mathewhe/aqua_rat huggingface dataset:
Question: At the time of marriage, a man was 8 years elder to his wife. 15 years after their marriage, his age is 5/4 times the age of his wife. What was wife's age at the time of marriage ? Choose one answer.
(A) 15 years
(B) 30 years
(C) 18 years
(D) 17 years
(E) 26 years
Rationale: let wifes age= x
husband age = x+8
now after 15 years of mrg x+15 wifes age
x+8+15 husbands age
5/4(x+15)=x+8+15
after solving x=17
ANSWER:D
Answer: (D) 17 years
Question: It is being given that (2^32 + 1) is completely divisible by a whole number. Which of the following numbers is completely divisible by this number?
(A) 2^16
(B) 7 * 2^23
(C) 7 * 2^33
(D) 5 * 2^32
(E) 2^96 + 1
Rationale: Assume 2^32 = x
Therefore , (2^32 + 1) = (x + 1) --------eq. 1
2^96 + 1 = (2^32)^3 + 1
= x^3 + 1 = x^3 + 1^3
= (x + 1) (x^2 - x +1)---------eq. 2
From eq. 1 and 2
Option E is correct.
Answer: (E) 2^96 + 1
Question: List L: ABC, BCA, CAB
In list L above, there are 3 positive integers, where each of A, B, and C is a different nonzero digit. Which of the following is the sum of all the positive integers that MUST be factors of the sum of the integers in list L?
(A) 47
(B) 114
(C) 152
(D) 161
(E) 488
Rationale: Sum = (100A + 10B + C) + (100B + 10C + A) + (100C + 10A + B) = 111*(A + B + C).
So, we have that the sum will be a multiple of 111=3*37.
As for A + B + C: if A=1, B=2 and C=4, then A + B + C = 7, so the sum will also be divisible by 7 BUT if A=1, B=2 and C=8, then A + B + C = 11, so the sum will also be divisible by 11. This implies that A + B + C will not produce the same factors for all possible values of A, B and C.
Therefore, we can say that 111*(A + B + C) MUST be divisible only by 111 --> so, by 1, 3, 37, and 111 --> 1 + 3 + 37 + 111 = 152.
Answer: C.
Answer: (C) 152
Question: If the cost price of 50 articles is equal to the selling price of 46 articles, then the gain or loss percent is?
(A) 22
(B) 65
(C) 78
(D) 33
(E) 8.69
Rationale: Given that, cost price of 50 article is equal to selling price of 46 articles.
Let cost price of one article = Rs. 1
Selling price of 46 articles = Rs. 50
But Cost price of 46 articles = Rs. 46
Therefore, the trader made profit.\Percentage of profit = 4/46 * 100 = 8.69%
Answer:E
Answer: (E) 8.69
Question: The ratio between the present age of P and Q is 6 : 7. if Q is 4 years old then P, what will be the ratio of the ages of P and Q after 4 year ?
(A) 3 : 4
(B) 3 : 5
(C) 7 : 8
(D) 4 : 3
(E) None of these
Rationale: Solution
Let P's age and Q's age be 6x years and 7x years respectively.
Then, 7x - 6x = 4 ⇔ x = 4.
∴ Required ratio = (6 x + 4) : (7 x + 4) = 28 : 32 = 7 : 8 .Answer C
Answer: (C) 7 : 8
Question: A die is thrown twice and the sum of the numbers appearing is observed to be 6.
find the conditional probability that the number 4 has appeared at least once?
(A) 2/5
(B) 3/5
(C) 3/7
(D) 3/11
(E) None
Rationale: Let E be the event that ‘number 4 appears at least once’ and F be
the event
that ‘the sum of the numbers appearing is 6’.
Then, E = {(4,1), (4,2), (4,3), (4,4), (4,5), (4,6), (1,4), (2,4), (3,4),
(5,4), (6,4)}
and F = {(1,5), (2,4), (3,3), (4,2), (5,1)}
We have P(E) = 11/36
and P (F) = 5/36
Also EnF = {(2,4), (4,2)}
Therefore P(EnF) = 2/36
the required probability
P(E|F) = P(EnF)/P(F) = (2/36)/(5/36) = 2/5.
