MU-NLPC/Calc-aqua_rat huggingface dataset:
Two trains start from A & B and travel towards each other at
speed of 50kmph and 60kmph resp. At the time of the meeting the
second train has traveled 100km more than the first.the distance
between them.	Options:
A) 800 km  B) 900 km  C) 1000 km  D) 1100 km  E) 1200 km

Solution: Let the distance traveled by the first train be x km   then distance covered by the second train is x + 100km   x/50 = x+100 / 60   x= 500   so the distance between A & B is x + x + 100 = 1100 km   Answer is 1100 km.
Answer: D
John is going with 10 friends on a trip to Sidney for spring break. Airfare and hotel costs a total of $12100.00 for the group of 11 friends. How much does each person have to pay for their hotel and airfare? Choose the correct answer:
A) $1010  B) $1100  C) $1110  D) $1101  E) $1200

Solution: Answer= $1100   The total cost of the trip ($12100.00) divided by 11 equals $1100.00.
Answer: B
In an election between two candidates A and B, the number of valid votes received by A exceeds those received by B by 15% of the total number of votes polled. If 20% of the votes polled were invalid and a total of 8720 votes were polled, then how many valid votes did B get?
Choose the correct option:
A) 2160
B) 2420
C) 2834
D) 3150
E) 3250

Solution: Let the total number of votes polled in the election be 100k.   Number of valid votes = 100k - 20% (100k) = 80k   Let the number of votes polled in favour of A and B be a and b respectively.   a - b = 15% (100k) => a = b + 15k   => a + b = b + 15k + b   Now, 2b + 15k = 80k and hence b = 32.5k   It is given that 100k = 8720   32.5k = 32.5k/100k * 8720 = 2834   The number of valid votes polled in favour of B is 2834.   ANSWER:283432.5 /100  * 8720= 
32.5 /100  * 8720 = 2_834
2834   The number of valid votes polled in favour of B is 2834.   ANSWER:2834
Answer: C
If $30,000 interest is invested in x percent simple annual interest for 5 years, which of the following represents the total amount of interest, in dollars, that will be earned by this investment in the n years?	Pick one
A) 2000x
B) 3000x
C) 4500x
D) 1200x
E) 1500x

Solution: 30000*x/100*5 = 1500 x   Answer : 1500x
Answer: E
In what time a sum of money double itself at 3% per annum simple interest?
Choices
A) 33 1/7% B) 33 1/3% C) 33 1/2% D) 33 7/3% E) 33 5/3%

Solution: P = (P*3*R)/100   R = 33 1/3%   Answer: 33 1/3%
Answer: B
Solve the given two equations and find the inequality of X and Y. (a) X^2- 365 = 364 and (b) y- (324) ^(1/2) = (81)^(1/2)  Choose the correct choice from the following choices.
A) If x>y B) If x>=y C) If x < y D) If x<=y E) x=y or relationship cannot be established

Solution: Solution:-   X= +27, -27   Y= +27   If x<=y
Answer: D
If x/y = 3/z, then 4x^2 =
Choose the correct answer:	A) y/z	B) xy	C) y²/z²	D) 36y²/z²	E) 15y²/z²

Solution: This question is most easily solved by isolating y in the equation and substituting into the expression 4x²:   x/y = 3/z   x = 3y/z   If we substitute 3y/z into the expression for x, we get:   4(3y/z)² = 4(9y²/z²) = 36y²/z².   The correct answer is choice (36y²/z²).
Answer: D
If the sum of the first n positive integers is S, what is the sum of the first n positive integers divisible by 3, in terms of S ?
Pick:
A) S/2	B) S	C) 2S	D) 3S	E) 4S

Solution: Answer is 3S   Given sum of 1 2 3.....n = S   sum of 3 , 6 , 9 ....3n = 3[sum(1 2 3....n) ] = 3S
Answer: D
An equal number of desks and bookcases are to be placed along a library wall that is 15 meters long. Each desk is 2 meters long, and each bookshelf is 1.5 meters long. If the maximum possible number of desks and bookcases are to be placed along the wall, then the space along the wall that is left over will be how many meters K long?	Choose the correct choice from the following
A) 0.5	B) 1	C) 1.5	D) 2	E) 3

