MU-NLPC/Calc-aqua_rat huggingface dataset:
The parameter of a square is equal to the perimeter of a rectangle of length 16 cm and breadth 14 cm. Find the circumference of a semicircle whose diameter is equal to the side of the square. (Round off your answer to two decimal places)  Choose the correct option:  A) 23.57  B) 23.54  C) 23.50  D) 23.55  E) 23.51

Solution: Let the side of the square be a cm.   Parameter of the rectangle = 2(16 + 14) = 60 cm Parameter of the square = 60 cm   i.e. 4a = 60   23.57 = 15   Diameter of the semicircle = 15 cm   Circimference of the semicircle   = 1/2(∏)(15)   = 1/2(22/7)(15) = 330/14 = 23.57 cm to two decimal places   23.57nswer: 23.57
Answer: A
find the odd man out:1,3,10,21,64,129,356,777
Choose the correct answer:
A) 3
B) 10
C) 21
D) 64
E) 356

Solution: 1=1   3=3   10=1+0= 
1+0 = 1
1   21=2+1= 
2+1 = 3
3   64=6+4= 
6+4 = 10
10=1+0= 
1+0 = 1
1   129=1+2+9= 
1+2+9 = 12
12=1+2= 
1+2 = 3
3   356=3+5+6= 
3+5+6 = 14
14=1+4= 
1+4 = 5
5( wrong one.. it should be 1)   777=7+7+7= 
7+7+7 = 21
21=2+1= 
2+1 = 3
3   Alternative 1 and 3 series..   ANSWER:64
Answer: D
A certain boxer has agreed to pay his opponent a fee of 2.5% of his total purse for every pound over the specified weight limit he weighs in. If the boxer pays his opponent a fee of $225,000 after weighing in eight pounds over the specified limit, what was the boxer's purse?  Choose the correct choice from the following answers
A) $65,625 B) $105,000 C) $150,000 D) $183,750 E) $1,125,000

Solution: .025*8= 
.025*8 = 0.2
.2   225000/.2= $1,125,000   Answer: $1,125,000
Answer: E
In a party attended by 12 persons, each clinch their glass with every other. How many glass clinches? Select the correct option.
A) 51	B) 52	C) 53	D) 66	E) 55

Solution: Total no. of person = 12   Total no. of glass clinches = n(n-1)/2   =12*11/2= 
12*11/2 = 66
66   ANSWER:66
Answer: D
In an exam, Amar scored 64 percent, Bhavan scored 36 percent and Chetan 44 percent. The maximum score awarded in the exam is 800. Find the average mark scored by all the three boys?
Choose the correct option.
A) 384 B) 826 C) 207 D) 269 E) 208

Solution: 384verage mark scored by all the three boys =   [64/100 (800) + 36/100 (800) + 44/100 (800)] / 3   = 384   384nswer: 384
Answer: A
A group of 55 adults and 70 children go for trekking. If there is meal for either 70 adults or 90 children and if 28 adults have their meal, find the total number of children that can be catered with the remaining food.
Answers.
A) 42	B) 54	C) 90	D) 70	E) 80

Solution: Explanation:   As there is meal for 70 adults and 28 have their meal, the meal left can be catered to 42 adults.   Now, 70 adults = 90 children   7 adults = 9 children   Therefore, 42 adults = 54 children   Hence, the meal can be catered to 54 children   ANSWER 54
Answer: B
Life expectancy is defined by the formula 2SB/G, where S = shoe size, B = average monthly electric bill in dollars, and G = GMAT score. If Melvin's GMAT score is twice his monthly electric bill, and his life expectancy is 70, what is his shoe size?	Choose the correct choice from the following answers:	A) 75	B) 70	C) 65	D) 40	E) 50

Solution: Solution -   Given that, G = 2B and Life expectancy(L) = 70   L=2SB/G -> 70 = 2SB/2B --> S=70.   ANS 70
Answer: B
The average of runs of a cricket player of 10 innings was 32. How many runs must he make in his next innings so as to increase his average of runs by 4?
Choose the correct option:
A) 56 B) 86 C) 25 D) 76 E) 63