A)
Answer: (A) 2/5
Question: A 1200 m long train crosses a tree in 120 sec, how much time will I take to pass a platform 700 m long?
(A) 333 Sec
(B) 190 Sec
(C) 176 Sec
(D) 2687 Sec
(E) 1876 Sec
Rationale: L = S*T
S= 1200/120
S= 10 m/Sec.
Total length (D)= 1900 m
T = D/S
T = 1900/10
T = 190 Sec
Answer:B
Answer: (B) 190 Sec
Question: A, B can Complete a work in 15 days &10 days respectively. They started doing thework together after 2 days B had to leave and A alone completed the remaining work.The whole work wascompleted in how many days?
(A) 8 days
(B) 10 days
(C) 12 days
(D) 14 days
(E) 16 days
Rationale: A and B can complete whole work in
30/(2+3)=6 days
Part of work completed together in
3 days =2/6=1/3 part
Now 2/3 part will be completed by A in
2/3*15=10 days
Hence, whole work will be completed in
2+10=12 days
C
Answer: (C) 12 days
Question: Baseball's World Series matches 2 teams against each other in a best-of-seven series. The first team to win four games wins the series and no subsequent games are played. If you have no special information about either of the teams, what is the probability E that the World Series will consist of fewer than 7 games?
(A)  12.5%
(B)  25%
(C)  31.25%
(D)  68.75%
(E)  75%
Rationale: Your explanation is very close toManhattan GMAT's official answer - it's quite uncanny:
"There are many other ways this could happen. Using the permutation formula, there are 6!/(3!)(3!) = 20 ways for the two teams to split the first 6 games (3 wins for each).
There are then 2 possible outcomes to break the tie in Game 7. Thus, there are a total of 202 = 40 ways for the World Series to last the full 7 games.
The probability that any one of these 40 ways occurs can be calculated from the fact that the probability of a team winning a game equals the probability of a team losing a game = 1/2.
Given that 7 distinct events must happen in any 7 game series, and that each of these events has a probability of 1/2, the probability that any one particular 7 game series occurs is.
Since there are 40 possible different 7 game series, the probability that the World Series will last exactly 7 games is: (1/2)^7 = 1/128
40*1/128 = 40/128 = 31.25%
Thus the probability E that the World Series will last less than 7 games is 100% - 31.25% = 68.75%.
The correct answer is D."
Answer: (D)  68.75%
Question: Find the sum of first 30 natural numbers
(A) 470
(B) 468
(C) 465
(D) 463
(E) 485
Rationale: Explanation:
Sum of n natural numbers
=n(n+1)2
=30(30+1)2=30(31)2=465
Answer: Option C
Answer: (C) 465
Question: What should come in place of the question mark(?) in the following equation?
4 1⁄2 × 4 1⁄3 - 8 1⁄3 ÷ 5 2⁄3 = ?
(A) 8
(B) 18 1⁄34
(C) 13 3⁄34
(D) 7⁄17
(E) None of these
Rationale: ? = 9⁄2 × 13⁄3 - 25⁄3 × 3⁄17
= 39⁄2 - 25⁄17 = 663−50/34=613/34=18 1/34
Answer B
Answer: (B) 18 1⁄34
Question: Tina’s cat weighs 3.2 kilograms. Her dog weighs 5 times as much as her cat. How much does her dog weigh in kilograms?
(A) A)10.4kg
(B) B)38kg
(C) C)22kg
(D) D)48kg
(E) E)16kg
Rationale: 3.2*5=16kg.Answer is E.
Answer: (E) E)16kg
Question: A certain telephone company company charges 3.10 cents for the first 1/5 of a minute plus 0.40 cents for each additional 1/5 of a minute. What would this company charge for a talk time of 8 minutes long?
(A) 15.60
(B) 16.0
(C) 17.8
(D) 18.7
(E) 19.1
Rationale: first 1/5 minute charge = 3.10 cents
rest of the minute = 8 - (1/5) = 39/5
charge for the rest of the minute = 39 *0.4 = 15.6
total charge = 3.10+15.6 = 18.7 cents
Answer is D.