Solution: Let x be the number of desks and bookcases that are placed along the library wall.   2x + 1.5x < 15   3.5x < 15   Since x is a non negative integer, the largest number x can be is 4.   When x is 4, the desks and bookcases take up 3.5 * 4= 
3.5 * 4 = 14
14m=K, leaving 1m of empty space.   Thus, I believe the answer is 1) 1
Answer: B
20 business executives and 7 chairmen meet at a conference. If each business executive shakes the hand of every other business executive and every chairman once, and each chairman shakes the hand of each of the business executives but not the other chairmen, how many handshakes would take place?	Choose the most appropriate option.
A) 144	B) 131	C) 330	D) 390	E) 445

Solution: there are 20 business exec and in each handshake 2 business execs are involved.   hence 20C2=190   Also, each of 20 exec will shake hand with every 7 other chairmen for total of 140 handshake.   total=190+140= 
190+140 = 330
330   ANS: 330
Answer: C
A train passes a station platform in 36 seconds and a man standing on the platform in 21 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?	Pick one.
A) 225	B) 240	C) 288	D) 267	E) 211

Solution: Speed = (54 * 5/18) m/sec = 15 m/sec. Length of the train = (15 x 21)m = 315 m. Let the length of the platform be x meters. Then, (x + 315)/36 = 15 ==> x + 315 = 540 ==> x = 225 m.225nswer: 225
Answer: A
A, B, C are three consecutive positive integers (A>B>C). What is the value of the expression 2A +B +2C? Choices:
A) 6A+7.	B) 5A+1.	C) 5A-5.	D) 6A-5.	E) 6A-7.

Solution: B = A-1   5A-5.= A-2   Putting these values in 2A +B +25A-5. we get 5A-5   5A-5. is the answer
Answer: C
The average weight of 7 persons increases by 1.5 kg. If a person weighing 65 kg is replaced by a new person, what could be the weight of the new person? Choose one.
A) 76 kg  B) 77 kg  C) 75.5 kg  D) Data inadequate  E) None of these

Solution: total weight increases = 7 × 1.5 = 10.5 kg   so the weight of new person = 65 + 10.5= 
65 + 10.5 = 75.5
75.5 kg   Answer 75.5 kg
Answer: C
A company assigns product codes consisting of all the letters in the alphabet.How many product codes are possible if the company uses at most 7 letters in its codes, and all letters can be repeated in any one code?
Choose the correct choice from the following choices
A) A.17576 B) B.456976 C) C.11881376 D) D.308915776 E) E.8353082582

Solution: The no of ways in which the company can make codes of 1 letter : 26   # for 2 letters :   26*26= 
  26*26 = 676
676   # for 3 letters :   26 * 26*26= 
  26 * 26*26 = 17_576
17576   # for 4 letters :   26 * 26*26*26= 
  26 * 26*26*26 = 456_976
456976   # for 5 letters :   26 * 26*26*26*26= 
  26 * 26*26*26*26 = 11_881_376
11881376   # for 6 letters :   26 * 26*26*26*26*26= 
  26 * 26*26*26*26*26 = 308_915_776
308915776   # for 7 letters :   26 * 26*26*26*26*26*26= 
  26 * 26*26*26*26*26*26 = 8_031_810_176
8031810176   The total : By adding all of them , 26+676+17576+456976+11881376+308915776+8031810176=8353082582   E.8353082582
Answer: E
If in a kindergarten class, there are five children 3 feet 4 inches tall (indicated by notation 3'4"), two children 4'3" tall and thirteen children 2'5" tall, which of the following is the median height of the children?	Choose the correct answer
A) 2'5"
B) 2'6"
C) 3'3"
D) 3'4"
E) 4'3

Solution: Total number of children in class = 20   so median must be between 10th and 11th child when they are arranged in ascending order.   When arranged in ascending order 5th and 6th child will have the height of 3'4"   so required median height = (2'5"+2'5")/2 = 2'5"   2'5"ns:Option 2'5"
Answer: A
When Jessica withdrew $200 from her bank account, her account balance decreased by 2/5. If she deposits an amount equal to 1/2 of the remaining balance, what will be the final balance in her bank account?	Choose the correct choice from the following options:
A) 300 B) 375 C) 450 D) 500 E) 575

Solution: As per the question 200=2a/5   thus- a which is the total amount =500   The amount thus left =300   She then deposited 1/2 of 300=150   total amount in her account =450   Answer 450
Answer: C
Two cogged wheels of which one has 32 cogs and other 54 cogs, work into each other. If the latter turns 80 times in three quarters of a minute, how often does the other turn in 8 seconds? Choose the correct answer
A) 48 B) 24 C) 38 D) 36 E) 35

