mathewhe/aqua_rat huggingface dataset:
Question: In a division sum, the remainder is 6 and the divisor is 5 times the quotient and is obtained by adding 22 to the thrice of the remainder. The dividend is
(A) 74
(B) 166
(C) 86
(D) 92
(E) 98
Rationale: Divisor = (6 * 3) + 22 = 40
5 * Quotient = 40
Quotient = 8.
Dividend = (Divisor * Quotient) + Remainder
Dividend = (20 * 8) + 6 = 166.
B)
Answer: (B) 166
Question: If the sides of a triangle are 26 cm, 22 cm and 10 cm, what is its area?
(A) 120
(B) 110
(C) 130
(D) 140
(E) 150
Rationale: The triangle with sides 26 cm, 22 cm and 10 cm is right angled, where the hypotenuse is 26 cm.
Area of the triangle = 1/2 * 22 * 10 = 110 cm2
Answer: Option B
Answer: (B) 110
Question: The original price of a suit is $100. The price increased 20%, and after this increase, the store published a 20% off coupon for a one-day sale. Given that the consumers who used the coupon on sale day were getting 20% off the increased price, how much did these consumers pay for the suit?
(A) $88
(B) $96
(C) $100
(D) $106
(E) $110
Rationale: 0.8*(1.2*100) = $96
The answer is B.
Answer: (B) $96
Question: If x, y, and z are positive integers and x = 5y = 9z, then the least possible value of x + y - z is
(A) 33
(B) 40
(C) 49
(D) 61
(E) 84
Rationale: x + y - z = x/5 + x - x/9
= (45 + 9 - 5 )x/45 = 49x/45
49 is not divisible by 45, so for least value, x = 45
C
Answer: (C) 49
Question: A pump can fill a tank with water in 3 hours. Because of a leak, it took 3 1/3 hours to fill the tank. The leak can drain all the water of the tank in?
(A) 17 hr
(B) 19 hr
(C) 30 hr
(D) 14 hr
(E) 16 hr
Rationale: Work done by the tank in 1 hour
= (1/3 - 3 1/3)
= 1/30 Leak will empty the tank in 30 hrs.
Answer:C
Answer: (C) 30 hr
Question: If z is a multiple of 9402, what is the remainder when z^2 is divided by 9?
(A) 0
(B) 2
(C) 4
(D) 6
(E) 8
Rationale: The sum of the digits is 9+4+2=15.
Thus 3 is a factor of 9402, so 3 is a factor of z.
Then 3^3 = 9 is a factor of z^2.
Then the remainder when z^2 is divided by 9 is 0.
The answer is A.
Answer: (A) 0
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) 2:3
(B) 4:3
(C) 6:7
(D) 9:16
(E) 10:8
Rationale: Explanation:
Let us name the trains A and B.
Then, (A's speed) : (B's speed)
= √b : √a = √16 : √9 = 4:3
ANSWER IS B
Answer: (B) 4:3
Question: What amount does Kiran get if he invests Rs.8000 at 10% p.a. compound interest for four years, compounding done annually?
(A) 9688
(B) 9687
(C) 9685
(D) 9682
(E) 11713
Rationale: A= P{1 + R/100}n
=> 8000{1 + 10/100}4 = Rs.11713
Answer:E
Answer: (E) 11713
Question: The area of a square is equal to three times the area of a rectangle of dimensions 25 cm * 27 cm. What is the perimeter of the square?
(A) 180 cm
(B) 190 cm
(C) 170 cm
(D) 150 cm
(E) 160 cm
Rationale: Area of the square = s * s = 3(25 * 27)
=> s = 3 * 5 * 3 = 45 cm
Perimeter of the square = 4 * 45 = 180 cm.
Answer: A
Answer: (A) 180 cm
Question: Two numbers are respectively 20% and 25% more than a third number. The percentage that is first of the second is?
(A) 98%
(B) 56%
(C) 96%
(D) 964%
(E) 16%
Rationale: I II III
120 125 100
125----------120
100-----------? => 96%
Answer:C
Answer: (C) 96%
Question: If n > 0 , which of the following must be true?
