mathewhe/aqua_rat huggingface dataset:
Question: At a Halloween party, 2/5 of the people were dressed as vampires, 1/3 were dressed as ghosts; everyone else at the party, were equally dressed as Pirates, Robin Hood, Fairies, and Princesses. If all of the Fairies leave the party, and the people who just arrived to the party are all dressed as ghosts, doubling the number of ghosts at the party, what proportion of the people at the party are vampires?
(A) 6/19
(B) 5/18
(C) 5/26
(D) 1/2
(E) 3/7
Rationale: Vampires = 2/5 = 6/15
Ghosts = 1/3 = 5/15
Pirates + Robin Hoods + Fairies + Princesses = 1 - (5/15 + 6/15) = 4/15, so each = 1/15
If Ghosts doubled (2)(5) = 10, and now Fairies = 0; then, total = 6 + 10 + 1 + 1 + 1 + 0 = 19. 6 are Vampires => proportion = 6/19.
Answer: A
Answer: (A) 6/19
Question: When n is divided by 18, the remainder is 6. When n is divided by 11, the quotient is equal to Z, and the remainder is equal to 6. Z must be divisible by which of the following numbers?
(A) 16
(B) 17
(C) 18
(D) 19
(E) 20
Rationale: N = 18 q + 6
N = 11 z + 6
Equating
18 Q + 6 = 11z+6
11z=18q
11z/18 = q
since q is an integer Z must be divisible by 18.
Hence C
Answer: (C) 18
Question: Tlaudia can choose any two of four different candles and any 8 of 9 different flowers for a centerpiece arrangement. Given these choices, how many candle + flower groupings can she select?
(A) 54
(B) 72
(C) 96
(D) 144
(E) 432
Rationale: Tlaudia can choose any two of four different candles and any 8 of 9 different flowers for a centerpiece arrangement. 2 candles from 4 candles: 4C2: 6
8 flowers from 9 flowers: 9C8 : 9
So total grouping
9*6= 54.
Answer is A.
Answer: (A) 54
Question: In a class, 6 students can speak Tamil, 15 can speak Gujarati and 6 can speak H. If two students can speak two languages and one student can speak all the three languages, then how many students are there in the class?
(A) 20
(B) 21
(C) 22
(D) 23
(E) 24
Rationale: T = 6
G = 15
H = 6
students can speak two languages (suppose Tamil & Gujarati) = 2
student can speak all the three languages = 1
student can speak only Tamil language = 6-2-1 = 3
student can speak only Gujarati language = 15-2-1 = 12
student can speak only H language = 6-1 = 5
So, Total number of student = 2+1+3+12+5 = 23
ANSWER:D
Answer: (D) 23
Question: Divide 2379 into 3 parts so that their amounts after 2, 3 and 4 years respectively may be equal, the rate of interest being 5% per annum at simple interest. The first part is:
(A) 759
(B) 792
(C) 818
(D) 828
(E) None of these
Rationale: Let the parts be x, y and [2379 – (x + y)].
x + (x × 2 × 5⁄100) = y + (y × 3 × 5⁄100)
= z + (z × 4 × 5⁄100)
⇒ 11x⁄10 = 23y⁄20 = 6z⁄5 = k ⇒ x = 10k⁄11, y = 20k⁄23, z = 5k⁄6
But x + y + z = 2379.
⇒ 10k⁄11 + 20k⁄23 + 5k⁄6 = 2379
⇒ 1380 k + 1320 k + 1256 k = 2379 × 11 × 23 × 6
⇒ k = 2379×11×23×6/3965=3×11×23×6/5
∴ x = (10/11×3×11×23×6/5)=828
Hence, the first part is 828.
Answer D
Answer: (D) 828
Question: Sum of two numbers is 15. Two times of the first exceeds by 5 from the three times of the other. Then the numbers will be?
(A) 5
(B) 9
(C) 11
(D) 13
(E) 15
Rationale: Explanation:
x + y = 15
2x – 3y = 5
x = 10 y = 5
A)
Answer: (A) 5
Question: How many three digits numbers greater than 600 can be formed by using the digits 4,5,6,7,8?
(A) 45.
(B) 55.
(C) 65.
(D) 85.
(E) 75.
