mathewhe/aqua_rat huggingface dataset:
Question: The grade point average of the entire class is 88. If the average of one third of the class is 94, what is the average of the rest of the class?
(A) 82
(B) 83
(C) 84
(D) 85
(E) 86
Rationale: Let x be the number of students in the class.
Let P be the average of the rest of the class.
88x = (1/3)94x + (2/3)(P)x
264 = 94 + 2P
2P = 170
P = 85.
The answer is D.
Answer: (D) 85
Question: If the cost of 15 kgs of rice is Rs.780/-, what is the cost of 112 kgs of rice?
(A) Rs.5824/-
(B) Rs.5720/-
(C) Rs.5616/-
(D) Rs.5512/-
(E) None of these
Rationale: Explanation:
Cost of 1 kg of rice = Rs.780/15 = Rs.52.
Therefore, cost of 112 kgs. = Rs.52x112 = Rs.5824/-
Answer: Option A
Answer: (A) Rs.5824/-
Question: The cost price of a radio is Rs.1500 and it was sold for Rs.1230, find the loss %?
(A) 18%
(B) 17%
(C) 78%
(D) 13%
(E) 19%
Rationale: 1500 ---- 270
100 ---- ? => 18%
Answer: A
Answer: (A) 18%
Question: A child received a gift of six different soccer team flags, including Liverpool and Arsenal. If he only has space in his bedroom to display four flags in a row, how many arrangements are possible if he cannot display the Liverpool and Arsenal flags at the same time?
(A) 162
(B) 216
(C) 272
(D) 360
(E) 414
Rationale: The total number of ways to choose and arrange 4 flags out of 6 is C^46∗4!=360(or directly P^46).
We cannot have Liverpool and Arsenal flags at the same time. The number of ways to have and arrange Liverpool and Arsenal flags at the same time is C24∗4!=144 (choosing 2 flags out of 4 remaining, without Liverpool and Arsenal, and then arranging 4 flags with 4!);
Total - Restriction = 360 - 144 = 216.
Answer: B.
Answer: (B) 216
Question: In a panel of 10 light bulbs, the odds of any light bulb to burn out are 0.02 at any given 10 minutes. Should a light bulb burn out, the whole panel would instantly turn off. What are the odds that the panel would be turned off within the first 10 minutes after it was switched on?
(A) 1-0.02^10
(B) 1-0.98^10
(C) (1-0.98)^10
(D) 0.06
(E) 1-10*0.06
Rationale: ans B.
Prob that light will not turned off = 0.98^10. Hence prob (turn off) = 1 - prob (not turn off).
Answer: (B) 1-0.98^10
Question: 15 years hence, Karthik will be just Quadrice as old as he was 15 years ago, How old is Karthik at now? [ Quadrice = 4 Times ]
(A) 25
(B) 26
(C) 22
(D) 29
(E) 28
Rationale: A
25
Let the current age of Karthikh = A years
Then, A+15 = 4(A – 15)
Therefore A = 25
Answer: (A) 25
Question: If the 11th day of a month is three days earlier than Friday, What day will it be on the 20th day of the month?
(A) Thursday
(B) Monday
(C) Sunday
(D) Wednesday
(E) Friday
Rationale: Explanation:
Given that 11th day of a month is three days earlier than Friday
=> 11th day is Tuesday
=> 18th is Tuesday
=> 20th is Thursday
Answer: Option A
Answer: (A) Thursday
Question: Twenty times a positive Integer is less than its square by 96. What is the integer?
(A) 4
(B) 25
(C) 24
(D) 16
(E) 27
Rationale: Let the Integer be x.
Then X2 - 20X = 96
X2 - 20X - 96 = 0
X2 + 4X - 24X - 96 = 0 ===> X(X + 4) -24(X + 4)
===> (X + 4)(X-24)
X = -4 or 24. as the Integer is positive the correct answer is
option C)24
Answer: (C) 24
Question: A train running at the speed of 60 km/hr crosses a pole in 12 seconds. What is the length of the train?