Answer: (D) 18.7
Question: How many numbers with 3 different digits can be formed using only the even-numbered digit?
(A) 10
(B) 24
(C) 40
(D) 60
(E) 120
Rationale: Odd digits are 2, 4, 6, 8.
We want 3 different digits.
First digit can be chosen in 4 ways.
Second digit can be chosen in 3 ways.
Third digit can be chosen in 2 ways.
Total ways = 4*3*2
= 24
Hence option (B).
Answer: (B) 24
Question: A list of measurements in increasing order is 4, 5, 6, 8, 15 and x. If the median of these measurements is 3/4 times their arithmetic mean, what is the value of x?
(A) 16
(B) 18
(C) 20
(D) 22
(E) 24
Rationale: The median is (6+8)/2 = 7
The mean is (4+5+6+8+15+x)/6 = (38+x)/6
(38+x) /6 * 3/4 = 7
x = 56-38 = 18
The answer is B.
Answer: (B) 18
Question: If a boat goes upstream at 5 km/hr and downstream at 7 km/hr what is the speed of the stream?
(A) 1.5 kmph
(B) 1.2 kmph
(C) 1.1 kmph
(D) 1.3 kmph
(E) 1 kmph
Rationale: Sol.
Speed of stream = 1/2(7 -5) kmph = 1 kmph.
Answer E
Answer: (E) 1 kmph
Question: 4 friends went for a cinema, and everyone decided to contribute equally to the total bill of $60. If one of the friends had a coupon for 8% off the total bill, and if each friend still contributed equally after the coupon was applied to the bill, how much did each friend pay?
(A) 13
(B) 13.1
(C) 13.2
(D) 13.8
(E) 14
Rationale: At the non-discounted price, each friend would pay $15, as $60 divided by 4 friends is $15 per friend. But if the bill is 8% off, then each friend would pay 8% less. 8% of $15 is $1.2, so each friend saves $1.2 and pays the remaining 13.8
CORRECT OPTION:OPTION D
Answer: (D) 13.8
Question: A rectangular lawn of dimensions 80 m * 60 m has two roads each 10 m wide running in the middle of the lawn, one parallel to the length and the other parallel to the breadth. What is the cost of traveling the two roads at Rs.3 per sq m?
(A) Rs.3990
(B) Rs.3967
(C) Rs.3927
(D) Rs.3900
(E) Rs.3282
Rationale: Area = (l + b – d) d
(80 + 60 – 10)10 => 1300 m2
1300 * 3 = Rs.3900
Answer: D
Answer: (D) Rs.3900
Question: Distance between two stations A and B is 778 km. A train covers the journey from A to B at 84 km per hour and returns back to A with a uniform speed of 56km per hour. Find the average speed of the train during the whole journey?
(A) 67.8
(B) 67.4
(C) 67.2
(D) 67.6
(E) 67.0
Rationale: If a car covers a certain distance at x kmph and an equal distance at y kmph. Then,
average speed of the whole journey = (2xy)/x+y kmph.
By using the same formula, we can find out the average speed quickly.
Average speed
=(2×84×56)/(84+56)
=(2×84×56)/140
=(2×21×56)/35
=(2×3×56)/5
=3365=67.2
Answer is C.
Answer: (C) 67.2
Question: A reduction of 40% in the price of bananas would enable a man to obtain 64 more for Rs.40. What is the reduced price/dozen?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 9
Rationale: Sol. lie purchases 6a bananas mere for 4096 of Rs 40 or, Rs 16. Reduced price per do 3
A
Answer: (A) 3
Question: A soccer store typically sells replica jerseys at a discount of 30 percent to 50 percent off list price. During the annual summer sale, everything in the store is an additional 20 percent off the original list price. If a replica jersey's list price is $80, approximately what percent of the list price is the lowest possible sale price?
