mathewhe/aqua_rat huggingface dataset:
Question: The average height of 35 boys in a class was calculated as 184cm. It has later found that the height of one of the boys in the class was wrongly written as 166 cm whereas his actual height was 106 cm. Find the actual average height of the boys in the class (Round off your answer to two decimal places).?
(A) 178.27 cm
(B) 182.29 cm
(C) 978.29 cm
(D) 178.89 cm
(E) 176.29 cm
Rationale: Calculated average height of 35 boys = 184 cm.
Wrong total height of 35 boys = 184 * 35 cm. This was as a result of an actual height of 106 cm being wrongly written as 166 cm. Correct total height of 35 boys = 184 cm - (166 cm - 106 cm)/35
= 184 cm - 60 /35 cm
= 184 cm - 1.71 cm = 182.29 cm.
Answer: B
Answer: (B) 182.29 cm
Question: The distance between 2 cities A and B is 1000km. A train starts from A at 1 p.m. and travels towards B at 100 km/hr. Another starts from B at 2 p.m. and travels towards A at 150 km/hr. At what time do they meet?
(A) 11am.
(B) 6p.m.
(C) 3pm.
(D) 2p.m.
(E) 1p.m.
Rationale: Suppose they meet x hrs after 1 p.m.
Distance moved by first in x hrs + Distance moved by second in (x-1)hrs = 1000
100x + 150 (x-1) = 1000
x = 4.60 = 5 hrs
They meet at 1+5 = 6 p.m.
Answer is B
Answer: (B) 6p.m.
Question: in a tennis match the probability for A to win the match is 2/3 and he has to win 3 sets to win the match so what is the probability for A to win the match
(A) 182/243
(B) 172/243
(C) 162/243
(D) 192/243
(E) 292/243
Rationale: The sequence of winning as follows:
Sequence Probability
----------------- -----------
W W L W 8/81
W W L L W 8/243
W W W 8/27
W L L W W 8/243
W L W L W 8/243
W L W W 8/81
L L W W W 8/243
L W L W W 8/243
L W W L W 8/243
L W W W 8/81
Thus, by adding all the above probabilities, we get the probability for A to win the match as : 192/243
ANSWER:D
Answer: (D) 192/243
Question: Two trains 140 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is?
(A) 10
(B) 11
(C) 12
(D) 10.8
(E) 13
Rationale: Relative speed = 60 + 40 = 100 km/hr.
= 100 * 5/18 = 250/9 m/sec.
Distance covered in crossing each other = 140 + 160 = 300 m.
Required time = 300 * 9/250 = 54/5 = 10.8 sec.
Answer: Option D
Answer: (D) 10.8
Question: A small pool filled only with water will require an additional 300 gallons of water in order to be filled to 80% of its capacity. If pumping in these additional 300 gallons of water will increase the amount of water in the pool by 30%, what is the total capacity of the pool in gallons?
(A) 1000
(B) 1250
(C) 1300
(D) 1600
(E) 1625
Rationale: Since pumping in additional 300 gallons of water will increase the amount of water in the pool by 30%, then initially the pool is filled with 1,000 gallons of water.
So, we have that 1,000 + 300 = 0.8*{total} --> {total} = 1,625.
Answer: E.
Answer: (E) 1625
Question: For all integers a and b, a%b = (a + b)(a - b). If 7%x = 13, then which of the following could be a value of x?
(A) -6
(B) -5
(C) 2
(D) 3
(E) 6
Rationale: 7%x = (7+x)(7-x)
49-x^2 = 13
x^2 = 36
x=-6,6
Ans: A
Answer: (A) -6
Question: A firm is comprised of partners and associates in a ratio of 2:61. If 75 more associates were hired, the ratio of partners to associates would be 4:137. How many partners are currently in the firm?
(A) 12
(B) 14
(C) 16
(D) 18
(E) 20
Rationale: The ratio 2:61 = 4:122 so the ratio changed from 4:122 to 4:137.
137-122 = 15 which is 1/5 of the increase in 75 associates.
The ratio changed from 20:610 to 20:685.