I 2n - 1 > 0
II n - n^2 < 0
III n^2 > 1
(A) I only
(B) II only
(C) none
(D) I and II only
(E) III only
Rationale: I. True for all values of n except 1
When n = 1 ; n^2 = 1
II. True for all values of n except 1
When n = 1 ; n - n^2 = 1 - 1 =>0
III	True for all values of n
Hence the correct answer will be (C)
Answer: (C) none
Question: Ranjani can buy watches at a price of X dollars per watch, which she marks up by a certain percentage before selling. If she makes a total profit of T by selling N watches, then in terms of X and T and N, what is the percent of the markup from her buy price to her sell price?
(A) 100T-X
(B) 100T/NX
(C) 100TX/N
(D) 100TX
(E) 100N/TX
Rationale: Algebraic Solution:If she makes a total profit of T for N watches, then that must be a profit of T/N for each watch. That must be the markup above cost on each watch, the amount of the increase. Well, percent increase = (amount of increase)/(starting amount) x 100% = (T/N)/X *100 = 100T/(NX)
Answer : B
Answer: (B) 100T/NX
Question: The ratio of buses to cars on River Road is 1 to 17. If there are 80 fewer buses than cars on River Road, how many cars are on River Road?
(A) 40
(B) 85
(C) 60
(D) 30
(E) 20
Rationale: B/C=1/17
C-B=80.........> B=C-80
(C-80)/C=1/17
Testing answers. Clearly Eliminate ACDE
Put C=85.........> (85-80)/85=5/85=1/17
Answer: B
Answer: (B) 85
Question: David paid $7,000 for 100 shares of stock X and $5,000 for 100 shares of stock Y. He later sold the same shares of both stocks, gaining 3/4 the amount he paid for stock Y. If the prices he had paid for the stocks had been reversed and everything else remained the same, then the net result would have been:
(A) A Gain of 1.67 times as much
(B) A Gain of 1.4 times as much
(C) A Gain of 2 times as much
(D) A Gain of 1.6 times as much
(E) A Gain of 1.7 times as much
Rationale: A = 7000; B = 5000; Profit = (3/4)*5000 = 3750
After prices are reversed:
A = 5000; B =7000; Profit = (3/4)*7000 =5250
5250 --> Gain of 1.4 times 3750
Answer: B
Answer: (B) A Gain of 1.4 times as much
Question: In a manufacturing plant, it takes 36 machines 4 hours of continuous work to fill 6 standard orders. At this rate, how many hours of continuous work by 72 machines are required to fill 12 standard orders?
(A) 4
(B) 6
(C) 8
(D) 9
(E) 12
Rationale: the choices give away the answer..
36 machines take 4 hours to fill 8 standard orders..
in next eq we aredoubling the machines from 36 to 72, but thework is not doubling(only 1 1/2 times),= 4*48/72*12/6 = 4
Ans A
Answer: (A) 4
Question: One hour after Yolanda started walking from X to Y, a distance of 10 miles, Bob started walking along the same road from Y to X. If Yolanda's walking rate was 3 miles per hour and Bobт's was 4 miles per hour, how many miles had Bob walked when they met?
(A) 24
(B) 23
(C) 22
(D) 21
(E) 4
Rationale: When B started walking Y already has covered 3 miles out of 10, hence the distance at that time between them was 10-3=7 miles.
Combined rate of B and Y was 3+4=7 miles per hour, hence they would meet each other in 7/7=1 hours. In 6 hours B walked 1*4=4 miles.
Answer: E.
Answer: (E) 4
Question: The second angle of a triangle is 45° more than the smallest angle. The third angle is three times
the smallest. How many degrees are there in each angle?
(A) L=6/W=18
(B) L=18/W=6
(C) L=7/W=19
(D) L=19/W=7
(E) L=10/W=20
Rationale: We are looking for three angles.
! 1 - x
! 2 - x + 45
! 3 - 3x
You would not be able to solve this problem unless you knew that the sum of the interior angles
of a triangle is 180°.