(A) 20
(B) 25
(C) 30
(D) 40
(E) 50
Rationale: Let the list price be 2x
for min sale price, the first discount given should be 50%, 2x becomes x here
now, during summer sale additional 20% off is given ie sale price becomes 0.8x
it is given lise price is $80
=> 2x = 80
=> x = 40
and 0.8x = 32
so lowest sale price is 32, which is 40% of 80
hence, D is the answer
Answer: (D) 40
Question: The probability that a man will be alive for 10more yrs is 1/4 & the probability that his wife will alive for 10 more yrs is 1/3. The probability that none of them will be alive for 10 more yrs, is
(A) 1/2
(B) 1
(C) 2/3
(D) 3/5
(E) 3/8
Rationale: Sol. Required probability = Pg.) x P(B) = (1— D x(1 —I) =: x 1=1/2
Ans.(A)
Answer: (A) 1/2
Question: A, B, C subscribe Rs. 50,000 for a business, A Subscribes Rs. 4000 more than B and B Rs. 5000 more than C. Out of a total profit of Rs. 35,000, C receives :
(A) 8400
(B) 14703
(C) 37798
(D) 13777
(E) 14778
Rationale: Explanation:
Let C = x. Then, B = x + 5000 and A = x + 5000 + 4000 = x + 9000.
So, x + x + 5000 + x + 9000 = 50000 <=> 3x = 36000 <=>
x = 12000.
A : B : C = 21000 : 17000 : 12000 = 21 : 17 : 12.
C's share = Rs. (35000 * 12/50 ) = Rs. 8,400.
Answer: A)
Answer: (A) 8400
Question: A computer program generates a single digit by a random process, according to which the probability of generating any digit is directly proportional to the reciprocal of one more than that digit. If all digits are possible to generate, then the probability R of generating an odd prime digit is between
(A) 0 and 1/6
(B) 1/6 and 1/3
(C) 1/3 and 1/2
(D) 1/2 and 2/3
(E) 2/3 and 5/6
Rationale: K (1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 1/7 + 1/8 + 1/9+ 1/10) =1
Note that 1/10 is least value and is equal to 0.1 so we can write above series as
K (1+0.5+0.3+0.25+0.2+0.16+0.5+residual) = 1
K=1/3+
P (3 or 5 or 7) =K*13/24
Required probability R= 13/24 × 1/3+ = 4+/24 > 1/6
Answer should be B
P.s. 3+ denotes a value little greater than 3 .
Same for 4+.
Answer: (B) 1/6 and 1/3
Question: P and Q invested in a business. The profit earned was divided in the ratio 2 : 3. If P invested Rs 40000, the amount invested by Q is
(A) 30000
(B) 50000
(C) 40000
(D) 20000
(E) 60000
Rationale: Let the amount invested by Q = q
40000:q=2:3
⇒40000×3=2q
⇒q=(40000×3)/2=60000
Answer is E.
Answer: (E) 60000
Question: The speed of a boat in upstream is 70 kmph and the speed of the boat downstream is 80 kmph. Find the speed of the boat in still water and the speed of the stream?
(A) 5 kmph
(B) 13 kmph
(C) 65 kmph
(D) 55 kmph
(E) 14 kmph
Rationale: Speed of the boat in still water
= (70+80)/2
= 75 kmph. Speed of the stream
= (80-70)/2
= 5 kmph.
Answer: A
Answer: (A) 5 kmph
Question: Square X is inscribed in circle Y. If the perimeter of X is 100, what is the circumference of Y?
(A) 30√ 2π
(B) 2√ 2π
(C) 5√ 2π
(D) 4√ 2π
(E) 25√ 2π
Rationale: square forms two right angled triangles.
Any time we have a right angle triangle inside a circle, the hypotenuse is the diameter.
hypotenuse here = diagonal of the square = 25 sqrt(2) = diameter
=> radius = 12.5 sqrt(2)
Circumference of the circle = 2pi r = 25 pi sqrt(2)
Answer is E.
Answer: (E) 25√ 2π
Question: A painting is painted on a cardboard 19 cm and 14 cm wide, such that there is a margin of 1.5 cm along each of its sides. Find the total area of the margin.
