MU-NLPC/Calc-aqua_rat huggingface dataset:
What is the sum of the multiples of 4 between 19 and 130 inclusive?
Select the correct option: A) 2012 B) 2044 C) 2060 D) 2072 E) 2080

Solution: the fastest way in an AP is to find the average and multiply with total integers..   between 19 and 130, the smallest multiple of 4 is 20 and largest =128..   average=(20+128)/2=148/2= 
148/2 = 74
74.   total numbers= (128-20)/4 + 1= 27+1=28..   sum=28*74= 
28*74 = 2_072
2072   ans 2072
Answer: D
The average of first five prime numbers greater than 3 is?  Pick one:
A) 32.2  B) 10.6  C) 32.3  D) 32.8  E) 32.4

Solution: 5 + 7 + 11 + 13 + 17= 
5 + 7 + 11 + 13 + 17 = 53
53/5= 
53/5 = 53/5 = around 10.6
10.60   Answer= 10.6
Answer: B
Find compound interest on Rs. 7500 at 4% per annum for 2 years, compounded annually Answers
A) Rs 312 B) Rs 412 C) Rs 512 D) Rs 612 E) None of these

Solution: Explanation:   Please apply the formula   Amount=P(1+R100)nC.I. = Amount - P   Answer: Rs 612
Answer: D
A can contains a mixture of liquids A and B is the ratio 7:5. When 9 litres of mixture are drawn off and the can is filled with B, the ratio of A and B becomes 7:9. How many liter E of liquid A was contained by the can initially? Choose the most appropriate option.
A) 10	B) 20	C) 21	D) 25	E) 27

Solution: As A:B::7:5 ---> only option C is a multiple of 7 and hence it is a good place to start. Also A:B::7:5 means that , A = (712)*Total and B = (5/12)*Total   If A = 21 , B = 15 ---> remove 9 litres ---> you remove (7/12)*9 of A ---> A remaining = 21-(7/12)*9 = 63/4   Similarly, for B, you remove (5/12)*9 ---> B remaining = 15 - (5/12)*9 = 45/4 and then add 9 more litres of B ---> 9+45/4 = 81/4   Thus A/B (final ratio) = (45/4)/(81/4) = 7:9 , the same as the final ratio mentioned in the question.   Hence C is the correct answer.   A/B = 7/9 = (7x-(7/12)*9)/ (5x-(5/12)*9+9), where 7x and 5x are initial quantities of A and B respectively.   Thus, 7/9 = (7x-(7/12)*9)/ (5x-(5/12)*9+9) ---> giving you x=3. Thus A (original) E= 7*3 = 21.21
Answer: C
Kate is 12 years old. His age is 4 times the age of Robbie. Find the age of Robbie.	Choose the correct choice from the following.
A) 1yrs B) 2yrs C) 3yrs D) 4yrs E) 5yrs

Solution: Let Kate age, x = 12   robbie = x/4   =12/4= 
12/4 = 3
3yrs   ANSWER:3yrs
Answer: C
Five years ago, the average age of A, B, C and D was 45 years. With E Joining them now, the average of all the five is 51 years. The age of E is?  Choose the correct choice:
A) 45 B) 47 C) 55 D) 49 E) 46

Solution: Solution   5 years ago average age of A,B,C,D = 45 years   => 5 years ago total age of A, B, C, D = 45 x 4 = 180 years   => Total present age of A, B, C, D = 180 + 5x4 = 200 years   If E's present age is x years = 200+x/5= 51   x=55 years. Answer 55
Answer: C
At a certain high school, a student’s popularity is determined by his or her locker number. Whoever has the locker number with the greatest number of distinct prime factors is the most popular student in the school. If Dhoni ,Kamal, Gokul, and Dinesh get lockers with the numbers 50, 400, 150, and 25, respectively, who is the most popular student?	Select:
A) Dhoni B) Kamal C) Gokul D) Dinesh E) They have equal popularity

