mathewhe/aqua_rat huggingface dataset:
Question: The total number of digits used in numbering the pages of a book having 266 pages is
(A) 732
(B) 990
(C) 109
(D) 130
(E) 690
Rationale: Total number of digits
= (No. of digits in 1- digit page nos. + No. of digits in 2-digit page nos. + No. of digits in 3- digit page nos.)
= (1 x 9 + 2 x 90 + 3 x 167) = (9 + 180 + 501) = 690.
ANSWER:E
Answer: (E) 690
Question: A rectangular-shaped carpet that measures x feet by y feet is priced at $12. What is the cost of the carpet, in dollars per square yard? (1 square yard = 9 square feet)
(A) 108/(xy)
(B) 90xy
(C) xy/90
(D) xy/10
(E) 10/(xy)
Rationale: The area of the carpet in feet is xy.
The area in square yards is xy / 9.
The price per square yard is 12 / (xy/9) = 108/(xy).
The answer is A.
Answer: (A) 108/(xy)
Question: If it takes 4 identical printing presses exactly 4 hours to print 8,000 newspapers, how long would it take 2 of these presses to print 6,000 newspapers?
(A) 6 hours
(B) 8 hours
(C) 7 hours
(D) 5 hours
(E) 9 hours
Rationale: 4 presses - 8,000 newspapers - 4 hours ;
2 presses - 4,000 newspapers - 4 hours ; (240 mins)
2 presses - 6,000 newspapers - 240/4000*6000 = 360 mins = 6 hrs
Answer : A
Answer: (A) 6 hours
Question: Three numbers are in the ratio 2:3:5 and their H.C.F is 30. The numbers are:
(A) 2, 3, 5
(B) 5, 10, 15
(C) 10, 20, 30
(D) 60, 90, 150
(E) 12, 24, 39
Rationale: Let the required numbers be 2x, 3x and 5x. Then, their H.C.F = x. So, x = 30.
The numbers are 60, 90, 150.
ANSWER:D
Answer: (D) 60, 90, 150
Question: TOM traveled the entire 100 miles trip. If he did the first 50 miles of at a constant rate 20miles per hour and the remaining trip of at a constant rate 50 miles per hour, what is the his average speed, in miles per hour?
(A) 28.36 mph
(B) 26.55 mph
(C) 28.57 mph
(D) 25.56 mph
(E) 28.45 mph
Rationale: avg speed = total distance/ total time = (d1+d2)/(t1+t2) = (50+50) / ((50/20)+(50/50)) = 60*2/3 = 28.57 mph
C
Answer: (C) 28.57 mph
Question: Two trains, each 100 m long, moving in opposite directions, cross other in 10 sec. If one is moving twice as fast the other, then the speed of the faster train is?
(A) 76 km/hr
(B) 66 km/hr
(C) 48 km/hr
(D) 67 km/hr
(E) 22 km/hr
Rationale: Let the speed of the slower train be x m/sec.
Then, speed of the train = 2x m/sec.
Relative speed = ( x + 2x) = 3x m/sec.
(100 + 100)/10 = 3x => x = 20/3.
So, speed of the faster train = 40/3 = 40/3 * 18/5 = 48 km/hr.
Answer:C
Answer: (C) 48 km/hr
Question: In the first twelve overs of a cricket game, the run rate was only 4.6. What should be the run rate in the remaining 38 overs to reach the target of 249 runs?
(A) 5.75
(B) 5.1
(C) 6.5
(D) 6.75
(E) None of these
Rationale: Explanation :
Required run rate = (249 - (4.6 x 12))/38
= 193.8/38
= 5.1
Answer : B
Answer: (B) 5.1
Question: A large research project was scheduled over the course of a 100-month period, and a budget of $250,000 was allotted for the course of the entire project. After 10 months, the project had spent $26,000. Was the project at this point over budget or under budget, and by how much?
(A) under, $4200
(B) under, $1200
(C) under, $700
(D) over $1800
(E) over $1000
Rationale: cost per month = 250,000/100 = 2,500.
Now, multiply by seven months: 10*($2500) = $25,000. That would be the budgeted amount, the amount theoretically supplied to the project. The real amount spent is more than this, so it is over budget.