(A) 80
(B) 85
(C) 88
(D) 90
(E) 92
Rationale: Length of the cardboard = 19 cm
Breadth of the cardboard = 14 cm
Area of the cardboard = 19 × 14 cm² = 266 cm²
Length of the painting excluding the margin = [19 - (1.5 + 1.5)] cm = 16 cm
Breadth of the painting excluding the margin = 14 - (1.5 + 1.5) = 11 cm
Area of the painting excluding the margin = (16 × 11) cm² = 176 cm²
Therefore, area of the margin = (266 - 176) cm² = 90 cm²
ANSWER : OPTION D
Answer: (D) 90
Question: When processing flower-nectar into honey bees' extract, a considerable amount of water gets reduced. How much flower-nectar must be processed to yield 1kg of honey, if nectar contains 50% water, and the honey obtained from this nectar contains 30% water?
(A) 1.2 kg
(B) 1.5 kg
(C) 1.4 kg
(D) 1.9 kg
(E) None of these
Rationale: Explanation :
Flower-nectar contains 50% of non-water part.
In honey this non-water part constitutes 70% (100-30).
Therefore 0.5 X Amount of flower-nectar = 0.70 X Amount of honey = 0.70 X 1 kg
Therefore amount of flower-nectar needed =
(0.70/0.51)kg=1.4 kgs
Answer : C
Answer: (C) 1.4 kg
Question: The variables a and b are non-zero integers W. If a = 2b^3/c, what happens to c when a is halved and b is doubled?
(A) c is not changed.
(B) c is halved.
(C) c is doubled.
(D) c is multiplied by 4.
(E) c is multiplied by 16.
Rationale: a=2b^3/c
c=2b^3/a
when a is halved and b is doubled
c=2(2b)^3/(a/2)
c=16*2b^3/a
Ans. E c is multiplied by 16.
Answer: (E) c is multiplied by 16.
Question: A certain psychologist charges $40 more for the first hour of therapy than for each additional hour. If the total charge to a patient who receives 5 hours of therapy is $375, what is the total charge to a patient who receives only 2 hours of therapy ?
(A)  $120
(B)  $135
(C)  $150
(D)  $174
(E)  $192
Rationale: Let the charge for first hour = x+40
then charge for each additional hour = x
x+40 + 4x = 375
=> 5x = 335
=> x = 67
Total charge for patient for 3 hours of therapy = x+40 + x = 2x+40
= 174 $
Answer D
Answer: (D)  $174
Question: 20% of employees are women with fair hair. 40% of fair-haired employees are women. What percent of employees have fair hair?
(A) 25
(B) 30
(C) 50
(D) 55
(E) 60
Rationale: 20% of employees are women with fair hair.
40% of fair-haired employees are women.
So,
20% * Employees = 40% * Fair Haired Employees (because both are equal to the number of fair haired women employees)
(1/2) * Employees = Fair Haired Employees
Answer (C)
Answer: (C) 50
Question: At 11:00 a.m., Tom begins traveling on a certain bike path from Riverdale at a constant rate of 10 mph. If, at 1:00 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) 3:00 p.m.
(B) 4:00 p.m.
(C) 5:00 p.m.
(D) 6:00 p.m.
(E) 7:00 p.m.
Rationale: By the time Jim starts, Tom has already covered = 2 hr * 10 mph = 20 miles
Relative speed = 20- 10 = 10mph
To catch up, Jim needs to cover 20 miles which can be covered in = 20/10= 2 hours
If Jim leaves at 1 pm, he will catch Tom at 3 pm
Answer: A
Answer: (A) 3:00 p.m.
Question: Students are in cultural program as follows: music-10, Dance-15, and skits -6. No student is in all three cultural program , but 4 are in both music and Dance, 3 are in both music and skits, and 2 are in Dance and skits.
How many different students are in at least one of the three cultural program?
(A) 34
(B) 28
(C) 26
(D) 22
(E) 18
Rationale: Total students = M + D + S - (sum of 2-group overlaps) + (all three)
Total students = 10 + 15 + 6 - (3 + 4 + 2) + 0 = 22 students.
