mathewhe/aqua_rat huggingface dataset:
Question: Three pipes, A, B, & C are attached to a tank. A & B can fill it in 20 & 30 minutes respectively while C can empty it in 20 minutes. If A, B & C are kept open successively for 1 minute each, how soon will the tank be filled?
(A) 2 hours
(B) 4 hours
(C) 1 hour 30 min
(D) 5 hours
(E) 6 hours
Rationale: in three minute 1/20+1/30-1/20=2/60 = 1/30 part is filled
3 min--------1/30 parts
x min--------- 1 part(full)
x=90 min =1 hour 30 min
ANSWER:C
Answer: (C) 1 hour 30 min
Question: In a fort, there are 1200 soldiers. If each soldier consumes 3 kg per day, the provisions available in the fort will last for 30 days. If some more soldiers join, the provisions available will last for 25 days given each soldier consumes 2.5 kg per day. Find the number of soldiers joining the fort in that case?
(A) 273
(B) 528
(C) 539
(D) 538
(E) 723
Rationale: Assume X soldiers join the fort. 1200 soldiers have provision for 1200(days for which provisions last them)(rate of consumption of each soldier)
= 1200(30)(3) kg
Also provisions available for (1200 + x) soldiers is (1200 + x)(25)(2.5) kg
As the same provisions are available
=> 1200(30)(3) = (1200 + x)(25)(2.5)
x = [1200(30)(3)]/[(25)(2.5)] - 1200
x = 528
Answer: Option B
Answer: (B) 528
Question: Total of ages of A,B and C at present is 90 years. If ratio of this ages is 2 : 3 : 4 what will be the age of C after 2 years?
(A) 45 years
(B) 42 years
(C) 40 years
(D) 37 years
(E) None of the above
Rationale: 2+3+4=9
4*(90/9)=40yrs
after 2yrs=42
ANSWER:B
Answer: (B) 42 years
Question: If $30,000 interest is invested in 10 percent simple annual interest for 2 years, which of the following represents the total amount of interest, in dollars, that will be earned by this investment in the 2 years?
(A) $6000
(B) $4000
(C) $5000
(D) $3000
(E) $2000
Rationale: 30000*10/100*2 = $6000
Answer : A
Answer: (A) $6000
Question: Teas worth Rs. 126 per kg and Rs. 135 per kg are mixed with a third variety in the ratio 1 : 1 : 2. If the mixture is worth Rs 156 per Kg , the price of the third variety per Kg will be?
(A) Rs. 147.50
(B) Rs. 785.50
(C) Rs. 178.50
(D) Rs. 258.50
(E) None of these
Rationale: Explanation :
Since first and second varieties are mixed in equal proportions.
So, their average price =Rs. (126+135)/2.
=>Rs. 130.50.
So, the mixture is formed by mixing two varieties, one at Rs. 130.50 per kg and the other at say, Rs. x per kg in the ratio 2 : 2, i.e., 1 : 1.
We have to find x.
By the rule of alligation, we have:
Cost of 1 kg Cost of 1 kg
of 1st kind of 2nd kind
(Rs. 130.50) (Rs. x)
\ /
Mean Price
(Rs. 156)
/ \
xâˆ’156 22.50
=>xâˆ’(156/22.50)=1.
=>xâˆ’156=22.50.
=>x= 178.50 Rs.
Answer : C
Answer: (C) Rs. 178.50
Question: What is the % change in the area of a rectangle when its length increases by 35% and its width decreases by 35%?
(A) 0%
(B) 20% increase
(C) 20% decrease
(D) 12% decrease
(E) Insufficient data
Rationale: (135/10)*(65/10) = 8775/100~88 of original area
0.88 is a 12% decrease from 100/100 ->D
Answer: (D) 12% decrease
Question: A jar contains 7 marbles consisting of an equal number of red, green, and blue marbles. Three marbles are removed from the jar and discarded. What is the probability that only two colors will remain in the jar after the Three marbles have been removed?
(A) 1/45
(B) 3/35
(C) 1/81
(D) 1/35
(E) 1/25
Rationale: Jar contains {4-red, 4-green, 4-blue} marbles. We are asked to find the probability that after removing 3 marbles only 2 colours remain in the jar, i.e., the probability of removing EITHER red, OR green, OR blue.
