MU-NLPC/Calc-aqua_rat huggingface dataset:
In a box there are 8 red, 7 blue and 6 green balls. One ball is picked up randomly. What is the probability that it is neither red nor green?	Pick:
A) 7⁄19  B) 2⁄3  C) 3⁄4  D) 9⁄21  E) None of these

Solution: If the drawn ball is neither red nor green, then it must be blue, which can be picked in 7C1 = 7 ways. One ball can be picked from the total(8 + 7 + 6 = 21) in 21C1 = 21 ways.   ∴ Reqd probability = 7⁄21 = 1⁄3   Answer None of these
Answer: E
A tank is filled by 3 pipes with uniform flow. The first two pipes operating simultaneously fill the tan in the same time during which the tank is filled by the third pipe alone. The 2nd pipe fills the tank 5 hours faster than first pipe and 4 hours slower than third pipe. The time required by first pipe is
Select the correct option
A) 13 hours	B) 45 hours	C) 15 hours	D) 12 hours	E) 11 hours

Solution: If first pipe fills tank in x hrs, then second pipe fills tank in x-5 hrs and 3rd pipe fills tank in x-9 hrs, then   as per given condition   1/x +1/(x-5) = 1/(x-9)   solving it, we get x= 15 hrs   ANSWER:15 hours
Answer: C
A and B can finish a work in 16 days while A alone can do the same work in 32 days. In how many days B alone will complete the work?  Choose the correct choice from the following choices.
A) 76 days
B) 48 days
C) 98 days
D) 32 days
E) 22 days

Solution: B = 1/16 – 1/32 = 1/32 => 32 days   Answer: 32 days
Answer: D
Convert 2/5 to a decimal Select the correct option:
A) 0.1
B) 0.2
C) 0.3
D) 0.4
E) 0.5

Solution: 0.4ivide 2 by 5: 2 / 5 = 0.4   Answer:   2/5= 
  2/5 = 2/5 = around 0.4
0.4 (0.4)
Answer: D
Last year 28 members of a certain club traveled to England, 28 members traveled to France, and 30 members traveled to Italy. Last year no members of the club traveled to both England and France, 6 members traveled to both England and Italy, and 11 members traveled to both France and Italy. How many members of the club traveled to at least one of these three countries last year?  Pick:  A) 52  B) 69  C) 71  D) 73  E) 79

Solution: n(E or F or I) = n(E) + n(F) + n(I) - n(E and F) - n(F and I) - n(I and E) +n(E and F and I)   n(E or F or I) = 28+ 28 + 30 - 0 - 11 - 6 + 0   Why is the number of people who traveled to E and F and I 0? Because no one traveled to both England and France. So obviously, no one would have traveled to England, France and Italy.   n(E or F or I) = 69   Answer (69)
Answer: B
The batting average of a particular batsman is 62 runs in 46 innings. If the difference in his highest and lowest score is 150 runs and his average excluding these two innings is 58 runs, find his highest score. Select: A) 179 B) 208 C) 210 D) 225 E) 229

Solution: Explanation:   Total runs scored by the batsman = 62*46= 
62*46 = 2_852
2852 runs   Now excluding the two innings the runs scored= 58*44= 
58*44 = 2_552
2552 runs   Hence the runs scored in the two innings= 2852 – 2552 = 300 runs.   Let the highest score be x, hence the lowest score = x – 150   x + (x - 150) = 300   2x = 450   x = 225 runs   ANSWER 225
Answer: D
A person bought 118 glass bowls at a rate of Rs. 12 per bowl. He sold 102 of them at Rs. 15 and the remaining broke. What is the percentage gain for A?  Choose one
A) 40  B) 300/11  C) 243/7  D) 475/59  E) 279/8

Solution: CP=118*12= 
118*12 = 1_416
1416 and SP=102*15= 
102*15 = 1_530
1530   Gain %= 100*(1530-1416)/1100= 11400/1416=475/59   ANSWER:475/59
Answer: D
There are three secretaries who work for four departments. If each of the four departments have one report to be typed out, and the reports are randomly assigned to a secretary, what is the probability T that all three secretary are assigned at least one report?	Select the correct option
A) 8/9  B) 64/81  C) 4/9  D) 16/81  E) 5/9