Solution: Distinct prime factors of 50 (Dhoni) : 2,5   Distinct prime factors of 400 (Kamal): 2 and 5.   Distinct prime factors of 150 (Gokul): 2,3, and 5   Distinct prime factors of 25 (Dinesh): 5.   So most popular student - Gokul   Answer Gokul
Answer: C
If 4 and 11 are the lengths of two sides of a triangular region, which of the following can be the length of the third side?
I. 5
II. 13
III. 15
Answers
A) I only
B) II only
C) I and II only
D) II and III only
E) I, II, and III

Solution: The length of any side of a triangle must be larger than the positive difference of the other two sides, but smaller than the sum of the other two sides.   i.e let us assume the third side be c and other sides be a and b, then as per rule   c > a - b and c < a + b.   Let's take options   option 1. the three sides will be 5 , 4 and 11..   then 11 > 5-4 --Yes   11 < 4+9...NO   option 2... 13, 4 and 11.   then 13 > 11-4...Yes   13 < 11+4...Yes   Option 3..15 ,4 and 11.   15 < 11+4...No   15 > 11-4...Yes...   Only 13 is correct .   Answer: option II only is correct..
Answer: B
Tim and Élan are 90 miles away from one another. They are starting to move towards each other simultaneously, Tim at a speed of 10 Mph and Élan at a speed of 5 Mph. If every hour they double their speeds, what is the distance that Tim will pass until he meets Élan? Options.
A) 30 miles.	B) 35 miles.	C) 45 miles.	D) 60 miles.	E) 65 miles.

Solution: In 1st hour: Relative speed of the two will be  10+5= 
 10+5 = 15
15 miles / hour. As they move towards each other, The distance between them reduces by 15 miles. Distance left between them:   90 - 15= 
  90 - 15 = 75
75 miles.   In 2nd hour: Speed of Tim: 20Mph, That of Elan: 10 Mph. Relative speed of the two will be   20+ 10= 
  20+ 10 = 30
30 miles / hour. As they move towards each other, The distance between them reduces by 30 miles. Distance left between them:   75 - 30= 
  75 - 30 = 45
45 miles.   In 3rd hour: Speed of Tim: 40 Mph, That of Elan: 20 Mph. Relative speed of the two will be   40+ 20= 
  40+ 20 = 60
60 miles / hour.   Now in order to cover the remaining distance of 45 miles. They will take: (45/ 60) hrs.= (3/4) hour.   Distance travelled by Tim?   In first hour: 1 hour * (10 miles per hour) = 10 miles   In second hour: 1 hour * (20 miles per hour) = 20 miles   In third hour: (3/4) hour * (40 miles per hour) = 30 miles   Total distance travelled:   10+20+30= 
  10+20+30 = 60
60 miles.   60 miles. is the answer
Answer: D
Peeta asks Katniss, 'It is 10 am as per my watch right now.Do you know what will be the time 23, 999, 999 hours later?'
Katniss knows the answer. Do you ? Choose the correct choice:
A) 5pm  B) 6pm  C) 4am  D) 7am  E) 8pm

Solution: D   7pm   The time after 24, 000, 000 hours will be the same as it is now. We want the time 3 hours before that and thus you can deduct three hours from 9 pm. So the time will be 6 pm.
Answer: D
A certain country is divided into 6 provinces. Each province consists entirely of Progressives and Traditionalists. If each province contains the same number of Traditionalists and the number of Traditionalists in any given province is 1/18 the total number of Progressives in the entire country, what fraction of the country is Traditionalist?	Choices.
A) 1/5 B) 1/3 C) 1/2 D) 2/3 E) 3/4

Solution: Let P be the number of Progressives in the country as a whole.   In each province, the number of traditionalists is P/18   The total number of traditionalists is 6P/18 = P/3.   The total population is P + P/3 = 4P/3   P / (4P/3) = 3/4   The answer is 3/4.
Answer: E
There was a cycle race going on. 1/5th of the those in front of a person and 5/6th of those behind him gives the total number of participants. How many people took part in the race?
Answers:
A) 30	B) 31	C) 32	D) 33	E) 34