(A) 200 metres
(B) 180 metres
(C) 324 metres
(D) 150 metres
(E) 100 meters
Rationale: Speed=60 x5/18m/sec=50/3	m/sec.
Length of the train = (Speed x Time).
Length of the train =	50/3	x 12m = 200 m.
ANSWER:A
Answer: (A) 200 metres
Question: In Badminton game, one player throws two fair, six-sided die at the same time. If the player receives at least a five or a one on either die, that player wins. What is the probability that a player wins after playing the game once?
(A) 1/3
(B) 4/9
(C) 5/9
(D) 2/3
(E) 3/4
Rationale: In Badminton game, Probably the easiest approach would be to find the probability of the opposite event and subtract it from 1:
P(win) = 1- P(not win) = 1 - 4/6*4/6 = 5/9.
Answer: C.
Answer: (C) 5/9
Question: The profit earned by selling an article for Rs. 832 is equal to the loss incurred when the same article is sold for Rs. 448. What should be the sale price for making 70% profit?
(A) 277
(B) 1088
(C) 277
(D) 266
(E) 121
Rationale: Let C.P. = Rs. x.
Then, 832 - x = x - 448
2x = 1280 => x = 640
Required S.P. = 170% of Rs. 640 = 170/100 * 640 = Rs. 1088.
Answer: B
Answer: (B) 1088
Question: 1100 male students and 700 female students are examined in a monthly test; 42% of the male students and 30% of the female students only pass in the examination. Find the percentage of the total failed?
(A) 62*2/3
(B) 40*2/3
(C) 55*2/3
(D) 50*2/3
(E) 35*2/3
Rationale: Total number = 1100 + 700 = 1800.
tot students passed = (42% of 1100 + 30% of 700) - (462 + 210) = 672.
Number of failures = 1800-672 = 1128.
Percentage of failure = (1128/1800 * 100 )% = 62 * 2/3 %.
ANSWER A
Answer: (A) 62*2/3
Question: The decimal 0.1 is how many times greater than the decimal (0.0001)^3?
(A) 10^9
(B) 10^10
(C) 10^11
(D) 10^12
(E) 10^13
Rationale: 0.1 = 10^-1
(0.0001)^3 = (10^-4)^3 = 10^-12
10^11 * 10^-12 = 10^-1
The answer is C.
Answer: (C) 10^11
Question: John throws a coin until a series of five consecutive heads or three consecutive tails appears. What is the probability that the game will end after the sixth throw?
(A) 1/32
(B) 2/16
(C) 3/16
(D) 7/16
(E) 9/16
Rationale: Let's consider the routes that would lead to ending the game on the fourth toss. In order to be a win at that point, tosses #2#3#4 would all have to be the same, either H or T, and in order for the game NOT to end on the third toss, the first toss would have to be different from the other four. Thus, the only two possible sequences are
H-T-T-T-T-T ----> P = (1/2)^6 = 1/64
T-H-H-H-H-H ----> P = (1/2)^6 = 1/64
Either one of these would satisfy the condition, so we could have one or the other. OR means add in probability.
1/64 + 1/64= 2/64 = 1/32
Answer(A).
Answer: (A) 1/32
Question: A can do a work in 8 days. B can do the same work in 4 days. Both A&B together will finish the work and they got $1000 from that work. Find their shares?
(A) 600,400
(B) 500,500
(C) 400,200
(D) 800,200
(E) 550,450
Rationale: Ratio of their works A:B = 8:4
Ratio of their wages A:B = 2:1
A's share = (2/5)1000 = 400
B's share = (1/5)1000 = 200
correct option is C
Answer: (C) 400,200
Question: 4 mat-weavers can weave 4 mats in 4 days. At the same rate, how many mats would be woven by 8 mat-weavers in 8 days?
(A) 16
(B) 77
(C) 88
(D) 26
(E) 29
Rationale: Explanation:
Let the required number of bottles be x.