Solution: I got the same answer: Here's my reasoning   First Report you have 3 choices   Second Report you have 2 choices   Third Report you have 1 choice   Fourth report 3 choices again   Then total number of ways is: 3*2*1*3=3^2*2   This is not correct. You have assumed that the 4th report must go to someone who already has a report. There is no such constraint. You can easily give the 1st and 2nd reports to secretary 1, 3rd report to secretary 2 and 4th report to secretary 3. But you have ignored all such cases.   The number of ways of ensuring at least one report goes to each secretary is 44/92 (select 2 reports out of 4 which go to the same person)*34/91 (select the person who must type 2 reports)*2! (since you have 2 reports left which you must distribute to the 2 remaining people such that each person gets one) = 36   Required probability T= 36/81.4/9
Answer: C
A bike covers a certain distance at the speed of 64km/h in 8 hrs. If the bike was to cover the same distance in approximately 6 hrs, at what approximate speed should the bike travel?
Answers
A) 80.56 km/h B) 85.34 km/h C) 95.05 km/h D) 98 km/h E) 99.56 km/h

Solution: Ans.(B)   Sol. Total distance = 64 × 8 = 512 km   Now speed = 512/6 = 85.34 km/h
Answer: B
A train 400 m long can cross an electric pole in 20 sec and then find the speed of the train?
Choose one:	A) 34	B) 56	C) 72	D) 35	E) 32

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: Option 72
Answer: C
Peter invested a certain sum of money in a simple interest bond whose value grew to $400 at the end of 4 years and to $ 500 at the end of another 2 years. What was the rate of interest in which he invested his sum?
Pick one
A) 12%
B) 12.5%
C) 67%
D) 25%
E) 33%

Solution: Lets assume the Principal Amount (initial amount invested) to be P   rate of interest to beRand time as T. We need to find R   Now After a time of 4years the principal P amounts to $400 and after a time of 6years ( question says after another 6years so 4+2) P becomes $500.   Formulating the above data   Amount (A1) at end of 4years   A1= P(1 + 4R/100) = 400   Amount (A2) at end of 6years   A2 = P(1 + 2R/100) = 500   25%ividing A2 by A1 we get   (1 + 4R/100)/(1 + 2R/100) = 5/4   after cross multiplication we are left with 4R =100 which gives R = 25%   Option: 25%
Answer: D
A certain university will select 1 of 7 candidates eligible to fill a position in the mathematics department and 2 of 8 candidates eligible to fill 2 identical positions in the computer science department. If none of the candidates is eligible for a position in both departments, how many different sets of 3 candidates are there to fill the 3 positions?  Choose the correct choice from the following
A) 42  B) 70  C) 140  D) 196  E) 315

Solution: Ans: 196   7C1 * 8C2   Answer 196)
Answer: D
Find the sum of prime numbers lying between 58 and 76?
Answers:
A) 198  B) 201  C) 252  D) 272  E) 331

Solution: Solution   Required sum	= 59 + 61 + 67 + 71 + 73)   = 331.   Answer 331
Answer: E
If a positive integer n is divided by 5 , the remainder is 3. which of the number below yields a remainder of 0 when it is divided by 5
Choose one:
A) n+3
B) n+2
C) n-2
D) n-1
E) n+1

Solution: Correct Answer : n+2   n is divided by 5 , the remainder is 3   n=5k+3 (k is integer)   add 2 to both sides of the above equation   n+2=5k+5   =5(k+1)   n+2 divided by 5 yields a remainder to zero.
Answer: B
On a game show, a contestant spins two different wheels; each wheel is numbered 1 to 15. What is the probability that the contestant will spin all tens? Choose the correct choice from the following:
A) 25  B) 64  C) 8/7  D) 4/6  E) 1/225

Solution: All 15s:   1st wheel = 15 = 1/15   2nd wheel = 15 = 1/15   (1/15)(1/15)= 1/225   Answer: 1/225
Answer: E
The second of two numbers is two less than three times the first. Find the numbers if there sum is
54.	Choose the correct answer:
A) 7-19
B) 8-20
C) 10-16
D) 14-40
E) 20-6

Solution: We are looking for two numbers.   #1 - x   #2 - 3x â€“ 2   The sum is 54. #1 + #2 = 54   Substituting x + 3x â€“ 2 = 54   4x â€“ 2 = 54   4x = 56   x = 14   The first number is 14, the second number is two less than three times 14 or 40.   correct answer 14-40
Answer: D
The price of a bushel of corn is currently $3.20, and the price of a peck of wheat is $10.80. The price of corn is increasing at a constant rate of 5x cents per day while the price of wheat is decreasing at a constant rate of x(2^1/2) - x cents per day. What is the approximate price when a bushel of corn costs the same amount as a peck of wheat? Choose the correct choice from the following answers
A) $4.50 B) $10.2 C) $5.30 D) $5.50 E) $5.60

