mathewhe/aqua_rat huggingface dataset:
Question: Four points lie on the circumference of a circle. What is the positive difference between the number of triangles and the number of quadrilaterals that can be created by connecting these points?
(A) 3
(B) 5
(C) 6
(D) 15
(E) 20
Rationale: Number of triangles can be formed out of 6 points= 4C3=4
Number of quadrilaterals can be formed out of 6 points= 4C4=1
4-1=3.
Answer=A
Answer: (A) 3
Question: Two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 18 kmph and 21 kmph respectively. When they meet, it is found that one train has traveled 60 km more than the other one. The distance between the two stations is?
(A) 288
(B) 468
(C) 877
(D) 278
(E) 178
Rationale: 1h ----- 5
? ------ 60
12 h
RS = 18 + 21 = 39
T = 12
D = 39 * 12 = 468
Answer: B
Answer: (B) 468
Question: In a hockey championship, there are 153 matches played. Every two team played one match with each other. The number of teams participating in the championship is:
(A) 18
(B) 19
(C) 17
(D) 16
(E) 15
Rationale: Explanation :
Let there were x teams participating in the games, then total number of matches:
=>nC2.
=153
On solving, we get n=−17 and n=18.
It cannot be negative so n=18.
Answer : A
Answer: (A) 18
Question: The length of a rectangular plot is 20 metres more than its breadth. If the cost of fencing the plot @ Rs. 26.50 per metre is Rs. 6095, what is the length of the plot in metres?
(A) 333
(B) 200
(C) 230
(D) 276
(E) 1999
Rationale: Let length of plot = L meters, then breadth = L - 20 meters
and perimeter = 2[L + L - 20] = [4L - 40] meters
[4L - 40] * 26.50 = 6095
[4L - 40] = 6095 / 26.50 = 230
4L = 270
L = 270/4= 67.5 meters.
Answer: C
Answer: (C) 230
Question: John's grade was 80th percentile of the 100 grades for his class. Of the 60 grades from another class, 20 were higher than John's, and the rest were lower. If no other grade was the same as John's grade, then John's grade was what percentile of the grades of the two classes of two classes combined?
(A) 72nd
(B) 75th
(C) 83rd
(D) 85th
(E) 94th
Rationale: 72nd/75th/83rd/85th/94th
Correct option: B
Answer: (B) 75th
Question: The total of the ages of Mahesh, Suresh, Ramesh is 111years. Ten years ago, the ratio of their ages was 2:3:4. What is the present age of Mahesh?
(A) 32years
(B) 46years
(C) 42years
(D) 35years
(E) 30years
Rationale: Let ages of Mahesh, Suresh, Ramesh 10years ago be 2x,3x,4x
2x+10 + 3x+10 +4x+10 = 111
x = 9
Ramesh present age = 4*9+10 = 46 years
Answer is B
Answer: (B) 46years
Question: Ajay can walk 6km in 1 hour. In how many hours he can walk 70km?
(A) 5hrs
(B) 11.6hrs
(C) 15.6hrs
(D) 20.1hrs
(E) 30hrs
Rationale: 1 hour he walk 6km
he walk 70km in = 70/6 * 1 = 11.6hours
Answer is B
Answer: (B) 11.6hrs
Question: What is the average (arithmetic mean) of all multiples of 10 from 10 to 500 inclusive?
(A) 190
(B) 255
(C) 200
(D) 205
(E) 210
Rationale: This question can be solved with the Average Formula and 'bunching.'
We're asked for the average of all of the multiples of 10 from 10 to 500, inclusive.
To start, we can figure out the total number of terms rather easily:
1(10) = 10
2(10) = 20
...
50(10) = 500
So we know that there are 50 total numbers.
We can now figure out the SUM of those numbers with 'bunching':
10 + 500 = 510
20 + 490 = 510
30 + 480 = 510
Etc.
Since there are 50 total terms, this pattern will create 25 'pairs' of 510.
Thus, since the average = (Sum of terms)/(Number of terms), we have...
(25)(510)/(50) =
255
Final Answer:
B
Answer: (B) 255
Question: If 65% of a number is greater than 5% of 60 by 23, what is the number?