Sample space = 7C3 = 35.
Probability of choosing 3 red = 3C3/7C3 = 1/35.
Probability of choosing 3 green = 3C3/7C3 = 1/35.
Probability of choosing 3 blue = 3C3/7C3 = 1/35.
Required probability = 1+1+1/495 = 3/35 Ans (B).
Answer: (B) 3/35
Question: A canoe has two oars, left and right. Each oar either works or breaks. The failure or non-failure of each oar is independent of the failure or non-failure of the other. You can still row the canoe with one oar. The probability that the left oar works is 3/5. The probability that the right oar works is also 3/5. What is the probability R that you can still row the canoe?
(A) 9/25
(B) 10/25
(C) 6/10
(D) 2/3
(E) 21/25
Rationale: Simply look at the question from the other side. What is the probability that you can’t row the canoe? This would be 2/5 x 2/5 = 4/25.
Using the idea that the probability of something happening is 1 – the probability that it doesn’t happen, you can use the following equation to reach the right answer R: 1 – 4/25 = 21/25.Answer choice E.
Answer: (E) 21/25
Question: In your bucket you have 6.35 $, and you want to travel to the next state by train and its ticket costs 1.35 $. How many times can you use this train between the two stations?
Suppose that the cost of ticket is the same in both ways!
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
Rationale: As the ticket costs 1.35 $ for one way, so the two-way trip costs 2.7$, and the two tow-way trips cost 5.4$.
So if you have 6.35$, you are able to go and return just two times according to your money in your bucket.
So the correct choice is A
Answer: (A) 4
Question: a wall clock rings after every 1 hr and a wrist watch beep after every 25 min.they voice together at 12 a.m,time taken to voice again simultaneously?
(A) 4 a.m
(B) 5 a.m
(C) 6 a.m
(D) 7 a.m
(E) 8 a.m
Rationale: 1 hr = 60 minutes
So, L.C.M. of 60 and 25 is = 300
300 minutes = 5 hr
So after 5 hr that is at 5 a.m both will voice again simultaneously.
ANSWER:B
Answer: (B) 5 a.m
Question: For integers U and V, when U is divided by V, the remainder is even. Which of the following must be true?
(A) U is odd
(B) At least one of U and V is odd
(C) The sum U + V is odd
(D) U and V share no common factors other than 1
(E) UV is odd.
Rationale: At least one of U and V is odd
B
Answer: (B) At least one of U and V is odd
Question: Lisa's grade was 75th percentile of the 40 grades for her class. Of the 50 grades from another class, 8 were higher than Lisa's, and the rest were lower. If no other grade was the same as Lisa's grade, then Lisa's grade was what percentile of the grades of the two classes of two classes combined?
(A) 62nd
(B) 74th
(C) 80th
(D) 87th
(E) 92nd
Rationale: 62nd/74th/80th/87th/92nd
Correct option: C
Answer: (C) 80th
Question: 16 is divided into two parts in such a way that seventh part of first and ninth part of second are equal. Find the smallest part?
(A) 14
(B) 12
(C) 11
(D) 8
(E) 7
Rationale: x/7 = y/9 => x:y = 7:9
7/16 * 16 = 7
ANSWER:E
Answer: (E) 7
Question: The sum of the squares of three numbers is 225, while the sum of their products taken two at a time is 200. Their sum is:
(A) 10
(B) 30
(C) 40
(D) 25
(E) None of these
Rationale: x^+y^2+z^2=225
xy+yz+zx=200
as we know.. (x+y+z)^2=x^2+y^2+z^2+2(xy+yz+zx)
so (x+y+z)^2=225+(2*200)
(x+y+z)^2=625
so x+y+z=25
ANSWER:D
Answer: (D) 25
Question: In a shop, the marked price of an article is worked out in such a way that it generates a profit of 33133313. What should be the discount percent allowed on the marked price during a sale, so that the final profit made is 20%?