$25,000 â€“ #26,000= $1000
Answer = (E)
Answer: (E) over $1000
Question: The sum of all consecutive odd integers from −25 to 35, inclusive, is
(A) 130
(B) 135
(C) 155
(D) 195
(E) 235
Rationale: The sum of the odd numbers from -25 to +25 is 0.
Let's add the remaining numbers.
27+29+31+33+35 = 5(31) = 155
The answer is C.
Answer: (C) 155
Question: The present ages of three persons are in proportions 4:7:9. Eight years ago, the sum of their ages was 136. Find their present ages.
(A) 20, 28
(B) 28, 36
(C) 35, 45
(D) 56, 72
(E) of these
Rationale: Let their present ages be 4x, 7x and 9x years respectively.
Then, (4x - 8) + (7x - 8) + (9x - 8) = 136
20x = 160 => x = 8
Their present ages are 32, 56 and 72 years respectively.
ANSWER:D
Answer: (D) 56, 72
Question: The distance between Delhi and Mathura is 110 kms. A starts from Delhi with a speed of 20 kmph at 7 a.m. for Mathura and B starts from Mathura with a speed of 25 kmph at 8 p.m. from Delhi. When will they meet?
(A) 10 a.m
(B) 10 a.m
(C) 90 a.m
(D) 18 a.m
(E) 20 a.m
Rationale: D = 110 – 20 = 90
RS = 20 + 25 = 45
T = 90/45 = 2 hours
8 a.m. + 2 = 10 a.m.
Answer:B
Answer: (B) 10 a.m
Question: A man can row downstream at 28 kmph and upstream at 16 kmph. Find the speed of stream ?
(A) 8
(B) 5
(C) 4
(D) 6
(E) 3
Rationale: Let the speed of the man in still water and speed of stream be x kmph and y kmph respectively.
Given x + y = 28 --- (1)
and x - y = 16 --- (2)
From (1) & (2) 2x = 44 => x = 22, y = 6.
Answer:D
Answer: (D) 6
Question: An auction house charges a commission of 18% on the first $50,000 of the sale price of an item, plus 10% on the amount of of the sale price in excess of $50,000. What was the price of a painting for which the house charged a total commission of $24,000?
(A) $115,000
(B) $160,000
(C) $200,000
(D) $240,000
(E) $365,000
Rationale: Say the price of the house was $x, then 0.18*50,000+0.1*(x-50,000)=24,000 --> x=$200,000 (18% of $50,000 plus 10% of the amount in excess of $50,000, which is x-50,000, should equal to total commission of $24,000).
Answer: C.
Answer: (C) $200,000
Question: A certain list of 200 test scores has an average (arithmetic mean) of 80 and a standard deviation of d, where d is positive. Which of the following two test scores, when added to the list, must result in a list of 202 test scores with a standard deviation less than d ?
(A)  80 and 80
(B)  80 and 85
(C)  80 and 90
(D)  85 and 85
(E)  85 and 90
Rationale: The standard deviation of a set shows how much variation there is from the mean, how widespread a given set is. So, a low standard deviation indicates that the data points tend to be very close to the mean, whereas high standard deviation indicates that the data are spread out over a large range of values.
So when we add numbers, which are far from the mean we are stretching the set making SD bigger and when we add numbers which are close to the mean we are shrinking the set making SD smaller.
According to the aboveadding two numbers which are closest to the mean will shrink the set most, thus decreasing SD by the greatest amount.
Closest to the mean are 80 and 80 (actually these numbers equal to the mean) thus adding them will definitely shrink the set, thus decreasing SD most.
Answer: a.
Answer: (A)  80 and 80
Question: A farmer travelled a distance of 61 km in 9 hours. He travelled partly on foot at 4 km/hr and partly on bicycle at 9 km/hr. The distance travelled on foot is :
(A) 1 hr 16 min
(B) 1 hr 17 min
(C) 1 hr 18 min
(D) 1 hr 19 min
(E) None
Rationale: Sol.
Let the distance travelled on foot be x km.
then, distance travelled on bicycle = (61 - x) km.
So, x/4 + (61-x)/9 = 9
⇔ 9x + 4 (61 - x) = 9 * 36
⇔ 5x = 80
⇔ x = 16 km.