(A) 65
(B) 40
(C) 55
(D) 30
(E) 60
Rationale: Explanation:
65/100 * x - 5/100 * 60 = 23
65/100 * x - 3 = 23
65/100 * x = 26
x = 26 * 100 / 65
x = 40
Answer: Option B
Answer: (B) 40
Question: Kamal started a business investing Rs. 9000. After five months, Sameer joined with a capital of Rs. 8000. If at the end of the year, they earn a profit of Rs. 6970, then what will be the share of Sameer in the profit?
(A) Rs.2323
(B) Rs.2380
(C) Rs.2329
(D) Rs.2329
(E) Rs.2312
Rationale: Kamal : Sameer = (9000 * 12) : (8000 * 7)
= 108:56 = 27:14
Sameer's share = 6970 * 14/41
= Rs.2380.
Answer: B
Answer: (B) Rs.2380
Question: 135 liters of a mixture of milk and water contains in the ratio 3:2. How much water should now be added so that the ratio of milk and water becomes 3:4?
(A) 12 liters
(B) 32 liters
(C) 41 liters
(D) 54 liters
(E) 34 liters
Rationale: Milk = 3/5 * 135 = 81 liters
Water = 54 liters
81 : (54+P) = 3:4
162 + 3P = 324 => P = 54
54 liters of water are to be added for the ratio become 3:4.
Answer:D
Answer: (D) 54 liters
Question: Out of a classroom of 5 boys and 6 girls, the teacher randomly chooses a president for the student board, a vice president, and a secretary. What is the probability that only girls will be selected for all three positions?
(A) 2/11
(B) 2/33
(C) 4/33
(D) 8/165
(E) 19/165
Rationale: The number of ways to choose three people is 11C3=165.
The number of ways to choose three girls is 6C3=20.
P(only girls are chosen)=20/165=4/33
The answer is C.
Answer: (C) 4/33
Question: Mr. Karan borrowed a certain amount at 6% per annum simple interest for 9 years. After 9 years, he returned Rs. 8010/-. Find out the amount that he borrowed.
(A) s. 5266
(B) s. 5269
(C) s. 5228
(D) s. 5201
(E) s. 52192
Rationale: Explanation:
Let us assume Mr. Karan borrowed amount is Rs. A. (the principal)
By formula of simple interest, S.I. = PRT / 100
Where P = The principal, R = Rate of interest as a %, T = Time in years
S.I. = (P * 6 * 9)/100 = 54 P/100
Amount = Principal + S.I.
8010 = P + (54P/100)
8010 = (100P + 54P)/100
8010 = 154P/100
P = (8010 * 100)/154 = Rs. 5201.298
ANSWER: D
Answer: (D) s. 5201
Question: Find the value of x when the sum of 20x,(2x+15),(3x-12)and (12x+5) is 674?
(A) 15
(B) 12
(C) 18
(D) 20
(E) 22
Rationale: sum = 20x+(2x+15)+(3x-12)+(12x+5) = 37x+8
37x+8 = 674
x = 666/37 = 18
Answer is C
Answer: (C) 18
Question: If u > 1 and v = 2^(u −1), then 4^u =
(A) 16v^2
(B) 4v^2
(C) v^2
(D) v^2/4
(E) v^2/16
Rationale: If u > 1 and v = 2^(u −1), then 4^u
Given u>1, so let's assume u=2
v=2^(u-1) = 2^(2-1) = 2, so v=2
hence, 4^u = 4^2 = 16
only 1 ans. choice can satisfy this:
A) 16v^2 --> clearly > 16
B) 4v^2 --> 4*2^2 = 16(we can stop after this as there can be only 1 right answer)
C) v^2 --> clearly < 16
D) v^2/4 --> clearly < 16
E) v^2/16 --> clearly < 16
Ans. B) 4v^2
Answer: (B) 4v^2
Question: What is the sum of the squares of the first 20 natural numbers (1 to 20)?