Solution: let total =x   1/5*(x-1)+5/6(x-1)=x by solving this we will get 31   ANSWER:31
Answer: B
A retailer sold two articles at a profit percentage of 10% each. The cost price of one article is three – fourth that of the other. Find the ratio of the selling price of the dearer article to that of the cheaper one  Choose the correct choice from the following answers.
A) 4:3  B) 3:4  C) 41:31  D) 51:41  E) 61:41

Solution: Let C.P of one of the article be X, Then C.P of the other = ¾X,   S.P 1 = 11X/10, S.P2 =3/4*11/10X,   S.P1/S.P2 = 11X/10 *40/33X = 4/3   S.P1: S.P2 = 4 : 3   4:3NSWER:4:3
Answer: A
A tradesman by means of his false balance defrauds to the extent of 20%? in buying goods as well as by selling the goods. What percent does he gain on his outlay?
Choose the correct choice from the following answers:
A) 56%	B) 44%	C) 78%	D) 55%	E) 33%

Solution: 44%   g% = 20 + 20 + (20*20)/100= 
20 + 20 + (20*20)/100 = 44
44%
Answer: B
A crow leaves its nest, and flies back and forth from its nest to a nearby ditch to gather worms. The distance between the nest and the ditch is 400 meters. In one and a half hours, the crow manages to bring worms to its nest 15 times. What is the speed of the crow in kilometers per hour? Choose the correct option
A) 2 B) 4 C) 6 D) 8 E) 10

Solution: The distance between the nest and the ditch is 400 meters.   15 times mean = A crow leaves its nest, and flies back ( going and coming back) i.e. 2 times we get total 30 rounds.   So the distance is  30 * 400= 
 30 * 400 = 12_000
12000.   8= ST   12000/1.5 = T , I think we can take 12000 meters as 12km, then only we get T = 8.( 1000 meters = 1 km)   8)
Answer: D
Fifteen identical machines, running continuously at the same constant rate, take 10 days to complete a shipment. How many additional machines, each running at the same constant rate, would be needed to reduce the time required to complete a shipment by five days?  Pick one:
A) 2 B) 3 C) 4 D) 6 E) 9

Solution: From the question you know that 15R = 1/10. The question asks you (partially) to make the rate from 1/10 to 1/5 (drop from 10 day to 5). So the only thing that you need to do is to find the magic number than can convert 1/10 to 1/5.   So 1/10 * x = 1/5 (1 equation with one unknown). So by solving this you get x = 10/5 or 2/1. Thats it then! Take the magic number 4/3 and multiply BOTH sides of the original equation and you have:   12*(2/1)*R = (2/1) * 1/10   12 * 2 * R = 1/5, Hence 24R = 1/5, therefore 9 more machines!   9
Answer: E
If the least common multiple of two prime numbers x and y is 10, where x > y, then the value of 2x + y is	Choose the correct choice from the following answers:  A) 7  B) 9  C) 11  D) 12  E) 21

Solution: LCM of two prime numbers will basically be multiple of those numbers. LCM = 10 = 2*5, both of which are prime.   Now we know x>y, so x=5 and y =2.   2x+y = 2*5 + 2 = 10 + 2= 
10 + 2 = 12
12.   ANSWER:12
Answer: D
When a is divided by b, the quotient is c with remainder 5. What is a in terms of 5, b, and c?  Pick: A) bc-5 B) 5bc C) 5b/c D) b/c E) bc+5

Solution: a/b =c with remainder 5   i.e, a-5 = bc   a= bc+5   Answer : bc+5
Answer: E
In a board game, a stack of 46 cards, 8 of which have pictures of fruit, are shuffled and then placed face down. If the first 2 cards selected do not have pictures of fruit, what is the probability that the third card selected will have a picture of fruit?  Answers.
A) 2/11 B) 1/6 C) 1/8 D) 3/7 E) 4/23