! 1 + ! 2 + ! 3 = 180°
x + x + 45 + 3x = 180°
5x + 45 = 180°
5x = 135°
x = 27°
That means the first angle is 27°, the second angle is 27 + 45 or 72°, and the third angle is 3 times
27 or 81°.
Try this on your own. The length of a rectangle is three times the width and its perimeter is 48 ft.
Find the length and width. The answers are length is 18 and the width is 6 ft.
correct answer B
Answer: (B) L=18/W=6
Question: A basket contains 9 apples, of which 1 is spoiled and the rest are good. If we select 2 apples from the basket simultaneously and at random, what is the probability that the 2 apples selected will include the spoiled apple?
(A) 2/3
(B) 2/5
(C) 2/7
(D) 2/9
(E) 2/11
Rationale: The total number of ways to choose 2 apples is 9C2 = 36
The number of ways that include the spoiled apple is 8C1 = 8
P(the spoiled apple is included) = 8/36 = 2/9
The answer is D.
Answer: (D) 2/9
Question: A jogger running at 10 km/hr along side a railway track is 340 m ahead of the engine of a 120 m long train running at 46 km/hr in the same direction. In how much time will the train pass the jogger?
(A) 76 sec
(B) 67 sec
(C) 98 sec
(D) 46 sec
(E) 23 sec
Rationale: Speed of train relative to jogger = 46 - 10 = 36 km/hr.
= 36 * 5/18 = 10 m/sec.
Distance to be covered = 340 + 120 = 460 m.
Time taken = 460/10 =46 sec.
Answer:D
Answer: (D) 46 sec
Question: Manish, Rahul and Bharti have some stones with each of them. Five times the number of stones with Rahul equals seven times the number of stones with Manish while five times the number of stones with Manish equals seven times the number of stones with Bharti. What is the minimum number of stones that can be there with all three of them put together?
(A) 113
(B) 109
(C) 93
(D) 97
(E) 66
Rationale: Explanation :
Let the stones with Manish, rahul and Bharti be m,r and b respectively.
Given,
=>5r=7m and 5m=7b.
=>25r=35m and 35m=49b.
=>25r=35m=49b=k.
=>r/49=m/35=b/25.
The least possible integral values for r,m,b will be r=49, m=35 and b=25.
=>Total=49+35+25=109.
Answer : B
Answer: (B) 109
Question: A football matches has been organized in such a fashion, every participating team plays a match against every other team once and only once.
If 36 matches are totally played, how many teams participated?
(A) 7
(B) 8
(C) 9
(D) 10
(E) 11
Rationale: For a match u need 2 teams.
Suppose there are totally 'n'teams.
Now we have to choose 2 teams out of 'n' teams.
nC2 = 36;
Solve to get n=9.
n(n-1)/2 = 36
9(9-1)/2 = 36
9(8)/2 = 36
72/2 = 36
So, answer is 9 If 36 matches are totally played.
ANSWER:C
Answer: (C) 9
Question: A sum of salary is distributed among A,B,C,D in the proportion of 2:3:4:6. If D gets $700 more than C, what is the B's share?
(A) $1050
(B) $2500
(C) $3000
(D) $3400
(E) $8000
Rationale: Let the shares of A,B,C,D are 2x,3x,4x,6x
6x-4x = 700
x = 350
B's share = 3x = $1050
Answer is A
Answer: (A) $1050
Question: A rectangular cube has a volume of 6 cubic feet. If a similar cube is twice as long, twice as wide, and twice as high, then the volume, in cubic feet of such cube is?
Choices
(A) 24
(B) 48
(C) 64
(D) 80
(E) 100
Rationale: Lets say the sides of the rectangular cube are x, y and z. Problem states volume is 6.
i.e,
x*y*z = 6 .
If every side is increased twice as before. then new volume is
2x*2y*2z = 8*(x*y*z) = 8*6 = 48.
Answer is B
Answer: (B) 48
Question: Little John had $5.10. He spent $1.05 on sweets and gave to his two friends $1.00 each. How much money was left?