Answer A
Answer: (A) 1 hr 16 min
Question: A and B can do a piece of work in 4 days, B and C in 5 days, C and A in 6 days. How long will C take to do it?
(A) 140/11 days
(B) 120/7 days
(C) 100/13 days
(D) 80/7 days
(E) 60/7 days
Rationale: 2c = 1/5 + 1/6 – 1/4 = 7/60
c = 7/120 => 120/7 days
The answer is B.
Answer: (B) 120/7 days
Question: A store has announced a 10% rebate for the entire day. If Amy only has Rs.500 in her pocket and needs Rs.20 to get back home, how many bottles of juice can she buy at the most from the store, with each juice costing Rs.50 before the discount?
(A) 8
(B) 9
(C) 10
(D) 11
(E) 12
Rationale: Explanation:
Amy has 500 - 20 = 480 to spend.
Each juice costs 50 * (1 - 10%) = 50 * 0.90 = 45.
480 / 45 = 10.67
Since you cannot buy juice in halves, Amy can buy 10 bottles at the most.
Correct Option : C
Answer: (C) 10
Question: A grocer has a sale of Rs. 5700, Rs. 8550, Rs. 6855, Rs. 3850 for 4 consecutive months. How much sale must he have in the fifth month so that he gets an average sale of Rs. 7800?
(A) s. 14991
(B) s. 49930
(C) s. 14045
(D) s. 14999
(E) s. 14578
Rationale: Total sale for 4 months = Rs. (5700 + 8550+ 6855 + 3850 ) = Rs.24955
Required sale = Rs. [ (7800 x 5) - 24955 ]
= Rs. (39000 - 24955)
= Rs. 14045
Option C
Answer: (C) s. 14045
Question: For every $20 that a billionaire spends, a millionaire spends the equivalent of 20 cents. For every $2 that a millionaire spends, a yuppie spends the equivalent of $1. The ratio of money spent by a yuppie, millionaire, and billionaire can be expressed as
(A) 1 : 4 : 400
(B) 1 : 2 : 200
(C) 20 : 4 : 1
(D) 100 : 4 : 1
(E) 400 : 4 : 1
Rationale: B.........M........Y
20.....0,20......Y
B.........2........1
What I did first was to turn 0.20 to 2 (by multiplying by 10), so that it is easy to find the LCM. This led me to this:
B.........M........Y
200.....2.........Y
B........20......10
Then I multiplied every row by 20 (the LCM of 2 and 20), which led me to this:
B.........M........Y
2000...20.......10
Then I got rid of the extra zero, and in the correct order this is Y:M:B=1:2:200
ANS B
Answer: (B) 1 : 2 : 200
Question: A train 100 m long crosses a platform 200 m long in 15 sec; find the speed of the train?
(A) 94 kmph
(B) 58 kmph
(C) 72 kmph
(D) 94 kmph
(E) 59 kmph
Rationale: D = 100 + 200 = 300
T = 15
S = 300/15 * 18/5 = 72 kmph
Answer:C
Answer: (C) 72 kmph
Question: Find the average of all prime numbers between 1 and 10
(A) 2.5
(B) 1.35
(C) 4.25
(D) 6.12
(E) 7.13
Rationale: Prime numbers between 1 and 10 are 2,3,5,7
Required average = (2+3+5+7)/4 = 17/4 = 4.25
Answer is C
Answer: (C) 4.25
Question: Bill’s compact disc player randomly plays a song, so that no song is repeated before the entire album is played. If Bill plays a disc with 13 songs, what are the chances that the third song he hears will be his favorite?
(A) 1/13
(B) 1/12
(C) 1/11
(D) 3/14
(E) 1/3
Rationale: The player plays the songs on the album at random, so there are 13 songs that can be the third one played. Only 1 of these ways will result in Bill's favorite song being the third one played.
Total outcomes ==> 13
Total positive outcomes ==> 1
Correct answer is A) 1/13
Answer: (A) 1/13
Question: The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling alongthe oundary of the park at the speed of 12 km/hr completes one round in 8 minutes, then the area of the park (in sq. m) is
(A) 124345 m
(B) 233234 m
(C) 153600 m
(D) 123567 m
(E) 168999 m
Rationale: Perimeter = Distance covered in 8 min. = 12000	x 8	m = 1600 m.