Thus the number of partners is 20.
The answer is E.
Answer: (E) 20
Question: The distance that light travels in one year is approximately 5,870,000,000,000 miles. The distance light travels in 10000 years is:
(A) 111 × 1827 miles
(B) 999× 1238 miles
(C) 587 x 10^14 miles
(D) 247 × 1012 miles
(E) 587 × 1012 miles
Rationale: The distance of the light travels in one years is:
5,870,000,000,000 = 587 * 10 ^10
The distance of the light travels in 10000 years is:
= 587 * 10^10 x 10 ^4 = 587 x 10^14 miles
Answer :C
Answer: (C) 587 x 10^14 miles
Question: John bought a shirt on sale for 25% off the original price and another 25 % off the discounted price. If the final price was $16, what was the price before the first discount?
(A) $28.44
(B) $38.44
(C) $48.44
(D) $58.44
(E) $68.44
Rationale: let x be the price before the first discount. The price after the first discount is
x - 25%x (price after first discount)
A second discount of 25% of the discounted price after which the final price is 16
(x - 25%x) - 25%(x - 25%x) = 16
Solve for x
x = $28.44
correct answer A
Answer: (A) $28.44
Question: On a game show, a contestant is given three keys, each of which opens exactly one of three identical boxes. The contestant assigns each key to one of the boxes and wins the amount of money contained in any box that is opened by the key assigned to it. The first box contains $1.5, the second $150, and the third $1500. What is the probability that a contestant will win more than $1500?
(A) 1/9
(B) 2/3
(C) 1/6
(D) 1/3
(E) 1/2
Rationale: Let's call the boxes that contain $1.5, $150, and $1500, respectively, Box A, Box B, Box C. These are opened, respectively, by Key A, Key B, and Key C.
We want to know the probability of winning more than $1500. Notice that if the distribution of keys is:
Box A = Key B
Box B = Key A
Box C = Key C
then the contestant wins exactly $1500, not more than $1500. The only configuration that leads to winning more than $1000 is:
Box A = Key A
Box B = Key B
Box C = Key C
i.e., getting all three keys correct. That's the only way to be more than $1500. So, really, the question can be rephrased: what is the probability of guessing the order of keys so that each key matches the correct box?
Well, for a set of three items, the number of possible permutations is 3! = 3*2*1 = 6.
Of those 6 possible permutations, only one of them leads to all three keys being paired with the right box. So, the answer is
Probability = 1/6
Answer = C
Answer: (C) 1/6
Question: The three competitors in a race have to be randomly chosen from a group of three men and three women. How many different such trios contain at least one woman?
(A) 13
(B) 15
(C) 17
(D) 19
(E) 21
Rationale: The total number of ways to choose three runners 6C3 = 20
The number of trios with only males is 3C3 = 1
The number of trios which include at least one woman is 19.
The answer is D.
Answer: (D) 19
Question: For a race a distance of 224 meters can be covered by P in 28 seconds and Q in 32 seconds. By what distance does P defeat Q eventually?
(A) 32m
(B) 38m
(C) 34m
(D) 31m
(E) 36m
Rationale: Explanation:
This is a simple speed time problem. Given conditions:
=>Speed of P= 224/28 = 8m/s
=>Speed of Q=224/32 = 7m/s
=>Difference in time taken = 4 seconds
Therefore, Distance covered by P in that time= 8m/s x 4 seconds = 32 metres
ANSWER: A
Answer: (A) 32m
Question: If B and C are digits and 8BC is a 3-digit number that is divisible by 7, which of the following is a possible product of B and C?