(A) $2.15
(B) $2.05
(C) $2.45
(D) $2.25
(E) $2.85
Rationale: John spent and gave to his two friends a total of
1.05 + 1.00 + 1.00 = $3.05
Money left
5.10 - 3.05 = $2.05
Answer :B
Answer: (B) $2.05
Question: Every person at a birthday party either wants candy or a wants cake, but not both. The ratio of people who want cake to people who want candy is 9 to 6 . If 9 people decided they wanted candy instead of cake, the ratio of people who want cake to people who want candy will be 1 to 1. How many people could be at the party?
(A) 60
(B) 50
(C) 90
(D) 45
(E) Both C and D
Rationale: By checking the answer choices:
Since we have an initial ratio of 9:6, the total count should be divisible by 15.
A. 60/15=4, Cake People = 36, Candy People = 24, Since 36-9 is not equal to 24+9 this can not be the answer.
B. Out, Since not divisible by 15.
C. 90/15=6, Cake People = 54, Candy People = 36, Since 54-9 is equal to 36+9, this is the correct answer.
D. 45/15=3, Cake People = 27, Candy People = 18, Since 27-9 is not equal to 18+9 this as well can not be the answer.
E. Since choice D is not correct, choice E is also not correct.
C is the correct answer.
Answer: (C) 90
Question: A man rows his boat 65 km downstream and 45 km upstream, taking 2 1/2 hours each time. Find the speed of the stream?
(A) 5 kmph
(B) 4 kmph
(C) 9 kmph
(D) 8 kmph
(E) 1 kmph
Rationale: Speed downstream = d/t = 65/(2 1/2) = 26 kmph
Speed upstream = d/t = 45/(2 1/2) = 18 kmph
The speed of the stream = (26 - 18)/2 = 4 kmph
Answer:B
Answer: (B) 4 kmph
Question: The volume of a rectangular swimming pool is 840 cubic meters and water is flowing into the swimming pool. If the surface level of the water is rising at the rate of 0.5 meters per minute, what is the rate T, in cubic meters per minutes, at which the water is flowing into the swimming pool?
(A) 0.125
(B) 0.25
(C) 0.5
(D) 0.75
(E) Not enough information to determine the rate
Rationale: The correct answer is E.
There are not enough info to answer the question.
A 840 cubic meters rectangle is built from: height*length*width.
From the question we know the volume of the pool and the filling rate.
A pool can have a height of 10*width8.4*length10 and have a volume of 840 cubic meters, and it can have a height of 1 meter, width of 100 meters and length of 8.4. In both cases the pool will fill up in a different rate = E
Answer: (E) Not enough information to determine the rate
Question: A big container is 40% full with water. If 28 liters of water is added, the container becomes 3/4 full. What is the capacity of the big container in liters?
(A) 68
(B) 72
(C) 76
(D) 80
(E) 84
Rationale: 28 liters is 35% of the capacity C.
28 = 0.35C
C = 28/0.35 = 80 liters.
The answer is D.
Answer: (D) 80
Question: Two trains are running in opposite directions with the same speed. If the length of each train is 120 m and they cross each other in 6 sec, then the speed of each train is?
(A) 30
(B) 31
(C) 72
(D) 25
(E) 24
Rationale: Let the speed of each train be x m/sec.
Then, relative speed of the two trains = 2x m/sec.
So, 2x = (120 + 120)/6 => x = 20
Speed of each train = 20 m/sec.
= 20 * 18/5 =72km/hr.
Answer: Option C
Answer: (C) 72
Question: In a certain series, each term is m greater than the previous term. If the 19th term is 760 and the 16th term is 700, what is the first term?
(A) 200
(B) 300
(C) 400
(D) 450
(E) 500
Rationale: a + 18m = 760 (17th term)
a + 15m = 700 (16th term)
You get a = 400 and m = 20
Answer: C
Answer: (C) 400
Question: Working at a constant rate, P can finish a job in 4 hours. Q, also working at a constant rate, can finish the same job in 20 hours. If they work together for 3 hours, how many more minutes will it take P to finish the job, working alone at his constant rate?