More weavers, More mats (Direct Proportion)
More days, More mats (Direct Proportion)
{\color{Blue} \left.\begin{matrix} weavers &4:8 \\ days& 4:8 \end{matrix}\right\}::4:x}
{\color{Blue}\therefore }4 x 4 x x = 8 x 8 x 4
{\color{Blue}\Rightarrow x=\frac{8\times 8\times 4}{4\times 4} }
{\color{Blue} \Rightarrow }x = 16.
Answer: A) 16
Answer: (A) 16
Question: In the formula V = 1/(4r)^2, if r is halved, then V is multiplied by
(A) 64
(B) 8
(C) 4
(D) 64
(E) 1/64
Rationale: Say r=2 => V1 = 1/64
when r=1; V2 = 1/16
V2 = 4*V1.
Answer=C=4
Answer: (C) 4
Question: The ratio of the cost price and the selling price is 4:5. The profit percent is?
(A) 75%.
(B) 27%.
(C) 25%.
(D) 45%.
(E) 15%.
Rationale: Let C.P. = Rs. 4x. Then, S.P. = Rs. 5x
Gain = (5x - 4x) = Rs. x
Gain % = (x * 100)/ 4x = 25%.
Answer:C
Answer: (C) 25%.
Question: The number of ways in which six boys and six girls can be seated in a row for a photograph so that no two girls sit together is?
(A) 8! * ⁷P₆
(B) 6! * ⁷P₆
(C) 9! * ⁷P₆
(D) 5! * ⁷P₆
(E) 2! * ⁷P₆
Rationale: We can initially arrange the six boys in 6! ways.
Having done this, now three are seven places and six girls to be arranged. This can be done in ⁷P₆ ways.
Hence required number of ways
= 6! * ⁷P₆
Answer: B
Answer: (B) 6! * ⁷P₆
Question: When the oil from a circular cylinder leaked, the formula for the speed of the leak is V = kh^2, where h was the height of the remaining oil and k was constant. If the height of the cylinder is 4, the speed of the leak is Vâ€™, When the height of the oil remaining is 12, what was the speed of the leak, in terms of Vâ€™?
(A) 9Vâ€™
(B) 4Vâ€™
(C) Vâ€™/2
(D) Vâ€™/4
(E) Vâ€™
Rationale: When h=4 v=V'
So V' = k.16
Hence k = V'/16
Now when h=12
v=(V'/16).12^2
v=V'.144/16
v=9V'
Ans : A
Answer: (A) 9Vâ€™
Question: If a committee of 3 people is to be selected from among 6 married couples so that the committee does not include two people who are married to each other, how many such committees are possible?
(A) 20
(B) 40
(C) 50
(D) 80
(E) 160
Rationale: You now have your Committee of 3 people. But you've selected them in an order, when order doesn't matter.
Selection #1 = Jack
Selection #2 = Susan
Selection #3 = Mary
Assume this is a good committee where Jack is not married to Susan or Mary and Susan and Mary are not married. The above committee will be the same as the following committee:
Selection #1 = Susan
Selection #2 = Mary
Selection #3 = Jack
To account for the fact that the order does not matter, we must divide out the number of ways a single committee can be the same members but in different order. 3 places = 3!, 3*2*1 = 6.
12*10*8 / 6 = 160. Answer E.
Answer: (E) 160
Question: A, B and C can do a piece of work in 20, 30 and 60 days respectively. In how many days can A do the work if he is assisted by B and C on every third day?
(A) 13 days
(B) 15 days
(C) 17 days
(D) 21 days
(E) None
Rationale: A's 2 day's work = 1	x 2 =	1	.
20	10
(A + B + C)'s 1 day's work = 1	+	1	+	1 =	6	=	1	.
20	30	60	60	10
Work done in 3 days = 1	+	1 =	1	.
10	10	5
Now,	1	work is done in 3 days.
5
Whole work will be done in (3 x 5) = 15 days.
