3x years respectively.
Then, 4x + 4 = 32 => x = 7
Deepak's age = 3x = 21 years.
Answer: E
Answer: (E) 21
Question: Two numbers A and B are such that the sum of 5% of A and 4% of B is two-third of the sum of 6% of A and 8% of B. Find the ratio of A : B.
(A) 2:1
(B) 1:2
(C) 1:1
(D) 4:3
(E) 3:2
Rationale: Explanation:
5% of A + 4% of B
=2/3(6% of A + 8% of B)
A/B=4/3
A : B = 4 : 3
ANSWER IS D
Answer: (D) 4:3
Question: What is the sum of all the multiples of 10 between 0 and 85?
(A) 500
(B) 620
(C) 450
(D) 360
(E) 440
Rationale: The multiples of 10 between 0 and 85 are 10, 20, 30, 40, 50, 60, 70, 80. If these are all added together, the result is 360.
Final Answer:
D
Answer: (D) 360
Question: Which number can we add to 897326 to get a number exactly divisible by 456?
(A) 58
(B) 66
(C) 74
(D) 82
(E) 90
Rationale: 897326 / 456 = 1967 with a remainder of 374.
We need to add 456 - 374 = 82
The answer is D.
Answer: (D) 82
Question: A, B and C started a business A's investment is 2 times of B's investment is 5 times of C's investment. Find the profit of B in the total profit of Rs. 16000.
(A) Rs. 25600
(B) Rs. 5000
(C) Rs. 7200
(D) Rs. 8000
(E) None of these
Rationale: Explanation:
A = 2B and B = 5C
=> A : B = 2:1 and B : C = 5 : 1
=> A : B : C = 10 : 5 : 1
Ratio of capitals of A, B and C = 10 : 5 : 1
B's share = Rs.[(5/16) × 16000] = Rs. 5000
Answer: Option B
Answer: (B) Rs. 5000
Question: How many seconds does a train 130 meters long, traveling at 72 km/h, take to completely cross a bridge of 210 meters in length?
(A) 13
(B) 15
(C) 17
(D) 19
(E) 21
Rationale: 72 km/h = 72000/3600 = 20 m/s
Time = 340 / 20 = 17 seconds
The answer is C.
Answer: (C) 17
Question: Sandy buys an old scooter for $900 and spends $300 on its repairs. If Sandy sells the scooter for $1320, what is the gain percent?
(A) 2%
(B) 4%
(C) 6%
(D) 8%
(E) 10%
Rationale: selling price / total cost = 1320/1200 = 1.1
The gain percent is 10%.
The answer is E.
Answer: (E) 10%
Question: A girl was asked to multiply a certain number by 43. She multiplied it by 34 and got his answer less than the correct one by 1242. Find the number to be multiplied.
(A) 130
(B) 132
(C) 134
(D) 136
(E) 138
Rationale: Let the required number be x. Then,
43x – 34x = 1242 or 9x = 1242 or x = 138.
Required number = 138.
ANSWER:E
Answer: (E) 138
Question: The average age of a group of 14 students was 20. The average age increased by 2 years when two new students joined the group. What is the average age of the two new students who joined the group?
(A) 22 years
(B) 30 years
(C) 36 years
(D) 32 years
(E) None of these
Rationale: Answer
The average age of a group of 14 students is 20.
Therefore, the sum of the ages of all 14 of them = 14 * 20 = 280
When two new students join the group, the average age increases by 2. New average = 22.
Now, there are 16 students.
Therefore, the sum of the ages of all 16 of them = 16 * 22 = 352
Therefore, the sum of the ages of the two new students who joined = 352 - 280 = 72
And the average age of each of the two new students = 72/2 = 36 years.
Answer C
Answer: (C) 36 years
Question: Bill has d animals, 16 of which were sold at a profit of 10% each while the rest were sold at a loss of 20% each. Overall, Bill made neither a profit nor a loss. Which of the following is equal to d?