Solution: After 2 cards have been selected, there are 44 cards remaining.   P(third card has a picture of fruit) = 8/44 = 2/11   The answer is 2/11.
Answer: A
Seed mixture X is 40% ryegrass and 60% bluegrass by weight; seed mixture Y is 25% ryegrass and 75% fescue. If a mixture of X and Y contains 37% ryegrass, what percent of the weight of the mixture is from mixture X?
Choose one:
A) 20% B) 40% C) 50% D) 60% E) 80%

Solution: 37% is 12%-points above 25% and 3%-points below 40%.   Thus the ratio of mixture Y to mixture X is 1:4.   The percent of mixture X is 4/5 = 80%.   The answer is 80%.
Answer: E
Jacob is now 13 years younger than Michael. If 9 years from now Michael will be twice as old as Jacob, how old will Jacob be in 4 years?  Options:
A) 8
B) 7
C) 15
D) 21
E) 25

Solution: Jacob=x years, Michael=x+13 years   9 years from now,   2(x+9)=x+22   2x+18=x+22   x=4   x+4=8 years   8nswer 8
Answer: A
Lakshmi invested some money in 25% stock at 500.If Usha wants to invest in an equally good 50% stock ,he must purchase a stock worth of :  Options
A) Rs. 1000 B) Rs. 1200 C) Rs. 1300 D) Rs. 1400 E) Rs. 1500

Solution: Solution   For an income of Rs. 25, investment = Rs. 500   For an income of Rs. 50, investment = Rs.(500/25x50) = Rs. 1000   Rs. 1000nswer Rs. 1000
Answer: A
The size of a flat-screen television is given as the length of the screen’s diagonal. How many square inches greater is the screen of a square 24-inch flat-screen television than a square 17-inch flat-screen television?  Choose the correct answer:	A) 143.5	B) 154	C) 160	D) 148.75	E) 142.25

Solution: If we take a square with side length x and draw a diagonal, we get two isosceles right triangles.   If we focus on one such right triangle, we see that the legs have length x.   square 24-inch flat-screen television   The diagonal (hypotenuse) = 24   So, we can apply the Pythagorean Theorem to get x² + x² = 24²   Simplify: 2x² = 24²   Divide both sides by 2 to get: x² = 24²/2   Since the area of the square = x², we can see that the area of this square is 24²/2   square 17-inch flat-screen television   The diagonal (hypotenuse) = 17   So, we can apply the Pythagorean Theorem to get x² + x² = 17²   Simplify: 2x² = 17²   Divide both sides by 2 to get: x² = 17²/2   Since the area of the square = x², we can see that the area of this square is 17²/2   DIFFERENCE IN 143.5RE143.5S =24²/2-17²/2   = 288 -144.5 i.e = 143.5   143.5
Answer: A
A man said to his son, "I was two-third of your present age when you were born". If the present age of the man is 48 years, find the present age of the son?  Choose the correct choice: A) 25.7 years B) 28 years C) 29.3 years D) 28.8 years E) 28.9 years

Solution: Present age of the son be P, he was born P years ago.   The age of the man was: (48 - P).   His age when the son was born should be equal to 2/3 of P.   (48 - P) = 2/3 P   5P = 144 => P = 28.8   ANSWER:28.8 years
Answer: D
what is the sum of the first 25 odd natural numbers
Choices
A) 300  B) 400  C) 625  D) 600  E) 700

Solution: sum of first n odd natural nuber is = n^2   so sum of the first 25 odd natural numbers=(25)^2=625   ans 625   ANSWER:625
Answer: C
Find the smallest number which when divided by 13 and 16 leaves respective remainders of 2 and 5. Select.
A) 187  B) 197  C) 207  D) 219  E) 227

Solution: Let 'N' is the smallest number which divided by 13 and 16 leaves respective remainders of 2 and 5.   Required number = (LCM of 13 and 16) - (common difference of divisors and remainders) = (208) - (11)= 
(208) - (11) = 197
197.   ANSWER:197
Answer: B
Mike weighs twice as much as Mary. Mike's weight is 150% of Michelle's weight. Alan weighs 140% of Charlie's weight. Charlie weighs 180% of Mary's weight. Which of these 5 people weighs the highest? Select the correct option
A) Mary
B) Mike
C) Michelle
D) Alan
E) Charlie