Solution: Explanation:   Less Cogs more turns and less time less turns   Number of turns required=80 Ã— Ã— = 24 times   ANSWER IS 24
Answer: B
A store sells a certain product at a fixed price per unit. At the product's current price, A units cost a total of exactly $300. If the price were lowered by $5 from its current value, then A + 2n units would cost exactly $300; if the price were raised by $5, then A – n units would cost exactly $300. What is the value of A?	Pick one
A) 10
B) 15
C) 20
D) 25
E) 30

Solution: It got too complicated when I used algebra. Using plugging in, it was quite fast.   Price Quantity total value   p a pa = 300   p-5 a+2n (p-5)(a+2n) = 300   p+5 a-n (p+5)(a-n) = 300   Solving three equations for three unknowns. Tough!!   Plugging in, I always start with C. 20 was the answer here, so saved calculation!   Putting values in above equations:   Price Quantity total value   15 20 300   10 20+2n 300 -> 10(20 + 2n)=300 -> 200 +20n = 300 -> 20n = 100 -> n =5   20 15 300   So a = 20 satisfies all equations!!
Answer: C
The average weight of 46 students in a class is 52 kg. 5 of them whose average weight is 48 kg leave the class and other 5 students whose average weight is 54 kg join the class. What is the new average weight (in kg) of the class ?  Choose the most appropriate option:
A) 51 1⁄23
B) 52 15/23
C) 52 15⁄3
D) 43.42
E) None of these

Solution: Total weight of 46 students   = 46 × 52 = 2392 kg   Total weight of 5 students who leave   = 5 × 48 = 240 kg   Total weight of 5 students who join   = 5 × 54 = 270 kg   Therefore, new total weight of 46 students   = 2392 – 240 + 270 = 2422   ⇒ New average weight = 2422⁄46 = 52 15/23 kg   Answer 52 15/23
Answer: B
The number of arrangements that can be made with the letters of the word MEADOWS so that the vowels occupy the even places?
Pick
A) 14
B) 144
C) 777
D) 992
E) 221

Solution: The word MEADOWS has 7 letters of which 3 are vowels.   -V-V-V-   As the vowels have to occupy even places, they can be arranged in the 3 even places in 3! i.e., 6 ways. While the consonants can be arranged among themselves in the remaining 4 places in 4! i.e., 24 ways.   Hence the total ways are  24 * 6= 
 24 * 6 = 144
144.   Answer:144
Answer: B
If 72/x is an integer and 108/x is an integer, which of the following must be true?
I. 9/x is an integer.
II. 12/x is an integer.
III. 36/x is an integer.
Options:
A) III only B) I and II only C) I, II, and III D) II and III only E) I only

Solution: The largest possible value of x is 36 (the greatest common factor of 72 and 108), and if x=36 then   III only
Answer: A
Which of the following equations has a solution in common with 2x^2 - 5x - 42?	Choose the correct answer
A) 2x^2 + 8x - 42 = 0  B) x^2 - 14x + 24 = 0  C) 2x^2 - 8x + 8 = 0  D) x^2 + 13x + 13 = 0  E) none of the above

Solution: Given : 2x^2 - 5x - 42 => (2x + 7) (x - 6) = 0 => -7/2 and 6 are the roots..   A. 2x^2 + 8x - 42 = 0 => (2x - 6) (x + 7)   B. x^2 - 14x + 24 = 0 => (x - 6) (x - 8)   C. x^2 + 13x + 13 = 0 => (2x -7) ( x - 1)   D. x^2 + 13x + 13 = 0 => (x + 6) (x + 7)   None of the answer equations have exactly both the same roots as the question equation, but at least one of them does share one of the two roots.   So IMO "B" is correct answer... because it shares the one root (part of the solution), -3, from the (x+3) portion of its factoring
Answer: B
Look at this series: 7, 10, 8, 11, 9, 12, ... What number should come next?
Choose the correct choice from the following answers:
A) 7 B) 10 C) 12 D) 13 E) 14

Solution: Explanation: This is a simple alternating addition and subtraction series. In the first pattern, 3 is added; in the second, 2 is subtracted.   Answer: Option 10
Answer: B
There are 48 students in a class. Find the numbers of ways in which a committee of 2 students is to be formed?
Select the correct option:	A) 1128	B) 1978	C) 2546	D) 3121	E) 2400