60
Let length = 3x metres and breadth = 2x metres.
Then, 2(3x + 2x) = 1600 or x = 160.
Length = 480 m and Breadth = 320 m.
Area = (480 x 320) m2 = 153600 m
C
Answer: (C) 153600 m
Question: A person travels equal distances with speeds of 2km/hr, 4km/hr, 6km/hr. and takes a total time of 11minutes. Find the total distance ?
(A) 1km
(B) 500mts
(C) 600mts
(D) 2km
(E) 250mts
Rationale: Let the each distance be x km
total distance = 3x
then total time,
(x/2)+(x/4)+(x/6) = 11/60
x=0.2
total distance = 3*0.2 = 0.6km = 600meters
correct option is C
Answer: (C) 600mts
Question: The length of a room is 5.5 m and width is 3.75 m. Find the cost of paying the floor by slabs at the rate of Rs. 1400 per sq.metre.
(A) Rs. 15,000
(B) Rs. 15,500
(C) Rs. 15,600
(D) Rs. 28,875
(E) None
Rationale: Solution
Area of the floor	= (5.5 x 3.75)m²
= 20.635m ²
Cost of paying	= Rs. (1400 x 20.625)
= Rs.28875.
Answer D
Answer: (D) Rs. 28,875
Question: The product of all the prime numbers less than 30 is closest to which of the following powers of 10?
(A) 10^9
(B) 10^8
(C) 10^7
(D) 10^6
(E) 10^9
Rationale: Quickly approximate
2, 3, 5, 7, 11, 13, 17, 19 ,23, 29
= 1*10^7 *2.3*2.9*10^9
=6.67*10^9
E
Answer: (E) 10^9
Question: The difference between a number and its two-fifth is 510. What is 10% of that number?
(A) 19
(B) 85
(C) 77
(D) 76
(E) 78
Rationale: Let the number be x. Then,
x - 2/5 x = 510
x = (510 * 5)/3 = 850
10% of 850 = 85.
Answer:B
Answer: (B) 85
Question: In a garment industry, 12 men working 8 hours per day complete a piece of work in 10 days. To complete the same work in 8 days, working 20 hours a day, the number of men required is:
(A) 4
(B) 5
(C) 6
(D) 8
(E) 9
Rationale: Explanation :
Let the required number of men be x.
Less days, More men (Indirect Proportion)
More working hrs per day, Less men (Indirect Proportion)
Days 8 : 10
Working Hrs 20 : 8 :: 12 : x
=> 8 x 20 x x = 10 x 8 x 12
=> x = 10 x 8 x 12 / (8 x 20)
=> x = 6
Answer : C
Answer: (C) 6
Question: What is the greatest integer m for which the number 40!/10^m is an integer?
(A) 7
(B) 8
(C) 9
(D) 10
(E) 11
Rationale: 10^m = 2^m*5^m.
Let's figure out how many 5's are in the prime factorization of 40!
The multiples of 5 are: 5, 10, 15, 20, 5*5, 30, 35, 40.
Thus 5^9 will divide 40! but 5^10 will not.
Clearly 2^9 will divide 40!
So m=9 is the largest possible integer.
The answer is C.
Answer: (C) 9
Question: Find the probability that a number selected from numbers 1, 2, 3,..., 20 is a prime number, when each of the given numbers is equally likely to be selected?
(A) 10/20
(B) 1/20
(C) 8/20
(D) 3/20
(E) 7/20
Rationale: Let X be the event of selecting a prime number.
X = {2, 3, 5, 7, 11, 13, 17, 19}
n(X) = 8,
n(S) = 20
Hence, the required probability is 8/20.
ANSWER:C
Answer: (C) 8/20
Question: If m= (n-1)(n+2), then what is the least possible value of m?