Solution: Average after 11 innings = 36   Required number of runs   = (36 * 11) - (32 * 10)   = 396 - 320= 
396 - 320 = 76
76.   Answer:76
Answer: D
For all integers a and b, a%b = (a + b)(a - b). If 8%x = 15, then which of the following could be a value of x? Choose the most appropriate option.
A) -7
B) -6
C) 2
D) 3
E) 6

Solution: 8%x = (8+x)(8-x)   64-x^2 = 15   x^2 = 49   x=-7,7   -7ns: -7
Answer: A
John makes $50 a week from his job. He earns a raise and now makes $60 a week. What is the % increase?
Choose the correct choice from the following options
A) 16%
B) 16.66%
C) 17.9%
D) 18.12%
E) 20%

Solution: Increase = (10/50)*100 = (1/5)*100= 
(1/5)*100 = 20
20%.   20%
Answer: E
One card is drawn from a pack of 52 cards. What is the probability that the card drawn is a face card?  Choose the correct answer: A) 4/13 B) 5/16 C) 9/17 D) 2/5 E) 3/9

Solution: Out of 52 cards there will be 16 face cards are there.   probability of getting a face card = 16/52 = 4/13   4/13nswer is 4/13
Answer: A
The average salary of all the workers in a workshop is Rs. 8000. The average salary of 7 technicians is Rs. 18000 and the average salary of the rest is Rs. 6000. The total number of workers in the workshop is	Choose the correct answer.
A) 20 B) 42 C) 22 D) 23 E) NONE

Solution: Sol.   Let the total number of workers be x. Then,   8000x = (18000 × 7) + 6000 ( x – 7)   ‹=› 2000x = 84000   ‹=› x = 42.   Answer 42
Answer: B
Find the number of selections that can be made taking 4 letters from the word "ENTRANCE". Options
A) 70  B) 36  C) 35  D) 72  E) 32

Solution: We have 8 letters from which 6 are unique.   Possible scenarios for 4 letter selection are:   A. All letters are different;   B. 2 N-s and other letters are different;   C. 2 E-s and other letters are different;   D. 2 N-s, 2 E-s.   Let's count them separately:   A. All letters are different, means that basically we are choosing 4 letters form 6 distinct letters: 6C4=15;   B. 2 N-s and other letters are different: 2C2(2 N-s out of 2)*5C2(other 2 letters from distinct 5 letters left)=10;   C. 2 E-s and other letters are different: 2C2(2 E-s out of 2)*5C2(other 2 letters from distinct 5 letters left)=10;;   D. 2 N-s, 2 E-s: 2C2*2C2=1.   15+10+10+1= 
15+10+10+1 = 36
36   Answer: 36.
Answer: B
The average of 30 numbers is 25. If each number is multiplied by 5, find the new average?  Choose one.
A) 115  B) 125  C) 135  D) 145  E) 155

Solution: Sum of the 30 numbers = 30 * 25= 
30 * 25 = 750
750   If each number is multiplied by 5, the sum also gets multiplied by 5 and the average also gets multiplied by 5.   Thus, the new average= 25 * 5= 
25 * 5 = 125
125.   ANSWER:125
Answer: B
During a clearance sale, a retailer discounted the original price of its TVs by 25% for the first two weeks of the month, then for the remainder of the month further reduced the price by taking 20% off the sale price. For those who purchased TVs during the last week of the month, what percent of the original price did they have to pay? Choose the correct choice from the following answers.
A) 40%	B) 45%	C) 55%	D) 60%	E) 62.5%