(A) 2870
(B) 2000
(C) 5650
(D) 6650
(E) 7650
Rationale: n(n+1)(2n+1)/6
20(21)(21)/6
=2870
ANSWER:A
Answer: (A) 2870
Question: A deer is standing 60 meters in from the west end of a tunnel. The deer sees a train approaching from the west at a constant speed ten times the speed the deer can run. The deer reacts by running toward the train and clears the exit when the train is 33 meters from the tunnel. If the deer ran in the opposite direction it would barely escape out the eastern entrance just as the train came out of the eastern entrance. How long is the tunnel in meters?
(A) 127
(B) 132
(C) 137
(D) 142
(E) 147
Rationale: Let x be the length of the tunnel.
When the deer runs 60 meters west , the train goes 600 meters to a point 33 meters from the west entrance of the tunnel.
When the deer runs east, the deer runs x-60 meters while the train goes x + 600 + 33 meters.
x + 600 + 33 = 10(x-60)
9x = 1233
x = 137 meters
The answer is C.
Answer: (C) 137
Question: The value of (10^8-10^2)/(10^5-10^3) is closest to which of the following?
(A) 1
(B) 10
(C) 10^2
(D) 10^3
(E) 10^4
Rationale: Because the question asks for what value isclosestthe question invites approximation.
Let's look at the numerator:
10^8 - 10^2
10^8 is HUGE compared to 10^2.
So 10^8 - 10^2 is very close to 10^8 itself. (Just as 100 - 0.0001 is very close to 100 itself).
Likewise, 10^5 is HUGE compared to 10^3.
So 10^5 - 10^3 is very close to 10^5.
So we have:
10^8/10^5
or 10^(8-5) = 10^3.
Choose D.
Answer: (D) 10^3
Question: What is the units digit of (6!*4! + 6!*5!)/12?
(A) 0
(B) 3
(C) 2
(D) 1
(E) 4
Rationale: (6!*4! + 6!*5!)/12
=6!(4! + 5!)/12
=720 ( 24 + 120)/12
=(720 * 144)/12
= 720 * 12
Units digit of the above product will be equal to 0
Answer A
Answer: (A) 0
Question: A batsman scores 26 runs and increases his average from 14 to 15. Find the runs to be made if he wants top increasing the average to 19 in the same match ?
(A) 74
(B) 25
(C) 27
(D) 91
(E) 11
Rationale: Number of runs scored more to increse the ratio by 1 is 26 - 14 = 12
To raise the average by one (from 14 to 15), he scored 12 more than the existing average.
Therefore, to raise the average by five (from 14 to 19), he should score 12 x 5 = 60 more than the existing average. Thus he should score 14 + 60 = 74.
Answer: A
Answer: (A) 74
Question: The difference between the length and breadth of a rectangle is 24 m. If its perimeter is 210 m, then its area is:
(A) 1520 m2
(B) 2420 m2
(C) 2480 m2
(D) 2520 m2
(E) 2600 m2
Rationale: We have: (l - b) = 25 and 2(l + b) = 210 or (l + b) = 105
Solving the two equations, we get: l = 65 and b = 40
Area = (l x b) = (65 x 40) m2 = 2600 m2
hence E
Answer: (E) 2600 m2
Question: The average earning of a mechanic for the first-four days of a week is Rs. 18 and for the last four days is Rs. 22. If he earns Rs . 13 on the fourth day, his average earning for the whole week is ?
(A) Rs . 18.95
(B) Rs 16
(C) Rs. 21
(D) Rs. 25.71
(E) None of these
Rationale: Answer
Total earning for the week = Sum of earning of first four days + Sum of earning of last four days - Earning of 4th day
= 4 x18 + 4 x 22 -13
= Rs. 147
âˆ´ Average earning = 147 / 7
= Rs. 21
Correct Option: C
Answer: (C) Rs. 21
Question: In a race of 1000 m, A can beat by 100 m, in a race of 800m, B can beat C by 100m. By how many meters will A beat C in a race of 1000 m?
(A) 122.9 m
(B) 127.5 m.
(C) 122.2 m
(D) 222.9 m
(E) 212.5 m
Rationale: When A runs 1000 m, B runs 900 m and when B runs 800 m, C runs 700 m.
When B runs 900 m, distance that C runs = (900 * 700)/800
= 6300/8
= 787.5 m.