(A) 13 1/3
(B) 12 1/2
(C) 10%
(D) 8 1/2
(E) 6 2/3
Rationale: soln:-
lets consider the cost price of an article as $60 (take a number whose 33.33% can be calculated easily)
so marked price = 1.3333*60 = 80
profit to be earned = 20%
final selling price = 1.2*60 = 72
therefore discount to be given = 8/80 = 10%
answer - C
Answer: (C) 10%
Question: If x^2 +2x = 15, then one possible value of x – 4 =
(A) -8
(B) -5
(C) -3
(D) -1
(E) 5
Rationale: x^2 +2x = 15
i.e. x^2 +2x - 15 = 0
i.e. x^2 +5x -3x - 15 = 0
i.e. (x+5)(x-3) = 0
i.e. x =-5 or 3
i.e. x-4 = -5-4 or 3-4
i.e. x-4 = - 9 or -1
Answer: Option D
Answer: (D) -1
Question: A sum of Rs.1460 is divided into 14 students so that each boy gets Rs.120 while each girl gets Rs.100. Find the number of boys and number of girls
(A) 8B, 5G
(B) 5B, 8G
(C) 3B, 9G
(D) 9B, 4G
(E) 9B, 5G
Rationale: 120B+100G=1460-----i
B+G=12-------ii
from i
100B+20B+100G=1460
100(B+G)+20B=1460
100(14)+20B=1460
By simplifing we get
B=3;G=9
ANSWER:C
Answer: (C) 3B, 9G
Question: The probability of Sam passing the exam is 1/4. The probability of Sam passing the exam and Michael passing the driving test is 1/6. What is the probability of Michael passing his driving test?
(A) 1/24
(B) 1/2
(C) 1/3
(D) 2/3
(E) 2/5
Rationale: let p(s) and p(m) denote probability of sam passing the exam and michael passing the driving test respectively
as per the question
p(s)=1/4 and
p(s) * p(m)=1/6
therefore,
p(m)=(1/6)*4=2/3
Answer:D
Answer: (D) 2/3
Question: The average age of a husband and his wife was 23 years at the time of their marriage. After five years they have a one year old child. The average age of the family now is
(A) 19 years
(B) 23 years
(C) 28.5 years
(D) 29.3 years
(E) None
Rationale: Solution
Sum of the present ages on husband, wife and child	=(23x2+5x2)+1
= 57 years
Required average
= (57/3)
= 19 years.
Answer A
Answer: (A) 19 years
Question: If 6 men can reap 60 acres of land in 10 days, how many acres of land can 12 men reap in 20 days?
(A) 120
(B) 360
(C) 240
(D) 182
(E) 1000
Rationale: 6 men 60 acres 10 days
12 men ? 20 days
60 * 12/6 * 20/10
60 * 2* 2
60 * 4 = 240
Answer:C
Answer: (C) 240
Question: The true discount on Rs. 1760 due after a certain time at 12% per annum is Rs. 160. The time after which it is due is
(A) 11
(B) 66
(C) 77
(D) 10
(E) 81
Rationale: P.W. = Rs. (1760 -160) = Rs. 1600.
S.I. on Rs. 1600 at 12% is Rs. 160.
Time = 100 x 160 =	5	years = 5	x 12	months = 10 months.
1600 x 12	6	6
Answer: D
Answer: (D) 10
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) 180 sec
(B) 190 sec
(C) 170 sec
(D) 175 sec
(E) 185 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: If one positive integer is greater than another positive integer by 4, and the difference of their cubes is 208, what is their sum?
(A) 8
(B) 10
(C) 12
(D) 14
(E) 16
Rationale: 1^3 = 1
2^3 = 8
3^3 = 27
4^3 = 64
5^3 = 125
6^3 = 216
The two numbers are 2 and 6.
The answer is A.
Answer: (A) 8
Question: There are 5women and 6 men in an office. In how many ways can a person can be selected?
(A) 10
(B) 11
(C) 12
(D) 15
(E) 20
Rationale: Number of ways in which a person can be selected = 5+6 = 11 ways
Answer is B
Answer: (B) 11
Question: The Shopkeeper increased the price of a product by 25% so that customer finds it difficult to purchase the required amount. But somehow the customer managed to purchase only 72% of the required amount. What is the net difference in the expenditure on that product?