Option B
Answer: (B) 15 days
Question: A farmer spent $35 on feed for chickens and goats. He spent 40% money on chicken feed, which he bought at a 30% discount off the full price, and spent the rest on goat feed, which he bought at full price. If the farmer had paid full price for both the chicken feed and the goat feed, what amount would he have spent on the chicken feed and goat feed combined?
(A) $37.80
(B) $38.50
(C) $39.20
(D) $39.50
(E) $41
Rationale: A farmer spent 40% money on chicken feed, so he spent 0.4*$35=$14 on chicken feed, thus he spent the remaining 35-14=$21 on goat feed.
Now, since he bought chicken feed at a 30% discount then the original price of it was x*0.7=$14 --> x=$20.
Therefore if the farmer had paid full price for both the chicken feed and the goat feed, then he would he have spent 20+21=$41.
Answer: E.
Answer: (E) $41
Question: Lucy's personal library had 1/20 the capacity as the town library. Lucy decided to donate 1/2 of her book collection to the town library. What fraction of the town library's capacity would Lucy's book donation fill?
(A) 3/16
(B) 1/10
(C) 1/6
(D) 1/18
(E) 1/4
Rationale: Assuming that the town library has space for 100 books, that would mean that Lucy's personal library had 20 books. If Lucy donated a 1/2 of her books, that would mean she donated 10 books. Those 10 books would make 10/100 of the town library's collection. 10/100 simplifies to 1/10. (Answer: B)
Answer: (B) 1/10
Question: Two cars A and B start from Boston and New York respectively simultaneously and travel towards each other at constant speeds along the same route. After meeting at a point between Boston and New York the two cars A and B proceed to their respective destinations of New York and Boston. Car A reaches New York 80 minutes after the two cars have met and Car B reaches Boston 90 minutes after they have met. How long did Car A take to cover the distance between Boston and New York?
(A) 1 hour
(B) 1 hour 10 minutes
(C) 2 hours 30 minutes
(D) 1 hour 40 minutes
(E) 2 hours 20 minutes
Rationale: Both cars leave at the same time
Both cars travel at constant speed
Stealing a useful piece of information from Paragkan:
If two objects A and B start from opposite points and, after having met en route, reach their respective destinations in a and b mins (or any other measure of time) respectively, then the ratio of their speeds
ratio of speed: (a/b) = sq. rt(b/a)
sq. rt(b/a)
sq. rt(90/80)
sq. rt(3/2)
So, for every three units of distance A travels, B travels two. Because we know the ratio of speed and the time it took B to travel the distance A hasn't yet covered, we can find the time it took A to cover the distance B did in 90 minutes.
90*(2/3)where 2/3 represents the lesser amount of time it took A to travel the distance B did in 90 minutes.
= 60 minutes.
Therefore, A took 80 minutes to travel the first portion then 60 minutes to travel the distance B did in 90 minutes. A spent (80+60)=140 minutes on the road.
E. 2 hours 20 minutes
Answer: (E) 2 hours 20 minutes
Question: Arithmetic mean and standard deviation of a certain normal distribution are 13 and 1.5. What value is exactly 2 standard deviations less than the mean?
(A)  10.5
(B)  10
(C)  11.5
(D)  12
(E)  12.5
Rationale: The value which is exactly two SD below the mean is: mean-2*SD=13-2*1.5=10.
Answer: B.
Answer: (B)  10
Question: Mrs. Rodger got a weekly raise of $146. If she gets paid every other week, write an integer describing how the raise will affect her paycheck.
(A) $140
(B) $141
(C) $142
(D) $147
(E) $146
Rationale: Let the 1st paycheck be x (integer).
Mrs. Rodger got a weekly raise of $ 146.
So after completing the 1st week she will get $ (x+146).
Similarly after completing the 2nd week she will get $ (x + 146) + $ 146.