Solution: As it's a percentage problem, start with $100.   The first discount is 25% of $100, so the sales prices is 75% of $100 = $75.   The second discount is 20% of $75. Move the decimal once to the left and double it = $7.5*2= 
7.5*2 = 15
$15.   The final sales price is $75-$15 = $60, which is 60% of $100.   The correct answer is 60%  75- 15= 
  75- 15 = 60
$60, which is 60% of $100.   The correct answer is 60%
Answer: D
Find the greatest number which is such that when794, 858 and 1351 are divided by it, the remainders are all same.	Pick one: A) 1 B) 5 C) 6 D) 7 E) 8

Solution: Given, the remainders are same i.e. differences of that numbers are exactly divisible. Hence, you have to find HCF (x–y, y–z, z–x). 858–794 = 64; 1351–794 = 557; 1351–858 = 493. HCF of (64, 557, 493) = 1.   1nswer:1
Answer: A
Find the annual income derived by investing $ 6800 in 50% stock at 136.
Choose one: A) 550 B) 2500 C) 250 D) 3000 E) 400

Solution: By investing $ 136, income obtained = $ 50.   By investing $ 6800, income obtained = $ [(50/136)*6800= 
(50/136)*6800 = 2_500
$ 2500.   Answer 2500.
Answer: B
A train with 120 wagons crosses John who is going in the same direction, in 36 seconds. It travels for half an hour from the time it starts overtaking the John (he is riding on the horse) before it starts overtaking the Mike(who is also riding on his horse) coming from the opposite direction in 24 seconds. In how much time (in secs) after the train has crossed the Mike do the John meets to Mike? Choose one
A) 3576 s B) 3589 s C) 3596 s D) 3598 s E) 3576 s

Solution: Let the length of the train be L metres and speeds of the train Arun and Sriram be R, A and S respectively, then   ---------- (i)   and ---------(ii)   From eq.(i) and (ii)   3(R - A ) = 2 (R + K)   R = 3A + 2K   In 30 minutes (i.e 1800 seconds), the train covers 1800R (distance) but the Arun also covers 1800 A (distance) in the same time. Therefore distance between Arun and Sriram, when the train has just crossed Sriram   = 1800 ( R - A) - 24 ( A + K)   Time required =   = (3600 - 24)= 
(3600 - 24) = 3_576
3576 s   3576 s
Answer: E
How many even multiples of 15 are there between 149 and 301?	Choose the correct option
A) 5	B) 6	C) 9	D) 10	E) 11

Solution: 150 = 10*15   300 = 20*15   The even multiples are 15 multiplied by 10, 12, 14, 16, 18, and 20 for a total of 6.   The answer is 6.
Answer: B
A team P of 20 engineers can complete work or task in 32 days. Another team Q of 16 engineers can complete same task in 30 days.Then the ratio of working capacity of 1 member of P to the 1 member of Q is
a. 3 : 2
Choose the correct choice from the following:
A) 22 B) 34 C) 77 D) 29 E) 21

Solution: Explanation:   Let the capacity of an engineer in P = x units, and in Q = y units.   Working capacity of P = x × 32 × 20   Working capacity of Q = y × 16 × 30   As the total work is same, we equate the above equations.   ⇒ x × 32 × 20 = y × 16 × 30   ⇒ xy=16×3032×20=34   Answer: 34
Answer: B
8 gentlemen and 3 gentlewomen are candidates for 2vacancies. A voter has to vote for 2 candidates. In how many ways can one cast his vote?	Select the correct option
A) 51	B) 52	C) 55	D) 56	E) 57

Solution: There are 11 candidates and a voter has to vote for any two of them.   So, the required number of ways is,   = 11C2 = 55.   55
Answer: C
A can do a half of certain work in 70 days and B one third of the same in 35 days. They together will do the whole work in. Pick:	A) 88 days	B) 27 days	C) 78 days	D) 60 days	E) 17 days

Solution: A = 140 days   B = 105 days   1/140 + 1/105 = 7/420 = 1/60   =>60 days   Answer: 60 days
Answer: D
What is the least common multiple of 8,12,32,14	Select:
A) 672  B) 682  C) 328  D) 964  E) 285