(A) 1
(B) 2
(C) 5
(D) 6
(E) 14
Rationale: Try with the options -
A. If BC = 1 , both B and C must be 1
B. If BC = 2 , either B or C must be 1 or 2 ; In that case sum of the digits will be 8 + 1 + 2 = 11 which is not divisible by 3
C. If BC = 5 , either B or C must be 1 or 5 ; In that case sum of the digits will be 8 + 1 + 5 = 14 which is not divisible by 3
D. If BC = 6 , then we can have the following possibilities
i. Either B or C must be 2 or 3 ; In that case sum of the digits will be 8 + 2 + 3 = 13 which is not divisible by 3
ii. Either B or C must be 1 or 6 ; In that case sum of the digits will be 8 + 1 + 6 = 15 which is divisible by 3
E. If BC = 14 , then either B or C must be 2 or 7 ; In that case sum of the digits will be 8 + 2 + 7 = 17 which is not divisible by 7
Thus answer is (E)
Answer: (E) 14
Question: Ratio of two numbers x and y is 3:7. If x is increased by 50% and y is increased by 2 then the new ratio becomes 1:2. What is the ratio 2y:(2x+6)
(A) 16:15
(B) 4:5
(C) 7:12
(D) 4:9
(E) 6:5
Rationale: Let:
x = 3n
y = 7n
4.5n/(7n+5) = 1/2
9n = 7n+2
n = 1
So, x =3; y=7
2y/(2x+6) = 14/12 = 7:6
Answer = C
Answer: (C) 7:12
Question: The difference between a two-digit number and the number after interchanging the position of the two digits is 27. What is the difference between the two digits of the number?
(A) 4
(B) 6
(C) 3
(D) Cannot be determined
(E) None of these
Rationale: Let the two-digit no. be l0x + y.
Then, (10x + y) â€“ (10y + x) = 27
or, 9(x â€“ y) = 27
or, x â€“ y = 3
Answer C
Answer: (C) 3
Question: The cost price of a radio is Rs.1500 and it was sold for Rs.1230, find the loss %?
(A) 18
(B) 99
(C) 77
(D) 66
(E) 55
Rationale: 1500 ---- 270
100 ---- ? => 18%
Answer: A
Answer: (A) 18
Question: The speed of a train is 90 kmph. What is the distance covered by it in 10 minutes?
(A) 277
(B) 266
(C) 300
(D) 767
(E) 211
Rationale: 1/2:1/3:1/4 = 6:4:3
3/13*1300 = 300
Answer:C
Answer: (C) 300
Question: When positive integer m is divided by positive integer n, the remainder is 12. If m/n = 24.2, what is the value of n ?
(A)  120
(B)  60
(C)  30
(D)  24
(E)  12
Rationale: n = decimal part of 24.2 * remainder i.e. (12)
Hence 0.2 * n = 12
n = 60.B
Answer: (B)  60
Question: Q is an much younger than R as he is older than T. If the sum of the ages of R and T is 50 years,what is definitely the difference between R and Q's age ?
(A) 15 years
(B) 25 years
(C) 2 years
(D) 1 year
(E) cannot be determined.
Rationale: R-Q=R-T
Q=T. also, R+T=50
R+Q=50.
so,(R-Q) cannot be determined.
Answer is E
Answer: (E) cannot be determined.
Question: There are 15 members in a family. it takes 180 days for a women to complete the work, however man completes in 120 days. They take 17days to complete the work if men work on alternate days and women work every third day. if all of them started together on the 1st day, then how many men are there in the family
(A) 9
(B) 10
(C) 11
(D) 12
(E) 13
Rationale: Let the number of men be m and so the number of women = 15-m
Out of 17 days, men and women work together on 1,4,7,10,13,16th days (Total of 6 days) from the start.
Men work on alternate days, that is 1,3,5,7,9,11,13,15,17th days (Total of 9 days).
Let the total work be 360 units (LCM of 180 and 120).
1 man does 360/120 = 3 units per day
1 woman does 360/180 = 2 units per day
Based on above facts,
Total work by men + women in these 17 days = 360 units
m*9*3 + (15-m)*6*2 = 360,
27m + 180 -12m = 360, Solving m=12.
Num of men = 12
ANSWER:D
Answer: (D) 12
Question: In a mixture of milk and water, the proportion of milk by weight was 80%. If, in a 180 gm mixture, 36 gms of pure milk is added, what would be the percentage of milk in the mixture formed?
