MU-NLPC/Calc-aqua_rat huggingface dataset:
The integer x is divisible by both 7 and 21. Which of the following must be an integer? Choose the correct option:
A) x/25
B) x/34
C) x/52
D) x/45
E) x/21

Solution: Prime factorization of 7 = 1*7   Prime factorization of 21= 3*7   LCM of 7 and 21 = 7 * 3= 
7 * 3 = 21
21   Therefore x/21 must be an integer   Answer x/21
Answer: E
Tanks A and E are each in the shape of a right circular cylinder. The interior of tank A has a height of 10 meters and a circumference of 8 meters, and the interior of tank E has a height of 8 meters and a circumference of 10 meters. The capacity of tank A is what percent of the capacity of tank E?  Select the correct option:
A) 75%
B) 80%
C) 100%
D) 120%
E) 125%

Solution: B.   For A, r=8/2pi. Its capacity = (4pi)^2 * 10= 160pi   For E, r=10/pi. Its capacity = (5pi)^2 *8 = 200pi   A/E = 160pi/200pi = 0.8160  /200= 
160  /200 = 4/5 = around 0.8
0.8=80%.
Answer: B
15 years hence, Rohan will be just four times as old as he was 15 years ago.How old is Rohan at present? Select the correct option:
A) 20	B) 25	C) 30	D) 35	E) 40

Solution: Let the present age of Rohan be x years   Then, given: x + 15 = 4 (x - 15)   x = 25   ANSWER:25
Answer: B
The average age of a group of 10 students was 20. The average age increased by 2 years when two new students joined the group. What is the average age of the two new students who joined the group?  Choices:  A) 22 years  B) 30 years  C) 44 years  D) 32 years  E) None of these

Solution: Answer   The average age of a group of 10 students is 20.   Therefore, the sum of the ages of all 10 of them = 10 * 20= 
10 * 20 = 200
200   When two new students join the group, the average age increases by 2. New average= 22.   Now, there are 12 students.   Therefore, the sum of the ages of all 12 of them = 12 * 22= 
12 * 22 = 264
264   Therefore, the sum of the ages of the two new students who joined= 264 - 200= 
264 - 200 = 64
64   And the average age of each of the two new students= 64/2= 
64/2 = 32
32 years.   Answer 32 years
Answer: D
If a car had traveled 30 kmh faster than it actually did, the trip would have lasted 30 minutes less. If the car went exactly 90 km, at what speed did it travel?	Choose the correct option:
A) 35 kmh	B) 45 kmh	C) 60 kmh	D) 75 kmh	E) 90 kmh

Solution: Time = Distance/Speed   Difference in time = 1/2 hrs   90/x - 90/(x + 30) = 1/2   Substitute the value of x from the options. --> x = 60 --> 90/60 - 90/90 = 3/2 - 1 = 1/2   Answer: 60 kmh
Answer: C
Find the smallest number which when divided by 11 and 13 leaves respective remainders of 4 and 6.	Choose the correct choice from the following choices:	A) 187	B) 197	C) 207	D) 136	E) 227

Solution: Let 'N' is the smallest number which divided by 11 and 13 leaves respective remainders of 4 and 6.   Required number = (LCM of 11 and 13) - (common difference of divisors and remainders) = (143) - (7)= 
(143) - (7) = 136
136.   ANSWER:136
Answer: D
The area of a square is 4096 sq cm. Find the ratio of the breadth and the length of a rectangle whose length is twice the side of the square and breadth is 24 cm less than the side of the square?
Choose one:
A) 5:16 B) 5:12 C) 5:19 D) 5:18 E) 5:14

Solution: Let the length and the breadth of the rectangle be l cm and b cm respectively. Let the side of the square be a cm.   a2 = 4096 = 212   a = (212)1/2 = 26 = 64   L = 2a and b = a - 24   b : l = a - 24 : 2a = 40 : 128 =   5:16   Answer:5:14
Answer: E
The number of degrees that the hour hand of a clock moves through between noon and 2.30 in the afternoon of the same day is?	Answers.
A) 38  B) 27  C) 75  D) 28  E) 21

