MU-NLPC/Calc-aqua_rat huggingface dataset:
What is the average of 1/2, 2/5 and 7/10?	Choose the correct choice.
A) 1/5 B) 3/10 C) 8/15 D) 1/2 E) 6/5

Solution: Sum of 1/2,2/5,7/10 =16/10   Average = 16/10*1/3 =8/15   Answer 8/15 8/15
Answer: C
A, B, C rent a pasture. A puts 10 oxen for 7 months, B puts 12 oxen for 5 months and C puts 15 oxen for 3 months for grazing. If the rent of the pasture is Rs. 175, how much must C pay as his share of rent?
Choose the correct choice from the following choices.
A) 45 B) 23 C) 38 D) 27 E) 28

Solution: Explanation:   A:B:C = (10×7):(12×5):(15×3)   = 70 :60 :45   = 14 :12 :9   C's rent = Rs.(175×9/35)   =Rs. 45.   Answer: A) Rs. 45
Answer: A
When a certain number X is divided by 143, the remainder is 59 Which of the following numbers, if added to X, would result in a number divisible by 13?  Choose the correct option:
A) 7
B) 21
C) 34
D) 47
E) 6

Solution: Now X= 143q + 58 = 11*13*q + 58..so we have to make only 58 div by 13..   59 + 6= 
59 + 6 = 65
65 divisible by 13 ..add 6   ans 6
Answer: E
What is the value of M and N respectively if M39048458N is divisible by 8 and 11, where M and N are single digit integers? Answers:
A) 7, 4
B) 8, 6
C) 6, 4
D) 3, 2
E) None of these

Solution: Sol. (c) A number is divisible by 8 if the number formed by the last three digits is divisible by 8.   i.e., 58N is divisible by 8.   Clearly,N = 4   Again, a number is divisible by 11 if the difference between the sum of digits at even places and sum of digits at the odd places is either 0 or is divisible by 11.   i.e (M + 9 + 4 + 4 + 8) - (3 + 0 + 8 + 5 + N)   = M + 25 - (16 + N)   = M - N + 9 must be zero or it must be divisible by 11.   i.e M - N = 2   => M = 2 + 4= 
2 + 4 = 6
6   Hence, M= 6 , N = 4   Answer 6, 4
Answer: C
In a division sum, the quotient is 18, the divisor 43 and the remainder 12, find the dividend?
Choose the correct choice from the following answers
A) 586
B) 766
C) 796
D) 786
E) 686

Solution: Explanation:   18 * 43 + 12= 
18 * 43 + 12 = 786
786   Answer : 786
Answer: D
Your new cell phone battery needs to be charged for 3 hours and 45 minutes before
using it. If you plug the battery into the charger at 8:20 a.m., you should wait till what
time before using it?  Choose the correct choice from the following answers.
A) 09:05 a.m.  B) 11:05 a.m.  C) 12:05 p.m.  D) 13:05 p.m.  E) 15:05 p.m.

Solution: 8:20 + 3 hours = 11:20   + 0:45 minutes = 12: 05 P.m.   Answer: 12:05 p.m.   correct answer 12:05 p.m.
Answer: C
A man whose speed is 4.5 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 1.5 kmph, find his average speed for the total journey? Answers.
A) 1 kmph	B) 4 kmph	C) 9 kmph	D) 5 kmph	E) 5 kmph

Solution: Explanation:   M = 45   S = 1.5   DS = 6   US = 3   AS = (2 * 6 * 3) /9= 
(2 * 6 * 3) /9 = 4
4   Answer: Option 4 kmph
Answer: B
Two kinds of Vodka are mixed in the ratio 1:2 and 2:1 and they are sold fetching the profit 10% and 35% respectively. If the vodkas are mixed in equal ratio and the individual profit percent on them are increased by 4/3 and 5/3 times respectively, then the mixture will fetch the profit of	Choose the correct choice from the following answers
A) 18%  B) 20%  C) 21%  D) 35%  E) Cannot be determined