Solution: I Tried using Time/Rate approach:-   Initial Price Difference = 10.80 - 3.20= 
10.80 - 3.20 = 7.6
7.60   Price of Corn increasing by 5x   Price of Wheat decreasing by x(1.4)-x= .4x   Since both the quantities are moving towards reducing the Price Gap hence:-   Relative Increase = 5x +.4x   Let T be the Time by which GAP is filled so,   7.6 = T(5.4x) -> T= (7.6)/5.4X   Final Price = 3.20 + 5X * T -> 3.20 + 5*7.6/5.4 = 10.2   Answer $10.2.
Answer: B
Of the total amount that Jill spent on a shopping trip, excluding taxes, she spent 40 percent on clothing, 30 percent on food, and 30 percent on other items. If Jill paid a 4 percent tax on the clothing, no tax on the food, and an 8 percent tax on all other items, then the total tax that she paid was what percent of the total amount that she spent, excluding taxes?	Pick one
A) 2.8% B) 3.6% C) 4% D) 5.2% E) 6.0%

Solution: Let amount spent by Jill = 100   4%lothing=40, Food=30, others=30   Tax on clothing= 1.6   Tax on others=2.4   Percentage= 4/100= 4%   Answer: 4%
Answer: C
Harriet planned to complete a certain task on Wednesday, January 1, but because of illness the completion date was postponed 47 days. On which day of the week in February was the task completed?	Choices
A) Monday
B) Tuesday
C) Wednesday
D) Thursday
E) Friday

Solution: This type of story problem is essentially just about a repeating pattern and a 'remainder.'   We're told that Harriet planned to complete a certain task on WEDNESDAY, January 1, but because of illness the completion date was postponed 47 DAYS. We're asked on what day of the week the task was actually completed on.   Since the task was supposed to be completed on a Wednesday....   A 1 day postponement would be Thursday   A 2 day postponement would be Friday   A 3 day postponement would be Saturday   A 4 day postponement would be Sunday   A 5 day postponement would be Monday   A 6 day postponement would be Tuesday   A 7 day postponement would be Wednesday   A 8 day postponement would be Thursday   Etc.   So this question is ultimately asking how many 'groups of 7' are there, and how many 'leftover days' are there, when you postpone 47 days.   47/7 = 6 remainder 5   This means that there are 6 full weeks AND 5 extra days after a Wednesday....Thus, the task was completed on a Monday.   Monday
Answer: A
A certain farmer pays $30 per acre per month to rent farmland. How much does the farmer pay per month to rent a rectangular plot of farmland that is 360 feet by 1210 feet? (43,560 square feet = 1 acre) Choose the most appropriate option
A) $5,330
B) $3,360
C) $1,350
D) $300
E) $150

Solution: Basically the question an error. 1 acre = 43,560 square feet and if it is then the answer is 300 ($300)
Answer: D
Anand and Deepak started a business investing Rs. 22,500 and Rs. 35,000 respectively. Out of a total profit of Rs. 13,800, Deepak's share is:? Options:  A) Rs.8467  B) Rs.8428  C) Rs.8400  D) Rs.8429  E) Rs.8420

Solution: Ratio of their shares   = 22500 : 35000   = 9:14   Deepak's share   = 13800 * 14/23   = Rs.8400.   Answer:Rs.8400
Answer: C
How many ways are there for 6 males and 3 females to sit (around a circular table) if no male should sit next to a male (and no female next to female) and Mary wants to sit with her back on the wall?	Choose the correct choice:
A) 6 B) 12 C) 72 D) 100 E) 1440

Solution: So Mary has her own chair, fixed position. Other two females around the table can sit in 2 ways: the first to the left of Mary and the second to the right or vise-versa. Now, if 6 males will sit between them then no two female or two male will sit next to each other (female-male-female-male-female-male). But these males on their spots can also sit in different ways, namely in 6! different ways, so total 2*6!=1440   Answer 1440.
Answer: E
With a uniform speed a car covers the distance in 8 hours. Had the speed been increased by 2 km/hr, the same distance could have been covered in 7 1/2 hours. What is the distance covered? Choose the correct option
A) 187 km	B) 480 km	C) 278 km	D) 240 km	E) 671 km

Solution: Let the distance be x km. Then,   x/(7 1/2) - x/8 = 2   2x/15 - x/8 = 2 => x = 240 km.   Answer:240 km
Answer: D
Miguel is 41 years old. He is 5 years older than twice his son’s age. Find the age of his son.
Pick one: A) 11years B) 12years C) 13years D) 14years E) 18years