(A) 3
(B) -9/4
(C) 2
(D) 1
(E) 0
Rationale: Answer : B
Answer: (B) -9/4
Question: (786×74) ÷ ? = 2423.5
(A) A)24
(B) B)48
(C) C)58
(D) D)68
(E) E)48
Rationale: Explanation:
58164/x = 2423.5 => x = 58164/2423.5 = 24
Answer: Option A
Answer: (A) A)24
Question: What will come in place of the x in the following Number series? 65536, 32768, 16384, 8192, 4096, x
(A) 2048
(B) 2046
(C) 2045
(D) 2044
(E) 2043
Rationale: Go on dividing by 2 to the next number
Answer : A
Answer: (A) 2048
Question: The rate of spin of a certain gyroscope doubled every 10 seconds from the moment a particular stopwatch started. If after a minute and a half the gyroscope reached a speed of 800 meters per second, what was the speed, in meters per second, when the stopwatch was started?
(A) 25/3
(B) 25/4
(C) 25/8
(D) 25/16
(E) 25/32
Rationale: Let x be the original speed when the stopwatch was started.
In 90 seconds, the speed doubled 9 times.
2^9 * x = 800
x = (2^5 * 25) / 2^9 = 25/16
The answer is D.
Answer: (D) 25/16
Question: A ball dropped from H height and moves 80% of height each time. Total distance covered is
(A) 4H
(B) 5H
(C) 7H
(D) 9H
(E) 8H
Rationale: First time distance is H
Second time 80H/100=4H/5
similarly third time 80%of 4H/5=H(4^2)/(5^2)
and so on...
this will lead to infinite terms of geometric progression
i.e
H+2*4H/5+2*16H/25............
sum = H+ 2*4H/(5(1-4/5))=9H
ANSWER:D
Answer: (D) 9H
Question: A boat having a length 3 m and breadth 2 m is floating on a lake. The boat sinks by 1 cm when a man gets on it. The mass of the man is:
(A) 12 kg
(B) 60 kg
(C) 72 kg
(D) 85 kg
(E) 96 kg
Rationale: Volume of water displaced	= (3 x 2 x 0.01) m3
= 0.06 m3.
Mass of man	= Volume of water displaced x Density of water
= (0.06 x 1000) kg
= 60 kg.
answer :B
Answer: (B) 60 kg
Question: If each of 4 digit code is formed of integers from 1 to 50, inclusively, and each of the digits are different, how many possible codes are there?
(A) 5527200
(B) 5586300
(C) 5598600
(D) 5547800
(E) 2569800
Rationale: Code consists of 4 digits and no digit is repeated.
First digit of the code can have 50 possibilities
Second digit can have 49 possibilities
Third digit can have 48 possibilities
fourth digit can have 47 possibilities
Total number of possible codes = 50*49*48*47 = 5527200
Answer: A
Answer: (A) 5527200
Question: You have been given a physical balance and 7 weights of 40, 42, 36, 33, 47, 52 and 67 kgs. Keeping weights on one pan and object on the other, what is the maximum you can weigh less than 169 kgs.
(A) 163
(B) 166
(C) 162
(D) 164
(E) 165
Rationale: 67 + 52 + 47 = 166
Answer: E
Answer: (E) 165
Question: Chris mixed 4 pounds of raisins with 4 pounds of nuts. If a pound of nuts costs 3 times as much as a pound of raisins, then the total cost of the raisins was what fraction of the total cost of the mixture?
(A)  1/7
(B)  1/5
(C)  1/4
(D)  1/3
(E)  3/7
Rationale: 1 lbs of raisin = $1
4 lbs of raisin = $4
1 lbs of nuts = $3
4 lbs of nuts = $12
Total value of mixture = 12+4 = 16
Fraction of the value of raisin = 4/16 = 1/4
Ans:C
Answer: (C)  1/4
Question: A gets 4 times as much money as B gets, B gets only Rs.25 more then what C gets. The three gets Rs.675 in all. Find the share of B?
(A) Rs.115.66
(B) Rs.116.66
(C) Rs.125
(D) Rs.115
(E) Rs.125.66
Rationale: A+B+C = 675
A = 4B
4B+B+B-25 = 675
6B = 700
B = 116.66
ANSWER:B
Answer: (B) Rs.116.66
Question: Steve traveled the first 2 hours of his journey at 40 mph and the last 3 hours of his journey at 80 mph. What is his average speed of travel for the entire journey?