Solution: The given numbers are 8,12,32,14   thus the l.c.m is   2*2*2*1*3*4*7= 
  2*2*2*1*3*4*7 = 672
672   the answer is 672
Answer: A
Look at this series: 70, 71, 76, __, 81, 86, 70, 91, ... What number should fill the blank?  Pick one:  A) 60  B) 70  C) 82  D) 77  E) 52

Solution: 70   70   In this series, 5 is added to the previous number; the number 70 is inserted as every third number.
Answer: B
The credit card and a global payment processing companies have been suffering losses for some time now. A well known company recently announced its quarterly results. According to the results, the revenue fell to $42.0 billion from $69.0 billion, a year ago. By what percent did the revenue fall?  Pick one:
A) 20.8 B) 30.4 C) 31.8 D) 39.1 E) 33.8

Solution: $69-$42=27$   (27/69)*10069- 42= 
69- 42 = 27
27$   (27/69)*100=39.13%   ANSWER:39.1
Answer: D
The difference between the value of a number increased by 12.5% and the value of the original number decreased by 25% is 30. What is the original number Q?
Select:	A) 60	B) 80	C) 40	D) 120	E) 160

Solution: (1 + 1/8)x - (1 - 1/4)x = 30   (9/8)x - (3/4)x = 30   x = 80=Q   Answer: 80
Answer: B
A large tanker can be filled by two pipes A and B in 60 minutes and 40 minutes respectively. How many minutes will it take to fill the tanker from empty state if B is used for half the time and A and B fill it together for the other half ?  Select the correct option
A) 15 min	B) 20 min	C) 27.5 min	D) 30 min	E) 35 min

Solution: et total time consumed in filling the tank is n.   (A+B)'s 1 minute work is 1/60 + 1/40 and (A+B) will take half of total time ie   (n/2)(1/60 + 1/40)----------(1)   and rest half will be filled by B only in half of total time means (n/2)(1/40)--(2)   (1)+(2)   (n/2)(1/60 + 1/40) + (n/2)(1/40)=1   n=30   ANSWER:30 min
Answer: D
What annual payment dischargea debit of Rs.12900, due in 4yrs.At 5% rate?
Choose one: A) 2000 B) 1300 C) 3000 D) 4300 E) 4500

Solution: A.P.=(200X12900)/[4(200+5X3)]=3000 Ans   Alternative   100+105+110+115=12900   430=12900   100=12900/(430)X100=3000   3000
Answer: C
Bullock likes to keep a spare tyre in his car every time. On a certain day, he travels 1, 00,000 km and just to make the most of all the tyres, he changes the tyres between his journey such that each tyre runs the same distance.
What is the distance traveled by each tyre?	Answers:
A) 50,000 km.
B) 60,000 km.
C) 70,000 km.
D) 80,000 km.
E) 90,000 km.

Solution: Solution:   80,000.   Explanation:   The distance traveled by each tyre:   4/5 * 1, 00, 000km = 80,000 km.   Answer 80,000 km.
Answer: D
One-third of 1206 is what percent of 400 ? Select the correct option:  A) 3  B) 30  C) 300  D) 100.5  E) 201.2

Solution: Answer   Let one-third of 1206 is N% of 400.   ∵ 1206/3 = (N x 400)/100   ∴ N = (402 x 100) / 400 = 100.5   Correct Option: 100.5
Answer: D
When 24 is divided by the positive integer i, the remainder is 4. Which of the following statements about i must be true?
I. i is even
II. i is a multiple of 5
III. i is a factor of 20	Choose the correct choice from the following answers
A) III only B) I and II only C) I and III only D) II and III only E) I, II, and III

Solution: 24= m*i + 4   m*i=20   put values of m   m=1 i=20   m=2 i=10   m=4 i=5   I. not true   II. true   III. true   D. correct
Answer: D
In ten years, David will be four times as old as Aaron. Twenty years ago, David was twice as old as Ellen. If David is nine years older than Ellen, how old is Aaron?	Choose the correct option:
A) 1.5–5
B) 6–10
C) 11–15
D) 16–20
E) 21–25