Solution: Mary < Michelle < Mike   Charlie < Alan   Let x be Mary's weight.   Mike's weight is 2x and Alan's weight is   1.4*1.8= 
  1.4*1.8 = 2.52
2.52x.   The answer is Alan.
Answer: D
A train 210 m long, running with a speed of 63 km/hr will pass a tree in?	Choose the correct choice from the following answers:
A) 18 sec
B) 16 sec
C) 76 sec
D) 12 sec
E) 17 sec

Solution: Speed = 63 * 5/18 = 35/2 m/sec   Time taken = 210 * 2/35= 
210 * 2/35 = 12
12 sec   Answer:12 sec
Answer: D
The average weight of 25 persons sitting in a boat had some value. A new person added to them whose weight was 46 kg only. Due to his arrival, the average weight of all the persons decreased by 5 kg. Find the average weight of first 25 persons?	Choose the correct choice from the following answers:
A) 2211  B) 2721  C) 227  D) 176  E) 167

Solution: 25x + 46 = 26(x – 5)   x = 176   Answer:176
Answer: D
There are 4 periods in each working day of a school. In how many ways can one organize 3 subjects such that each subject is allowed at least one period?  Choose the correct option:
A) 32
B) 36
C) 24
D) 34
E) None of these

Solution: 3 subjects can be arranged in 4 periods in 4P3 ways.   Remaining 1 period can be arranged in 3P1 ways.   Two subjects are alike in each of the arrangement. So we need to divide by 2! to avoid overcounting.   Total number of arrangements = (4p3 x 3P1)/2! = 36   ANSWER:36
Answer: B
Which one of the following is not a prime number?
Choose the correct choice from the following:
A) 2  B) 3  C) 5  D) 9  E) 7

Solution: 9 is divisible by 3. So, it is not a prime number.   Answer:9
Answer: D
At a company, the average wage of male employees is $5 per hour, and the average wage of female employees is $8 per hour. If the average wage of all employees is $7.5 per hour, what is the ratio of the number of male employees to the number of female employees?	Answers:
A) 1 to 5	B) 2 to 3	C) 3 to 2	D) 5 to 3	E) 2 to 1

Solution: 1 to 5verage hourly wage of male employees = 5 $   1 to 5verage hourly wage of female employees = 8 $   1 to 5verage hourly wage of all employees = 7.5 $   Let number of male employees = m   number of female employees = f   7.5 = (5m + 8f ) / m+f   =>7.5m + 7.5f = 5m + 8f   => 2.5m = .5f   => m/f = 2.5/.5 = 1/5   1 to 5nswer 1 to 5
Answer: A
In a class, there are 15 boys and 10 girls. Three students are selected at random. The probability that 1 girl and 2 boys are selected, is: Choose the correct choice from the following answers:  A) 21/46  B) 25/117  C) 1/50  D) 3/25  E) 2/13

Solution: Let S be the sample space and E be the event of selecting 1 girl and 2 boys.   Then, n(S)	= Number ways of selecting 3 students out of 25   = 25C3 `   =(25 x 24 x 23)/(3 x 2 x 1)   = 2300.   n(E)	= (10C1 x 15C2)   =10 x((15 x 14)	/(2 x 1))   = 1050.   P(E) =	n(E)/n(S)	=1050/2300=21/46   Option 21/46
Answer: A
Find the probability that a leap year selected at random will have 53 Mondays	Pick.
A) 6/7	B) 5/7	C) 4/7	D) 3/7	E) 2/7