Solution: Explanation:   The hour hand moves from pointing to 12 to pointing to half way between 2 and 3. The angle covered between each hour marking on the clock is  360/12= 
 360/12 = 30
30. Since the hand has covered 2.5 of these divisions the angle moved through is 75.   Answer: 75
Answer: C
After driving to a riverfront parking lot, Bob plans to run south along the river, turn around, and return to the parking lot, running north along the same path. After running 3.25 miles south, he decides to run for only 50 minutes more. If Bob runs at a constant rate of 8 minutes per mile, how many miles farther south can he run and still be able to return to the parking lot in 50 minutes?
Choose the correct choice from the following answers.
A) 1.5	B) 2.25	C) 3.0	D) 3.25	E) 4.75

Solution: For the first 3.25 miles, Bob takes 3.25x8=26minutes   Say he runs 'x' miles further south. So the total distance he covers is (3.25+2x+3.25) in (50+26) minutes   So we have 6.5+2x=76/8 => x=1.5   1.5nswer 1.5
Answer: A
There is 60% increase in an amount in 6 years at S.I. What will be the C.I. of Rs. 12,000 after 3 years at the same rate?	Choose the correct choice from the following choices
A) Rs.3389  B) Rs.3923  C) Rs.3972  D) Rs.3928  E) Rs.3929

Solution: Let P = Rs. 100. Then, S.I. Rs. 60 and T = 6 years.   R = (100 * 60)/(100 * 6)= 
(100 * 60)/(100 * 6) = 10
10% p.a.   Now, P= Rs. 12000, T = 3 years and R = 10% p.a.   C.I. = [12000 * {(1 + 10/100)3 - 1}]   = 12000 * 331/1000 =Rs.3972   Answer:Rs.3972
Answer: C
A garrison of 2000 men has provisions for 54 days. At the end of 15 days, a reinforcement arrives, and it is now found that the provisions will last only for 20 days more. What is the reinforcement?	Pick:
A) 1898
B) 9801
C) 1987
D) 1900
E) 8373

Solution: 2000 ---- 54   2000 ---- 39   x ----- 20   x*20 = 2000*39   x = 3900   2000   -------   1900   Answer:1900
Answer: D
Find the length of the wire required to go 15 times round a square field containing 69696 m2.	Choose the correct answer: A) 15840 m B) 16840 m C) 15820 m D) 15640 m E) 16640 m

Solution: a2 = 69696 => a = 264   4a = 1056   1056 * 15= 
1056 * 15 = 15_840
15840   15840 mNSWER:15840 m
Answer: A
Ram get 450 marks in his exam which is 90% of total marks. What is the total marks? Select the correct option:
A) 475
B) 600
C) 550
D) 500
E) 525

Solution: X * (90/100) = 450   X = 5 * 100= 
5 * 100 = 500
500   Answer: 500
Answer: D
Jack, Jill, and Sandy each have one try to make a basket from half court. If their individual probabilities of making the basket are 1/6, 1/7, and 1/8 respectively, what is the probability that all three will miss? Select.
A) 3/8
B) 5/8
C) 7/16
D) 9/16
E) 23/32

Solution: The probability that all three will miss is 5/6*6/7*7/8=5/8.   The answer is 5/8.
Answer: B
M and N invested in a shop. The profits were divided in the ratio of 4 : 5 respectively. If M invested Rs. 40,000, the amount invested by N is: Pick one:
A) 35000	B) 40000	C) 50000	D) 60000	E) None