Rationale: Clearly repetition of digits allowed. Since the three digits number greater than 600 will have 6,7 or 8 at hundreds place. So hundreds place can be filled in 3 ways. Each of ten's and one's place can be filled in 5 ways. Hence, total number of required number =3x5x5 =75. Answer : E
Answer: (E) 75.
Question: What is the greatest of 3 consecutive integers whose sum is 39?
(A) 14
(B) 15
(C) 16
(D) 17
(E) 18
Rationale: 39 / 3 = 13
The three numbers are 12, 13, and 14.
The answer is A.
Answer: (A) 14
Question: The average weight of 10 oarsmen in a boat is increased by 1.8kg when one of the crew, who weight 53kg is replaced by a new man. Find the weight of the new man.
(A) 59kg
(B) 62kg
(C) 74kg
(D) 85kg
(E) 71kg
Rationale: Total weight increased = 1.8*10 = 18kg
Weight of the new man = 53+18 = 71 kg
Answer is E
Answer: (E) 71kg
Question: Ann and Bob drive separately to a meeting. Ann's average driving speed is greater than Bob's avergae driving speed by one-third of Bob's average driving speed, and Ann drives twice as many miles as Bob. What is the ratio E of the number of hours Ann spends driving to the meeting to the number of hours Bob spends driving to the meeting?
(A) 8:3
(B) 3:2
(C) 4:3
(D) 2:3
(E) 3:8
Rationale: Say the rate of Bob is 3mph and he covers 6 miles then he needs 6/3=2 hours to do that.
Now, in this case the rate of Ann would be 3+3*1/3=4mph and the distance she covers would be 6*2=12 miles, so she needs 12/4=3 hours for that.
The ratio E of Ann's time to Bob's time is 3:2.
Answer: B.
Answer: (B) 3:2
Question: What is the area of a square field whose diagonal of length 22 m?
(A) 288
(B) 289
(C) 242
(D) 112
(E) 178
Rationale: d2/2 = (22 * 22)/2
= 242
Answer: C
Answer: (C) 242
Question: How many 5 letter words ( with or without meaning) can be formed using all the following 5 letters P,Q,R,S,and W so that letter P is to the left of letter R?
(A) 70
(B) 50
(C) 60
(D) 90
(E) 100
Rationale: Two positions can be selected out of 5 positions in 5C2 ways = 10 ways.
And the remaining 3 letters can be placed in 3 posions in 3! Ways = 6 ways.
So the final Answer = number of ways letters P and R can be arranged x number
of ways the other 3 letters can be arranged
Final Answer = 10 x 6 = 60 ways
C
Answer: (C) 60
Question: In a group of ducks and cows, the total number of legs are 28 more than twice the no. of heads. Find the total no.of buffaloes.
(A) 11
(B) 12
(C) 14
(D) 16
(E) 18
Rationale: Let the number of buffaloes be x and the number of ducks be y
=> 4x + 2y = 2 (x + y) + 28
=> 2x = 28 => x = 14
C
Answer: (C) 14
Question: Susan weighs m pounds more than Anna does, and together they weigh a total of n pounds. Which of the following represents Anna’s weight in pounds?
(A) (n - m)/2
(B) (n + m)/2
(C) n/2 - m
(D) 2n − m
(E) n − 2m
Rationale: Let Anna's weight = a
Susan's weight = a + m
Together their weight is 2a + m = n
2a = n-m
Hence a = #(n-m)/2#
ANSWER:A
Answer: (A) (n - m)/2
Question: The sum of three integers is 33. The largest integer is 3 times the middle integer, and the smallest integer is 23 less than the largest integer. What is the product of the three integers?
(A) 192
(B) 203
(C) 214
(D) 225
(E) 236
Rationale: Let x be the middle integer. Then the largest is 3x and the smallest is 3x - 23.
3x - 23 + x + 3x = 33
x = 8
The three integers are 1, 8, and 24.
The product is 1*8*24 = 192
The answer is A.
Answer: (A) 192
Question: If a:b=1:2 and b:c=3:4 find a:b:c?