(A) 60 mph
(B) 56.67 mph
(C) 53.33 mph
(D) 64 mph
(E) 66.67 mph
Rationale: Answer
Average speed of travel = Total distance travelled/Total time taken
Total distance traveled by Steve = Distance covered in the first 2 hours + distance covered in the next 3 hours.
Distance covered in the first 2 hours = speed * time = 40 * 2 = 80 miles.
Distance covered in the next 3 hours = speed * time = 80 * 3 = 240 miles.
Therefore, total distance covered = 80 + 240 = 320 miles.
Total time taken = 2 + 3 = 5 hours.
Hence, average speed = Total distance travelled/Total time taken=320/5 = 64 miles per hour.
Choice D
Answer: (D) 64 mph
Question: what is the average of odd numbers from 1 to 79?
(A) 30
(B) 25
(C) 35
(D) 40
(E) 45
Rationale: Sum of n odd natural number is given by,
Sum of n odd natural numbers = n*n
Average of n odd natural numbers is given by,
= (n*n)/n = n.
Here,
n = Number of terms= (79 +1)/2 = 40.
So, required average = 40.
answer : D
Answer: (D) 40
Question: A SHAM bought toy at 60 for a rupee. How many for a rupee must he sell to gain 20%?
(A) 7200
(B) 200
(C) 3000
(D) 400
(E) 540
Rationale: C.P. of 60 toffees = Re. 10
S.P. of 60 toffees = 1200% of Re. 10 = Rs. 120
For Rs. 120, toffees sold = 60.
For Re. 10, toffees sold = 120*60 = 7200
Answer A
Answer: (A) 7200
Question: Two numbers are in the ratio of 5:7. If 25 be subtracted from each, they are in the ratio of 35:59. Find the numbers?
(A) 60,87
(B) 60,81
(C) 60,88
(D) 60,84
(E) 60,89
Rationale: (5x-25):(7x-25) = 35:59
x = 12 => 60,84
Answer:D
Answer: (D) 60,84
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
(B) 17 1/1
(C) 17 1/7
(D) 17 1/9
(E) 17 1/2
Rationale: Explanation:
1/20 + 1/30 - 1/40 = 7/120
120/7 = 17 1/7
Answer:C
Answer: (C) 17 1/7
Question: An electric pump can fill a tank in 3 hours. Because of a leak in the tank, it took 3 hours 30 min to fill the tank. In what time the leak can drain out all the water of the tank and will make tank empty ?
(A) 10 hours
(B) 13 hours
(C) 17 hours
(D) 21 hours
(E) 23 hours
Rationale: Explanation:
We can get the answer by subtrating work done by leak in one hour by subtraction of filling for 1 hour without leak and with leak, as
Work done for 1 hour without leak = 1/3
Work done with leak =
3 1/2=7/2
Work done with leak in 1 hr= 2/7
Work done by leak in 1 hr =1/3−2/7=1/21
So tank will be empty by the leak in 21 hours.
Option D
Answer: (D) 21 hours
Question: Two numbers N and 16 have LCM = 52 and GCF = 8. Find N.
(A) 35
(B) 26
(C) 76
(D) 87
(E) 24
Rationale: The product of two integers is equal to the product of their LCM and GCF. Hence.
16* N = 52 * 8
N = 52*8 / 16 = 26 correct answer B
Answer: (B) 26
Question: Hector runs a one-product widget shop. Each month, his fixed costs, whether he produces anything or not, amount to x dollars. The marginal cost of producing and selling one widget is a constant y dollars, regardless of the number he produces. He generally can sell widgets for q dollars each. What is the minimum number of widgets he must produce, assuming he sells every widget he produces, to break even (neither make a profit nor incur a loss) in a given month?
(A) x/(y - q)
(B) x/(q - y)
(C) x
(D) x/q
(E) x/y
Rationale: Two ways...
1) let t be the total number, so cost = t*y+x and selling price=t*q..
No profit no loss....t*y+x=t*q.....T=x/(q-y)...
B
Answer: (B) x/(q - y)
Question: A man took a loan at rate of 12% per annum simple interest. After 3 years he had to pay 5400 interest. The principal amount borrowed by him was.