Solution: sons age=x   41-2x=5   x=18years   ANSW18yearsR:18years
Answer: E
A certain shade of gray paint is obtained by mixing 3 parts of white paint with 5 parts of black paint. If 2 gallons of the mixture is needed and the individual colors can be purchased only in one gallon or half gallon cans, what is the least amount of paint, in gallons, that must be purchased in order to measure out the portions needed for the mixture?
Options:
A) 2  B) 2 1/2  C) 3  D) 3 1/2  E) 4

Solution: Ratio; white: black: gray = 3: 5: (3+5) = 3: 5: 8   If 2 gallons of the mixture is needed <==> Need 2 gallons of gray paint.   Then,   3: 5: 8 = x: y: 2   3/8 = x/2; x = 3/4   5/8 = y/2; y = 5/4   You need 3/4 gallon of white. You have to buy 1 gallons.   You need 5/4 gallons of black. You have to buy 1 gallon and another 1/2 gallon of black.   The least amount of paint = 1 + 1 + 1/2 = 2.5.   ANSWER:2 1/2
Answer: B
A class contains five juniors and five seniors. If one member of the class is assigned at random to present a paper on a certain subject, and another member of the class is randomly assigned to assist him, what is the probability T that both will be juniors? Choose the correct answer:	A) 1/10	B) 1/5	C) 2/9	D) 2/5	E) 1/2

Solution: I think you're right. The other way to do it (but the long way) is to figure out the probability that it is not two Juniors.   2 seniors = P(Senior) * P(Senior) = 2/9   1 Senior and 1 Junior = (1/2) *(5/9)*2 = 5/9   Probability that it is not two Juniors is 5/9+2/9 = 7/9 so the probability T that it is two juniors is 1- (7/9) = 2/9.2/9
Answer: C
If a tire rotates at 400 revolutions per minute when the car is traveling 120km/h, what is the circumference of the tire?  Pick one:
A) 2 meters	B) 6 meters	C) 5 meters	D) 3 meters	E) 7 meters

Solution: 400 rev / minute = 400 * 60 rev / 60 minutes   = 24,000 rev / hour   24,000 * 5 meters = 120,000 m : 5 meters is the circumference   5 meters = 5 meters   correct answer 5 meters
Answer: C
A can do a piece of work in 15 days. A does the work for 5 days only and leaves the job. B does the remaining work in 12 days.In how many days B alone can do the work?  Select the correct option.
A) 5days B) 7 days C) 12 days D) 9 days E) 18 days

Solution: 18 daysxplanation:   A’s 5 day work = 5*1/15=1/3   Remaining work = 1-1/3=2/3   B completes 2/3 work in 6 days   B alone can do in x days   2/3*x=12   X=18 days   Answer: Option 18 days
Answer: E
Solve:-
666 x 666 x 666 + 555 x 555 x 555 = ?(666 x 666 - 666 x 555 + 555 x 555)	Choices
A) 888
B) 333
C) 555
D) 1221
E) 889

Solution: Given Exp. = (a3 + b3) = (a + b) = (666 + 555)= 
(666 + 555) = 1_221
1221(a2 - ab + b2)   Answer 1221
Answer: D
Sreedhar and Sravan together can do a work in 25 days. With the help of Pavan, they completed the work in 8 days and earned Rs. 225. What is the share of Sravan, if Sreedhar alone can do the work in 75 days?  Choose the correct choice from the following choices.
A) 33	B) 77	C) 48	D) 99	E) 12

Solution: Sravan's one day's work = 1/25 - 1/75 = 2/75   Sravan worked for 8 days. So, his 8 days work = 8 * 2/75 = 16/75   Sravan completed 16/75th of total work.   So, his share is 16/75 * 225 = Rs. 48.   Answer: 48
Answer: C
If y exceeds x by 30%, then x is less than y by?	Choose the correct choice from the following options.
A) 16 2/9%  B) 16 3/3%  C) 16 2/3%  D) 23 1/13%  E) 16 1/3%

Solution: X=100	y=130   130------30   100-------? => 23 1/13%   Answer:23 1/13%
Answer: D
A certain number of men can do a work in 20days. If there were 4 men less it could be finished in 5days more. How many men are there?
Answers
A) 10	B) 20	C) 25	D) 30	E) 35