In a race of 1000 m, A beats C by (1000 - 787.5) = 212.5 m to C.
In a race of 1000 m, the number of meters by which A beats C = (1000 * 212.5)/1000
= 212.5 m.
Answer:E
Answer: (E) 212.5 m
Question: A grocery shop has a sale of Rs. 6635, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 6500?
(A) 4857
(B) 4184
(C) 4012
(D) 4791
(E) 5291
Rationale: Let the sale in the sixth month =x
Then
(6635+6927+6855+7230+6562+x)/6 =6500
=>6635+6927+6855+7230+6562+x =6×6500
=> 34209+x=39000
=> x=39000−34209
=4791
ANSWER:D
Answer: (D) 4791
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 $17, what was the price before the first discount?
(A) $45.10
(B) $30.22
(C) $28.44
(D) $67.54
(E) $65.23
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 17
(x - 25%x) - 25%(x - 25%x) = 17
Solve for x
x = $30.22
correct answer B
Answer: (B) $30.22
Question: When m is divided by 7, the remainder is 5. When m is divided by 13, the remainder is 6. If 1 < m < 200, what is the greatest possible value of m?
(A) 5
(B) 19
(C) 61
(D) 74
(E) 110
Rationale: Answer is E.
I started with E.110 and it fits the bill . 105 is divisible by 7 and 104 is divisible by 13. so its E.
Modular approach would be the proper way, but this worked at first attempt.
Answer: (E) 110
Question: Albert and Bob are painting rooms at constant, but different rates. Albert takes 1 hour longer than Bob to paint n rooms. Working side by side, they can paint a total of 3n/4 rooms in 4/3 hours. How many hours would it take Albert to paint 3n rooms by himself?
(A) 7
(B) 9
(C) 12
(D) D.13
(E) 15
Rationale: rate of bob to paint n rooms is n/T(bob)
rate of Albert to paint n rooms is n/T(albert).
albert paints the room 1 hour slower than bob, so T (albert) = T(bob) -1
Together they paint the 3n/5 rooms in 4/3 hours. Rate is equal to work over time
Therefore
n/x + n/x-1 = (3n/5)/(4/3) =
n/x + n/x-1 = 9n/20. Fastest way for me is to think how would make the denominator 20. 4*5 = 20 and it fits x and x-1 or you can solve the quadratic
4n/20 + 5n/20 = 9n/20. Therefore you know it takes Albert 5 hours to paint n room, since Albert's rate is n/5.
4*3 = 3n
12 = 3n.
Answer is C
Answer: (C) 12
Question: Jar X is 1/3 full of water. Jar Y, which has half the capacity of Jar X, is 1/2 full of water. If the water in Jar Y is poured into Jar X, then Jar X will be filled to what fraction of its capacity?
(A) 5/6
(B) 5/12
(C) 7/12
(D) 7/18
(E) 11/18
Rationale: Let P be the capacity of Jar X.
The amount of water in Jar Y is 1/2*P/2=P/4
Then the total amount in Jar X is P/3+P/4=7P/12
The answer is C.
Answer: (C) 7/12
Question: The ratio of the volumes of two cubes is 729 : 125. What is the ratio of their total surface areas?
(A) 81 : 21
(B) 81 : 22
(C) 81 : 24
(D) 81 : 25
(E) 81 : 29
Rationale: Ratio of the sides = 3√729 : 3√125= 9 : 5
Ratio of surface areas = 9^2 : 5^2 = 81 : 25
Answer: Option D
Answer: (D) 81 : 25
Question: There are 5 bags three of which each contains 5 white and 2 black balls, and remaining 2 bags each contains 1 white and 4 black ball; a white ball has been drawn, find the chance that it came from second group.
(A) 2/7
(B) 6/35
(C) 8/25
(D) 14/89
(E) 3/5
Rationale: Chances of selecting a white ball from group 1: 2/7----------------------Chances of selecting a white ball from group 2: 4/5
Thus combined probability of section of white ball from group 1:
3/5 x 5/7 = 3/7
Thus combined probability of section of white ball from group 2:
2/5 x 1/5 = 2/25
Out of these chances, chance of occurrence of first case : (2/25) / (3/7 + 2/25) = 14/89
D
Answer: (D) 14/89
Question: -84x19+100=?