(A) 3:5:8
(B) 3:6:8
(C) 3:7:8
(D) 3:6:4
(E) 3:6:9
Rationale: a:b = 1:2, b:c = 3:4
1:2
3:4
(a = 1 × 3 = 3, b = 2 × 3 = 6 and c = 2 × 4 = 8)
(a = a × b, b = b × b and c = b × c)
a:b:c = 3:6:8
B
Answer: (B) 3:6:8
Question: By selling a watch for Rs.640/-, a man loses 20% what is that watch cost price?
(A) Rs. 600/-
(B) Rs. 700/-
(C) Rs. 800/-
(D) Rs. 850/-
(E) Rs. 900/-
Rationale: 80 % ------> 640 (80 * 8 = 640)
100 % ------>800 (100 * 8 = 800)
Cost price = Rs. 800/-
C)
Answer: (C) Rs. 800/-
Question: A football coach must choose 3 freshers from a team of 12players. How many different ways can the coach choose the freshers?
(A) 220
(B) 650
(C) 729
(D) 800
(E) 890
Rationale: Choose 3 starters from a team of 12 players. Order is not important.
\inline {\color{Black} 12C_{3}}= 220
A
Answer: (A) 220
Question: In the first round of the elections, the only two candidates got exactly the same number of votes. During the second round, 24,000 votes switched from the first candidate to the second one. The total number of votes remained the same in both rounds, and no other votes switched sides. If, in the second round, the winning candidate got four times as many votes as the other candidate, how many people have voted in each round?
(A) 15,000
(B) 25,000
(C) 80,000
(D) 50,000
(E) 60,000
Rationale: Let A be the first candidate and B be the second one.
Given x+24000 = 4(x-24000) => x = 40000
2x = 80000
IMO option C.
Answer: (C) 80,000
Question: Find the probability that a number selected from numbers 1, 2, 3,..., 40 is a prime number, when each of the given numbers is equally likely to be selected?
(A) 10/40
(B) 12/40
(C) 8/40
(D) 3/40
(E) 7/40
Rationale: Let X be the event of selecting a prime number.
X = {2, 3, 5, 7, 11, 13, 17, 19,23,29,31,37}
n(X) = 12,
n(S) = 40
Hence, the required probability is 12/40.
ANSWER:B
Answer: (B) 12/40
Question: If logX = (logY)/2 = (logZ)/5, then X4.Y3.Z-2 =?
(A) 2
(B) 10
(C) 1
(D) 0
(E) 3
Rationale: (log X)/1 = (logY)/2 = (logZ)/5 = K
=> logX = K, log Y = 2k, log Z = 5K
Thus, log(X4.Y3.Z-2) = 4logX +3logY - 2logZ = 0.
=> X4.Y3.Z-2 = 1.
ANSWER:C
Answer: (C) 1
Question: In the quiet town ofNothintodothere are 850 inhabitants, 400 are unemployed and 300 are somnambulists. If half of the somnambulists are unemployed, how many are employed and are not somnambulists?
(A) 50.
(B) 100.
(C) 150.
(D) 200.
(E) 300.
Rationale: Total = 850
unemployed=400
employed=850-400=450
som=300
unemployed som = 300/2=150
employed som = 150
employed that are not som = 450-150=300
Answer : E
Answer: (E) 300.
Question: In how many ways can the letters of word TREATMENT be arranged such that all the vowels as well as all the Consonants always appear together?
(A) 9!
(B) 3!*6!*2!
(C) 5!*5!
(D) 5!*4!*2!
(E) 6!*4!
Rationale: Since all the vowels and consonants have to be together there can only be there are 3! way to order the vowels and 6! to order the consonants. But they must be together either vowels come first or consonants so you multiply by 2.
So 3!6!2! (B)
Answer: (B) 3!*6!*2!
Question: The number of arrangements that can be made with the letters of the word MEADOWS so that the vowels occupy the even places?
(A) 156
(B) 144
(C) 165
(D) 182
(E) 716
Rationale: The word MEADOWS has 7 letters of which 3 are vowels.
-V-V-V-
As the vowels have to occupy even places, they can be arranged in the 3 even places in 3! i.e., 6 ways. While the consonants can be arranged among themselves in the remaining 4 places in 4! i.e., 24 ways.
Hence the total ways are 24 * 6 = 144.