Solution: Answer: 35%.
Answer: D
There are 6 people in the elevator. Their average weight is 170 lbs. Another person enters the elevator, and increases the average weight to 151 lbs. What is the weight of the 7th person.
Pick
A) 37
B) 168
C) 189
D) 190
E) 200

Solution: Solution   Average of 7 people after the last one enters = 151 .   âˆ´ Required weight = (7x151)-(6x170)   = 1057- 1020= 
1057- 1020 = 37
37.   37nswer 37
Answer: A
Rs 60000 is divided into two parts One part is given to a person with 10% interest and another part is given to a person with 20 % interest. At the end of first year he gets profit 7000 Find money given by 10%? Choices:
A) 30000  B) 40000  C) 50000  D) 60000  E) 70000

Solution: let first parrt is x and second part is y then x+y=60000----------eq1   total profit=profit on x +profit on y   7000=(x*10*1)/100 + (y*20*1)/100   70000=x+2y-----------------------------------eq2   70000=60000+y   so y=10000 then x =50000-10000= 
50000-10000 = 40_000
40000   first part=40000   ANSWER:40000
Answer: B
An article sold at a profit of 20%. If both the cost price and selling price would be Rs.20/- less, the profit would be increased by 10%. What is the price of that article?
Pick
A) Rs 60	B) Rs 50	C) Rs 65	D) Rs 62	E) Rs 68

Solution: Actual price = Rs 60 and selling price with 20% profit = Rs. 72.   If CP and SP is Rs 20 less, then   CP=Rs 40 and SP = Rs 52 and hence, the profit is 30%.   CP = Rs 60.   Rs 60NSWER:Rs 60
Answer: A
A lemonade stand sold only small and large cups of lemonade on Tuesday. 4/5 of the cups sold were small and the rest were large. If the large cups were sold for 7/6 as much as the small cups, what fraction of Tuesday's total revenue was from the sale of large cups?	Pick one
A) 7/31
B) 7/15
C) 10/21
D) 17/35
E) 1/2

Solution: Let the total # of cups be 10.   # of small cups sold 4/5*10= 
4/5*10 = 8
8;   # of large cups sold  10-8= 
 10-8 = 2
2;   Let the price of small cup be $6, then the price of larges cup would be 7/6*6= 
7/6*6 = 7
$7;   Revenue from small cups:8*$6=$48   Revenue from large cups cups: 2*$7 8* 6= 
 8* 6 = 48
$48   Revenue from large cups cups: 2*$7=$14;   Fraction of total revenue from large cups: 14/(14+48)2* 7= 
2* 7 = 14
$14;   Fraction of total revenue from large cups: 14/(14+48)=7/31.   7/31nswer: 7/31.
Answer: A
The least whole number which when subtracted from both the terms of the ratio 6 : 7 to give a raƟo
less than 16 : 21, is  Choose one:
A) 3	B) 4	C) 5	D) 6	E) 7

Solution: Explanation:   Let x is subtracted.   Then,   (6−x)(7−x)<162121(6�x)<16(7�x)=>5x>14=x>2.8   Least such number is 3   3nswer: 3
Answer: A
The ratio of spinsters to cats is 2 to 7. If there are 40 more cats than spinsters, how many spinsters are there?  Choose the most appropriate option:
A) 14  B) 16  C) 18  D) 20  E) 22

Solution: Let 2x be the number of spinsters. Then 7x is the number of cats.   7x-2x=40   x=8 and the number of spinsters is 2(8)=16.   The answer is 16.
Answer: B
The ratio of ages of Aman, Bren, and Charlie are in the ratio 5:8:7 respectively. If 8 years ago, the sum of their ages was 76, what will be the age of Bren 10 years from now? Pick one: A) 17 B) 25 C) 27 D) 35 E) 50

Solution: Let the present ages of Aman, Bren, and Charlie be 5x, 8x and 7x respectively.   5x-8 + 8x-8 + 7x-8 = 76   x = 5   Present age of Bren = 8*5= 
8*5 = 40
40   Bren's age 10 years hence= 40+10= 
40+10 = 50
50   Answer= 50
Answer: E
Find the invalid no.from the following series 13, 18, 25, 30, 37, 40
Choose the correct answer
A) 30	B) 35	C) 40	D) 47	E) 50