(A) 83.33
(B) 84
(C) 85
(D) 76
(E) 80
Rationale: Percentage of milk in the mixture formed = [80/100 (180) + 36] / (180 + 36) * 100% = (144 + 36)/216 * 100% = 5/6 * 100% = 83.33%.
ANSWER A
Answer: (A) 83.33
Question: A person purchased a TV set for Rs. 1600 and a DVD player for Rs. 625. He sold both the items together for Rs. 31150. What percentage of profit did he make?
(A) 1250%
(B) 35%
(C) 1300%
(D) 1200%
(E) None of these
Rationale: The total CP = Rs. 1600 + Rs. 625= Rs. 2225 and SP = Rs. 31150
Profit(%) = (31150 - 2225)/2225* 100 = 1300%
ANSWER:C
Answer: (C) 1300%
Question: A 340-liter solution of Kola is made from 75% water, 5% concentrated Kola and the rest is made from sugar. If 3.2 liters of sugar, 12 liter of water and 6.8 liters of concentrated Kola were added to the solution, what percent of the solution is made from sugar?
(A) 6%.
(B) 7.5%.
(C) 19.6%.
(D) 10.5%.
(E) 11%.
Rationale: Denominator:
340+12+3.2+6.8=362
Numerator:
340(1-.75-.05)+3.2
340(0.2)+3.2
68+3.2
71.2
Ratio:
71.2/362=0.196
Answer: C
Answer: (C) 19.6%.
Question: There are three vessels of equal capacity .Vessel A contains Milk and water in the ratio 4:3 ;Vessel B contains Milk and water in the ratio 2:1 and Vessel C contains Milk and water in the ratio 3:2 .If the mixture in all the three vessels is mixed up.What will be the ratio of milk and water ?
(A) 9:6
(B) 3:2
(C) 118:126
(D) 193:122
(E) 201:132
Rationale: m=portion of milk in solution
m=(4/7+2/3+3/5)/3➡193/315
315-193=122
122/315=portion of water in solution
ratio of milk to water=193/122
ANSWER:D
Answer: (D) 193:122
Question: The Avg age of a class of 22 subject areas in 21 years. The avg increased by one when the lecturer’s age also involved. What is the age of the Lecturer?
(A) 48 years
(B) 45 years
(C) 46 years
(D) 47 years
(E) 44 years
Rationale: E
44 years
Average * Subject Areas = Total Age
So => 21 years x 22 numbers = 462 years … (1)
=> 22 years x 23 numbers = 506 years … (2)
Therefore Lecturer’s age = Eqn(2) – Eqn(1)
= 506 – 462
= 44 Years.
Answer: (E) 44 years
Question: If log 27 = 1.437, then the value of log 9 is:
(A) 0.934
(B) 0.945
(C) 0.954
(D) 0.958
(E) 0.987
Rationale: log 27 = 1.437
log (33 ) = 1.437
3 log 3 = 1.437
log 3 = 0.479
log 9 = log(32 ) = 2 log 3 = (2 x 0.479) = 0.958.
Answer: Option D
Answer: (D) 0.958
Question: Find the least number of complete years in which a sum of money put out at 25% compound interest will be more than double of itself?
(A) 12
(B) 33
(C) 6
(D) 4
(E) 7
Rationale: 4 years
Answer:D
Answer: (D) 4
Question: A three-digit code for certain locks uses the digits 0, 1, 2, 3, 4, 5, 6, 7, 8 according to the following constraints. The first digit cannot be 0 or 1, the second digit must be 0 or 1, and the second and third digits cannot both be 0 in the same code. How many different codes are possible?
(A) 119
(B) 152
(C) 160
(D) 168
(E) 176
Rationale: The first digit can be filled in 7 ways
For second digit , it can either be 0 or 1
Case 1 -
If second digit is 1 ,Third digit can take 10 values
number of codes = 7 * 1 * 9 = 63
Case 2 -
If second digit is 0,Third digit can take 8 values ( Third digit can't be zero)
number of codes = 7 * 1 * 8= 56
Total number of codes = 119
Answer A
Answer: (A) 119
Question: A envelop weight 8.5 gm,if 850 of these envelop are sent with an advertisement mail. How much wieght?