Solution: Let David's present age be 'd', 1.5–5aron's present age be 'a' and Ellen's present age be 'e'   In ten years, David will be four times as old as 1.5–5aron --> d+10 = 4(a+10)   Twenty years ago, David was twice as old as Ellen --> d-20 = 2(e-20)   David is seven years older than Ellen --> d = e + 9   e+9-20 = 2e-40   e-11 = 2e-40   e = 29   d = 36   46 = 4a + 40   a = 1.5   1.5–5nswer: 1.5–5
Answer: A
A certain industrial machine requires 15 quarts (480 ounces) of oil every day, and it is given a mixture of oil A and oil B. Oil A consists of 5% special additives while oil B consists of 8% special additives. If the machine needs exactly 40 ounces of the special additives to ensure smooth operation, then how much of oil A, in ounces, should be in the mixture? Choose the correct choice from the following answers
A) a.	A – 53.33  B) b.	B – 280  C) c. C – 290  D) d.	D – 300  E) e.	E – 320

Solution: 5%*x + 8% *(480-x)=40   1.6 = 3 %*x   x=53.33   a.	A – 53.33
Answer: A
How many positive integers y less than 30 have no common prime factor with 30?	Options:
A) 5
B) 6
C) 7
D) 8
E) 9

Solution: y=30=2*3*5. So, the number must be less than 30 and not have primes 2, 3, or 5.   This means that the number could be: 1, 7, 11, 13, 17, 19, 23, or 29. Total of 8 numbers.   Answer: 8.
Answer: D
Pipe A runs 30 liters of water per minute out of a pool that has a total volume of 3,600 liters. Pipe B empties a third of the pool in 6 hours.
Working together how long will it take both pipes to empty the pool?	Choose the correct choice from the following.
A) 2 hours and 36 minutes  B) 1.5 hours  C) 9 hours and 12 minutes  D) 15 hours  E) 1 hour and 48 minutes.

Solution: Pipe A has a rate of 30 liters per minute which equals a rate of 1800 liters per hour.   Pipe B has a rate of 200 liters per hour.   200 + 1800 (A+B) = Together they have a rate of 2000 liters per hour.   3600 (The pool) / 2000 = 9/5 = 108 / 60 = 1 Hour and 48 minutes   Answer -1 hour and 48 minutes.
Answer: E
A man covered a certain distance at a speed of 8 Kmph and returned at a speed of 4 Kmph. Find the average speed of whole journey?	Choose the most appropriate option.
A) 5 2/3 Kmph
B) 5 1/3 Kmph
C) 5 4/3 Kmph
D) 6 1/3 Kmph
E) None

Solution: Option '5 1/3 Kmph'
Answer: B
Look at this series: 21, 9, 21, 11, 21, 13, 21, ... What number should come next?
Pick one:
A) 14	B) 15	C) 21	D) 23	E) None of these

Solution: Explanation:   In this alternating repetition series, the random number 21 is interpolated every other number into an otherwise simple addition series that increases by 2, beginning with the number 9.   Answer is 15
Answer: B
The number of bacteria in a petri dish increased by 50 percent every 2 hours. If there were 108 million bacteria in the dish at 2: 00 p.m., at what time were there 32 million bacteria in the dish?
Select the correct option
A) 6: 00 p.m. B) 8: 00 p.m. C) 6: 00 a.m D) 8: 00 a.m. E) 10: 00 a.m.