Solution: The differences between two successive terms from the beginning are 7, 5, 7, 5, 7, 5. So, 40 is wrong.   40
Answer: C
If Dale works at full efficiency he needs a break of 1 day after every 2 days of work and he completes a job in a total of 14 days. If he works at reduced efficiency, he can work without break and finish that same job in 14 days. Dale's output at reduced efficiency is what fraction of his output at full efficiency?	Choose the correct answer
A) 3/9
B) 4/5
C) 3/2
D) 4/6
E) 5/2

Solution: We're told that there are 2 ways for Dale to complete a job:   1) Full Efficiency: 2 days of work followed by 1 dayofffor a total of 14 days.   2) Reduced Efficiency: 14 straight days with no days off.   Working at Full Efficiency creates the following pattern:   2 days on, 1 day OFF, 2 days on, 1 day OFF, 2 days on, 1 day OFF, 2 days on = 2+1+2+1+2+1+2+1+2= 
2+1+2+1+2+1+2+1+2 = 14
14 days   Totals: 10 days on, 4 days off   Reduced Efficiency means that Dale will do 10 days of work in 14 days, thus those Reduceddaysare 10/4=5/2 of Full Efficiency.   Answer : 5/2
Answer: E
The average salary of 20 workers in an office is Rs.1900 per month. If the manager's salary is added, the average salary becomes Rs.2000 p.m. What is the manager's annual salary?  Choose the most appropriate option
A) Rs.24,000 B) Rs.25,200 C) Rs.45,600 D) None of these E) Cannot be determined

Solution: Explanation:   Manager's salary per month   = (Rs.21×2000−20×1900)) = Rs.4000   Manager's Annual salary = Rs.(4000×12)=Rs.48000   Correct Option:None of these
Answer: D
A, B, C, and D are four points, any three of which are non-collinear. Then, the number of ways to construct three lines each joining a pair of points so that the lines do not form a triangle is	Choose the most appropriate option:
A) 7  B) 8  C) 9  D) 24  E) 23

Solution: To construct 2 lines, three points can be selected out of 4 in 4 x 3 x 2 = 24 ways. Now, if third line goes from the third-point to the first point, a triangle is formed, and if it goes to the fourth point, a triangle is not formed. So, there are 24 ways to form a triangle and 24 ways of avoiding triangle.   ANSWER:24
Answer: D
What percentage of numbers from 1 to 50 have squares that end in the digit 4? Pick.
A) 1
B) 14
C) 25
D) 21
E) None of the these

Solution: Clearly, the numbers which have 1 or 9 in the unit's digit, have squares that end in the digit 4. Such numbers from 1 to 50 are 2,8,12,18,22,28,32,38,42,48.   Number of such numbers = 10.   Required percentage = (10/50 * 100)= 
(10/50 * 100) = 20
20%   ANSWNone of the theseR:None of the these
Answer: E
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? Choose the correct answer.
A) Rs. 9400 B) Rs. 8900 C) Rs. 8400 D) Rs. 3400 E) Rs. 8440

Solution: Ratio of their shares = 22500 : 35000 = 9:14   Deepak's share = 13800 * 14/23 = Rs. 8400.   Answer:Rs. 8400
Answer: C
Two numbers are in the ratio of 5:7. If 7 is subtracted from each number, they are in the ratio of 2:3. What are the two numbers? Choices:
A) 35, 49
B) 40, 56
C) 45, 63
D) 50, 70
E) 55, 77

Solution: (5x-7):(7x-7) = 2y:3y   5x - 7 = 2y   7x - 7 = 3y   49-35 = 15y - 14y   14 = y   5x-7 = 28   x = 7   The two numbers are 5x and 7x which are 35 and 49.   The answer is 35, 49.
Answer: A
A wooden box of dimensions 8 m x 10 m x 6 m is to carry rectangularboxes of dimensions 4 cm x 5 cm x 6 cm. The maximum number ofboxes that can be carried in the wooden box, is	Choices:
A) 9800000
B) 1000000
C) 7500000
D) 4000000
E) None of these