(A) 6
(B) 12
(C) 18
(D) 24
(E) 36
Rationale: Total d animals, suppose each has price of x - total price = dx
now 16 were sold at profit of 10%, making equation - - 16*1.1x
now d-16 were sold at loss of 20%, making eqn --- (d-16)*0.8x
Now he made no profit or loss so,
dx = 16*1.1x + (d-16)*0.8x
solving for d, we get d=24
Ans D
Answer: (D) 24
Question: A train which has 300 m long, is running 80 kmph. In what time will it cross a person moving at 16 kmph in same direction ?
(A) 25 sec
(B) 35 sec
(C) 15 sec
(D) 45 sec
(E) 20 sec
Rationale: Time taken to cross a moving person = length of train/ relative speed
Time taken = 300/((80-16) (5/18) = 300/ 64*(5/18) = 300/20= 15 sec
Answer: C
Answer: (C) 15 sec
Question: Two trains each 250 m in length are running on the same parallel lines in opposite directions with the speed of 80 kmph and 70 kmph respectively. In what time will they cross each other completely?
(A) 16 sec
(B) 87 sec
(C) 12 sec
(D) 18 sec
(E) 12 sec
Rationale: D = 250 m + 250 m = 500 m
RS = 80 + 70 = 150 * 5/18 = 125/3
T = 500 * 3/125 = 12 sec
Answer: C
Answer: (C) 12 sec
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) 90%
(C) 60%
(D) 40%
(E) 21%
Rationale: SP2 = 2/3 SP1
CP = 100
SP2 = 80
2/3 SP1 = 80
SP1 = 120
100 --- 20 => 20%
Answer: A
Answer: (A) 20%
Question: The length of the bridge, which a train 140 metres long and travelling at 45 km/hr can cross in 30 seconds, is?
(A) 876 m
(B) 157 m
(C) 235 m
(D) 156 m
(E) 167 m
Rationale: Speed = [45 X 5/18] m/sec
= [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (140 + x)/30 = 25/2
=> 2(140 + x) = 750 => x
= 235 m.
Answer: C
Answer: (C) 235 m
Question: How many more years will it take to get another Rs.500 compound interest, if the initial principal of Rs.250 doubled in 5 years when compounded annually.
(A) 3 years
(B) 4 years
(C) 5 years
(D) 7 years
(E) 6 years
Rationale: Explanatory Answer
Rs.250 invested in compound interest becomes Rs.500 in 6 years.
The amount will double again in another 6 years.
i.e., the amount will become Rs.1000 in another 6 years.
So, to earn another Rs.500 interest, it will take another 6 years.
Answer E
Answer: (E) 6 years
Question: A thief is noticed by a policeman from a distance of 225 m. The thief starts running and the policeman chases him. The thief and the policeman run at the rate of 10 km and 11 km per hour respectively. What is the distance between them after 6 minutes ?
(A) 50 meter
(B) 100 meter
(C) 110 meter
(D) 125 meter
(E) 130 meter
Rationale: Explanation:
Relative speed of the thief and policeman = (11 – 10) km/hr = 1 km/hr
Distance covered in 6 minutes =
1/60∗6=1/10=100meters
So distance between them after 6 minutes = 225 - 100
= 125 meters
Option D
Answer: (D) 125 meter
Question: A person can row at 9 kmph and still water. He takes 4 1/2 hours to row from A to B and back. What is the distance between A and B if the speed of the stream is 1 kmph?
(A) 28
(B) 20
(C) 998
(D) 21
(E) 35
Rationale: Let the distance between A and B be x km.
Total time = x/(9 + 1) + x/(9 - 1) = 4.5
=> x/10 + x/8 = 9/2 => (4x + 5x)/40 = 9/2 => x = 20 km. Answer: B
Answer: (B) 20
Question: A wheel that has 6 cogs is meshed with a larger wheel of 14 cogs. If the smaller wheel has made 35 revolutions, what will be the number of revolutions made by the larger wheel?
(A) 15
(B) 12
(C) 21
(D) 9
(E) 22
Rationale: Explanation:
Let the number of revolutions made by the larger wheel be x
More cogs, less revolutions (Indirect proportion)
Hence we can write as
(cogs) 6 : 14 :: x : 35
â‡’6Ã—35=14 Ã— x
â‡’x = 15
Answer: Option A
Answer: (A) 15
Question: 48% of respondents to a survey consisted of those who used both M and N and those who used neither M nor N. 46% of respondents did not use M. 42% used N. What percent of respondents used only N?