Answer is D
Answer: (D) 22
Question: You are distributing vegetable oil. there are 21 bottles in total out of which 7 are full, 7 half empty, 7 empty. the oil has to be distributed among three people. how will you distribute so that each person gets equal number of bottles and the same quantity of oil
(A) 1st person : 3 full, 1 half, 3 empty , 2nd person: 3 full, 1 half, 3 empty,, 3rd person : 1 full, 5 half, 1 empty
(B) 1st person : 1 full, 1 empty ,1half , 2nd person: 3 full, 1 half, 2 empty, 3rd person : 1 full, 2 half, 4 empty
(C) 1st person : 1 full, 2 half, 3 empty , 2nd person: 3 full, 1 empty , 3 empty, 3rd person : 3 full, 5 half, 2 empty
(D) 1st person : 1 full, 1 half, 2 empty , 2nd person: 2 full, 1 half, 1 empty, 3rd person : 1 full, 5 half, 2 empty
(E) None
Rationale: Correct Answer : A
Answer: (A) 1st person : 3 full, 1 half, 3 empty , 2nd person: 3 full, 1 half, 3 empty,, 3rd person : 1 full, 5 half, 1 empty
Question: Two cars start at the same time from opposite ends of a highway that is 45 miles long. One car is riding at 14 mph and the second car is riding at 16 mph. How long after they begin will they meet?
(A) 1
(B) 1.2
(C) 1.25
(D) 1.35
(E) 1.5
Rationale: As cars are moving in opposite directions their speeds will be added. So their relative speeds: 16+14 = 30 mph
Total distance to be covered = 45 miles.
Time taken would be: 45 miles/30 mph = 1.5 hours
E is the answer.
Answer: (E) 1.5
Question: If 3x=8y=z, what is x+y, in terms of z?
(A) z/2
(B) 2z
(C) 11z/24
(D) 3z/5
(E) z/9
Rationale: 3x=8y=z
x = z/3
and y = z/8
x+y = z/3 + z/8 = 11z/24
Answer is C
Answer: (C) 11z/24
Question: A man walks from B to C, a distance of x miles, at 10 miles per hour and returns at 15 miles per hour. What is his average speed?
(A) 10 mph
(B) 12 mph
(C) 8.8 mph
(D) 8.4 mph
(E) 14 mph
Rationale: Total distance covered = 2x
Time taken12miles / hour = x/15 hrs
Time taken @ 8 miles / hour = x/10 hrs
Avg speed = 2x / (x/10 + x/15) = 12 mph
Ans is B
Answer: (B) 12 mph
Question: When x is divided by y, the quotient is z with remainder t. Which of the following is equal to t?
(A) yz – x
(B) y/x−z
(C) x – y – z
(D) x – yz
(E) zx – y
Rationale: (x/y)=z(+t)
(18/8)=2(+2)
x-yz
which is 18-(8*2)=2
Answer is D
Answer: (D) x – yz
Question: A list of numbers has six positive integers. Three of those integers are known: 4, 5 and 24 and three of those are unknown: x, y and z. The three unknowns are known to be distinct. It is also known that the mean of the list is 10 and the median lies between 7 and 8 (exclusive). Which of the following CANNOT be the value of any one of the unknowns?
(A) 13
(B) 12
(C) 11
(D) 10
(E) 5
Rationale: Mean = 10
Therefore sum of the 6 digits = 6*10 = 60 -------- (1)
The 3 digits are 4,5 & 24 -------------- (2)
Now, 7 < median < 8
-> 7 < (sum of 2 digits)/2 < 8
-> 14 < (sum of 2 digits) < 16
Therefore the sum of 2 digits = 15.
The 2 digits whose sum is 15 & whose median is b/w 7 & 8 can be :
1. 7, 8,
2. 6, 9,
3. 5, 10, or
But as soon as we take 4, 11 -> the series becomes 4,4,5,11,12,24 &
11 pairs up with 5 to give median as 8.
Hence the number can't be 11 !!
Answer : C
Answer: (C) 11
Question: Find the number of ways of arranging the boy and 12 guests at a circular table so that the boy always sits in a particular seat?
(A) 3!
(B) 8!
(C) 11!
(D) 12!
(E) 14!