Solution: Suppose N invested Rs. x. Then, 40000/x = 4/5 or y = [40000 x 5/ 4] = 50000.   Answer 50000
Answer: C
7.51 8.22 7.86 8.36
8.09 7.83 8.30 8.01
7.73 8.25 7.96 8.53
A vending machine is designed to dispense 8 ounces of coffee into a cup. After a test that recorded the number of ounces of coffee in each of 1000 cups dispensed by the vending machine, the 12 listed amounts, in ounces, were selected from the data above. If the 1000 recorded amounts have a mean of 7.5 ounces and a standard deviation of 0.3 ounces, how many of the 12 listed amounts are within 1.7 standard deviation of the mean? Choose the correct choice from the following choices:  A) Four  B) Six  C) Nine  D) Ten  E) Eleven

Solution: Mean = 7.5   Standard Deviation = 0.3   within 1.7 standard deviation of the mean   i.e. 1.7 standard deviation ASixOVE the mean = 7.5+1.7*0.3= 
7.5+1.7*0.3 = 8.01
8.01   and 1.7 standard deviation SixELOW the mean= 7.5-1.7*0.3= 
7.5-1.7*0.3 = 6.99
6.99   hence, 6 values fall within 1.7 SD from Mean   Answer: Option Six
Answer: B
If integer k is equal to the sum of all even multiples of 25 between 200 and 600, what is the greatest prime factor of k? Answers:	A) 5	B) 7	C) 11	D) 13	E) 17

Solution: if we break down what the stem is asking what is the sum of all mult of 50 between 200 and 600.   using arithmetic progression to find n : 600 = 200 + (n - 1) 50   400+ 50 = 50n   450 = 50n => n = 9   the sum would be: 9* mean   mean = [600 + 200] / 2 = 400   9*400= 
9*400 = 3_600
3600   13
Answer: D
If José reads at a constant rate of 2 pages every 6 minutes, how many seconds will it take him to read N pages?
Pick:  A) 180  B) 2N  C) 5/2*N  D) 24N  E) 150

Solution: Jose would read 1 page in 6/2 min   Jose would read N page in (6/2)*N min i.e. (6/2)*N*60 Seconds = 180N Seconds.   Option 180 is the correct 180nswer.
Answer: A
An amount of money is to be divided between P, Q and R in the ratio of 3:7:12. If the difference between the shares of P and Q is Rs.2400, what will be the difference between Q and R's share?  Choose the correct answer:
A) 3000  B) 2887  C) 2666  D) 2578  E) 2771

Solution: 4 --- 2000   5 --- ? => 3000   3000nswer: 3000
Answer: A
The first three terms of a proportion are 6, 12 and 24. The fourth term is? Choose the correct choice from the following answers.
A) 22
B) 28
C) 27
D) 36
E) 48

Solution: (12*24)/6= 
(12*24)/6 = 48
48   Answer:48
Answer: E
How much time will take for an amount of Rs. 320 to yield Rs. 81 as interest at 4.5% per annum of simple interest?	Pick one
A) 8 years  B) 4 years  C) 3 years  D) 5 years 7 months  E) 5 years

Solution: Time = (100 * 81) / (320 * 4.5)   = 5 years 7 months   Answer: 5 years 7 months
Answer: D
If 2^5, 3^3, and 11^2 are all factors of the product of 936 and w where w is a positive integer, what is the smallest possible value of w? Choose the correct answer.
A) 132  B) 39  C) 42  D) 65  E) 156

Solution: Here 156 has three two's   two three's   and one 11   rest of them must be in w   so w= 11*3*4= 
11*3*4 = 132
132   Smash 132
Answer: A
Amy has to go to three different stores this week. How many ways can she go to one or more stores today? Options
A) 19
B) 26
C) 24
D) 9
E) 7

Solution: Amy has to visit at least one of three stores.   = > 2^3 - 1 = 7   7
Answer: E
A sum of money is to be distributed among A, B, C, D in the proportion of 5 : 2 : 4 : 3. If C gets $500 more than D, what is A's share?
Choices.
A) $1200  B) $1600  C) $2000  D) $2500  E) $3000