(A) 12
(B) 15
(C) 20
(D) 21
(E) 24
Rationale: Each hour they complete 1/4 + 1/20 = 3/10 of the job.
In 3 hours, they complete 3(3/10) = 9/10 of the job.
The time for P to finish is (1/10) / (1/4) = (2/5) hour = 24 minutes
The answer is E.
Answer: (E) 24
Question: 7+2+2^2+2^3+2^4+2^5=？
(A) (2^3-1)(2^3+1)
(B) 2^6+5
(C) 2^5-1
(D) 2^5+1
(E) 2^5-2
Rationale: From 7+2+2^2+2^3+2^4+2^5=69,
2^6+5=69
the correct answer is B.
Answer: (B) 2^6+5
Question: Q-1) Of the 84 parents who attended a meeting at a
school, 35 volunteered to supervise children during
the school picnic and 11 volunteered both to supervise
children during the picnic and to bring refreshments to
the picnic. If the number of parents who volunteered
to bring refreshments was 3 times the number of
parents who neither volunteered to supervise children
during the picnic nor volunteered to bring
refreshments, how many of the parents volunteered to
bring refreshments?
(A) 25
(B) 36
(C) 22
(D) 42
(E) 45
Rationale: i used the following formula: total = group1 + group2 + neither - both
using the information from the question stem, we have:
84 total people
35 who supervise (group1)
x who neither supervise nor bring refreshments
3x people who bring refreshments (group2)
11 who supervise AND bring refreshments (both)
therefore...
84 = 35 + 3x + x - 11
solving, we get x = 15.
since we want the value of those who bring refreshments AND supervise:
1.5(15) = 22
answer is C
Answer: (C) 22
Question: A student committee that must consists of 4 members is to be formed from a pool of 8 candidates. How many different committees are possible
(A) 5
(B) 8
(C) 70
(D) 56
(E) 336
Rationale: Out of 8 people, any 4 can be selected for a committee. So 8c4=70 is the answer
C
Answer: (C) 70
Question: A car travelling with 5/7 of its actual speed covers 42 km in 1 hr 40 min 48 sec. Find the actual speed of the car.
(A) 55 km/hr.
(B) 25 km/hr.
(C) 65 km/hr.
(D) 35 km/hr.
(E) 45 km/hr.
Rationale: D
35 km/hr.
Time taken = 1 hr 40 min 48 sec = 1 hr 40 4/5 min. = 126/75 hrs.
Let the actual speed be x km/hr.
Then, (5/7)x X 126/75 = 42
--> x = 35 km/hr.
Answer: (D) 35 km/hr.
Question: In an election between the two candidates, the candidates who gets 70% of votes polled is winned by 280 vote’s majority. What is the total number of votes polled?
(A) 750
(B) 700
(C) 800
(D) 850
(E) None of these
Rationale: Explanation:
Note: majority (40 %) = difference in votes polled to win (70 %) & defeated candidates (30 %)
40 % = 70 % - 30 %
40% -----> 280 (40*7 = 280)
100% -----> 700 (100*7 = 700)
Answer: Option B
Answer: (B) 700
Question: If $120 invested at a certain rate of simple interest amounts to $240 at the end of 3 years,How much will $150 amount to at the same rate of interest in 6 years?
(A) $190
(B) $180
(C) $200
(D) $340
(E) $450
Rationale: 120 amounts to 240 in 3 years.
i.e (principal + interest ) on 120 in 3 years = 240
120 + 120*(r/100)*(3) = 240 => r = 100/3
150 in 6 years = principal + interest
= 150 + 150*(r/100)*(6)
= 450
Answer is E.
Answer: (E) $450
Question: A man bought an article and sold it at a gain of 5 %. If he had bought it at 5% less and sold it for Re 3 less, he would have made a profit of 10%. The C.P. of the article was
(A) 344
(B) 218
(C) 200
(D) 600
(E) 211
Rationale: Explanation:
Let original Cost price is x
Its Selling price = (105/100) * x = 21x/20
New Cost price = (95/100) * x = 19x/20
New Selling price = (110/100 )* (19x/20 )= 209x/200
[(21x/20) - (209x/200)] = 3
=> x = 600
Answer: D) Rs 600
Answer: (D) 600
Question: Find the least number of five digits which is exactly divisible by 12, 15 and 18?