= $ (x + 146 + 146)
= $ (x + 292)
So in this way end of every week her salary will increase by $ 146.
correct answer E)$146
Answer: (E) $146
Question: Anna and Carol buy CDs and tapes at a music store that sells each of its CDs for a certain price and each of its tapes for a certain price. Anna spends twice as much as Carol spends, buying three times as many CDs and the same number of tapes. If Carol spends $90.00 on four CDs and five tapes, how much does one tape cost?
(A) $5.00
(B) $6.25
(C) $12.00
(D) $25.00
(E) $9.00
Rationale: CD => C
Type => T
Carol: 4C+5T=90
Anna: 12C+5T=180
12C-4C=90
8C=90
C=11.25
4C+5T=90
45+5T=90
5T=45
T=9
Answer is E
Answer: (E) $9.00
Question: A train of 50 carriages, each of 60 meters length, when an engine also of 60 meters length is running at a speed of 60 kmph. In what time will the train cross a bridge 1.5 km long?
(A) 6
(B) 3
(C) 4
(D) 4.5
(E) 2
Rationale: D = 50 * 60 + 1500 = 3000 m
T = 4500/60 * 18/5 = 270 sec = 4.5 mins
Answer:D
Answer: (D) 4.5
Question: A specialized type of sand consists of 40% mineral X by volume and 60% mineral Y by volume. If mineral X weighs 2.5 grams per cubic centimeter and mineral Y weighs 2 grams per cubic centimeter, how many grams does a cubic meter of specialized sand combination weigh? (1 meter = 100 centimeters)
(A) 5,500,000
(B) 2,200,000
(C) 55,000
(D) 28,000
(E) 280
Rationale: Let the volume be 1 m^3 = 1m * 1m * 1m = 100cm * 100cm * 100cm = 1,000,000 cm^3
By volume
40% is X = 400,000 cm^3
60% is Y = 600,000 cm^3
By weight,
In 1 cm^3, X is 2.5 gms
In 400,000 cm^3 , X = 2.5 * 400,000 = 1,000,000 grams
In 1 cm^3, Y is 2 gms
In 600,000 cm^3, Y = 2 * 600,000 = 1,200,000 gms
Total gms in 1 m^3 = 1,000,000 + 1,200,000 = 2,200,000
ANSWER:B
Answer: (B) 2,200,000
Question: A train speeds past a pole in 15 sec and a platform 100 m long in 25 sec, its length is?
(A) 299
(B) 150
(C) 267
(D) 551
(E) 121
Rationale: Let the length of the train be x m and its speed be y m/sec.
Then, x/y = 15 => y = x/15
(x + 100)/25 = x/15 => x = 150 m.
Answer: B
Answer: (B) 150
Question: What percent of a day is 10 hours?
(A) 12%
(B) 12.5%
(C) 13%
(D) 41.6%
(E) None of these
Rationale: Explanation :
Solution: required percentage = (10/100 * 24) = 41.6%
Answer : D
Answer: (D) 41.6%
Question: A fair coin with sides marked heads and tails is to be tossed eight times. What is the probability that the coin will land tails side up more than seven times?
(A) 37/256
(B) 56/256
(C) 65/256
(D) 70/256
(E) 1/256
Rationale: More than 7 times tails = 8times = 8C8 = 1
2 2 2 2 2 2 2 2
2^8 times total events and 1 events where tails side up .
So probability = 1/2^8 = 1/256 (Answer E)
Answer: (E) 1/256
Question: Two pipes A and B can fill a cistern in 20 and 30 minutes respectively, and a third pipe C can empty it in 40 minutes. How long will it take to fill the cistern if all the three are opened at the same time?
(A) 17 1/8 min
(B) 17 2/7 min
(C) 17 1/7 min
(D) 17 1/6 min
(E) 17 3/7 min
Rationale: Explanation:
1/20 + 1/30 - 1/40
= 7/120
120/7
= 17 1/7
Answer:C
Answer: (C) 17 1/7 min
Question: Suppose son name is 120,his brother name is 150 and his mother name is 220.find out his father's name???