Answer: B
Answer: (B) 144
Question: If the median of a list of numbers is m, the first quartile of the list is the median of the numbers in the list that are less than m. What is the first quartile of the list of numbers 42, 24, 30, 22, 26, 27, 33 and 35 ?
(A) 33
(B) 28
(C) 27
(D) 24
(E) 25
Rationale: It is given that a quartile is the middle number of all numbers less than median..
so lets arrange the number in ascending order- 42, 24, 30, 22, 26, 27, 33 and 35
22, 24, 26, 27, 30, 33, 35, 42,...
numbers less than median are 22, 24, 26, 27..
the median of these numbers = center of 24 and 26 = 25
E
Answer: (E) 25
Question: While driving from A-ville to B-town, Harriet drove at a constant speed of 110 kilometers per hour. Upon arriving in B-town, Harriet immediately turned and drove back to A-ville at a constant speed of 140 kilometers per hour. If the entire trip took 5 hours, how many minutes did it take Harriet to drive from A-ville to B-town?
(A) 138
(B) 148
(C) 150
(D) 162
(E) 168
Rationale: 5hr = 300min.
If harriet spend equal hrs on each leg she will spend 150min on each. Since speed A-B is less than speed B-A and distance on each leg is the same, time spent on A-B is more than 150min, which mean we can eliminate ans. A, B and C.
Now let plug in ans. D or E and verify which one give same distance on each leg.
E. t= 168min
* leg A-B ---> d = 110.168/60 = 18480/60
* leg B-A ----> d = 140*132/60 = 18480/60
so the correct ans. isE
Answer: (E) 168
Question: In a class of 40 students, 2 students did not borrow any books from the library, 12 students each borrowed 1 book, 10 students each borrowed 2 books, and the rest borrowed at least 3 books. If the average number of books per student was 2, what is the maximum number of books any single student could have borrowed?
(A) 3
(B) 5
(C) 8
(D) 13
(E) 15
Rationale: Total # of students = 40
Avg # of books per student = 2
Total # of books = 40*2 = 80
# of student borrowed at least 3 books = 40-2-12-10 = 16
# of books borrowed by above 16 students = 80-(12*1)-(10*2) = 48
Considering that 15 out of above 16 students borrowed only 3 books, # of books borrowed = 15*3 = 45
So maximum # of books borrowed by any single student = 48-45 = 3
option A
Answer: (A) 3
Question: The some of present ages of father and son is 60.If 6 years ago fathers age was five times the sons age,then what will be sons age after six years??
(A) 15
(B) 18
(C) 20
(D) 22
(E) 24
Rationale: Let f nd s be the present ages of father nd son
f + s = 60
f = 60 - s
(f-6) = 5(s-6)
f-6 = 5s - 30
f = 5s - 24
Equate "f"
60 - s = 5s - 24
6s = 84
s = 14
f = 60 - 14
f = 46
Present age of son is 14
Age of son after 6 years = 14+6 = 20
ANSWER:C
Answer: (C) 20
Question: The sum of ages of 5 children born at the intervals of 3 years each is 50 years. Find out the age of the youngest child?
(A) 9
(B) 8
(C) 7
(D) 6
(E) 4
Rationale: Let the age of the youngest child =x
Then, the ages of 5 children can be written as x,(x+3),(x+6),(x+9) and (x+12)
x+(x+3)+(x+6)+(x+9) +(x+12)=50
⇒5x+30=50⇒5x=20⇒x=205=4
Answer is E.
Answer: (E) 4
Question: A number when divided by a divisor leaves a remainder of 30. When twice the original number is divided by the same divisor, the remainder is 11. What is the value of the divisor?
(A) 12
(B) 13
(C) 35
(D) 43
(E) 59
Rationale: Let the number is N, the divisor = D,
I will make the two equations-
N = xD+30
2N = yD+11
where x and y are integers
Solving them: D(y-2x) = 43
as D is also integer and 43 is a prime number, the D should be 43 to satisfy the above equation.
Hence answer is 'D'
Answer: (D) 43
Question: Two employees X and Y are paid a total of Rs. 600 per week by their employer. If X is paid 120 percent of the sum paid to Y, how much is Y paid per week?