Solution: The original number of men = 4(20+5)/5 = 20men   Answer is 20
Answer: B
Janet covered a distance of 340 miles between city A and city B taking a total of 5 hours. If part of the distance was covered at 60 miles per hour speed and the balance at 80 miles per hour speed, how many hours did she travel at 60 miles per hour?	Select the correct option:
A) 1 hour 45 minutes	B) 2 hours	C) 2 hours 30 minutes	D) 3 hours	E) None of these

Solution: Janet covered a distance of 340 miles between city A and city B taking a total of 5 hours. time taken at 60:time taken at 80::(greater speed-average speed):(average speed-lower speed)   average speed is   340/5= 
  340/5 = 68
68   That gives the answer 3:2=3 hours
Answer: D
. A car covers a distance of 742 km in 7 hours. Find its speed?	Choose one.
A) 104
B) 55
C) 148
D) 150
E) 159

Solution: 742/5 = 148 kmph   Answer: 148
Answer: C
5216 x 51 = ? Choices
A) 212016 B) 266016 C) 266436 D) 216314 E) 216318

Solution: Normal way of multiplication may take time. Here are one alternative.   5216 x 51 = (5216 x 50) + 5216 = (5216 x 100)/2 + 5216   = 521600/2 + 5216 = 260800 + 5216= 
260800 + 5216 = 266_016
266016   Answer is 266016
Answer: B
A garrison of 400 men had a provision for 31 days. After 27 days 200 persons re-enforcement leave the garrison. Find the number of days for which the remaining ration will be sufficient? Choose the correct answer:
A) 65 days
B) 45 days
C) 8 days
D) 16 days
E) 18 days

Solution: 400 --- 31   400 --- 4   200 --- ?   400*4 = 200*x => x =8 days.   Answer: 8 days
Answer: C
A certain Deep Blue paint contains 45 percent blue pigment and 55 percent red pigment by weight. A certain green paint contains 35 percent blue pigment and 65 percent yellow pigment. When these paints are mixed to produce a brown paint, the brown paint contains 40 percent blue pigment. If the brown paint weighs 10 grams, then the red pigment contributes how many grams of that weight? Choices
A) 1.5	B) 2.5	C) 3.5	D) 2.75	E) 4.5

Solution: 10 Grams of combined mixture and 40% blue pigment means that the mixtures were mixed 50% each. Thus 5 grams a piece. Out of the 5 grams of the Dark Blue paint, 60% is red. Therefore, 5*.55 =2.75 Grams of red pigment
Answer: D
the sum of 7th and 23rd term of A.P. is equal to the sum of 8th , 15th and 13 th term . find the term which is 0 Choose one:
A) 6 B) 8 C) 10 D) 12 E) 14

Solution: t7 + t23 = t8 + t15 + t13   => a+6d + a+22d = a+7d + a+14d + a+12d   => a +5d = 0   => t6= 0 i.e. 6th term is zero.   6NSWER: 6
Answer: A
Two bullet trains of equal lengths take 10 seconds and 20 seconds respectively to cross a telegraph post. If the length of each bullet train be 120 metres, in what time (in seconds) will they cross each other travelling in opposite direction?	Choose the correct choice from the following answers
A) 11 sec. B) 15 sec. C) 13.3 sec. D) 17 sec. E) 19 sec.

Solution: Speed of the first bullet train = 120/10 m/sec = 12 m/sec.   Speed of the second bullet train = 120/20 m/sec = 6 m/sec.   Relative speed = (12 + 6)= 
(12 + 6) = 18
18 m/sec.   Required time= (120 + 120)/18 sec = 13.3 sec.   13.3 sec.
Answer: C
A train crosses a pole in 4 sec while travelling at a speed of 135 kmph, what is the length of the train?
Answers
A) 135 m B) 140 m C) 145 m D) 150 m E) 155 m

Solution: Explanation:   150 m = 135 * 5/18 * 4= 
135 * 5/18 * 4 = 150
150 m   Answer: Option 150 m
Answer: D
Tickets numbered 1 to 50 are mixed and one ticket is drawn at random. Find the probability that the ticket drawn has a number which is a multiple of 4 or 7?  Choices
A) 9/25  B) 9/50  C) 18/25  D) 13/20  E) None of these

Solution: EXPL9/25N9/25TION:   S = {1, 2, 3, … , 49, 50}   E = {4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 7, 14, 21, 35, 42, 49}   n(S) = 50   n(E) = 18   P(E) = n(E)/n(S) = 18/50   = 9/25   9/25NSWER IS 9/25
Answer: A
Mangala completes a piece of work in 10 days, Raju completes the same work in 60 days. If both of them work together, then the number of days required to complete the work is?
Choose the correct choice from the following answers
A) 60/7 days
B) 10 days
C) 12 days
D) 14 days
E) 16 days