(A) 19.5%
(B) 21.5%
(C) 20%
(D) 18.5%
(E) 17.5%
Rationale: From the question, we can summarize the information as follows:
N Not N
M X
Not M Ans y 46
42 100
Then we can set a system of 3 equations 3 unknowns described below:
X + Y = 48
X + Ans = 42
Y + Ans = 46
Sum up all three equations to get 2X + 2Y + 2Ans = 136
Divide both sides by 2 to get X + Y + Ans = 68
Replace X + Y with 48 to get 48 + Ans = 68
Substract 48 from both sides to get Ans = 68 - 48 = 20
The answer must be C.
Answer: (C) 20%
Question: Zayn is a trail runner who decides to take a day off work to run up and down a local mountain. He runs uphill at an average speed of 6 miles per hour and returns along the same route at an average speed of 8 miles per hour. Of the following, which is the closest to his average speed, in miles per hour, for the trip up and down the mountain?
(A)  2.4
(B)  5.8
(C)  6.0
(D)  6.3
(E)  6.5
Rationale: to calculate average of 2 speeds a and b when distance is constant
Formula - 2ab/(a+b)
Here Zayn's uphill speed = 6 mph
Zayn's downhill speed = 8 mph
2*6*8/(6+8) = 96/40 = 2.4
Correct answer - A
Answer: (A)  2.4
Question: WHEN A PERSON SELLS TWO ITEMS $600 each, ONE AT A GAIN OF 20% AND OTHER AT A LOSS OF 20%.THEN THE SELLER INCURES A LOSS OR GAIN OF:
(A) 1% loss
(B) no loss no gain
(C) 4% loss
(D) 2% gain
(E) 5% gain
Rationale: When two items are sold at the same price, one at a profit of a% and other at a loss of a% (which means the cost price of one item was lower than the selling price and the cost price of the other item was higher than the selling price), there will always be a loss of (a^2)/100 %. e.g. Here a = 20, so loss % = (20)^2/100 % = 4%.
Answer : C
Answer: (C) 4% loss
Question: What is the smallest number which when diminished by 8, is divisible by 9, 6, 12 and 18?
(A) 50
(B) 45
(C) 44
(D) 60
(E) 65
Rationale: Explanation:
Required number = LCM of (9, 6, 12 and 18) + 8
= 36 + 8 = 44
Answer: Option C
Answer: (C) 44
Question: Each digit in the two-digit number G is halved to form a new two-digit number H. Which of the following could be the sum of G and H
(A) 153
(B) 150
(C) 137
(D) 123
(E) 89
Rationale: let the number be x, now x is halved => x/2..the question asks what is x?
x(number) + x/2 (half of that number) = something
=> 3x/2 = something
=> x = 2 (something) / 3
so the answer choice must be divisible by 3
eliminate C, E right away
check the rest
D satisfies
3x/ 2 = 123
=> x = 82
Verify. 82 + 41 = 123
Answer is D
Answer: (D) 123
Question: Five children — A, B, C, D and E — are going to sit in five chairs in a row. The children C & E have to sit next to each other, and the others can sit in any order in any remaining chairs. How many possible configurations are there for the children?
(A) 60
(B) 20
(C) 40
(D) 43
(E) 48
Rationale: for such questions , we can treat both as one then total person=4..
these 4 can be arranged in 4! ways.. but within these 4 , one consists of two people who can be arranged in 2 ways CE or EC.. so ans =4!*2=48
ans E
Answer: (E) 48
Question: Aarti can do a piece of work in 6 days. In how many days will she complete three time of work of same type?
(A) 6 days
(B) 18 days
(C) 21 days
(D) 3 days
(E) 13 days
Rationale: We have the important relation, More work, More time (days)
A piece of work can be done in 6 days.