(A) s.200.72
(B) s.250.72
(C) s.272.72
(D) s.300.72
(E) s.310.72
Rationale: Let the amount paid to X per week = x
and the amount paid to Y per week = y
Then x + y = 600
But x = 120% of y = 120y/100 = 12y/10
∴12y/10 + y = 600
⇒ y[12/10 + 1] = 600
⇒ 22y/10 = 600
⇒ 22y = 6000
⇒ y = 6000/22 = Rs.272.72
C
Answer: (C) s.272.72
Question: If x and y are positive real numbers such that x + y = 1, which of the following could be the value of 100x + 300y?
I. 80
II. 150
III. 299
(A) II only
(B) III only
(C) I and II
(D) I and III
(E) II and III
Rationale: We know that x and y are both between 0 and 1.
The minimum limit of 100x + 300y is 100, when x is close to 1 and y is close to 0.
The maximum limit of 100x + 300y is 300, when x is close to 0 and y is close to 1.
The expression can take on any value between 100 and 300.
The answer is E.
Answer: (E) II and III
Question: A train covers a distance of 18 km in 3 min. If it takes 4 sec to pass a telegraph post, then the length of the train is?
(A) 370
(B) 380
(C) 390
(D) 400
(E) 410
Rationale: Speed = (18/3 * 60) km/hr = (360 * 5/18) m/sec = 100 m/sec.
Length of the train = 100 * 4 = 400 m.
Answer: Option D
Answer: (D) 400
Question: The average runs scored by a batsman in 15 matches is 30. In the next 20 matches the batsman scored an average of 15 runs. Find his average in all the 30 matches?
(A) 31.56
(B) 25.65
(C) 21.43
(D) 28.36
(E) 27.96
Rationale: Total score of the batsman in 15 matches = 450.Total score of the batsman in the next 20 matches = 300.Total score of the batsman in the 35 matches = 750.Average score of the batsman = 750/35 = 21.43.Answer: C
Answer: (C) 21.43
Question: 16 boys or 24 girls can construct the wall in 6 days. the number of days that 8 boys and 6 girls Will take to construct?
(A) 7 days
(B) 14 days
(C) 6 days
(D) 8 days
(E) 9 days
Rationale: Explanation:
16 boys =24 girls, 1 boy = 24/16 girls
1 boy = 6/4 girls
8 boys +6 girls = 8 Ã— 6/4 + 12 = 12 + 6 = 18 girls
8 days to complete the work
Answer: Option D
Answer: (D) 8 days
Question: In how many ways can a leap year have 53 Sundays?
(A) 365C7
(B) 7
(C) 4
(D) 5
(E) 6
Rationale: Explanation :
In a leap year there are 366 days i.e. 52 weeks + 2 extra days.
So, to have 53 Sundays one of these two days must be a Sunday.
This can occur in only 2 ways.
i.e. (Saturday and Sunday) or (Sunday and Monday).
Thus, the required number of ways is 2.
Answer : D
Answer: (D) 5
Question: If the tens digit of positive integers h, y are 6, how many values of the tens digit of 2(h+y) can be there?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: If the tens digit of positive integers h, y are 6, how many values of the tens digit of 2(h+y) can be there?
A. 2
B. 3
C. 4
D. 5
E. 6
-> If h=y=60, 2(h+y)=240 is derived. If h=y=69, 2(h+y)=276 is derived, which makes 4,5,6,7 possible for the tens digit. Therefore, the answer is C.
Answer: (C) 4
Question: By investing Rs. 1620 in 8% stock, Michael earns Rs. 135. The stock is then quoted at:
(A) 96
(B) 70
(C) 75
(D) 80
(E) 100
Rationale: To earn Rs. 135, investment = Rs. 1620.
To earn rs 8 investment = (1620/135*8) = 96
Market value of rs 100 stock = rs 96
ANSWER A
Answer: (A) 96
Question: Machine A can make 350 widgets in 1 hour, and machine B can make 250 widgets in 1 hour. If both machines work together, how much time will it take them to make a total of 1500 widgets?