(A) 10080
(B) 1080
(C) 10025
(D) 10050
(E) 10024
Rationale: LCM = 180
180) 10000 (55
9900
---------
100
10000 + 180 - 100 = 10080
ANSWER A
Answer: (A) 10080
Question: A sum fetched a total simple interest of $4151.25 at the rate of 9 p.c.p.a. in 5 years. What is the sum?
(A) $8829
(B) $2840
(C) $6578
(D) $7782
(E) $8928
Rationale: E
8928
Principal
= $100 x 4151.25/9 x 5
= $415125/45
= $8928.
Answer: (E) $8928
Question: You have only 1 kg weight. You have to weight 31kg. Min number of measurements you have to done ?
(A) 21R
(B) 33R
(C) 35R
(D) 31R
(E) 38R
Rationale: You can do it in 5 steps.
1,2,4,8,16
Asume stone as S (Left Side) weight of 1kg as T (Right Side)
Move 1T to the same side as S and, Left Side is S+1T, Now weight 2T
Move 2T to the same side as S and, against S+3T, Now weight 4T
Move 4T to the same side as S and, against S+7T, weight 8T
Move 8T to the same side as S and, against S+15T, weight on right Side is 16T
15R + 16R = 31R.
ANSWER:D
Answer: (D) 31R
Question: If a tire rotates at 400 revolutions per minute when the car is traveling 168km/h, what is the circumference of the tire?
(A) 2
(B) 1
(C) 7
(D) 3
(E) 5
Rationale: 400 rev / minute = 400 * 60 rev / 60 minutes
= 24,000 rev / hour
24,000 * C = 168,000 m : C is the circumference
C = 7 meters
correct answer C
Answer: (C) 7
Question: Every second Saturday and all Sundays are holidays. How many working days will be there in a
month of 30 days beginning on a Saturday?
(A) 24
(B) 23
(C) 18
(D) 21
(E) 22
Rationale: Explanation :
Mentioned month has begins on a Saturday and has 30 days
Sundays = 2nd, 9th, 16th, 23rd, 30th
=> Total Sundays = 5
Second Saturdays = 8th and 22nd
Total Second Saturdays = 2
Total Holidays = Total Sundays + Total Second Saturdays = 5 + 2 = 7
Total days in the month = 30
Total working days = 30 - 7 = 23
Answer : Option B
Answer: (B) 23
Question: A car runs 10,000 miles using 5 tyres interchangeably. to have equal worn out by all tyres,how many miles each tyre should have run?
(A) 5000
(B) 8000
(C) 4000
(D) 3000
(E) 2000
Rationale: for 5 tyres running interchangeably 10,000 miles the car runs
for 1 tyre=10000/5=2000
as you all know i suppose the car has 4 tyre
to have equal worn out by 4 tyres we need=2000*4=8000
ANSWER:B
Answer: (B) 8000
Question: In a fuel station the service costs $1.75 per car, every liter of fuel costs 0.45$. Assuming that a company owns 12 cars and that every fuel tank contains 55 liters and they are all empty, how much money total will it cost to fuel all cars?
(A) 318$
(B) 380$
(C) 420$
(D) 450$
(E) 480$
Rationale: 12*1.75 + 0.45*12*55 = 318 hence - A
Answer: (A) 318$
Question: Rs.2500 is divided into two parts such that if one part be put out at 5% simple interest and the other at 6%, the yearly annual income may be Rs.120. How much was lent at 5%?
(A) 2333
(B) 2777
(C) 3000
(D) 1000
(E) 2871
Rationale: (x*5*1)/100 + [(2500 - x)*6*1]/100 = 120
X = 3000
Answer: C
Answer: (C) 3000
Question: January 1, 2007 was Monday. What day of the week lies on Jan. 1, 2008?