(A) 12.5%
(B) 10%
(C) 15%
(D) 17%
(E) 19%
Rationale: Quantity X Rate = Price
1 x 1 = 1
0.72 x 1.25 = 0.9
Decrease in price = (0.1/1) × 100 = 10%
B)
Answer: (B) 10%
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) 5/27
(C) 5/97
(D) 5/22
(E) 5/39
Rationale: Number of ways of (selecting at least two couples among five people selected) = (⁵C₂ * ⁶C₁)
As remaining person can be any one among three couples left.
Required probability = (⁵C₂ * ⁶C₁)/¹⁰C₅
= (10 * 6)/252 = 5/21
Answer: A
Answer: (A) 5/21
Question: A small beaker is 1/2 filled with salt water. Another beaker, which has five times the capacity of the small beaker, is 2/5 filled with fresh water. After dumping all of the salt water from the small beaker into the large beaker, to what fraction of its capacity will the large beaker be filled?
(A) 5/6
(B) 4/5
(C) 3/4
(D) 2/3
(E) 1/2
Rationale: 1/2 of the small beaker is 1/10 of the large beaker.
1/10 + 2/5 = 1/2
The answer is E.
Answer: (E) 1/2
Question: A football coach must choose 6 freshers from a team of 12 players. How many different ways can the coach choose the freshers?
(A) 500
(B) 650
(C) 729
(D) 800
(E) 924
Rationale: Choose 6 starters from a team of 12 players. Order is not important.
\inline {\color{Black} 12C_{6}}= 924
E
Answer: (E) 924
Question: Monica planned her birthday party. She prepared 5 muffins for each of her guests and kept aside two additional muffins in case someone will want extra. After the party, it turned out that one of the guests didn't come but every one of the guests that did come ate six muffins and 4 muffins remained. How many guests did Monica plan on?
(A) 3.
(B) 5.
(C) 4.
(D) 6.
(E) 7.
Rationale: 5N +2 = 4 + 6(N-1)
Solving N= 4
Hence C
Answer: (C) 4.
Question: Eleven bags are bought for Rs.1000 and sold at 10 for Rs.1400. What is the gain or loss in percentage?
(A) 10%
(B) 21%
(C) 24%
(D) 20%
(E) None of these
Rationale: Explanation:
As selling price is Rs.1400 for 10 bags, each bag is sold at Rs.140.
Hence, the profit is Rs.100 after selling 10 bags plus the selling price of 1 bag = 100 + 140 = Rs.240.
%profit = 240/1000 *100
= 24%
ANSWER C
Answer: (C) 24%
Question: A, B and C enter into a partnership and their shares are in the ratio 1/2 : 1/3 : 1/4. After 2 months, A withdraws half of his capital and after 10 months, a profit of Rs. 378 is divided among them. What is B's share ?
(A) 144
(B) 378
(C) 217
(D) 299
(E) 277
Rationale: Explanation:
Ratio of initial investments = 1/2 : 1/3 : 1/4 = 6 : 4 : 3.
Let their initial investments be 6x, 2x and 3x respectively.
A : B : C = (6x * 2 + 3x * 10) : (4x * 12) : (3x * 12) = 42 : 48 : 36 = 7 : 8 : 6.
B's share = = Rs. 144.
Answer: A) 144
Answer: (A) 144
Question: Mr. keth sold two pipes at $3 each. Based on the cost, his profit one was 30% and his loss on the other was 15%. On the sale of the pipes. Find the amount of his profit or loss?
(A) lost 10 cents
(B) lost 50 cents
(C) broke even
(D) gained 60 cents
(E) gained 40 cents
Rationale: 30 % profit on $ 3
= $ 30/100 ×3
= $ 0.30× 3
= $ 0.90
Similarly, 15% loss on $ 3
= $ 15/100 × 3
= $ 0.15 ×3
= $ 0.45
Therefore, in one pipe his profit is $ 0.90 and in the other pipe his loss is $ 0.45
so profit by amount $0.40.
Answer is E
Answer: (E) gained 40 cents
Question: Including Cara and Dan, there are seven members on the board of directors for a company. If the board is to be split up into a four-person subcommittee, what fraction of all the possible subcommittees that include Cara, also include Dan?