(A) Rs 14000
(B) Rs 15000
(C) Rs 16000
(D) Rs 17000
(E) None of these
Rationale: Explanation:
S.I.=P∗R∗T/100
=>P=S.I.∗100/R∗T
=>P=5400∗100/12∗3=Rs15000
Option B
Answer: (B) Rs 15000
Question: If the area of a circle is 100pi square feet, find its circumference.
(A) 65 pi feet
(B) 20 pi feet
(C) 42 pi feet
(D) 18 pi feet
(E) 64 pi feet
Rationale: The area is given by pi * r * r. Hence
pi * r *r = 100 pi
r *r = 100 ; hence r = 10 feet
The circumference is given by
2 *pi *r = 2 * pi * 10 = 20 pi feet
correct answer B
Answer: (B) 20 pi feet
Question: A $500 investment and a $1,500 investment have a combined yearly return of 16 percent of the total of the two investments. If the $500 investment has a yearly return of 7 percent, what percent yearly return does the $1,500 investment have?
(A) 9%
(B) 10%
(C) 105/8%
(D) 11%
(E) 19%
Rationale: The equation we can form the question :
Return on Total Investment = Sum of individual Investments
(500+1500)(16)=(500âˆ—7)+(1500x), where x is the return on investment of 1500.
Solving the equation, we get x = 19% ( Option E )	ANSWER:E
Answer: (E) 19%
Question: Zachary is helping his younger brother, Sterling, learn his multiplication tables. For every question that Sterling answers correctly, Zachary gives him 3 pieces of candy. For every question that Sterling answers incorrectly, Zachary takes away two pieces of candy. After 9 questions, if Sterling had answered 2 more questions correctly, he would have earned 31 pieces of candy. How many of the 9 questions did Zachary answer correctly?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 10
Rationale: i got two equations:
3x-2y=25
x+y=9
3x-2(9-x)=25
3x-18+2x=25
5x=43
x=8.6 or between 8 and 9. (ANS C)
Answer: (C) 8
Question: Let Q represent a set of three distinct prime numbers. If the sum of the numbers in Q is even and x is a member of Q, then what is the least possible value that x can be?
(A) 1
(B) 2
(C) 3
(D) 5
(E) 7
Rationale: Q = p1+p2+p3= even (and all primes are distinct)
if the least prime is 2 then we have sum of Q = even.
Ans. B. 2
Answer: (B) 2
Question: Alex and Brenda both stand at point X. Alex begins to walk away from Brenda in a straight line at a rate of 2 miles per hour. One hour later, Brenda begins to ride a bicycle in a straight line in the opposite direction at a rate of R miles per hour. If R > 8, which of the following represents the amount of time, in terms of R, that Alex will have been walking when Brenda has covered twice as much distance as Alex?
(A) R-4
(B) R/(R+4)
(C) R/(R-4)
(D) 8/(R-8)
(E) 2R - 4
Rationale: Let T be the time thatAlexwill have been walking when Brenda has covered twice as much distance as Alex.
In T hours Alex will cover 4T miles;
Since Brenda begins her journey 1 hour later than Alex then total time for her will be T-1 hours, and the distance covered in that time will be R(T-1);
We want the distance covered by Brenda to be twice as much as that of Alex: 2*2T=R(T-1) --> 4T=RT-R --> T=R/(R-4).
Answer: C.
Answer: (C) R/(R-4)
Question: 24 persons can manufacture 1000 soaps in 15 days, working 7 hours a day. In how many days will 18 persons, working 5 hours a day, manufacture the same 1000 soaps?
(A) 30
(B) 28
(C) 35
(D) 14
(E) 21
Rationale: Explanation :
Solution: Let the required number of days be x.
Less persons, more days (Indirect proportion)
more working hrs per day, less days (indirect proportion)
persons 18 : 24
} : : 15 : x.
Working hrs per day, less days 5 : 7
.'. 18*5*x = 24*7*15 <=> x = 28.
Answer : B
Answer: (B) 28
Question: The diameter of a cylindrical tin is 6cm and height is 5 cm. Find the volume of the cylinder?
(A) 30 pi cc
(B) 45 pi cc
(C) 150 pi cc
(D) 180 pi cc
(E) 200 pi cc
Rationale: r = 3 h = 5
Ï€ * 3 * 3 * 5 = 45 Ï€ cc
ANSWER B
Answer: (B) 45 pi cc