(A) 2 hour and 20 minutes
(B) 2 hour and 24 minutes
(C) 2 hour and 30 minutes
(D) 2 hour and 36 minutes
(E) 2 hour and 40 minutes
Rationale: (350+250)t=1500
600t=1500
t=5/2
t=2 hour and 30 minutes
Answer: C
Answer: (C) 2 hour and 30 minutes
Question: Pipe A can fill a tank in 4 hours, pipe B in 8 hours and pipe C in 8 hours. If all the pipes are open, in how many hours will the tank be filled?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: Answer:	Part filled by A + B + C in 1 hour = 1/4 + 1/8 + 1/8= 1/2
All the three pipes together will fill the tank in 2 hours.
Answer: A
Answer: (A) 2
Question: There are 10 female and 15 male in a work place. In how many ways can a person can be selected?
(A) 20
(B) 15
(C) 18
(D) 40
(E) 25
Rationale: No of ways = 10+ 15 = 25
ANSWER E
Answer: (E) 25
Question: A part of certain sum of money is invested at 9% per annum and the rest at 12% per annum, if the interest earned in each case for the same period is equal, then ratio of the sums invested is?
(A) 7:3
(B) 4:9
(C) 4:3
(D) 2:3
(E) 4:9
Rationale: 12:9
= 4:3
Answer:C
Answer: (C) 4:3
Question: A man pointing to a photo says "The lady in the photograph is my nephew’s maternal grandmother". How is the lady in the photograph related to the man’s sister who has no other sister ?
(A) Cousin
(B) Sister-in-law
(C) Mother
(D) Mother-in-law
(E) None of these
Rationale: Since the man is referring to his nephew, the nephew’s parent has to be a sibling to the man. Now the last part says that the man’s sister has no other sister and hence the brother-sister relationship is established between the man and his nephew’s mother. Now the lady in the picture is the grandmother of the nephew and hence she is the mother of the man’s sister.
ANSWER:C
Answer: (C) Mother
Question: Which of the following is a multiple of 4!+6?
(A) 2!+3
(B) 4!+12
(C) 5!+6
(D) 5!+30
(E) 8!+12
Rationale: considering prime factors:
4! + 6 = 4 * 3 * 2 + 6 = 6(4 + 1) = 6 * 5 = 2 * 3 * 5
So the correct answer is the one which is a multiple of 2, of 3 and of 5.
ANSWER:D
Answer: (D) 5!+30
Question: Aden and Brad can do a piece of work in 18 days. Brad can Cody can do it in 24 days and Cody and Aden can do it in 36 days. If Aden, Brad, Cody work together, in how many days will they finish the work?
(A) 10 days
(B) 12 days
(C) 14 days
(D) 16 days
(E) 17 days
Rationale: (Aden + Brad)’s 1 day’s work = 1/18
(Brad + Cody)’s 1 day’s work = 1/24
(Cody + Aden)’s 1 day’s work = 1/36
Therefore, 2 (Aden + Brad + Cody)’s 1 day’s work = 1/18 + 1/24 + 1/36
= (4 + 3 + 2)/72
= 9/72
= 1/8
(Aden + Brad + Cody)’s 1 day’s work = 1/2 × 8 = 1/16
Therefore, Aden, Brad, Cody together will complete this work in 16 days. ANSWER : D
Answer: (D) 16 days
Question: A man swims downstream 30 km and upstream 18 km taking 3 hours each time, what is the speed of the man in still water?
(A) 9
(B) 8
(C) 6
(D) 4
(E) 2
Rationale: 30 --- 3 DS = 10
? ---- 1
18 ---- 3 US = 6
? ---- 1 M = ?
M = (10 + 6)/2 = 8
Answer:B
Answer: (B) 8
Question: The average age of 37 students in a group is 14 years. When teacher's age is included to it, the average increases by one. What is the teacher's age in years ?
(A) 35 years
(B) 45 years
(C) 51 years
(D) 52 years
(E) None of these
Rationale: Explanation:
Age of the teacher = (38 * 15 - 37 * 14) years = 52 years. Answer: D
Answer: (D) 52 years
Question: The length of the bridge, which a train 130 m long and traveling at 45 km/hr can cross in 30 sec is?
(A) 257 m
(B) 632 m
(C) 245 m
(D) 737 m
(E) 243 m
Rationale: Speed = 45 * 5/18 = 25/2 m/sec.
Time = 30 sec
Let the length of bridge be x meters.
Then, (130 + x)/30 = 25/2
x = 245 m.