(A) Monday
(B) Tuesday
(C) Wednesday
(D) Friday
(E) Sunday
Rationale: The year 2007 is an ordinary year. So, it has 1 odd day.
day of the year 2007 was Monday
day of the year 2008 will be 1 day beyond Monday
Hence, It will be Tuesday. answer : B
Answer: (B) Tuesday
Question: What is 78% of 4/5?
(A) 6.9
(B) 69.0
(C) 0.6845
(D) 0.624
(E) 0.69
Rationale: 78%*(4/5)=0.78*0.8=0.624
Answer :D
Answer: (D) 0.624
Question: Addison High School’s senior class has 300 boys and 240 girls. If 30% of the boys did not attend the college then 70% of the total class attended college, what percentage of the girls class did not attend college?
(A) 70
(B) 45
(C) 50
(D) 46
(E) 30
Rationale: % of boy attending the college = 100-30 = 70%
Number of boys attending the college : 0.70*300 = 210
Total people = 300+240 = 540
Total number of students attending the college: 0.70*540 = 378
number of girls attending the college = 378-210 = 168
number of girls not attending the college = 240-168 = 72
% of girls not attending = 72/240 = 30%. E is the correct answer
Answer: (E) 30
Question: The radius of a wheel is 22.4 cm. What is the distance covered by the wheel in making 300 resolutions.
(A) 421 m
(B) 422 m
(C) 423 m
(D) 424 m
(E) 425 m
Rationale: In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 300 resolutions.
= 300 * 2 * 22/7 * 22.4
= 42200 cm
= 422 m
Answer: B
Answer: (B) 422 m
Question: A “Sophie Germain” prime is any positive prime number p for which 2p + 1 is also prime. The product of all the possible units digits of Sophie Germain primes greater than 4 is
(A) 3
(B) 7
(C) 189
(D) 227
(E) 234
Rationale: In that case, the Sophie prime numbers greater than 5 are 7,11,23,47,59, .. which yields units digit as 1,3,7 and 9
Product would be 1 x 3 x 7x9 =189 Answer should be C.
Answer: (C) 189
Question: If 0 < e< 1 < f, which of the following must be true?
(A) 1 < 1/e< 1/f
(B) 1/e< 1 < 1/f
(C) 1/e< 1/f< 1
(D) 1/f< 1 < 1/e
(E) 1/f< 1/e< 1
Rationale: 0<e<1<f. Let e=1/2 and f=2
Substituting values:
A. 1<2<1/2 ---Wrong
B. 2<1< 1/2 ---Wrong
C. 2<1/2<1 ---Wrong
D. 1/2<1<2 ---Correct
E. 1/2<2<1 ---Wrong
Hence answer is D
Answer: (D) 1/f< 1 < 1/e
Question: Andrew started saving at the beginning of the year and had saved $180 by the end of the year. He continued to save and by the end of 2 years had saved a total of $540. Which of the following is closest to the percent increase in the amount Andrew saved during the second year compared to the amount he saved during the first year?
(A) 11%
(B) 25%
(C) 44%
(D) 56%
(E) 100%
Rationale: Percent increase in the amount Andrew saved during the second year compared to the amount he saved during the first year.
Percentage Change = ( Change in value / Original value ) * 100
Percentage Change = [ (Saving in 2nd year - Saving in 1st year ) / Saving in 1st year ] * 100
Saving in 2nd year + Saving in 1st year = 540
Saving in 2nd year + 180 = 540
Saving in 2nd year = 540 - 180 = 360
Change in Value = 360 - 180 = 180
Original Value = 180
Percentage Increase = (180 / 180 ) * 100 = 100%..... Answer E......
Answer: (E) 100%
Question: A rectangular field has to be fenced on three sides leaving a side of 20 feet uncovered. If the area of the field is 680 sq. feet, how many feet of fencing will be required?
(A) 95
(B) 92
(C) 82
(D) 88
(E) 97
Rationale: AREA OF FIELD = 680 SQ FEET
LENGTH OF ADJ SIDES 20 FEET AND 680/20 = 34 FEET
REQ LENGTH OF THE FENCING = 20 + 34 + 34 = 88 FEET
ANSWER D
Answer: (D) 88