Rationale: Ans.(D)
Sol. Total number of persons = 13 Host can sit in a particular seat in one way. Now, remaining positions are defined relative to the host. Hence, the remaining can sit in 12 places => 12! Ways ... The number of required arrangements = 12! x 1= 12! = 12! ways
Answer: (D) 12!
Question: A survey was conducted to find out how many people in a housing colony of 144 residents could swim, dance and drive a car. It was found that the number of people who could not swim was 85, the number of people who could not dance was 100 and that the number of people who could not drive a car was 91. If the number of people who could do at least two of these things, was found to be 37 and the number of people who could do all these things was found to be 6, how many people could not do any of these things?
(A) 28
(B) 31
(C) 33
(D) 35
(E) 37
Rationale: T=n(A)+n(B)+n(C)-n(Exactly two of the events)-2*n(All 3 Events)+n(None of the events)
T=144
n(A)=T-n(A')=144-85=59
n(B)=T-n(B')=144-100=44
n(C)=T-n(C')=144-91=53
n(Exactly two of the events)=n(At least 2 Events)-n(All 3 Events)=37-6=31
n(All 3 Events)=6
144=59+44+53-31-2*6+n(None of the events)
n(None of the events)=144-55-44-53+31+12=31
Ans:B
Answer: (B) 31
Question: Excluding stoppages, the speed of a train is 54 kmph and including stoppages it is 40 kmph. Of how many minutes does the train stop per hour?
(A) A)13.55
(B) B)14.55
(C) C)15.55
(D) D)16.55
(E) E)17.55
Rationale: Explanation:
T = 14/54 * 60 = 15.55
Answer: Option C
Answer: (C) C)15.55
Question: Rajan borrowed Rs.4000 at 5% p.a compound interest. After 2 years, he repaid Rs.2210 and after 2 more year, the balance with interest. What was the total amount that he paid as interest?
(A) 635.50
(B) 635.58
(C) 635.52
(D) 635.59
(E) 635.51
Rationale: 4000
200 ---- I
200
10 ---- II
---------------
4410
2210
--------
2000
110 ---- III
110
5.50 ---- IV
-----------
2425.50
2210
-----------
4635.50
4000
----------
635.50
Answer: A
Answer: (A) 635.50
Question: In a group of ducks and cows, the total number of legs are 28 more than twice the number of heads. Find the total number of cows.
(A) 14
(B) 12
(C) 16
(D) 8
(E) 6
Rationale: Explanation :
Let the number of ducks be d
and number of cows be c
Then, total number of legs = 2d + 4c = 2(d + 2c)
total number of heads = c + d
Given that total number of legs are 28 more than twice the number of heads
=> 2(d + 2c) = 28 + 2(c + d)
=> d + 2c = 14 + c + d
=> 2c = 14 + c
=> c = 14
i.e., total number of cows = 14
Answer : A
Answer: (A) 14
Question: If i is a positive integer and i^2 is divisible by 12, then the largest positive integer that must divide i ^3 is
(A)  2^3
(B)  2^6
(C)  3^3
(D)  6^3
(E)  12^2
Rationale: Since i is an integer so i cannot have a 2 and sqrt 3 (because squaring this will give us a 2^2 and 3 (making the product as 12, and making i^2 as a multiple of 12))
i^2 is divisible by 12 (12 = 2*2*3), So, i should have at least one 2 and one 3 so that i^2 has a 2^2 and two 3
So, i will have a 2 and a 3. Or i will be a multiple of 6
So, largest possible integer than should divide i^3 is 6^3
So, Answer will be D
Answer: (D)  6^3
Question: What is the 4 digit number in which the 1st digit is 1/3 of the second, the 3rd is the sum of the 1st and 2nd, & the last is three times the second?
(A) 1234
(B) 1567
(C) 1349
(D) 1456
(E) 1356
Rationale: First digit is 1/3 second digit => The numbers can be 1 & 3, 2& 6, 3 & 9.
First + second = third => we can eliminate 3 & 9 since 3 + 9 = 12.
Last is 3 times the second => we can eliminate option 2 & 6 since 3 * 6 = 18.
Hence the number is 1349
C
Answer: (C) 1349