Three times of work of same type can be done in 6 x 3
= 18 days
Answer B
Answer: (B) 18 days
Question: A man invested Rs. 4940 in Rs. 10 shares quoted at Rs. 9.50. If the rate of dividend be 14%, his annual income is
(A) Rs.728
(B) Rs.648
(C) Rs.720
(D) Rs.622
(E) Rs.722
Rationale: Explanation :
Market Value of a share = Rs.9.50
Investment = Rs.4940
Number of shares = 4940/9.50 = 520
Face Value of a share = Rs.10
dividend = 14%
dividend per share = (10×14)100 = Rs. 1.4
His annual income = 520 × 1.4 = Rs.728
Answer : Option A
Answer: (A) Rs.728
Question: Twenty percent of the programmers in a startup company weigh 200 pounds or more. Twenty-five percent of the programmers that are under 200 pounds in that same company weigh 100 pounds or less. What percent of the programmers in the startup company weigh between 100 and 200 pounds?
(A) 15%
(B) 20%
(C) 25%
(D) 60%
(E) 75%
Rationale: Initially 80% and 20% split
80% is further divided as 25% and 75%
Q is asking about that 75%
let total be '100' then that 75% is (3/4)∗80
so, the required % is [(3/4)∗80/100]∗100 = 60%
ANSWER:D
Answer: (D) 60%
Question: At a dinner party, 4 people are to be seated around a circular table. Two seating arrangement are considered different only when the positions of the people are different relative to each other. What is the total number of different possible seating arrangements for the group?
(A) 5
(B) 10
(C) 6
(D) 32
(E) 120
Rationale: Has to be C.
Simple formula: There are (n - 1)! ways to arrange n distinct objects in a circle
hence (4-1)! = 3!= 6
Answer: (C) 6
Question: In an office in Singapore there are 60% female employees. 50 % of all the male employees are computer literate. If there are total 62% employees computer literate out of total 1100 employees, then the no. of female employees who are computer literate ?
(A) 462
(B) 674
(C) 672
(D) 960
(E) None
Rationale: Solution: Total employees,
= 1100
Female employees, 60% of 1100.
= (60 *1100) /100 = 660.
Then male employees,
= 440
50 % of male are computer literate,
= 220 male computer literate.
62 % of total employees are computer literate,
= (62 *1100) /100 = 682 computer literate.
Thus, Female computer literate = 682 - 220
= 462.
Answer: Option A
Answer: (A) 462
Question: Last year’s receipts from the sale of greeting cards during the week before Mother’s Day totaled $215 million, which represented 10 percent of total greeting card sales for the year. Total greeting card sales for the year totaled how many million dollars?
(A) 17,010
(B) 2,150
(C) 1,890
(D) 1,701
(E) 210
Rationale: 10% ---- 215 millions
for 100% => ( 215 * 100% )/10% = 2150.
Option B.
Answer: (B) 2,150
Question: A box contains 3 blue marbles, 2 red, 6 green marbles and 2 yellow marbles. If three marbles are picked at random, what is the probability that they are all blue?
(A) 1/286
(B) 2/455
(C) 1/91
(D) 4/455
(E) None of these
Rationale: Given that there are three blue marbles, two red marbles, six green marbles and one yellow marbles.
Probability that all the three marbles picked at random are blue = 3C₃/13C₃ = (1 * 3 * 2 * 1)/(13 * 12 * 11) = 1/286
ANSWER:A
Answer: (A) 1/286
Question: If a sample of data has mean of 20 and SD of 3, which of the following values is more than 2 SDs from the mean?
(A) a. 12
(B) b. 14.5
(C) c. 17
(D) d. 23.5
(E) e. 25.5
Rationale: Value ismore than 2SDfrom the mean means that the distance between the mean and the value must be more than 2SD=6. So the value either <20-6=14 or >20+6=26.
Answer: A.
Answer: (A) a. 12
Question: The lowest number which should be added to 11390 so that the sum is exactly divisible by 7, 9, 10 and 12 is:
(A) 1010
(B) 2210
(C) 1250
(D) 1210
(E) 1110
Rationale: L.C.M. of 7, 9, 10 and 12 = 1260.
On dividing 11390 by 1260, the remainder is 50.
Number to be added = (1260 - 50) = 1210. Answer: Option 'D'
Answer: (D) 1210
Question: A group consists of 8 men, 6 women and 4 children. In how many ways can 1 man , 2 woman and 2 child selected from the given group?