Solution: Let the shares of A, B, C and D be 5x, 2x, 4x and 3x respectively.   Then, 4x - 3x = 500   x = $500   A's share = 5x = 5*$500 = $2500   The answer is $2500.5* 500= 
5* 500 = 2_500
$2500   The answer is $2500.
Answer: D
For each 6-month period during a light bulb's life span, the odds of it not burning out from over-use are half what they were in the previous 6-month period. If the odds of a light bulb burning out during the first 6-month period following its purchase are 2/3, what are the odds of it burning out during the period from 6 months to 1 year following its purchase?	Choose the correct choice from the following answers: A) 5/27 B) 2/9 C) 1/3 D) 4/9 E) 2/7

Solution: P(of not burning out in a six mnth period)=1/2 of P(of not burning out in prev 6 mnth period)   P(of burning out in 1st 6 mnth)= 2/3   --->P( of not burning out in 1st 6 mnth)=1-2/3=1/3   ---->P(of not burning out in a six mnth period)=1/2 *1/3=1/6--->P(of burning out in a six mnth period)=1-1/3=2/3   now   P( of burning out in 2nd six mnth period)=P( of not burning out in 1st six mnth)*P(of burning out in a six mnth)   =2/3 * 1/6=2/7   Ans 2/7
Answer: E
In how many ways can a cricket eleven be chosen out of a batch of 15 players. Pick one
A) 1365 B) 2154 C) 1245 D) 4512 E) 7841

Solution: Required number of ways   = 15C 11 = 15C (15-11)   = 15C4   15C4 = 15 * 14 * 13 * 12 / 4 * 3 * 2 *1   = 1365   1365ns: 1365
Answer: A
For how many values n is 2^n = n^2 ?  Choose the most appropriate option.
A) None B) One C) Two D) Three E) More than Three

Solution: draw a graph with x^2 and 2^x, you'll see 3 intercepts between the 2 curves, but one is in the 2nd quadrant,Thus 3 are valid, and the answer is Three
Answer: D
A money lender finds that due to a fall in the annual rate of interest from 8% to 7 1/2 % his yearly income diminishes by Rs.61.50. his capital is  Choose the correct option.
A) 223.78 B) 37.78 C) 24.6 D) 278.88 E) 123.0

Solution: 123.0xplanation:   Capital = Rs.x , then   1/2 x=61.5   x = 123.00   Answer: 123.0) Rs.123.00
Answer: E
A train covers a distance of 6 km in 10 min. If it takes 12 sec to pass a telegraph post, then the length of the train is? Select
A) 120m  B) 180m  C) 240m  D) 220m  E) 280m

Solution: Speed = (6/10 * 60) km/hr = (36 * 5/18) m/sec = 10 m/sec.   Length of the train = 10 * 12= 
10 * 12 = 120
120 m.   120mNSWER:120m
Answer: A
The average (arithmetic mean) of four numbers is 5x + 9. If one of the numbers is 2x, what is the average of the other three numbers?
Choose the most appropriate option.
A) x + 1
B) 3x + 3
C) 5x + 1
D) 5x + 4
E) 6x + 12

Solution: The sum of all four numbers is 4 * (5x + 9) = 20x + 36.   If one of the numbers is 2x, the sum of the other 3 numbers is 18x+36.   The average of the remaining three numbers is (18x+36)/3 = 6x+12.   The answer is 6x + 12.
Answer: E
One fourth of a solution that was 15% sugar by weight was replaced by a second solution resulting in a solution that was 16 percent sugar by weight. The second solution was what percent sugar by weight? Options
A) 34%	B) 24%	C) 22%	D) 19%	E) 8.5%

Solution: Say the second solution (which was 1/4 th of total) was x% sugar, then 3/4*0.15+1/4*x=1*0.16 --> x=0.19. Alternately you can consider total solution to be 100 liters and in this case you'll have: 75*0.15+25*x=100*0.16 --> x=0.19.   Answer: 19%.
Answer: D
Find compound interest on Rs. 7500 at 4% per annum for 2 years, compounded annually. Choose the correct option:
A) Rs 712 B) Rs 812 C) Rs 912 D) Rs 512 E) Rs 612