Solution: Required number of ways = 48C2 = 48*47 / 2= 
48*47 / 2 = 1_128
1128   1128nswer is 1128
Answer: A
A machine P can print one lakh books in 8 hours, machine Q can print the same number of books in 10 hours while machine R can print them in 12 hours. All the machines are started at 9 A.M. while machine P is closed at 11 A.M. and the remaining two machines complete work. Approximately at what time will the work (to print one lakh books) be finished ?	Choose one:
A) 1:00 P.M.
B) 2:00 P.M
C) 1:30 P.M.
D) 2:30 P.M.
E) 12:30 P.M.

Solution: (P + Q + R)'s 1 hour's work =	(	1	+	1	+	1	)	=	37	.   8	10	12	120   Work done by P, Q and R in 2 hours =	(	37	x 2	)	=	37	.   120	60   Remaining work =	(	1 -	37	)	=	23	.   60	60   (Q + R)'s 1 hour's work =	(	1	+	1	)	=	11	.   10	12	60   Now,	11	work is done by Q and R in 1 hour.   60   So,	23	work will be done by Q and R in	(	60	x	23	)	=	23	hours = 2 hours.   60	11	60	11   So, the work will be finished approximately 2 hours after 11 A.M., i.e., around 1 P.M.   Option 1:00 P.M.
Answer: A
In a certain state, gasoline stations compute the price per gallon p, in dollars, charged at the pump by adding a 3 percent sales tax to the dealer's price per gallon d, in dollars, and then adding a gasoline tax of $0.18 per gallon. Which of the following gives the dealer's price per gallon d in terms of the price per gallon p charged at the pump? Choose the correct choice from the following answers:
A) d = (p-0.03)/1.18 B) d = p/1.21 C) d= (p-0.18)/1.03 D) d = p-0.20 E) d = p/1.03 - 0.18

Solution: Let dealers price (d) be 1. so adding 3% to dealers price is d+ 3% of d. i.e. 1 + 3% of 1 which is1 + 0.03. then add 0.18 to the value.   Now 1.03 + 0.18. this is now 1.21. you have the gasoline stations price (p) as 1.21 dollars.   Now sub 1.21 in the options to know which option gave you d = 1. d must equal 1 because you earlier picked 1 as the value of d in the question.   PS: always remember to start from E upwards.   Answer : d= (p-0.18)/1.03
Answer: C
How many squares are there between 2011 to 2300 ????
Select the correct option.
A) 3  B) 4  C) 5  D) 6  E) 7

Solution: nos. are 2025, 2116, 2209   3nswers is 3   3NSWER:3
Answer: A
A man sold 10 eggs for 5 rupees and gained 20%. How many eggs did he buy for 5 rupees?	Choose the correct answer
A) 10 eggs  B) 12 eggs  C) 14 eggs  D) 16 eggs  E) None of these

Solution: S.P. for 1 egg = 5⁄10 = 1⁄2   ∴ C.P. for 1 egg = 100/(100+20)×12=512   ⇒ He bought 12 eggs for 5 rupees.   Answer 12 eggs
Answer: B
Two sets of 4 consecutive positive even integers have exactly one integer in common. The sum of the integers in the set with greater numbers is how much greater than the sum of the integers in the other set?
Answers:	A) 14	B) 7	C) 18	D) 24	E) it cannot be determined from the information given.

Solution: A=(2,4,6,8), sum of this=20   B=(8,10,12,14), sum of this=44,   The differenct between   44-20= 
  44-20 = 24
24   Hence,24 is the answer i.e.24
Answer: D
In order to fulfill a local school’s request for a cakes, B parents agreed to each bake an equal number of cakes. If p of the parents did not bake any cakes, which of the following represents the additional number of cakes that each of the other parents had to bake in order for the school’s request for a cakes to be fulfilled?	Choices:
A) pa/(B(B-p))
B) pa/2
C) pa/B
D) p/B-p
E) pa/B

Solution: No of cakes each parent has to bake : a/B   No of parents did not bake cake = p   No of cakes that were not baked by p parents = p*a/B   No of parents has to bake additional cakes = B-p   additional number of cakes that each of the other parents had to bake in order for the school’s request for a cakes = pa/(B(B - P))   pa/(B(B-p))nswer pa/(B(B-p))
Answer: A
How many 1/2s are there in 37 1/2?
Choose the correct choice from the following choices: A) 75 B) 150 C) 300 D) 600 E) 700