Solution: There are 366 days in a leap year: 52 weeks and 2 more days. So, 52 Mondays and 2 days.   These 2 days can be: {Mon, Tue}, {Tue, Wed}, {Wed, Thu}, {Thu, Fri}, {Fri, Sat}, {Sat,Sun} and {Sun, Mon} (7 cases). In order to have 53 Mondays we should have either {Mon,Tuesday} or {Sun, Mon} case.   The probability of that is 2/7.   Answer: 2/7.
Answer: E
A person X working alone can complete a work in 6 days. A person Y completes the same amount of work in 15 days, and a person Z when working alone can complete the same amount of work in 30 days. All three people work together for 2 days but then X and Y leave. How many more days does Z need to complete the work after X and Y leave? Choose the correct option:
A) 12
B) 13
C) 14
D) 15
E) 16

Solution: The fraction of work completed in two days is 2/6 + 2/15 + 2/30 = 16/30   The fraction of work remaining is 1 - 16/30 = 14/30   The number of days required for Z is 14 days.   The answer is 14.
Answer: C
A and B entered into partnership with capitals in the ratio 4 : 5. After 3 months, A withdrew 1/4 of his capital and B withdrew 1/5 of his capital. The gain at the end of 10 months was Rs. 760. A's share in this profit is:
Choose the correct choice from the following options.
A) Rs. 330
B) Rs. 360
C) Rs. 380
D) Rs. 430
E) Rs. 450

Solution: If earlier their investmwnts were 4x and 5x for 3 months   and then   3x and 4x for next 7 months,   Then profit will be divided in ratio of (4x*3 + 3x*7) :( 5x*3+4x*7) or 33:43   Hence A's share in profit of Rs 760 = 760*33/76= 
760*33/76 = 330
Rs 330.   Rs. 330NSWER:Rs. 330
Answer: A
A student committee on academic integrity has 30 ways to select a president and vice president from a group of candidates. The same person cannot be both president and vice president. How many candidates are there? Choose the correct choice from the following choices
A) 7
B) 8
C) 9
D) 6
E) 11

Solution: xC1 * (x-1)C1=30   x^2 -x -30 =0   (X-6) (X+5) = 0   X= 6 , -5   -5 can't possible.   6
Answer: D
Three table runners have a combined area of 212 square inches. By overlapping the runners to cover 80% of a table of area 175 square inches, the area that is covered by exactly two layers of runner is 24 square inches. What is the area of the table that is covered with three layers of runner?  Pick.
A) 18 square inches	B) 20 square inches	C) 24 square inches	D) 28 square inches	E) 30 square inches

Solution: Total = a + b + c - (sum of EXA24 square inchesTLY 2-group overlaps) - 2*(all three) + Neither   80%*175 = 212 - 24 - 2*(all three) + 0   2*(all three) = 212 - 24 - 140   all three = 24   Answer: 24 square inches
Answer: C
In how many different ways can the letters of the word ‘PREPTY’ be arranged?  Choices
A) 250
B) 280
C) 300
D) 310
E) 360

Solution: Number of ways = 61/21 6X5X4X3X2X1 - 360   360
Answer: E
The traffic lights at 3 different roads change after every 9 sec, 72 sec, 108 sec respectively. If they all change simultaneously at 9:15 AM then at what time will they again change simultaneously.
Choose the correct choice from the following options
A) 9:18:36	B) 9:42:15	C) 10:15:24	D) 9:54:12	E) 10:01:20

Solution: LCM of 9,72,108 = 216 = 3mnts 36sec   The lines will change every 3m 36sec   The light will change again after 9:15 9:18:36M is = 9:15+0:03:36 = 9:18:36   9:18:36nswer is 9:18:36
Answer: A
If 15% of 30% of 50% of a number is 108, then what is the number?
Choose the correct choice from the following answers.
A) 4000
B) 3050
C) 4400
D) 4800
E) None of these

Solution: Let the number be a   Given, 15/100 * 30/100 * 50/100 * a = 108   => 3/20 * 3/10 * 1/2 * a = 108   => a = 10 * 20 * 10 * 2 = 4800.   ANSWER:4800
Answer: D
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?	Choices.
A) 85 km/h	B) 85.34 km/h	C) 87.67 km/h	D) 90.25 km/h	E) 90.64 km/h