(A) 2436
(B) 2801
(C) -1496
(D) -2071
(E) None of them
Rationale: Given exp.=-84x(20-1)+100
=-(84x20)+84+100
=-1680+184
=-1496
Answer is C
Answer: (C) -1496
Question: The first flight out of Phoenix airport had a late departure. If the next three flights departed on-time, how many subsequent flights need to depart from Phoenix on-time, for the airport's on-time departure rate to be higher than 70%?
I will see what is the quickest way to solve it then I will provide the explanation
(A) 6
(B) 7
(C) 5
(D) 10
(E) 11
Rationale: The following approach might be the easiest one and less error prone.
We need on-time departure rate to be higher than 7/10, so it should be at least 8/11, which means that 8 out of 11 flights must depart on time. Since for now 3 out of 4 flights departed on time then 8-3=5 subsequent flights need to depart on-time.
Answer: C
Answer: (C) 5
Question: A train of 24 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 4.5 km long?
(A) 4
(B) 3
(C) 5
(D) 6
(E) 9
Rationale: D = 25 * 60 + 4500 = 6000 m
T = 6000/60 * 18/5 = 360 sec = 6 mins
Answer: D
Answer: (D) 6
Question: In an election a candidate who gets 60% of the votes is elected by a majority of 900 votes. What is the total number of votes polled?
(A) A)4500
(B) B)5200
(C) C)6900
(D) D)7520
(E) E)6000
Rationale: Let the total number of votes polled be x
Then, votes polled by other candidate = (100-60)% of x = 40% of x
60% of x - 40% of x = 900
20x/100 = 900
x = 900*100/20 = 4500
Answer is A
Answer: (A) A)4500
Question: A and B invests Rs.10000 each, A investing for 8 months and B investing for all the 12 months in the year. If the total profit at the end of the year is Rs.45000, find their shares?
(A) s.17000, Rs.2500
(B) s.18000, Rs.35059
(C) s.16000, Rs.27000
(D) s.14000, Rs.25000
(E) s.18000, Rs.27000
Rationale: The ratio of their profits A:B
= 8:12 = 2:3
Share of A in the total profit
= 2/5 * 45000
= Rs.18000 Share of A in the total profit = 3/5 * 45000
= Rs.27000
Answer: E
Answer: (E) s.18000, Rs.27000
Question: The speed of a boat in still water is 20 km/hr and the rate of current is 5 km/hr. The distance traveled downstream in 15 minutes is:
(A) 9.25
(B) 5.25
(C) 7.25
(D) 6.25
(E) 5.1
Rationale: Explanation:
Speed downstream = (20+5) kmph = 25 kmph
Distance travelled = (25*(15/60)) km = 6.25 km.
ANSWER:D
Answer: (D) 6.25
Question: If 12 men and 16 boys can do a piece of work in 5 days and 13 men together will 24 boys can do it in 4 days. Compare the daily work done by a man with that of a boy.
(A) 1:1
(B) 2:1
(C) 3:1
(D) 5:1
(E) 4:1
Rationale: B
2:1
12M + 16B ----- 5 days
13M + 24B ------- 4 days
60M + 80B = 52M + 96B
8M = 16B => 1M = 2B
M: B = 2:1
Answer: (B) 2:1
Question: In how many ways can you sit 7 people on a bench if 2 of them must sit together?
(A) 720
(B) 1440
(C) 2,400
(D) 4,320
(E) 40,320
Rationale: In such questions, always tie the person that have to sit together. So we have effectively 5+1= 6 persons to arrange.
They can be arranged in 6! ways.
Now the 2 persons can themselves be arranged in 2! ways.
Total ways: 6!*2! = 1440.
B is the answer.
Answer: (B) 1440
Question: The average weight of A, B and C is 45 kg. If the average weight of A and B be 40 kg and that of B and C be 43 kg, then the weight of B is?
(A) 65 kg
(B) 26 kg
(C) 16 kg
(D) 31 kg
(E) 18 kg
Rationale: Let A, B, C represent their respective weights.