(A) 6.6kg
(B) 7.225kg
(C) 6.7kg
(D) 6.9kg
(E) 7.8kg
Rationale: 850*8.5
7225.0gm
7.225kg
ANSWER:B
Answer: (B) 7.225kg
Question: Find the ratio in which rice at Rs.7.20 a kg be mixed with rice at Rs.5.70 a kg to produce a mixture worth Rs.6.30 a kg?
(A) 1 : 3
(B) 2 : 3
(C) 3 : 4
(D) 4 : 5
(E) None of these
Rationale: Solution
Required ratio = 60 : 90 = 2 : 3
Answer B
Answer: (B) 2 : 3
Question: A tank is filled in 10 hours by three pipes A, B and C. Pipe C is twice as fast as B and B is twice as fast as A. How much time will pipe A alone take to fill the tank?
(A) 70 hours
(B) 30 hours
(C) 35 hours
(D) 50 hours
(E) 40 hours
Rationale: Efficiency of pipes A,B,C =1:2:4
Therefore, in 10 hours, part of the tank filled by A =17
Therefore, pipe A alone requires 10×7=70 hours to fill the tank.
Answer: Option A
Answer: (A) 70 hours
Question: In a psychology school the grade of the students is determined by the following method: At the end of the first year the grade equals to twice the age of the student. From then on, the grade is determined by twice the age of the student plus half of his grade from the previous year. If Joey’s grade at the end of the first year is 32, what will be his grade at the end of the third year?
(A) 44
(B) 51
(C) 62
(D) 75
(E) 80
Rationale: Cool question!
There's a lot of information given here, so let's eat slow here.
Joey scores a 32 at the end of his first year. That means that he's currently 16 years old (since given per instruction, after the first year one's grade is determined by doubling his/her age).
Now, come next year, or his second year at this psychology school, he's technically 17 years old. To find out the second year's grade, we want to double his age PLUS half of his previous grade.
Well, his second year is then going to be 17(2) + 16 = 50.
Now let's tackle the main question: what's his grade going to be the third year?
Well, he will be at an age of 18 on his third year at this school. Again, to find out his third year's grade, you're going to double his age (18x2), plus half of his previous year's grade (as calculated for his second year, his grade is 50; therefore, 50/2)
Having said that, the final answer would be 18(2) + 50/2 = 36 + 25 = 51 --> (B)
Answer: (B) 51
Question: Bill likes long bike rides. On one ride, he goes biking for seven hours. For the first hour, he bikes
at a speed of 16 miles per hour. For the next two hours, he bikes at a speed of 12 miles per
hour. He remembers biking 112 miles over the seven hours. Compute the average speed, in miles
per hour, Bill biked during the last four hours of his trip.
(A) 18
(B) 14
(C) 22
(D) 27
(E) 35
Rationale: He has to travel 112 - 16 - 12 * 2 = 72 miles in 4 hours
72 / 4 = 18 miles per hour
correct answer A
Answer: (A) 18
Question: An urn contains 5 red, 6 blue and 8 green balls. 4 balls are randomly selected from the urn, find the probability that the drawn ball are 1 blue and 3 red?
(A) 1/969
(B) 2/969
(C) 4/969
(D) 5/323
(E) 21/789
Rationale: Sample space = no. of ways 4 balls were drawn from urn = 19C4 = 3876
No. ways 1 blue balls and 3 red were drawn from bag = 6C1 * 5C3 = 60
Probability = 60 / 3876 = 5/323
Ans - D
Answer: (D) 5/323
Question: 45% of 750 - 25% of 480 = ?
(A) 216
(B) 217.5
(C) 236.5
(D) 245
(E) None
Rationale: Sol.
Given expression = (45/100 x 750) - (25/100 x 480)
= (337.50 - 120)
= 217.50
Answer B
Answer: (B) 217.5
Question: If a number between 0 and 1 is selected at random, which of the following will the number most likely be between?
(A) 0 and 3/20
(B) 3/20 and 1/5
(C) 1/5 and 1/4
(D) 1/4 and 3/10
(E) 3/10 and 1/2
Rationale: The number will most likely be between the largest range.