Solution: Ans.(B)   Sol. Total distance = 64 × 8 = 512 km   Now speed = 512/6 = 85.34 km/h
Answer: B
Two female friendstwo male friends will be pictured in a advertising photo. If the photographer wants to line them up in one row, with menwomen alternating. How many possible arrangements may she chose?  Pick:
A) 40320	B) 1680	C) 1152	D) 576	E) 8

Solution: now any of the alternate 2 places can be filled by 2 male or female in 2!   similarily,   other 2 alternate places can be filled in 2!   hence required probability= 2*2!*2!=8   hence 82*2 *2= 
2*2 *2 = 8
8   hence 8
Answer: E
If P(A)=0.4, P(B)=0.6 and P(A ∪ B)=0.8. What is the value of P(A∩B')=? Pick one.
A) 0.1  B) 0.2  C) 0.3  D) 0.4  E) None

Solution: Solution:   P(A∪0.2) = P(A) + P(0.2) - P(A∩0.2') =>   0.8=0.4 - P(A∩0.2) =>P(A∩0.2)=0.2   P(A∩0.2') = P(A) - P(A∩0.2) = 0.4 - 0.2= 
0.4 - 0.2 = 0.2
0.2   Answer 0.2
Answer: B
39 persons can repair a road in 12 days, working 5 hours a day. In how many days will 30 persons, working 6 hours a day, complete the work?
Choose the correct choice from the following:
A) 10
B) 13
C) 14
D) 15
E) 12

Solution: Let the required number of days be x.   Less persons, More days (Indirect Proportion)   More working hours per day, Less days (Indirect Proportion)   Persons 30	:	39 :: 12 : x   Working hours/day	6	:	5   Therefore 30 x 6 x x = 39 x 5 x 12   => x =(39 x 5 x 12)/(30 x 6)   => x = 13.   Correct answer is 13
Answer: B
When the positive integer z is divided by 9, the remainder is 5. What is the remainder when 3z is divided by 9? Choose the correct choice: A) 0 B) 1 C) 3 D) 4 E) 6

Solution: Lets take the number as z   when x is divided by 9 the remainder is 5 hence z can be written as   z=9k +5   Multiplying by 3 will give   3z = 27k + 15   we can also write   3z = 27k + 9 + 6   Now 27k and 9 are divisible by 9 leaving the remainder as 6 hence 6 is the answer.
Answer: E
How many three-digit integers between 310 and 400, exclusive, are divisible by 3 when the tens digit and the ones digit are switched? Choose the correct answer.
A) 3
B) 19
C) 30
D) 22
E) 90

Solution: Answer is 30   No of digits between 310 and 400 (exclusive) = 400-310-1= 
400-310-1 = 89
89   No Intergers divisble by 3=~ 89/3 ~ 30   Divsiblivity rule for 3 is Sum of all digits must be divisble by 3. It doesn't matter if ones digit and tens digits are switched.   e.g 372 is divisble by 3 (becae 3+7+2= 
3+7+2 = 12
12 (divisble by 3))   switch digits 732 also divisble by 3 (becae 7+3+2= 
7+3+2 = 12
12 (divisble by 3))   Divsiblivity rule for 3 is Sum of all digits must be divisble by 3. It doesn't matter if ones digit and tens digits are switched.   You have right. So it is enough to proceed like usual to find the numbers in a given range that are divisible by 3. So 399-312/3 +1=30.   Answer : 30
Answer: C
A beats B by 20metres ,B beats C by20 metres in a 100 m race .By how much A beats C  Choose the correct choice:  A) 35metres  B) 36metres  C) 37metres  D) 38metres  E) 39metres

Solution: A : B = 100 : 80   B : C = 100 : 80   A : C = (A/B * B/C)   = (100/80 * 100/80)   = (100/64)   Therefore A beats C by = (100-64)= 
(100-64) = 36
36metres.   ANSWER:36metres
Answer: B