Then, we have:
A + B + C = (45 * 3) = 135 --- (i)
A + B = (40 * 2) = 80 --- (ii)
B + C = (43 * 2) = 86 --- (iii)
Adding (ii) and (iii), we get: A + 2B + C = 166 --- (iv)
Subtracting (i) from (iv), we get: B = 31
B's weight = 31 kg.
Answer: D
Answer: (D) 31 kg
Question: P and Q started a business investing Rs. 85,000 and Rs. 45,000 respectively. In what ratio the profit earned after 2 years be divided between P and Q respectively?
(A) 17:6
(B) 17:0
(C) 17:4
(D) 17:9
(E) 17:3
Rationale: P:Q = 85000 : 45000
= 17:9.
Answer: D
Answer: (D) 17:9
Question: One man or two women or three boys can do a work in 44 days then one man, one women and one boy together?
(A) 24 days
(B) 25 days
(C) 26 days
(D) 27 days
(E) 28 days
Rationale: 1 man or 2 women or 3 boys can do in 44 days.
LCM of 1,2&3 is=6,each one do the unit of work 6,3 and 2 units.add the units(6+3+2=11)
They can do the work together 44*6/11=24 days.
ANSWER:A
Answer: (A) 24 days
Question: Solve this logic number sequence puzzle by the correct digit
8080 = 6
1357 = 0
2022 = 1
1999 = 3
6666 = ?
(A) 4
(B) 2
(C) 5
(D) 7
(E) 8
Rationale: A
4
No Of circles in the number.
Answer: (A) 4
Question: A train 90 m long is running with a speed of 60 km/hr. In what time will it pass a man who is running at 6 km/hr in the direction opposite to that in which the train is going?
(A) 7
(B) 6
(C) 8
(D) 5
(E) 4
Rationale: Speed of train relative to man = 60 + 6 = 66 km/hr.
= 66 * 5/18 = 55/3 m/sec.
Time taken to pass the men = 90 * 3/55
= 5 sec.
Answer D
Answer: (D) 5
Question: It takes 7 high school students, working at identical constant individual rates, 10 hours to paint a certain house. At what time will the house be fully painted if 7 students start painting at 9:00 am and one student, working at the same rate, is added per hour starting at 4:00 pm?
(A) 4:18 pm
(B) 4:45 pm
(C) 5:12 pm
(D) 5:48 pm
(E) 6:24 pm
Rationale: Each student paints at a rate of 1/70 of the house per hour.
In 7 hours, the 7 students can paint 49/70 of the house.
From 4 pm to 5 pm, 8 students paint another 8/70 for a total of 57/70.
From 5 pm to 6 pm, 9 students paint another 9/70 for a total of 66/70.
10 students can paint the remaining 4/70 of the house in 4/10 of an hour = 24 minutes.
The house is completed at 6:24 pm.
The answer is E.
Answer: (E) 6:24 pm
Question: When tossing two coins once, what is the probability of heads on both the coins?
(A) 1/3
(B) 5/8
(C) 1/9
(D) 1/4
(E) 2/5
Rationale: Total number of outcomes possible when a coin is tossed = 2 (∵ Head or Tail)
Hence, total number of outcomes possible when two coins are tossed, n(S) = 2 × 2 = 4
(∵ Here, S = {HH, HT, TH, TT})
E = event of getting heads on both the coins = {HH}
Hence, n(E) = 1
P(E) = n(E)/n(S)=1/4
Answer is D.
Answer: (D) 1/4
Question: In the city of San Durango, 60 people own cats, dogs, or rabbits. If 30 people owned cats, 40 owned dogs, 10 owned rabbits, and 10 owned exactly two of the three types of pet, how many people owned all three?
(A) 2
(B) 5
(C) 8
(D) 12
(E) 32
Rationale: You are considering a case when cat dogs and rabbit are not exactly equal to 12 .
The solution shall be 60=30+
Answer B
Answer: (B) 5
Question: If 5^z × 5^y = (125)^4, then what two values will satisfy z and y such that it equals the value of 125^4?