Solution: Required number = (75/2)/(1/2)   = (75/2 x 2/1)   = 75   75NSWER:75
Answer: A
Find the odd one out:
125, 106, 86, 76, 65, 58, 53 Choose one.
A) 33  B) 86  C) 26  D) 18  E) 222

Solution: Explanation:   This sequence represents a series in which from the reverse order a prime number is added:   53+5= 
53+5 = 58
58   58+7= 
58+7 = 65
65   65+11= 
65+11 = 76
76   76+13= 
76+13 = 89
89   89+17= 
89+17 = 106
106   106+19= 
106+19 = 125
125   Hence 86 is the answer.   ANSWER: 86
Answer: B
How many four digit numbers can be formed using the digits {1, 3, 4, 5, 7,9}(repetition of digits is not allowed)? Pick:
A) 360
B) 817
C) 145
D) 346
E) 342

Solution: The given digits are six.   The number of four digit numbers that can be formed using six digits is ⁶P₄   = 6 * 5 * 4 * 3= 
6 * 5 * 4 * 3 = 360
360.   360nswer: 360
Answer: A
The sum of all the integers k such that –25 < k < 24 is	Select the correct option
A) 0
B) -2
C) -25
D) -49
E) -47

Solution: -24------------------0-----------------23   values upto+23 cancels outwe are left with only -24-23 sum of which is - 47. hence option D.   -47
Answer: E
Crazy Eddie has a key chain factory. Eddie managed to decrease the cost of manufacturing his key chains while keeping the same selling price, and thus increased the profit from the sale of each key chain from 50% of the selling price to 50% of the selling price. If the manufacturing cost is now $50, what was it before the decrease?	Choose the correct choice from the following choices
A) $20 B) $40 C) $50 D) $80 E) $100

Solution: Deargoodyear2013,   I'm happy to help.This is a relatively straightforward problem, not very challenging. BTW,Crazy Eddiewas the actually name of an electronics chain on the East Coast of the USA back in the 1970s.   Manufacturing now is $50. They now are making a 50% profit, so the selling price must be $100.   They had this same selling price, $100, before they made the change, and had a profit of 50%, so the manufacturing must have been $50. Answer = ($50).
Answer: C
In the biology lab of "Jefferson" High School there are 0.036*10^5 germs, equally divided among 45000*10^(-3) Petri dishes. How many germs live happily in a single dish?	Pick:
A) 10	B) 20	C) 30	D) 60	E) 80

Solution: 0.036*10^5 can be written as 3600   45000*10^(-3) can be written as 45   Required= 3600/45= 
3600/45 = 80
80   ANSW80R:80
Answer: E
A shepherd has 1 million sheep at the beginning of Year 2010. The numbers grow by xx during the yr. A famine hits his village in the next year & many of his sheep die. The sheep population decreases by yy during 2001 and at the beginning of 2011 the shepherd finds that he is left with 1 million sheep. Which of the following is correct? Select the correct option:	A) x<y	B) x>y	C) x=y	D) x<=y	E) x>=y

Solution: Let us assume the value of xx to be 10%10%.   Therefore, the number of sheep in the herd at the beginning of year 2001 (end of 2000) will be 1 million + 10%10% of 1 million = 1.1 million   In 2001, the numbers decrease by y%y% and at the end of the year the number sheep in the herd = 1 million.   i.e., 0.1 million sheep have died in 2001.   In terms of the percentage of the number of sheep alive at the beginning of 2001,   it will be (0.1/1.1)×100%=9.09%(0.1/1.1)×100%=9.09%.   From the above illustration it is clear that x>y   x>y
Answer: B
If x is an integer, which of the following is a possible value of W=(x^2 +2x – 7)/9?
Pick:
A) -2.4
B) 0.268
C) 1.166 repeating
D) 4.555 repeating
E) 8.125

Solution: x is an integer, which of the following is a possible value of W= (x^2 +2x – 7)/9?   Used process of elimination   A. -2.4   when this is multiplied by 9, x is not an integer   B. 0.268   when this is multiplied by 9, x is not an integer   C. 1.166 repeating   when this is multiplied by 9, x is not an integer   D. 4.555 repeating   E. 8.125   when this is multiplied by 9, x is not an integer   Answer choice 4.555 repeating seems to fit.4.555 repeating
Answer: D
if Juan takes 14 seconds to run y yards, how many seconds will it take him to run x yards at the same rate?
Pick
A) 14x/y	B) 11y/x	C) x/11y	D) 11/xy	E) xy/11