Solution: Explanation: Number = (800*1000*600)/4*5*6 = 4000000 Answer: 4000000
Answer: D
What will be remainder when 17200 is divided by 18 ?
Choose one
A) 17  B) 16  C) 14  D) 1  E) 2

Solution: When n is even. (xn - an) is completely divisibly by (x + a)   (17200 - 1200) is completely divisible by (17 + 1), i.e., 18.   (17200 - 1) is completely divisible by 18.   On dividing 17200 by 18, we get 1 as remainder.   Option 1
Answer: D
A person travels equal distances with speeds of 7 km/hr, 8 km/hr and 9 km/hr and takes a total time of 47 minutes. The total distance is?	Choices
A) 6 km	B) 3 km	C) 7 km	D) 9 km	E) 2 km

Solution: Let the total distance be 3x km.   Then, x/7 + x/8 + x/9 = 47/60   36x/95 = 47/60 => x = 2.07.   Total distance = 3 * 2.07 = 6.2 km.   6 kmnswer:6 km
Answer: A
Pipes A and B can fill a cistern in 20 and 60 minutes respectively. They are opened an alternate minutes. Find how many minutes, the cistern shall be full?  Choose the correct answer: A) 30 B) 45 C) 32 D) 18 E) 19

Solution: :   1/20 + 1/60 = 1/15   15 * 2 = 30.30nswer:30
Answer: A
If x is the sum of six consecutive integers, then x is divisible by which of the following:
I. 6
II. 4
III. 11	Choose the correct choice from the following options:	A) I only	B) II,III only	C) III only	D) I,III only	E) II only

Solution: We're told that X is the SUM of 6 CONSECUTIVE INTEGERS. We're asked what X is divisible by....   Let's TEST VALUES....   IF we use the 6 consecutive integers: 3, 4, 5, 6, 7 and 8, then the sum = 33.   33 is divisible by 11   33 is NOT divisible by 4   33 is NOT divisible by 6   There's only one answer that 'fits' with these facts. Answer : III only
Answer: C
The greatest number which on dividing 1557 and 2037 leaves remainders 7 and 5 respectively, is:  Choose the correct choice from the following options:	A) 123	B) 127	C) 2	D) 305	E) 505

Solution: Explanation:   Required number = H.C.F. of (1557 - 7) and (2037 - 5)   = H.C.F. of 1550 and 2032 = 2. Answer: 2
Answer: C
A man can row his boat with the stream at 6 km/h and against the stream in 4 km/h. The man's rate is?  Answers:
A) 1 kmph  B) 2 kmph  C) 7 kmph  D) 8 kmph  E) 3 kmph

Solution: DS = 6   US = 4   S = ?   S = (6 - 4)/2= 
(6 - 4)/2 = 1
1 kmph   1 kmphnswer:1 kmph
Answer: A
1,2,3,4,5,6,7 are arranged such that sum of two successive numbers is a prime number. For example, 1234765 (i.e. 1+2=3, 2+3=5, 3+4=7....)
1. How many such possible combinations occur?
2. How many possible combination occurs if first number is 1/7 and last number is 7/1 (i.e 1xxxxx7 or 7xxxxx1)?
3. How many numbers will come on 4th position(xxx_xxx)? Choices.
A) How many such possible combinations occur?  B) How many possible combination occurs if first number is 1/7 and last number is 7/1 (i.e 1xxxxx7 or 7xxxxx1)?  C) How many numbers will come on 4th position(xxx_xxx)?  D) W3  E) 24