(A) 1/5
(B) 1/4
(C) 1/3
(D) 1/2
(E) 2/5
Rationale: The number of possible subcommittees with Cara is 6C3=20.
The number of possible subcommittees with Cara and Dan is 5C2=10.
The fraction of Cara's subcommittees which include Dan is 10/20=1/2.
The answer is D.
Answer: (D) 1/2
Question: In a deck of cards there are 52 cards numbered from 1 to 13. There are 4 cards of each number in the deck. If you insert 10 more cards with the number 10 on them and you shuffle the deck really good, what is the probability to pull out a card with a number 10 on it?
(A) 1/4.
(B) 7/31.
(C) 5/29.
(D) 4/13.
(E) 1/3.
Rationale: 4+10 tens/52+10 total cards=14/62=7/31
B
Answer: (B) 7/31.
Question: A certain number when divided by 65 leaves a remainder 25, what is the remainder if the same no.be divided by 15?
(A) 4
(B) 5
(C) 6
(D) 8
(E) 9
Rationale: Explanation:
65 + 25 =90/15 =6 (Remainder)
C
Answer: (C) 6
Question: Which of the following must be divisible by 2 if z is a positive integer?
(A) z^2*(z−5)
(B) (z^2−2)
(C) z(z+2)^3
(D) (z−1)*z*(z+1)
(E) z^2*(z−5)
Rationale: option D) (z−1)*z*(z+1) which represents the product of three consecutive integers
the product of 3 consecutive integers is divisible by both 2 and 3.
Answer is D
Answer: (D) (z−1)*z*(z+1)
Question: A sum of money is borrowed and paid back in two annual installments of Rs. 882 each allowing 5% C.I. The sum borrowed was?
(A) Rs.1648
(B) Rs.1640
(C) Rs.1289
(D) Rs.1282
(E) Rs.1633
Rationale: Principal = (P.W. of Rs. 882 due 1 year hence) + (P.W. of Rs. 882 due 2 years hence)
= [882/(1 + 5/100) + 882/(1 + 5/100)2]
= (882 * 20)/21 + (882 * 400)/441
= Rs.1640.
Answer:B
Answer: (B) Rs.1640
Question: Six lights begin to flash together at 12:00 noon and flash respectively at intervals of 4, 5, 6, 7, 8, and 9 seconds. Not including the flash at 12:00 noon, how many more times will all six lights flash together before 4:00 pm (i.e. four hours later)?
(A) 3
(B) 5
(C) 7
(D) 9
(E) 11
Rationale: The least common multiple is 2*2*2*3*3*5*7=2520.
14400 seconds / 2520 = 5 + remainder.
The answer is B.
Answer: (B) 5
Question: A and B rent a pasture for 10 months. A put in 80 cows for 7 months. How many can B put in for the remaining 3 months, if he pays half as much again as A?
(A) 388
(B) 277
(C) 266
(D) 280
(E) 191
Rationale: 80* 7: x* 3 = 1:1 1/2
560: 3x = 2: 3
x = 280
Answer: D
Answer: (D) 280
Question: Vishal and Raghu jointly started a business. Vishal invested three times as Raghu did and invested his money for double time as compared to Raghu. Raghu earned Rs. 4000. If the gain is proportional to the money invested and the time for which the money is invested then the total gain was ?
(A) Rs. 28,000
(B) Rs. 18,000
(C) Rs. 14,000
(D) Rs. 8,000
(E) None of these
Rationale: Explanation:
Investments ratio is = 3:1
Time period ratio is = 2:1
As they are proportional to gain
------
Gain ratio of Vishal and raghu = 6:1
But given Raghu got Rs. 4000,
=? 1 ----- 4000
7 ----- ?
=> Rs.28,000
The total gain = Rs.28,000
ANSWER IS A
Answer: (A) Rs. 28,000
Question: Sahil took a loan for 6 years at the rate of 5% per annum on Simple Interest, If the total interest paid was Rs. 1230, the principal was
(A) 4100
(B) 4200
(C) 4300
(D) 4400
(E) None of these
Rationale: Explanation:
S.I.=P∗R∗T /100=>P=S.I.∗100/ R∗T
By applying above formula we can easily solve this question, as we are already having the simple interest.