Solution: Answer is A.   The rate of running hards: 14 minutes per y hards.   Thus the time for running x hards = x hards * 14 minutes/y hards = 14x/y
Answer: A
A cylinder is sliced by a plane to form the solid
shown. The base edge of the solid is a circle
of radius 3. The top edge is an ellipse. The
highest point on the ellipse is 6 units above the
base. The lowest point on the ellipse is 2 units
above the base. What is the volume, in cubic
units, of the solid?  Answers.
A) 24π B) 30π C) 36π D) 42π E) 48π

Solution: The plane parallel to the base passing through the center of the ellipse will cross the ellipse   along its minor axis. If we cut the solid along this plane and flip the top piece that is sliced off 180   degrees around the minor axis, the solid becomes a cylinder with the base of area 9 and height     (2 + 6)/2= 
  (2 + 6)/2 = 4
4. The volume is therefore 36π.   correct answer 36π
Answer: C
The average salary of all the workers in a workshop is Rs. 8000. The average salary of 7 technicians is Rs. 20000 and the average salary of the rest is Rs. 6000. The total number of workers in the workshop is  Select the correct option:
A) 20
B) 49
C) 22
D) 23
E) NONE

Solution: Sol.   Let the total number of workers be x. Then,   8000x = (20000 × 7) + 6000 ( x – 7)   ‹=› 2000x = 98000   ‹=› x = 49.   Answer 49
Answer: B
A small company is planning to rent either computer A or computer B to print customer mailing lists. Both computer A and computer B must be rented on an hourly basis. The rental fee is based only on the amount of time the computer is turned on. It will cost 40 percent more per hour to rent computer A than to rent computer B. Computer B would, however, require 20 hours more than computer A to do the job. If either computer A, or computer B were rented the total cost to rent the computer would be $650.00. What would be the approximate hourly charge to rent computer B?	Choose the correct choice from the following answers.
A) $9.28	B) $11.30	C) $13.20	D) $17.80	E) $22.10

Solution: Pa = price of $9.28   Pb = price of B   Ta = time for $9.28 to complete the job   Tb = time for B to complete the job   Given   Pa = 1.4 Pb   Ta+20 = Tb   Pa*Ta = Pb*Tb=650   1.4Pb * (Tb-20) = Pb*Tb   1.4 Pb Tb - Pb Tb = 1.4 Pb * 20   0.4PbTb = 28Pb   Tb = 28/0.4= 
28/0.4 = 70
70   Pb=650/70 ~ 9.28   $9.28
Answer: A
Mr. Gangadhar, Mr. Ramesh and Mr. Shridhar together earned 19800. The ratio of earnings between Mr. Gangadhar and Mr. Ramesh is 2 : 1 while that between Mr.Ramesh and Mr. Shridhar is 3 : 2. How much did Mr. Ramesh earn?	Choices: A) 3600 B) 5400 C) 1800 D) 6300 E) None of these

Solution: Ratio of investment = 6 : 3 : 2   ∴ Share of Mr. Ramesh = 3⁄11 × 19800 = 5400   Answer 5400
Answer: B
A tea expert claims that he can easily find out whether milk or tea leaves were added first to water just by tasting the cup of tea. In order to check this claims 12 cups of tea are prepared, 6 in one way and 6 in other. Find the different possible ways of presenting these 12 cups to the expert.
Choose the correct choice from the following answers:
A) 252
B) 240
C) 300
D) 924
E) None

Solution: Solution:   Since, there are 6 cups of each kind, prepared with milk or tea leaves added first, are identical hence, total number of different people ways of presenting the cups to the expert is,   [12!/(6!x 6!)]= 924   Answer: Option 924
Answer: D
when W is divided by 13, the reminder is 0. if W is one more than it value and when divided by 10 its remainder is 0. what is the value of W ?	Choose the correct choice from the following answers
A) 39  B) 26  C) 14  D) 13  E) 52

Solution: W is divided by 13 so that is multiple of 14 as 13,26,39...   W+1 is divided by 10 the remainder is 0 so it is divisible by 10. Consider from option let us take the number is 39 it is divisible by 13 but 39+1 is divisible by 10 so ans is 39
Answer: A