Solution: We have to follow a systematic approach for this question. We know that if at all two consecutive numbers be prime, they should not be even in the first place. So we arrange even numbers in even places, odd numbers in odd places.   2 should not have 7 as its neighbor   4 should not have 5 as its neighbor   6 should not have 3 as its neighbor   Case 1:   __ 2 ____ 4 ____ 6 __   x7 x7,5 x5,3 x3   So fix, 3 or 1 in between 2 and 4. We get the following options with reverse case also.   5234167, 7614325   5234761, 1674325   1234765, 5674321   3214765, 5674123   Case 2:   __ 2 ____ 6 ____ 4 __   x7 x7,3 x3,5 x5   5216743, 3476125   3256147, 7416523   3256741, 1476523   1256743, 3476521   Case 3:   __ 4 ____ 2 ____ 6 __   x5 x5,7 x7,3 x33412567, 7652143   7432165, 5612347   7432561, 1652347   1432567, 7652341   Answer 1: Total possibilities are 24.   Answer 2: 4 possibilities.   Answer 3: 3 possibilities.   Answer:How many possible combination occurs if first number is 1/7 and last number is 7/1 (i.e 1xxxxx7 or 7xxxxx1)?
Answer: B
The length of rectangle is thrice its breadth and its perimeter is 120 m, find the area of the rectangle?
Choose the correct option:  A) 432 sq m  B) 356 sq m  C) 452 sq m  D) 428 sq m  E) 675 sq m

Solution: 2(3x + x) = 120   l = 45 b = 15   lb = 45 * 15= 
45 * 15 = 675
675   ANSW675 sq mR:675 sq m
Answer: E
The average runs scored by a batsman in 25 matches is 45. In the next 7 matches the batsman scored an average of 15 runs. Find his average in all the 32 matches?
Choices:	A) 31355	B) 38.44	C) 29.55	D) 97.66	E) 45.66

Solution: Total score of the batsman in 25 matches = 1125.Total score of the batsman in the next 7 matches = 105.Total score of the batsman in the 32 matches = 1230.Average score of the batsman = 1230/32 = 38.44.Answer: 38.44
Answer: B
If money is invested at r percent interest, compounded annually, the amount of investment will double in approximately 70/r years. If Pat's parents invested $ 10000 in a long term bond that pays 8 percent interest, compounded annually, what will be the approximate total amount of investment 18 years later, when Pat is ready for college?
Choices:
A) $40000 B) $15000 C) $12000 D) $10000 E) $9000

Solution: Since investment doubles in 70/r years then for r=8 it'll double in 70/8=~9 years (we are not asked about the exact amount so such an approximation will do). Thus in 18 years investment will double twice and become ($10,000*2)*2=$40,000 (after 9 years investment will become $10,000*2=$20,000 and in another 9 years it'll become $20,000*2=$40,000).   $40000nswer: $40000.
Answer: A
Car A leaves the airport at 9:00 am and travels at a constant rate of 30 km per hour. Car B leaves the airport at 9:30 am and travels in the same direction along the same highway at a constant rate of 34 km per hour. At what time will Car B be 12 km ahead of Car A? Choose one.
A) 3:45 pm	B) 4:00 pm	C) 4:15 pm	D) 4:30 pm	E) 4:45 pm

Solution: At 9:30 am, Car A will be 15 km ahead of Car B.   Car B travels at a rate 4 km per hour faster than Car A.   Car B needs to travel 27 km more than Car A in order to be 12 km ahead.   This will take 27 km/4 km per hour=6.75 hours.   Car B will be 12 km ahead at 4:15 pm.   The answer is 4:15 pm.
Answer: C
Shop Offered 20% offer for every Shirt, Smith bought a shirt at Rs. 560. and What was the shop's original selling Price?  Pick one:	A) 500	B) 550	C) 600	D) 700	E) 750

Solution: SP* (80/100) = 560   SP= 70 * 100 => CP = 700   Answer:700
Answer: D
Train P crosses a pole in 30 seconds and train Q crosses the same pole in one minute and 15 seconds. The length of train P is three-fourths the length of train Q. What is the ratio of the speed of train P to that of train Q?
Answers:
A) 15 : 8	B) 15 : 9	C) 15 : 5	D) 15 : 2	E) 15 : 1