Solution: Given:   he number of bacteria in a petri dish increased by 50 percent every 2 hours   There were 108 million bacteria in the dish at 2: 00 p.m   Since the bacteria is increasing by 50% every 2 hours, this means that the number is multiplied by 1.5 every 2 hours.   Required: At what time were there 32 million bacteria in the dish?   Assume that there were n intervals of 2 hours between 32 million and 108 million.   32 * (1.5)^n = 108   (3/2)^n = 108/32 = 27/8 = (3/2)^3   Hence n = 3 intervals.   Each interval was of 2 hours. Therefore, the number of hours = 6   Subtracting 6 hours from 2 PM, we get 8 AM as the answer.   Option 8: 00 a.m.
Answer: D
In a 200 m race, A beats B by 20 m and c by 38m. In a race of 600 m B will beat C by  Choose the correct choice
A) 20 m  B) 30 m  C) 25 m  D) 15 m  E) 60 m

Solution: It means, when A covers 200 m,   B covers only   (200-20)= 
  (200-20) = 180
180 m   and C covers only   (200-38)= 
  (200-38) = 162
162 m=> When C covers 162 m, B covers 180 m   => When B covers 600 m, C covers 162/180×600 = 540 m   Hence, B beats C by   600-540= 
  600-540 = 60
60 metre   ANSW60 mR:60 m
Answer: E
When positive integer n is divided by 3, the remainder is 1. When n is divided by 5, the remainder is 4. What is the smallest positive integer p, such that (n + p) is a multiple of 11?  Choose the correct choice from the following options
A) 1 B) 2 C) 5 D) 7 E) 20

Solution: When positive integer n is divided by 3, the remainder is 1 i.e., n=3x+1   values of n can be one of {1, 4, 7, 10, 13, 16, 19, 22..............49, 52, 59..................}   Similarly,   When n is divided by 5, the remainder is 5..i.e., n=5y+4   values of n can be one of {4, 9, 14, 19,...}   combining both the sets we get   n={4,19, 52, ...........}   What is the smallest positive integer p, such that (n + p) is a multiple of 11 or 11x   in case of n=4 p=7   so for min value of p, we take min value of n.   7 is the answer.
Answer: D
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?	Choose the correct option:
A) 1888
B) 2766
C) 2999
D) 1900
E) 1712

Solution: 2000 ---- 54   2000 ---- 39   x ----- 20   x*20 = 2000*39   x = 3900   2000   -------   1900   Answer: 1900
Answer: D
Due to construction, the speed limit along an 10-mile section of highway is reduced from 55 miles per hour to 25 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) 6.24 B) B) 13.1 C) C) 10 D) D) 15 E) E) 24

Solution: Old time in minutes to cross 10 miles stretch = 10*60/55 = 10*12/11 = 10.9   New time in minutes to cross 10 miles stretch = 10*60/25 = 10*12/5= 
10*12/5 = 24
24   Time difference= 13.1   Ans:13.1
Answer: B
By doing some calculation, 2+3=18, 3+5=42, 6+2=48 and find 5+6=??  Choose the correct choice from the following choices.
A) 74
B) 70
C) 72
D) 76
E) 78

Solution: Given 2+3=18==> (2^2+3^2)+(2+3)=18   3+5=42==> (3^2+5^2)+(3+5)=42   6+2=48==> (6^2+2^2)+(6+2)=48   So 5+6=72==> (5^2+6^2)+(5+6)=72   ANSWER:72
Answer: C
Average of money that group of 4 friends pay for rent each month is $800.After one persons rent is increased by 20% the new mean is $880.What was original rent of friend whose rent is increased?
Answers.
A) 800  B) 900  C) 1600  D) 1100  E) 1200

Solution: 0.2X = 4(880-800)   0.2X = 320   X = 1600   Answer 1600
Answer: C
Worldwide production of motor vehicles was 3.9 million vehicles in 1946 and 65.4 million in 1987. Of the following, which is closest to the average (arithmetic mean) annual increase, in millions, in worldwide production of motor vehicles during this period?
Choose the correct choice:	A) 0.08	B) 1.0	C) 1.1	D) 1.5	E) 41.8