Solution: Amount = Rs [7500*(1+(4/100)2] = Rs(7500 * (26/25) * (26/25)) = Rs. 8112.   therefore, C.I. = Rs. (8112 - 7500) = Rs. 612.   ANSWRs 612R Rs 612 612
Answer: E
An investor bought a 1-year $6,000 certificate of deposit that paid interest at an annual rate of 10 percent compounded semiannually. What was the total amount of interest paid on this certificate at maturity?	Choose the correct choice:
A) $325	B) $600	C) $615	D) $1000	E) $1230

Solution: 1.05*1.05*6000= 
1.05*1.05*6000 = 6_615
$6615   The answer is $615.
Answer: C
A man cheats while buying as well as while selling. While buying he takes 10% more than what he pays for and while selling he gives 20% less than what he claims to. Find the profit percent, if he sells at 9.09% below the cost price of the claimed weight. Choose the correct choice from the following choices.
A) 19.81%  B) 20%  C) 37.5%  D) 25%  E) 37.5%

Solution: (1 + m1%)(1 + m2%)(1 - d%) = (1 + p%)   11/10 * 5/4 * 10/11 = (1 + p%)   profit % = 25%   ANSWER:25%
Answer: D
A bag contains 7 green and 8 white balls. If two balls are drawn simultaneously, the probability that both are of the same colour is?  Choose the most appropriate option.
A) 7/15
B) 7/16
C) 7/19
D) 7/13
E) 7/11

Solution: Drawing two balls of same color from seven green balls can be done in 7C2 ways.   Similarly from eight white balls two can be drawn in ⁸8C2 ways.   = 7/15   7/15nswer: 7/15
Answer: A
During 2005, a company produced an average of 2,500 products per month. How many products will the company need to produce from 2006 through 2008 in order to increase its monthly average for the period from 2005 through 2008 by 300% over its 2005 average?  Answers: A) 450,000 B) 475,000 C) 500,000 D) 525,000 E) 550,000

Solution: Company produced 12*2500 = 30,000 products in 2005. If company produces X products from 2006 to 2008, then total amount of product produced in 4 years (2005 through 2008) is X+30,000. The gives the average of (X+30,000)/4.   This average needs to be 200% higher than that in 2005. In math terms, 30,000+300%(30,000) = 120,000. So:   (X+30,000)/4 = 120,000   X+30,000 = 480,000   X = 450,000   The answer is 450,000.
Answer: A
Yearly subscription to professional magazines cost a company $940.00. To Make a 50% cut in the magazine budget, how much less must be spent?  Choose the most appropriate option:  A) 654  B) 655  C) 656  D) 657  E) 470

Solution: total cost 940   940*50/100= 
940*50/100 = 470
470   so the cut in amount is 470   the less amount to be spend is  940-470= 
 940-470 = 470
470   ANSW470R:470
Answer: E
The weight of four dogs is determined to be 42 pounds, 38 pounds, 35 pounds and 41 pounds respectively. The weight of a fifth dog is determined to be y pounds. If the average (arithmetic mean) weight of the first four dogs is the same as that of all five dogs what is the value of y?  Select:
A) 31	B) 33	C) 35	D) 37	E) 39

Solution: Total weight of the 4 dogs = (42+38+35+41)= 
(42+38+35+41) = 156
156   Avg= 156/4= 
156/4 = 39
39   Total weight of 5 dogs= 156+y or 4(39)+y   Average of 5 dogs as per Question = 39   Equation:   4(39) + y = 5 (39), or y = 39.   Choose 39
Answer: E
By selling 150 mangoes, a fruit-seller gains the selling price of 30 mangoes. Find the gain percent?
Answers
A) 22  B) 25  C) 77  D) 88  E) 99