Solution: Given that train P crosses a pole in 30 seconds and train Q crosses the same pole in one minute and 15 seconds.   Let the length of train P be LP and that of train Q be LQ   given that LP = 3/4 LQ   15 : 8s the train P and Q crosses the pole in 30 seconds and 75 seconds respectively,   => Speed of train P = VP = LP/30   Speed of train Q = VQ = LQ/75   LP = 3/4 LQ   => VP = 3/4 LQ/(30) = LQ/40   Ratio of their speeds = VP : VQ   = LQ/40 : LQ/75 => 1/40 : 1/75 = 15 : 8   15 : 8nswer: 15 : 8
Answer: A
Assume that 20 cows and 40 goats can be kept for 10 days for Rs.460. If the cost of keeping 5 goats is the same as the cost of keeping 1 cow, what will be the cost for keeping 50 cows and 30 goats for 12 days?	Pick:
A) Rs.1104
B) Rs.1000
C) Rs.934
D) Rs.1210
E) Rs.1110

Solution: Rs.1104ssume that cost of keeping a cow for 1 day = c ,   cost of keeping a goat for 1 day = g   Cost of keeping 20 cows and 40 goats for 10 days = 460   Cost of keeping 20 cows and 40 goats for 1 day = 460/10= 
460/10 = 46
46= 20c + 40g = 46   = 10c + 20g = 23 ---(1)   Given that 5g = c   Hence equation (1) can be written as 10c + 4c = 23 =14c =23   = c=23/14   cost of keeping 50 cows and 30 goats for 1 day   = 50c + 30g   = 50c + 6c (substituted 5g = c)   = 56 c = 56×23/14   = 92   Cost of keeping 50 cows and 30 goats for 12 days = 12×92 = 1104 Rs.1104NSWER : Rs.1104
Answer: A
Exactly 3/7 of the people in the room are under the age of 21, and exactly 5/11 of the people in the room are over the age of 65. If the total number of the people in the room is greater than 50 and less than 100, how many people in the room are under the age of 21?  Choose the correct choice:
A) 21  B) 33  C) 39  D) 60  E) 65

Solution: The total number of the people in the room must be a multiple of both 7 and 11 (in order 3/7 and 5/11 of the number to be an integer), thus the total number of the people must be a multiple of LCM of 7 and 11, which is 77.   Since, the total number of the people in the room is greater than 50 and less than 100, then there are 77 people in the room.   Therefore there are   3/7*77= 
  3/7*77 = 33
33 people in the room under the age of 21.   Answer: 33.
Answer: B
A soccer store typically sells replica jerseys at a discount of 30 percent to 50 percent off list price. During the annual summer sale, everything in the store is an additional 20 percent off the original list price. If a replica jersey's list price is $80, approximately what Y percent of the list price is the lowest possible sale price?	Answers:
A) 20 B) 25 C) 30 D) 40 E) 50

Solution: Let the list price be 2x   for min sale price, the first discount given should be 50%, 2x becomes x here   now, during summer sale additional 20% off is given ie sale price becomes 0.8x   it is given lise price is $80   => 2x = 80   => x = 40   and 0.8x = 32   so lowest sale price is 32, which Y is 40% of 80   hence, 40 is the answer
Answer: D
Train X and Y, 455 miles apart, are traveling toward each other at constant rates and in the same time zone. If train X left at 4 pm traveling at a speed of 60 miles per hour, and train Y left at 5:45 pm and traveling at 45 miles per hour, then at what time would they pass each other?	Choices
A) 4.05pm  B) 5.05pm  C) 6.05pm  D) 7.05pm  E) 9.05pm

Solution: First, since X has a headstart then in that 1hr45min or 1.75hrs he travels 105 miles   Then remaining distance to be traveled will be   455 - 105= 
  455 - 105 = 350
350 miles   Now, using relative rates (105)(t)= 350   This gives 10/3 hours   Now 5.45pm + 10/3 hours gives us 9.05pm   Hence answer is 9.05pm
Answer: E
What is the least common multiple of 15, 18, and 34?	Choose the correct choice from the following options:  A) 60  B) 120  C) 240  D) 360  E) 1530