=>P=1230∗100/ 6∗5
=>P=4100
Option A
Answer: (A) 4100
Question: In March, Kurt ran an average of 2 miles an hour. If by June he had increased his pace by 10 seconds per mile, then which of the following expresses the number of hours it would take Kurt to complete one mile in June?
(A) 3590/60^2
(B) 2410/60^2
(C) 1790/60^2
(D) 3586/60
(E) 60^2/3590
Rationale: Kurt ran at an average of 2 miles/hour in march. So to run 1 mile he would take 1/2 hours = (60 * 60)/2 seconds = 1800 seconds.
If he increases his speed by 10 seconds, he will complete a mile in 1790 seconds. Converting in hours = 1790/(60 * 60) = 1790/(60^2)
ANSWER: C
Answer: (C) 1790/60^2
Question: Rs.8000 become Rs.8820 in a certain interval of time at the rate of 5% per annum of C.I. Find the time?
(A) 6 years
(B) 8 years
(C) 9 years
(D) 3 years
(E) 2 years
Rationale: 8820 = 8000(21/20)N
(21/20)^2 = (21/20)N => N = 2
. At the end of two years what will be the comp.Answer: E
Answer: (E) 2 years
Question: A can do a certain job in 20 days. B is 60% more efficient than A. How many days does B alone take to do the same job?
(A) 7 1/2 days
(B) 8 days
(C) 12 1/2 days
(D) 9 days
(E) None of them
Rationale: Ratio of times taken by A and B = 160 : 100 = 8 : 5.
Suppose B alone takes x days to do the job.
Then, 8 : 5 :: 20 : x = 8x = 5 x 20 =x = 12 1/2 days.
Answer is C.
Answer: (C) 12 1/2 days
Question: The length and breadth of a rectangle are raised in the proportion 3:4 and 4:5 correspondingly. What is the proportion of the previous place to the new?
(A) 2:3
(B) 3:5
(C) 5:7
(D) 7:9
(E) None of these
Rationale: Explanation :
-> If the real length = 3a
And the real breadth = 4a
Area = (3a)*(4a)
=12 a2
-> New Length is 4a and New breadth is 5a
New area is (4a)*(5a)
= 20 a2
Ratio of previous place to new place = 12 a2 : 20 a2
= 12 : 20
= 3 : 5
Answer : B
Answer: (B) 3:5
Question: A ship sails out to a mark at the rate of 18 kmph. and sails back at the rate of 14 kmph. The average rate of sailing is ?
(A) 5 km/hr
(B) 12 km/hr
(C) 16 km/hr
(D) 25 km/hr
(E) None
Rationale: Answer
Average = ( 2uv / u +v ) km/hr
= ( 2 x 18 x 14 ) / (18 +14 ) km/hr.
= 16 km/hr.
Correct Option: C
Answer: (C) 16 km/hr
Question: A businessman earns $28800 in December, thus decreasing his average annual (January to December) earnings by $1300. His average annual earnings would be
Source: CMAT Preparation
(A) $29000
(B) $33500
(C) $40200
(D) $41000
(E) $43100
Rationale: (x - 28,800)/11 - x/12 = 1,300
x = 517,200
x/12 = 43,100
Answer: E.
Answer: (E) $43100
Question: A batsman in his 17th innings makes a score of 85 and their by increasing his average by 3. What is his average after the 17thinnings?
(A) 88
(B) 16
(C) 128
(D) 37
(E) 12
Rationale: 16x + 85 = 17(x + 3)
x = 34 + 3 = 37
Answer:D
Answer: (D) 37
Question: A merchant has selected two items to be placed on sale, one of which currently sells for 25 percent less than the other. If he wishes to raise the price of the cheaper item so that the two items are equally priced, by what percentage must he raise the price of the less expensive item?
(A) 52 %
(B) 40%
(C) 30%
(D) 20%
(E) 10%
Rationale: Expensive item = $100;
Cheap item = $75;
We must increase $75 to $100, so by $25, which is approximately 30% increase: (100-75)/75 = 1/3 = ~0.33
Answer: C.