Solution: If A can complete a work in x days and B can complete the same work in y days, then, both   of them together can complete the work in x y/ x+ y days.   That is, the required No. of days = 10 Ã— 60/70 = 60/7 days   60/7 days)
Answer: A
For any positive x, y and z if x is n% of y and z is m% of y then what percentage R must x be of z?  Choose the correct choice from the following:
A) (n/m)%
B) (m × n)%
C) (100 / [m × n]) %
D) (100 × m/n)%
E) (100 × n/m)%

Solution: x is n% of y M(100 × n/m)%ANS x= (n/100 )* y------------------------eq1   z is m% of y M(100 × n/m)%ANS z= (m/100 )* y------------------------eq2   Find equation of xz   substitute value of y from 2nd equation into Ist equation   so x= (n/100)*(100z/m)   so x= (n/m)z   or x= (100n/m)z/100   so answer R is 100n/m %.(100 × n/m)%
Answer: E
Average of first five multiples of 5 is	Choices:
A) 9	B) 11	C) 13	D) 15	E) 16

Solution: Explanation:   Average=5(1+2+3+4+5)/5=15   Answer: Option 15
Answer: D
Earl can stuff advertising circulars into envelopes at the rate of 36 envelopes per minutes and Ellen requires a minutes and half to stuff the same number of envelops.Working together,how long will it take Earl and Ellen to stuff 360 envelopes  Choose the correct choice from the following options.
A) 6 minutes  B) 5 minutes  C) 7 minutes  D) 3 minutes  E) 4 minutes

Solution: earl takes 1 min. for 36 envelopes.   ellen takes 3/2 mins for the same. so ellen can stuff ((36)/(3/2)) in 1 min. i.e., 24 envlpes a min.   so both of them when work together can stuff 36+24= 
36+24 = 60
60 envelopes in 1 min.   for 360 envelopes they will take 360/60 mins. i.e., 6 mins.   6 minutesNSWER:6 minutes
Answer: A
If y is an integer, then the least possible value of |21 - 5y| is
Pick: A) 2 B) 1 C) 3 D) 4 E) 5

Solution: We know that 5y is a multiple of 5, so let’s first look at the multiples of 5 closest to 22. We have “20” and “25”. Let’s subtract both of these from 21 and see which one produces the smallest result. When 5y = 20, y is 4 and when 5y = 25, y is 5. Let’s start with letting y = 4.   |21-5(4)|   |21-20|   |1| = 1   Next, let’s let y equal 5.   |21-5(5)|   |21-25|   |-4| =4   We see that the smallest possible value of |21-5y| is 1.   Answer 1.
Answer: B
How many integers from 22 to 160, inclusive, are divisible by 3 but not divisible by 7?	Choose one:
A) 30	B) 35	C) 40	D) 50	E) 60

Solution: We should find # of integers divisible by 3 but not by 3*7= 
3*7 = 21
21.   # of multiples of 21 in the range from 22 to 160, inclusive is   (147-42)/21+1= 
  (147-42)/21+1 = 6
6;    46-6= 
 46-6 = 40
40.   Answer: 40.
Answer: C
A is twice efficient as B and together they do the same work in as much time as C and D together. If C and D can complete the work in 20 and 30 daysrespectively, working alone ,then in how many days A can complete the work individually:	Choices.
A) 12 days  B) 18 days  C) 24 days  D) 30 days  E) None of these

Solution: Explanation:   A + 18 days = C + D   | | | |   Ratio of efficiency 10x + 5x 9x + 6x   |________| |_________|   15x 15x   Therefore , ratio of efficiency of A:C =10:9   Therefore, ratio of days taken by A:C = 9:10   Therefore, number of days taken by A = 18 days   Answer: 18 days
Answer: B
Consider the equation K = (mv^2)/2.
If v and m are both doubled, by what factor is K increased?	Choose the correct choice:
A) 2 B) 6 C) 8 D) 10 E) 4

Solution: We have,   K = (mv^2)/2   On doubling both m and v,   K = [(2m)*(2v)^2]/2   K = (2m*4v^2)/2   K = (8mv^2)/2   K = 8*(mv^2)/2   Initially K = (mv^2)/2. After changing m and v, K = 8*(mv^2)/2   Hence, K increases by 8 times.   Answer = 8 = 8
Answer: C