Solution: Let us first write the numbers in the form of prime factors:   15 = 3*5   18 = 2*3^2   34 = 2 * 17^1   The LCM would be the largest powers of the prime numbers from all these three numbers.   Hence LCM = 1530   Option 1530
Answer: E
A man can row with a speed of 15 kmph in still water. If the stream flows at 10 kmph, then the speed in downstream is? Pick one
A) A)25  B) B)28  C) C)20  D) D)21  E) E)18

Solution: M = 15   S = 5   DS = 15 + 10= 
15 + 10 = 25
25   25nswer:25
Answer: A
Let the least number of six digits,which when divided by 4,6,10 and 15 leaves in each case the same remainder of 2, be N. The sum of the digits in N is : Choose the correct choice from the following.
A) 3	B) 4	C) 5	D) 6	E) 7

Solution: Solution   Least number of 6 digital is 100000. L.C.M. of 4,6,10 and 15 = 60.   on dividing 100000 by 60, the remainder obtained is 40.   So, least number of 6 digits divisible by 4,6,10 and 15 = 100000 +(60 - 40)= 
100000 +(60 - 40) = 100_020
100020.   So, N= (100020 + 2)= 
(100020 + 2) = 100_022
100022. sum of digits in N= (1 + 2 + 2)= 
(1 + 2 + 2) = 5
5. Answer 5
Answer: C
When a natural number N is successively divided by 10,20,30,40. the remainders are 50,60,70,80. What will be the sum of the remainders if the order of the division is reversed?	Options:
A) 16
B) 14
C) 28
D) 11
E) 9

Solution: 10 20 30 40   50 60 70 80   leave the top right- most number 8   start with bottom right-most number 5   80*30+70= 
80*30+70 = 2_470
2470   2470*20+60= 
2470*20+60 = 49_460
49460   49460*10+50= 
49460*10+50 = 494_650
494650   this is the number required   Now, do the successive division in the reverse order   The sum of the remainders is 28   Hence, the correct option is 28
Answer: C
On a certain plane, 2/5 of the passengers speak Tamil and 3/4 speak Hebrew. If all of the passengers on the plane speak at least one of these languages, what is the smallest number of passengers that could be on the plane?	Choose the correct answer
A) 12  B) 75  C) 80  D) 94  E) 96

Solution: Assume the total members = x   Tamil = .4x   Hebrew = .75x   Tamil + Hebrew = 1.15x, but this is not possible hence 15 people speak both languages.   Only Tamil = .25x, Only Hebrew = .6x, both = .15x   Since these are all people, all of these should be whole numbers.   Checking the options:   A. 12. Only Hebrew = 12*0.6= 
12*0.6 = 7.2
7.2 We do not get the people as whole numbers. INCORRECT   B. 15. Only Tamil= 0.25*15 Again we do not get the people as whole numbers. INCORRECT   C. 80 Only Tamil = .25*80= 
.25*80 = 20
20, Only Hebrew= .6*80= 
.6*80 = 48
48, both= .15*80= 
.15*80 = 12
12. We have the people as whole numbers. CORRECT   D. 94   E.96   Since we have to find the lowest number, no need to calculate for the rest of the options.   80orrect Option: 80
Answer: C
A man tosses three coins in the air. When they land, he finds that two of the coins have heads up and one has tails up.
What is the probability that when the coins are tossed again, they will land again with two heads up and one tails up.
Please note that the coins are unbiased. Choose one.
A) 50% B) 58% C) 45% D) 61% E) 45%

Solution: A   50%   Explanation:   When the coins are tossed there can be eight possible outcomes (2*2*2)   HHH   HTT   HTH   HHT   TTT   THH   THT   TTH   If you find out, we have only four favorable outcomes. Also, the events here are independent and thus we can calculate the probability by using these only.   Thus the probability is 50 percent.
Answer: A