A. 0 and 3/20 --> range 3/20;
B. 3/20 and 4/20 --> range 1/20;
C. 4/20 and 5/20 --> range 1/20;
D. 5/20 and 6/20 --> range 1/20;
E. 6/20 and 10/20 --> range 4/20.
Answer: E.
Answer: (E) 3/10 and 1/2
Question: Sam bought 2Q steaks for W dollars. Jerome buys R steaks for a 50% discount, how much will the steaks cost him in cents?
(A) 50RW/Q.
(B) 50QR/W.
(C) 25RQ/W.
(D) 25RW/Q.
(E) RW/(4Q).
Rationale: Sam bought 2Q steaks for W dollars, so 1 steak = W/2Q
Jerome buys R steaks for a 50% discount: r* (W/4Q)
in cents the answer will be : r* (100 W/4Q)= 25 RW/ Q=D
Answer: (D) 25RW/Q.
Question: A man sells a car to his friend at 11% loss. If the friend sells it for Rs.54000 and gains 20%, the original C.P.of the car was :
(A) Rs.25561.80
(B) Rs.37500.80
(C) Rs.50561.80
(D) Rs.60000
(E) None of these
Rationale: Explanation:
S.P = Rs.54,000. Gain earned = 20%
C.P = Rs.[100/120Ã—54000]
=Rs. 45000
This is the price the first person sold to the second at at loss of 11%.
Now S.P = Rs.45000 and loss = 11%
C.P. Rs.[100/89Ã—45000]= Rs.50561.80.
Correct Option : C
Answer: (C) Rs.50561.80
Question: Louie takes out a three-month loan of $3000. The lender charges him 10% interest per month compounded monthly. The terms of the loan state that Louie must repay the loan in three equal monthly payments. To the nearest dollar, how much does Louie have to pay each month?
(A) A)333
(B) B)383
(C) C)402
(D) D)1206
(E) E)483
Rationale: Here's the calculation for that case, assume monthly payment is X.
After 1st month: (3000)(1.1)-X = 3300-X
After 2nd month: (3300-X)(1.1)-X = 3630-2.21X
After 3rd month: (3630-2.21X)(1.1)-X = 3993-3.31X
Now, the amount after the last payment in 3rd month must bring the total to 0. Hence:
3993-3.31X = 0
X = 3993/3.31 = 1206.34
Answer D
Answer: (D) D)1206
Question: If rupee one produces rupees nine over a period of 30 years, find the rate of simple interest?
(A) 10 %
(B) 20 %
(C) 30 %
(D) 22 %
(E) 28 %
Rationale: 9 = (1*30*R)/100
R = 30 %
ANSWER:C
Answer: (C) 30 %
Question: A bag contains 6 white marbles and 6 black marbles. If each of 6 girls and 6 boys randomly selects and keeps a marble, what is the probability that all of the girls select the same colored marble?
(A) 1/35
(B) 1/10
(C) 1/3
(D) 1/462
(E) 1/252
Rationale: first, total ways to select for all boys and girls, i.e 12!/(6!*6!) = 12*11*10*9*8*7/6*5*4*3*2 =924
then there are one two way girls can have all same colors, either white or black.
The number of ways in which 6 girls can select 6 white balls = 6C6 = 1
The number of ways in which 6 girls can select 6 black balls = 6C6 = 1
Therefore, total favorable outcomes/total outcomes = 2/924 = 1/462
D
Answer: (D) 1/462
Question: Two trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 16 hours respectively. The ratio of their speeds is?
(A) 4:6
(B) 4:3
(C) 4:9
(D) 4:4
(E) 4:1
Rationale: Let us name the trains A and B.
Then, (A's speed) : (B's speed)
= √b : √a = √16 : √9 = 4:3
Answer:B
Answer: (B) 4:3
Question: Bag A contains red, white and blue marbles such that the red to white marble ratio is 1:3 and the white to blue marble ratio is 2:3. Bag B contains red and white marbles in the ratio of 1:4. Together, the two bags contain 18 white marbles. How many red marbles could be in bag A?