Answer:C
Answer: (C) 245 m
Question: A person purchased a TV set for Rs. 16000 and a DVD player for Rs. 5000. He sold both the items together for Rs. 25000. What percentage of profit did he make?
(A) 1.00%
(B) 15.21%
(C) 41.10%
(D) 19.04%
(E) 10.00%
Rationale: The total CP = Rs. 16000 + Rs. 5000
= Rs. 21000 and SP = Rs. 25000
Profit(%) = (25000 - 21000)/21000* 100
= 19.04%
Answer: D
Answer: (D) 19.04%
Question: A father is now three times as old as his son. Seven years back, he was four times as old as his son. The age of the son (in years) is
(A) 12
(B) 15
(C) 18
(D) 20
(E) 21
Rationale: If father's age is F and son's age is S, then
F=3S
and
F-7 = 4*(S-7)
3S-7 =4S-28
S=21
F=63 years
ANSWER:E
Answer: (E) 21
Question: If 'a' and 'b' are non-zero numbers such that their sum is five times the product, what is the value of 1/a + 1/b?
(A) 4
(B) 5
(C) 6
(D) 10
(E) 15
Rationale: a+b = 5ab
1/a + 1/b = (b + a)/(ab) = 5.
The answer is B.
Answer: (B) 5
Question: The G.C.D of 1.08, 0.36 and 0.9 is
(A) 0.13
(B) 0.17
(C) 0.18
(D) 0.12
(E) 0.11
Rationale: Given numbers are 1.08, 0.36 and 0.90.
H.C.F of 108, 36 and 90 is 18.
H.C.F of a given numbers = 0.18
Answer:C
Answer: (C) 0.18
Question: A shipment of 250 smartphones contains 76 that are defective. If a customer buys two smartphones at random from the shipment, what is the approximate probability that both phones are defective?
(A) 1/250
(B) 1/84
(C) 1/11
(D) 1/9
(E) 1/3
Rationale: Probability of chosing one defective phone from a lot of 250 which ontains 76 defective phones is = (76/250)
Probability of chosing one defective phone from a lot of 249(we already picked one) which ontains 75(we already picked one) defective phones is = (75/249)
Combined probability of series of events = product of the probabilities = (76/250)*(75/249)
76/250 is close to (7/23) and (75/249)= (25/83)
so answer is (7/23)*(25/83) = (1/11)
So, answer will be C
Answer: (C) 1/11
Question: Of the following values of n, the value of (-1/3 )^(-n) will be greatest for n =
(A) 3
(B) -3
(C) 0
(D) -2
(E) 2
Rationale: imo -2
(-1/3)^-2=
1/(1/9)=9
oops i meant 2
E
Answer: (E) 2
Question: The sum of four consecutive even numbers is 140. What would be the smallest number?
(A) 32
(B) 88
(C) 70
(D) 123
(E) 12
Rationale: Let the four consecutive even numbers be 2(x - 2), 2(x - 1), 2x, 2(x + 1)
Their sum = 8x - 4 =140 => x = 18
Smallest number is: 2(x - 2) = 32
Answer: A
Answer: (A) 32
Question: Carol budgeted 18 dollars for gifts for each of the 15 people on her Christmas list. After a disagreement with some of her neighbors, she reduces her Christmas list to 10 people. How much can she spend on each?
(A) 20
(B) 27
(C) 18
(D) 23
(E) 30
Rationale: A1*P1=A2*P2
18*15=A2*10 => A2=27
Answer:B
Answer: (B) 27
Question: In how many ways 2 boys and 2 girls can be seated in a row so that boys and girls are alternate?
(A) 7
(B) 8
(C) 9
(D) 10
(E) 11
Rationale: number of ways = 2*2!*2! = 8
Answer is B
Answer: (B) 8
Question: A goods train runs at the speed of 72 km/hr and crosses a 260 m long platform in 26 sec. What is the length of the goods train?
(A) 278
(B) 166
(C) 151
(D) 260
(E) 109
Rationale: Speed = 72 * 5/18 = 20 m/sec.
Time = 26 sec.
Let the length of the train be x meters.
Then, (x + 260)/26 = 20
x = 260 m.
Answer:D
Answer: (D) 260