MU-NLPC/Calc-aqua_rat huggingface dataset:
If 10 persons meet at a reunion and each person shakes hands exactly once with each of the others, what is the total number of handshakes?	Pick one.
A) 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1  B) 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1  C) 11 × 10  D) 55  E) 45

Solution: If 10 persons meet at a reunion and each person shakes hands exactly once with each of the others, what is the total number of handshakes?   1st person will have 9 handshakes, 2nd will have 8, ....9th will have 1 and 10th will have 0   = 9+8+7+6+5+4+3+2+1= 
9+8+7+6+5+4+3+2+1 = 45
45   if we generalize this: if there are n people then there will be n(n-1)/2 handshakes.   Ans.45) 45
Answer: E
The sum of two numbers is 72, and one of them is 12 more than the other. What are the two numbers?
Select.
A) 36-48
B) 50-34
C) 60-24
D) 30-42
E) 21-63

Solution: In this problem, we are asked to find two numbers. Therefore, we must let x be one of them. Let x, then, be the first number.   We are told that the other number is 12 more, x + 12.   The problem states that their sum is 72:   word problem = 72   The line over x + 12 is a grouping symbol called a vinculum. It saves us writing parentheses.   We have:   2x = 72 âˆ’ 12   = 60.   x = 60/2= 
60/2 = 30
30.   This is the first number. Therefore the other number is   x + 12= 30 + 12= 
30 + 12 = 42
42.   The sum of 30 + 42 is 72.   30-42
Answer: D
The ratio of the volumes of two cubes is 9261: 12167. What is the ratio of their total surface areas? Pick: A) 1:12 B) 85:31 C) 51:45 D) 58:67 E) 53:58

Solution: Ratio of the sides   = ³√9261 : ³√12167= 21 : 23   Ratio of surface areas   = 212 : 232 = 53:58   Answer:53:58
Answer: E
At the end of three years what will be the compound interest at the rate of 10% p.a. on an amount of Rs.30000?  Choices:	A) 6620	B) 3277	C) 2688	D) 2998	E) 9930

Solution: A = 30000(11/10)3   = 39930   = 30000   ----------   9930   Answer:9930
Answer: E
How much interest will $2,400 earn at an annual rate of 8% in one year if the interest is compounded every 4 months?	Choose the correct choice.
A) $141 B) $150 C) $197 D) $234 E) $312

Solution: Rate 8% compounded every 4 months = 8/3 %. Interest for the first 4 months = 8/3 % of 2400 = 8/3 * 2400 * 1/100= 
8/3 * 2400 * 1/100 = 64
64.   Now in this particular scenario, the next 4 months will earn an interest on 2400, and an interest on 64.   For approximation, let's calculate total interest without considering interest on the interest earned. Thus total interest earned will be 64*3= 
64*3 = 192
192   Now, we will earn some interest on this interest as well. So the total will be a little more than 192. And the only option that satisfies that is $197   . So the answer is option $197
Answer: C
A watch was sold at a loss of 10%. If it was sold for Rs.140 more, there would have been a gain of 5%. What is the cost price?	Choices.
A) s.933.33  B) s.1009  C) s.1007  D) s.1006  E) s.1002

Solution: Explanation:   90%   105%   --------   15% ---- 140   100% ---- ? => Rs.933.33   s.933.33nswer:s.933.33
Answer: A
Tough and Tricky questions: Number Properties.
If (z + 3)/9 is an integer, what is remainder when z is divided by 9? Pick:	A) 2	B) 3	C) 4	D) 5	E) 6

Solution: Assume the answer choices as the value of z   9/9= 
9/9 = 1
1   Ans 6
Answer: E
Camel and carriage for Rs. 5000. He SP the camel at a gain of 20% and the carriage at a loss of 10%. If he gains 3% on the whole, then find the CP of the camel?	Select:
A) Rs.2166.67 B) Rs.3210 C) Rs.3210.14 D) Rs.3344.24 E) Rs.4500.12