Answer: (C) 30%
Question: The ages of two persons differ by 16 years. 6 years ago, the elder one was
3 times as old as the younger one. What are their present ages of the elder person?
(A) 10
(B) 20
(C) 30
(D) 40
(E) 50
Rationale: Let present age of the elder person =x and
present age of the younger person =x−16
(x−6)=3(x−16−6)
x−6=3x−66
2x=60
x=60/2=30 Answer: Option C
Answer: (C) 30
Question: How many prime numbers D exist such that 90 < D < 106 and D is a factor of 99999919?
(A) 1. Zero
(B) 2. One
(C) 3. Two
(D) 4. Three
(E) 5. More than three
Rationale: I found that considering the constraint..D is a prime num in between 90 to 106 not inclusive , only 3 numbers (91,97 and 101) are present but those numbers are not the factors of the number mentioned....Therefore, i doubt the answer.C
Answer: (C) 3. Two
Question: A man bring 2 cats to his home to eliminate all the mice. They do a half of the work in 5 days, then the man brings 3 more cats. If they hunt at the same rate, how many days will take to hunt all the mice, since the first day?
(A)  7 days
(B)  8 days
(C)  9 days
(D)  10 days
(E)  11 days
Rationale: We have that: 2 cats----- 5 days, (2+3) C ----- X d, that is: (X d/ 2C) = (5 d/5P), then: X d = (5 d/5C)2C = 2d. Is to say, the 5 cats hunt the same quantity in 2 days; as it is only 1/2 of the work, all the mice would be hunt in: M = 5 d + 2 d = 7 days. Answer A.
Answer: (A)  7 days
Question: next term in series 3,32,405
(A) 5144
(B) 6144
(C) 7144
(D) 7582
(E) 8547
Rationale: first term 3*1^2=3
second term 4*2^3=32
third term 5*3^4=405
fourth term 6*4^5=6144
ANSWER:B
Answer: (B) 6144
Question: Find the invalid no.from the following series 3, 7, 15, 31, 63, 123, 255
(A) 3
(B) 7
(C) 27
(D) 63
(E) 123
Rationale: Go on multiplying the number by 2 and adding 1 to it to get the next number.So, 123 is wrong.
E
Answer: (E) 123
Question: A shopkeeper fixes the marked price of an item 40% above its cost price. The percentage of discount allowed to gain 8% is
(A) 23.85%
(B) 22.85%
(C) 21.85%
(D) 20.85%
(E) None of these
Rationale: Explanation:
Let the cost price = Rs 100
then, Marked price = Rs 140
Required gain = 8%,
So Selling price = Rs 108
Discount = 140 - 108 = 32
Discount% = (32/140)*100 = 22.85%
Option B
Answer: (B) 22.85%
Question: A single reservoir supplies the petrol to the whole city, while the reservoir is fed by a single pipeline filling the reservoir with the stream of uniform volume. When the reservoir is full and if 40,000 liters of petrol is used daily, the suply fails in 90 days.If 32,000 liters of petrol is used daily, it fails in 60 days. How much petrol can be used daily with out the supply ever failing?
(A) 64000 liters
(B) 56000 liters
(C) 78000 liters
(D) 60000 liters
(E) None of these
Rationale: Explanation:
Let x liter be the per day filling and v litr be the capacity of the reservoir, then
90x + v = 40000 × 90 -----(1)
60x + v= 32000 × 60 ------(2)
solving eq.(1) and (2) , we get
x = 56000
Hence , 56000 liters per day can be used without the failure of supply.
Answer: B
Answer: (B) 56000 liters
Question: A box contains 5 green, 4 yellow and 3 white balls. Three balls are drawn at random. What is the probability that they are not of same colour.
(A) 52/55
(B) 3/55
(C) 41/44
(D) 3/44
(E) None of these
Rationale: Explanation:
Total cases =12C3=12∗11∗10/3∗2∗1=220
Total cases of drawing same colour =5C3+4C3+3C3
5∗4/2∗1+4+1=15
Probability of same colur ==15/220=3/44
Probability of not same colur =1−3/44=41/44
Option C
Answer: (C) 41/44