(A) 2
(B) 3
(C) 4
(D) 6
(E) 8
Rationale: 6 is the answer.
Bag A-
R:W:B = 2:6:9
Let W in bag A be 6K
Bab B -
R:W = 1:4
Let W in bag B be 4P
W = 18 = 6K+4P
=> K =1, P=3
Total Red's in bag A will be 2K = 2
A
Answer: (A) 2
Question: A lemonade stand sold only small and large cups of lemonade on Tuesday. 3/5 of the cups sold were small and the rest were large. If the large cups were sold for 7/2 as much as the small cups, what fraction of Tuesday's total revenue was from the sale of large cups?
(A) (a) 7/16
(B) (b) 7/10
(C) (c) 10/21
(D) (d) 17/35
(E) (e) 1/2
Rationale: This problem is very good example how easy and quick plug-in method might be.
Let the total # of cups be 10.
# of small cups sold 3/5*10=6;
# of large cups sold 10-6=4;
Let the price of small cup be $6, then the price of larges cup would be 7/2*6=$21;
Revenue from small cups: 6*$6=$36;
Revenue from large cups cups: 4*$21=$84;
Fraction of total revenue from large cups: 84/(36+84)=7/10.
Answer: B.
Answer: (B) (b) 7/10
Question: Ravi can do a piece of work in 30 days while Prakash can do it in 40 days. In how many days will they finish it together?
(A) 14 1/7 days
(B) 11 1/7 days
(C) 16 1/7 days
(D) 17 1/7 days
(E) 24 1/7 days
Rationale: D
17 1/7 days
1/30 + 1/40 = 7/120
120/7 = 17 1/7 days
Answer: (D) 17 1/7 days
Question: The average weight of 8 person's increases by 2.5 kg when a new person comes in place of one of them weighing 66 kg. What might be the weight of the new person?
(A) 56 kg
(B) 90 kg
(C) 86 kg
(D) Data inadequate
(E) None of these
Rationale: C
86 kg
Total weight increased = (8 x 2.5) kg = 20 kg.
Weight of new person = (66 + 20) kg = 86 kg.
Answer: (C) 86 kg
Question: A vessel of capacity 90 litres is fully filled with pure milk. Nine litres of milk is removed from the vessel and replaced with water. Nine litres of the solution thus formed is removed and replaced with water. Find the quantity of pure milk in the final milk solution?
(A) 15.6 litres
(B) 72.9 litres.
(C) 22.8 litres
(D) 16 litres
(E) 92.3litres
Rationale: Explanation:
Let the initial quantity of milk in vessel be T litres.
Let us say y litres of the mixture is taken out and replaced by water for n times, alternatively.
Quantity of milk finally in the vessel is then given by [(T - y)/T]n * T
For the given problem, T = 90, y = 9 and n = 2.
Hence, quantity of milk finally in the vessel
= [(90 - 9)/90]2 (90) = 72.9 litres.
Answer:B
Answer: (B) 72.9 litres.
Question: In a card game, a combination of two kings beats all others. If Jose is the first to draw from a standard deck of 52 cards, what is the probability that he wins the game with the best possible combination?
(A) 1/221
(B) 13/221 C
(C) 2/52
(D) 3/51
(E) 4/51
Rationale: The best possible combination is the case when he wins in his first two draws
There are 52 cards in a deck of cards with 4 kings in it.
Probability of first card to be king = 4/52
Probability of Second card to be king = 3/51
Probability of Best possible case = (4/52)*(3/51) = 1/221
Answer: A
Answer: (A) 1/221
Question: Three numbers are in the ratio 1 : 3 : 6 and their average is 100. The largest number is :
(A) 180
(B) 98
(C) 27
(D) 21
(E) 22
Rationale: Explanation:
Let the numbers be x, 3x and 6x, Then, (x + 3x + 6x ) / 3 = 100
=> 10x = 100*3
=> x = 30
Largest number 6x = 6*30 = 180
Answer: A
Answer: (A) 180