Solution: SP = CP + g   150 SP = 150 CP + 30 SP   120 SP = 150 CP   120 --- 30 CP   100 --- ? => 25%   Answer:25
Answer: B
A qualified worker digs a well in 5 hours. He invites 2 apprentices, both capable of working 3/4 as fast and 3 trainees both working 1/5 as fast as he. If the five-person team digs the same well, how much time does the team need to finish the job?  Choose the correct choice from the following options:
A) 1:56	B) 1:34	C) 1:44	D) 1:54	E) 2:14

Solution: and answer is correct as you have calculated : 100/48 hrs that is 1.88 hrs - 1 hr and 56 minutes, so 1:56, hence, 1:56
Answer: A
Due to construction, the speed limit along an 5-mile section of highway is reduced from 40 miles per hour to 22 miles per hour. Approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ?  Pick one.
A) A) 3.12	B) B) 8	C) C) 10	D) D) 15	E) E) 6.13

Solution: Old time in minutes to cross 5 miles stretch = 5*60/40 = 5*3/2= 
5*3/2 = 15/2 = around 7.5
7.5   New time in minutes to cross 5 miles stretch= 5*60/22 = 5*30/11 = 13.63   Time difference = 6.13   Ans:6.13
Answer: E
A train 400 m long can cross an electric pole in 20 sec and then find the speed of the train?  Choose the correct answer
A) 76 Kmph	B) 88 Kmph	C) 72 Kmph	D) 55 Kmph	E) 44 Kmph

Solution: Length = Speed * time   Speed = L/T   S = 400/20= 
400/20 = 20
20 M/Sec   Speed= 20*18/5 (To convert M/Sec in to Kmph multiply by 18/5)   Speed = 72 Kmph   Answer: 72 Kmph
Answer: C
If a particular player is always chosen, in how many ways can a cricket-be chosen out of 15 players? Pick
A) 1000  B) 1123  C) 1245  D) 1350  E) 1365

Solution: A particular player is always chosen, it means that 10 players are selected out of the remaining 14 players.   =. Required number of ways = 14C10 = 14C4   = 14!/4!x19! = 1365   1365
Answer: E
A fruit seller had some apples. He sells 40% apples and still has 420 apples. Originally, he had: Choose the most appropriate option:	A) 701 apples	B) 708 apples	C) 720 apples	D) 730 apples	E) 700 apples

Solution: E   Suppose originally he had x apples.   Then, (100 - 40)% of x = 420.   60/100 x x = 420   x = (420 x 100)/60 = 700.
Answer: E
A person crosses a 500m long street in 5 minnutes. What is his speed in km per hour? Choose the correct option.
A) 6.01km/hr  B) 7.2km/hr  C) 9km/hr  D) 2.5km/hr  E) 3km/hr

Solution: Speed = 500/5*60 = 1.67m/sec   =1.67*18/5   =6.01km/hr   6.01km/hrnswer is 6.01km/hr
Answer: A
If 8 workers can build 8 cars in 8 days, then how many days would it take 4 workers to build 4 cars?
Choose the correct choice.
A) 2	B) 4	C) 8	D) 12	E) 16

Solution: 8 workers can build 1 car per day on average.   1 worker can build 1/8 of a car per day.   4 workers can build 1/2 car per day.   The time required to build 4 cars is 4 / (1/2)= 
4 / (1/2) = 8
8 days   The answer is 8.
Answer: C
A batsman in his 12th innings makes a score of 92 and thereby increases his average by 2 runs. What is his average after the 12th innings if he had never been ‘not out’?	Choose the most appropriate option
A) 42	B) 43	C) 70	D) 45	E) 46

Solution: Let ‘x’ be the average score after 12 th innings   ⇒ 12x = 11 × (x – 2) + 92   ∴ x = 70   Answer 70
Answer: C
What is the remainder of G=3^19 when divided by 10? Choose the correct choice
A) 0  B) 1  C) 5  D) 7  E) 9