(A) 190
(B) 210
(C) 230
(D) 240
(E) 250
Rationale: since difference between all name is =30
so father's name will be 220+30=250.
ANSWER:E
Answer: (E) 250
Question: A rectangle A has an area of 30 square centimeters. Square B has a perimeter of 16 centimeters. If square B is placed within square A and a random point is chosen within square A, what is the probability the point is not within square B?
(A) 9/30
(B) 14/30
(C) 4/9
(D) 3/5
(E) 6/25
Rationale: I guess it's mean that square B is placed within rectangle A entirely.
Since, the perimeter of B is 16, then its side is 16/4=4 and the area is 4^2=16;
Empty space between the squares is 30-16=14 square centimeters, so if a random point is in this area then it won't be within square B: P=favorable/total=14/30.
Answer: B.
Answer: (B) 14/30
Question: The edge of a cube is 5a cm. Find its surface?
(A) 24a8
(B) 150a2
(C) 24a1
(D) 24a2
(E) 24a7
Rationale: 6a2 = 6 * 5a * 5a = 150a2
Answer:B
Answer: (B) 150a2
Question: If a number between 10 and 40 (inclusive) at random. What is the probability that the tens digit is greater than ones digit?
(A) 31/41
(B) 1041
(C) 7/31
(D) 27/41
(E) 11/41
Rationale: If tens digi is 4 ---> ones digit : 0
If tens digi is 3 ---> ones digit : 0, 1, 2
If tens digi is 2 ---> ones digit : 0, 1
If tens digi is 1 ---> ones digit : 0
So the number of numbers whose tens digit is greater than ones digit is 11.
The total number is 40-10+1=31.
So the probability is 7/31.
The answer is (C).
Answer: (C) 7/31
Question: Two friends A and B leave point A and point B simultaneously and travel towards Point B and Point A on the same route at their respective constant speeds. They meet along the route and immediately proceed to their respective destinations in 32 minutes and 50 minutes respectively. How long will B take to travel the entire journey between Point B and point A?
(A) 65
(B) 70
(C) 90
(D) 75
(E) 80
Rationale: Let x per minute be the speed of A and y per minute be the speed of B.
After meeting at a point, A travels for 32 mins and B travels for 50 mins. So distance covered by each of them post point of crossing
A= 32x and B=50y
The distance covered by A and B before they cross each would be distance covered by B and A post crossing respectively.
Therefore distance covered by B before he meets A= 32x
Time taken by B cover 32x distance= 32x/y mins
Therefore total time taken by B= 32x/y + 50 mins ................. I
We need to find value of x in terms of y to arrive at final answer.
Total distance= 32x+50y
Combined speed of A and B= x+y
Therefore time taken before A and B meet en-route= (32x+50y)/(x+y)
Time taken by B reach destination after meeting A= 50 mins
Total travel time for B= [(32x+50y)/(x+y)]+50 mins ...................II
Equate I and II
32x/y+50= [(32x+50y)/(x+y)]+50
(32x+50y)/y=(82x+100y)/(x+y)
32x^2+50xy+32xy+50y^2=82xy+100y^2
32x^2+82xy-82xy+50y^2-100y^2=0
32x^2-50y^2=0
32x^2=50y^2
16x^2=25y^2
Taking square root.. (since x and y denote speed, square root can't be negative)
4x=5y
y=4x/5 ............ III
substitute in I
=32x/(4x/5) + 50
=32x*5/4x + 50
=40+50
=90 mins
C
Answer: (C) 90
Question: If the cost price of 20 articles is equal to the selling price of 40 articles, what is the % profit or loss made by the merchant?
(A) 25% loss
(B) 25% profit
(C) 20% loss
(D) 20% profit
(E) 50% loss
Rationale: Let the cost price of 1 article be $1.
Therefore, cost price of 20 articles = 20 * 1 = $20
The selling price of 40 articles = cost price of 40 articles = $40.
Now, we know the selling price of 40 articles. Let us find the cost price of 40 articles.
Cost price of 40 articles = 40 * 1 = $40.