(A) 780
(B) 750
(C) 720
(D) 620
(E) 650
Rationale: One man, two women and two child can be selected in 8C1 * 6C2 * 4C2 ways
8*6*5/2*1*4*3/2*1
= 720 ways
Answer : C
Answer: (C) 720
Question: For all real numbers v, an operation is defined by the equation v* = v - v/3. If (v*)* = 16, then v=
(A) 30
(B) 33
(C) 36
(D) 39
(E) 42
Rationale: (v*)* = (v - v/3) - (v - v/3) / 3
16 = 2v/3 - 2v/9 = 4v/9
v = 36
The answer is C.
Answer: (C) 36
Question: how many such letters pairs r in word SMUGGLER having same no. of letters left between them in the word as they have in the series
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: 2 letter pair.S-U,G-E.
ANSWER:B
Answer: (B) 2
Question: How many words can be formed by using all letters of the word “MANFUL”
(A) 720
(B) 240
(C) 750
(D) 860
(E) 140
Rationale: The word MANFUL contains 6 different letters.
Required number of words = 6p6 = 6! = (5x4x3x2x1) = 720.
Answer A.
Answer: (A) 720
Question: If the sum of two positive integers is 20 and the difference of their squares is 40, what is the product of the two integers?
(A) 108
(B) 99
(C) 128
(D) 135
(E) 143
Rationale: Let the 2 positive numbers x and y
x+ y = 20 -- 1
x^2 - y^2 = 40
=> (x+y)(x-y)=40 -- 2
Using equation 1 in 2 , we get
=> x-y = 2 -- 3
Solving equation 1 and 3 , we get
x= 11
y= 9
Product = 11*9 = 99
Answer B
Answer: (B) 99
Question: The sum of the present ages of A, B, C is 39 years. Three years ago their ages were in the ratio 1:2:3. What is the present age of A?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
Rationale: Three years ago:
a:b:c = 1:2:3
Let a = 1x, b = 2x, and c = 3x.
Today:
(x+3) + (2x+3) + (3x+3) = 39
x = 5
So the present age of A is x+3 = 8
The answer is D.
Answer: (D) 8
Question: Three consecutive odd integers are in increasing order such that the sum of the last two integers is 17 more than the first integer. Find the three integers?
(A) 11,13,15
(B) 7, 2, 10
(C) 7, 9, 10
(D) 7, 9, 11
(E) 7, 9, 29
Rationale: Explanation:
Let the three consecutive odd integers be x, x + 2 and x + 4 respectively.
x + 4 + x + 2 = x + 17 => x = 11
Hence three consecutive odd integers are 11, 13 and 15
Answer: A
Answer: (A) 11,13,15
Question: If n is an integer from 1 to 96, what is the probability for n*(n+1)*(n+2) being divisible by 8?
(A) a. 25%
(B) b. 50%
(C) c. 62.5%
(D) d. 72.5%
(E) e. 75%
Rationale: There is another way I approach such questions if I am short of time (otherwise I prefer the logical approach given above) - Brute Force/Pattern Recognition/Intuition - whatever you may want to call it.
We need to find the numbers in which the product is a multiple of 8. I know I get a multiple of 8 after every 8 numbers. I will also get an 8 when I multiply 4 by an even number. In first 8 numbers, I have exactly two multiples of 4.
Basically, I figure that I should look at the first 8 cases. In all other cases, the pattern will be repeated. It helps that n can be from 1 to 96 i.e. a multiple of 8:
1*2*3 N
2*3*4 Y
3*4*5 N
4*5*6 Y
5*6*7 N
6*7*8 Y
7*8*9 Y
8*9*10 Y
5 of the first 8 products are divisible by 8 so my answer would be 5/8 = 62.5% C
Answer: (C) c. 62.5%
Question: If 2 : 9 :: x : 18, then find the value of x
(A) 2
(B) 3
(C) 4
(D) 6
(E) 5
Rationale: Explanation:
Treat 2:9 as 2/9 and x:18 as x/18, treat :: as =
So we get 2/9 = x/18
=> 9x = 36
=> x = 4
ANSWER IS C
Answer: (C) 4