Solution: I looked for patterns:   ^2 - units digit 9   ^3 - units digit 7   ^4 - units digit 1   ^5 - units digit 3   hence, we can see that when raised to a power which is multiple of 4, the units digit is 1, and when to an even power not multiple of 4, the units digit is 9   and we can then see:   ^16 - units digit 1, or   ^18 - units digit 9   and ^19 - units digit 7   therefore, G=when divided by 10, the remainder must be 7.7
Answer: D
A watch was sold at a loss of 10%. If it was sold for Rs.140 more, there would have been a gain of 4%. What is the cost price?	Choose the correct choice from the following answers:
A) 1000  B) 2996  C) 2686  D) 1028  E) 1013

Solution: 90%   104%   --------   14% ---- 140   100% ---- ? => Rs.1000   1000nswer: 1000
Answer: A
Positive integer x has m factors; 3x has 3 factors; Which of the following values can m take?
I. 1
II. 2
III. 3 Select:  A) I or III  B) II or III  C) I or II  D) I only is true  E) II only is true

Solution: Squares have odd number of factors.The square which is a multiple of 3 is 9.   3 has factors 1,3 .   Therefore 2 factors   Answer II only is true
Answer: E
The owner of a furniture shop charges his customer 18% more than the cost price. If a customer paid Rs. 6000 for a computer table, then what was the cost price of the computer table?
Choose the correct option.
A) Rs.6289
B) Rs.6298
C) Rs.6290
D) Rs.5084
E) Rs.6708

Solution: CP = SP * (100/(100 + profit%))   = 6000(100/118) = Rs.5084.   Answer: Rs.5084
Answer: D
A clock is set at 5 a.m. The clock loses 16 minutes in 24 hours. What will be the true time when the clock indicates 10 p.m. on 4th day? Pick.
A) 9 p.m B) 10 p.m C) 11 p .m D) 12 p.m E) none

Solution: Solution   Time from 5 a.m on a day to 10 p.m.on 4th day	= 89 hours.   Now 23 hrs 44 min. of this clock	= 24 hours of correct clock.   Therefore 356 / 15 hrs of this clock	= 24 hours of correct clock.   89 hrs of this clock	= (24 x 15/356 x 89) hrs   = 90 hrs   So, the correct time is	11 p.m.   Answer 11 p .m
Answer: C
If B is the center of the circle in the figure above and the area of the shaded region is 16π, what is the length of arc ADC? Choose the correct choice:  A) 4  B) 4π  C) 16  D) 8π  E) 16

Solution: Area of 1/4th of the circle is 16pi   so area of the circle=64 pi   radius of circle=8 units   circumference= 2 pi* radius= 16 pi   1/4th the circumference= required length of ADC= 4pi   ANS:4π
Answer: B
If $50,000,000 is the initial amount placed in an account that collects 7% annual interest, which of the following compounding rates would produce the largest total amount after two years? Choose the most appropriate option: A) compounding annually B) compounding quarterly C) compounding monthly D) compounding daily E) All four of these would produce the same total

Solution: This will produce the maximum yield as the interest accured each day will be added the very next day to the Principal amount for further computation of interest.   This process will be repeated every day till the amount matures   Compounding annually will give least returns   Answer = compounding daily
Answer: D
Two trains 137 meters and 163 meters in length are running towards each other on parallel lines, one at the rate of 42 kmph and another at 48 kmpb. In what time will they be clear of each other from the moment they meet  Select:
A) 8 sec
B) 10 sec
C) 12 sec
D) 14 sec
E) 16 sec

Solution: Explanation:   Relative speed of the trains = (42 + 48)= 
(42 + 48) = 90
90 kmph= (90×5/18) m / sec = 25 m /sec.   Time taken by the trains to ‘pass each other   = Time taken to cover (137 + 163) m at 25 m /sec = (300/25)= 
(300/25) = 12
12 sec   Answer: Option 12 sec
Answer: C