Solution: Change in production of motor vehicles = 65.4 - 3.9= 
65.4 - 3.9 = 61.5
61.5 million in 41 years (1987 - 1946)   average increase per year= 61.5/41= 
61.5/41 = 1.5
1.5 million (apporx.)   Answer (1.5)
Answer: D
If C + D = 15 and C and D are any numbers, which of the following is a possible value for 8C + 5D? Pick.
A) 99 B) 29 C) 0 D) 09 E) 19

Solution: c + d = 15   8c + 5d = 3c + 5C + 5d = 5(c+d) + 3C = 5(15) + 3C=75 + 3C= c=-25   Now 3C is a multiple of 3, so the right answer should be 75 + multiple of 3.   c+d=15=-25+d=15=d=40   So, 0 is the right answer   Hence, 0 is the right answer.
Answer: C
If the consumer price index for a sample of goods and services purchased in Dallas rose from 100 at the end of 1967 to x at the end of 1985, what was the average T(arithmetic mean) annual increase in the index over this period?
Choose the correct choice from the following choices.
A) (x + 100)/18  B) x/18  C) (100 − x)/18  D) (x − 100)/18  E) 100x/18

Solution: CPI in end of 1967 = 100   CPI in end of 1985 = x   Number of years = 18   Average annual increase in CPI T= (x-100)/18   Answer (x − 100)/18
Answer: D
Each side of a certain parallelogram has length 8. If the area of the parallelogram is 24. Which of the following is the measure of one of its angles?  Answers.
A) 22 B) 45 C) 60 D) 90 E) 120

Solution: area of a parallelogram = b*h   b*h=24   h=24/8= 
24/8 = 3
3   sin theta=opp/hyp = 3/8   theta = sin inv of 3/8 = 22 deg   22
Answer: A
Find out the wrong number in the given sequence of numbers.
52, 51, 48, 43, 34, 27, 16  Pick one:	A) 22	B) 34	C) 77	D) 99	E) 21

Solution: Explanation:   Subtract 1, 3, 5, 7, 9, 11 from successive numbers.   So, 34 is wrong.   Answer: 34) 34
Answer: B
Two pipes P and Q can fill a tank in 5 hours and 10 hours respectively. If both pipes are opened simultaneously, how much time will be taken to fill the tank? Choose the correct choice from the following answers
A) 4 hours 20 min B) 5 hours 49 min C) 3 hours 20 min D) 3 hours 22 min E) 3 hours 42 min

Solution: Explanation:   Part filled by P in 1 hour = 1/5   Part filled by Q in 1 hour = 1/10   Part filled by (P + Q) in 1 hour = ( 1/5 + 1/10) = (3/10)   Time taken to fill the tank is (10/3) = 10/3*60= 
10/3*60 = 200
200 mins= 3 hrs 20 mins   ANSWER 3 hours 20 min
Answer: C
log3 N+log6 N what is 3 digit number N that will be whole number Choose the correct choice from the following options
A) 629	B) 729	C) 829	D) 929	E) 216

Solution: No of values N can take is 1   6^3=216   ANSW216R:216
Answer: E
What is the smallest positive integer x such that 450x is the cube of a positive integer?	Choose the correct choice from the following answers
A) 2
B) 15
C) 30
D) 60
E) 120

Solution: 450 = 2 x 3^2 x 5^2 now we need two 2s, one 3 and one 5 to make it perfect cube.   So x= 2^2 x 3 x 5 = 60.   Answer is 30.
Answer: C
There are 35 students in a hostel. If the no. of students increases by 10, the expenses of the mess increase by Rs.42/day while the average expenditure per head diminishes by Rs1. Find the original expenditure of the mess? Choose the correct choice from the following choices.
A) 304.5
B) 340.9
C) 342.9
D) 345.9
E) 380.9

Solution: Suppose the average join the mess , total expenditure = 35x + 42   Now, the average expenditure = (35x + 42)/ (35 + 10) = x – 1   or, 35x + 42 = 45x – 45   or, x = 8.7   Thus the original expenditure of the mess = 35 x 8.7 = Rs. 304.5   304.5
Answer: A