Therefore, profit made on sale of 40 articles = Selling price of 40 articles - cost price of 40 articles
= 20 - 40 = -$20.
As the profit is in the negative, the merchant has made a loss of $20.
Therefore, % loss = loss/cp * 100
% loss = -20/40 * 100 = 50% loss.
E
Answer: (E) 50% loss
Question: The average age of a group of 5 members is 20 years. Two years later, a new member joins the group. The average age of the group becomes 24 years. What is the age of the new member ?
(A) 20 years
(B) 21 years
(C) 34 years
(D) 23 years
(E) 24 years
Rationale: The average age of a group of 5 members is 20 years --> the sum of the ages is 5*20=100;
Two years later the sum of the ages of these 5 members would be 100+5*2=110;
Now, say the age of the new member is x years, so the sum of the ages of a new 6 member group is 110+x. Since given that the average age of this group of 6 members is 24 years then: 24*6=110+x --> x=34.
Answer: C.
Answer: (C) 34 years
Question: Three math classes: X, Y, and Z, take an algebra test.
The average score in class X is 83.
The average score in class Y is 76.
The average score in class Z is 85.
The average score of all students in classes X and Y together is 79.
The average score of all students in classes Y and Z together is 81.
What is the average score for all the three classes, taken together?
(A) 81
(B) 81.5
(C) 82
(D) 84.5
(E) None of these
Rationale: Explanation :
Let the number of students in classes X, Y and Z be a,
b and c respectively. Then
Total of X = 83a
Total of Y = 76b
Total of Z = 85c
And , (83a + 76b) / (a + b) = 79. i.e 4a = 3b.
Also, (76b + 85c) / (b + c) = 81. i.e 4c = 5b.
Hence, b= (4/3)a, c =(5/4)b = (5/4) x (4/3)a = (5/3)a.
Average of X, Y and Z = (83a + 76b + 85c ) / (a + b + c).
=> 83a+76∗(4/3)a+85∗(5/3)a /a+(4/3)a+(5/3)a .
=> 978/12
=> 81.5
Answer : B
Answer: (B) 81.5
Question: How many numbers are there between 20 and 60 which are divisible by 3 and the total of two digits is 9?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: Since number are
27,36,45,54
ANSWER:C
Answer: (C) 4
Question: Mother's age is 65 years. If he is 3 more than twice the age of his son, find the age of his son.
(A) 32 years
(B) 31 years
(C) 16 years
(D) 18 years
(E) 25 years
Rationale: Let Mike's son age be x.
3+ 2 x =65
x = 31
Hence Mike's son age is 31 years
Answer : B
Answer: (B) 31 years
Question: A big container is 30% full with water. If 9 liters of water is added, the container becomes 3/4 full. What is the capacity of the big container?
(A) 20 liters
(B) 40 liters
(C) 45 liters
(D) 54 liters
(E) 60 liters
Rationale: A big container is 30% full with water and after 9 liters of water is added, the container becomes 75% full. Hence these 9 liters account for 45% of the container, which means that the capacity of it is 9/0.45=20 liters.
OR: if the capacity of the container is x liters then: 0.3x+9=0.75x --> x=20 liters.
Answer: A.
Answer: (A) 20 liters
Question: When a person aged 39 is added to a group of n people, the average age increases by 2. When a person aged 15 is added instead, the average age decreases by 1. What is the value of Q?
(A)  7
(B)  8
(C)  9
(D)  10
(E)  11
Rationale: A simple and elegant solution.
As addition of 39, shifts mean by 2, and addition of 15, shifts mean by 1 to the other side, we have the mean lying between 3915, and in a ratio of 2:1
39-15 = 24
24 divide by 3 is 8.
Meaning mean of the n terms is 15+8 = 39-16 = 23
Now, from first statement, When a person aged 39 is added to a group of n people, the average age increases by 2.
Q*23 +39 = 25*(Q+1)
Q = 7
Ans. (A)
Answer: (A)  7