(A) 1, 5
(B) 2, 3
(C) 5, 7
(D) Both A and B
(E) Neither of the Above
Rationale: 5^z × 5^y = (125)^4
5^(z+y) = 5^12
since base is same, we can equate powers:
z+y =12
There are several values that can work, (i.e. 4 and 8, 3 and 9, 1 and 11, but the only one that works in the options given is C
Ans. C) 5, 7
Answer: (C) 5, 7
Question: The volume of the sphere QQ is (dfrac{37}{64}%)less than thevolume of sphere PP and the volume of sphere RR is (dfrac{19}{27}%) less than that of sphere QQ. By what is the surface areaof sphere RR less than the surfacearea of sphere PP?
(A) 40%
(B) 50%
(C) 75%
(D) 80%
(E) 90%
Rationale: Let the volume of sphere PP be 64 parts.
Therefore volume of sphere QQ
=64−3764%=64−3764% of 6464
=64−37=27=64−37=27 parts.
The volume of RR
=27−1927×27=27−1927×27
=27−19=8=27−19=8 parts.
Volume ratio:
=P:Q:R=64:27:8=P:Q:R=64:27:8
Radius ratio:
=P:Q:R=4:3:2=P:Q:R=4:3:2
The surface area will be 16:9:516:9:5
Surface area of RR is less than the surface area of sphere PP
16k−4k=12k16k−4k=12k
Now,
=12k16k×100=12k16k×100
=75%=75%
Thus surface area of sphere RR is less than the surface area of sphere P by 75%
C
Answer: (C) 75%
Question: A train passes a station platform in 36 sec and a man standing on the platform in 20 sec. If the speed of the train is 54 km/hr. What is the length of the platform?
(A) 280 m
(B) 240 m
(C) 152 m
(D) 639 m
(E) 239 m
Rationale: Speed = 54 * 5/18 = 15 m/sec.
Length of the train = 15 * 20 = 300 m.
Let the length of the platform be x m . Then,
(x + 300)/36 = 15 => x = 240 m.
Answer:B
Answer: (B) 240 m
Question: How many days are there in x weeks x days?
(A) 7x
(B) 8x
(C) 14x
(D) 2x
(E) 1x
Rationale: Explanation:
x weeks x days = (7x + x) days = 8x days.
Answer: B
Answer: (B) 8x
Question: At the wholesale store you can buy an 8-pack of hot dogs for $1.55, a 20-pack for $3.05, and a 250-pack for $22.95. What is the greatest number of hot dogs you can buy at this store with $250?
(A)  1,108
(B)  2,100
(C)  2,628
(D)  2,124
(E)  2,256
Rationale: To maximize number of hot dogs with 250$
Total number of hot dogs bought in 250-pack = 22.95*10 =229.5$
Amount remaining = 250 - 229.5 = 20.5$
Total number of hot dogs bought in 20-pack = 3.05*6 =18.3$
Amount remaining = 20.5 - 18.3 = 2.2$
Total number of hot dogs bought in 8-pack = 1.55*1 =1.55$
Amount remaining = 2.2 - 1.55 = 0.65$
This amount is too less to buy any 8- pack .
Greatest number of hot dogs one can buy with 250 $ = 250*10+20*6+8*1 = 2628
Answer C
Answer: (C)  2,628
Question: The total age of A and B is 14 years more than the total age of B and C. C is how many years younger than A?
(A) 12
(B) 14
(C) C is elder than A
(D) Data inadequate
(E) None
Rationale: Solution
[(A+B) - (B+C)]	= 14
â€¹=â€ºA - C
= 14.
Answer B
Answer: (B) 14
Question: A merchant gains or loses, in a bargain, a certain sum. In a second bargain, he gains 350 dollars, and, in a third, loses 60. In the end he finds he has gained 200 dollars, by the three together. How much did he gain or lose bv the first ?
(A) 80
(B) 90
(C) -90
(D) -80
(E) None
Rationale: In this sum, as the profit and loss are opposite in their nature, they must be distinguished by contrary signs. If the profit is marked +, the loss must be -.
Let x = the sum required.
Then according to the statement x + 350 - 60 = 200
And x = -90.
Answer C
Answer: (C) -90