Solution: Now, in this numerical, there is no common loss and gain %.   Hence, solve it making equations.   Let cost price of camel be x.   As cost of camel and carriage = Rs 5000   Cost of carriage = Rs. (5000 – x)   After selling camel he gains 20% and on carriage a loss of 10%. But on the whole he gains 3%.   Therefore,   20% of x – 10 % of (5000 – x) = 3 % of 5000   20	× x –	10	× (5000 – x) =	3	× 5000   100	100	100   x	–	(5000 – x)	= 150   5	10   10x	–	(5000 – x) × 10	= 150 × 10   5	10   2x-5000+x=1500   3x=1500+5000   x=2166.67   The cost of camel = Rs.2166.67   Option (Rs.2166.67) is the correct answer
Answer: A
The length of a rectangle ishalved, while its breadth is tripled. Watis the % change in area? Choose the most appropriate option:  A) 25%  B) 30%  C) 50%  D) 65%  E) 70%

Solution: Let original length = x and original breadth = y.   Original area = xy.   New length = x .   2   New breadth = 3y.   New area = x x 3y = 3 xy.   2 2   Increase % = 1 xy x 1 x 100 % = 50%.   2 xy   50%
Answer: C
Stacy and Heather are 25 miles apart and walk towards each other along the same route. Stacy walks at constant rate that is 1 mile per hour fast than heather's constant rate of 5 miles/hour. If Heather starts her journey 24 minutes after Stacy, how far from the original destination has Heather walked when the two meet?.
Choices
A) 9.0mile  B) 13.0mile  C) 11.0mile  D) 10.2 mile  E) 12 mile

Solution: Ss - Stacy's speed = 6m/hr   Sh - Heather's speed = 5m/hr   In 24 minutes Stacy will cover = (24/60)*6= 
(24/60)*6 = 12/5 = around 2.4
2.4miles   Now since both are walking in opposite directions, add their speeds - 6+5=11m/hr and distance to cover is  25 -2.4= 
 25 -2.4 = 22.6
22.6   Time taken= Distance/ Speed = 22.6/11 = 2.05 hrs   Heather will cover = 5*2.4 = 10.2 miles.   Answer 10.2 mile
Answer: D
The radius of a semi circle is 14 cm then its perimeter is?  Choose the correct choice from the following options.
A) 32.8
B) 32.4
C) 72
D) 32.2
E) 32.9

Solution: Diameter = 28 cm   1/2*22/7*28+28= 
1/2*22/7*28+28 = 72
72   Answer : 72
Answer: C
A letter lock consists of three rings each marked with six different letters. The number of distinct unsuccessful attempts to open the lock is at the most? Select:
A) 277 B) 269 C) 215 D) 177 E) 123

Solution: Since each ring consists of six different letters, the total number of attempts possible with the three rings is   = 6 * 6 * 6= 
6 * 6 * 6 = 216
216. Of these attempts, one of them is a successful attempt.   Maximum number of unsuccessful attempts= 216 - 1= 
216 - 1 = 215
215.   Answer:215
Answer: C
O(x) represents the least odd integer greater than x, whereas o(x) represents the greatest odd integer less than x. Likewise, E(x) represents the least even integer greater than x, whereas e(x) represents the greatest even integer less than x. According to these definitions, the value of O(5.3) + E(–6.7) + o(–3.3) + e(4.7) is: Answers: A) -3 B) -1 C) 0 D) 1 E) 3

Solution: O(5.3) + E(–6.7) + o(–3.3) + e(4.7) = 7 + (-6) + (-5) + 4= 
7 + (-6) + (-5) + 4 = 0
0   The answer is 0.
Answer: C
One woman and one man can build a wall together in five hours, but the woman would need the help of two girls in order to complete the same job in the same amount of time. If one man and one girl worked together, it would take them nine hours to build the wall. Assuming that rates for men, women and girls remain constant, how many hours would it take one woman, one man, and one girl, working together, to build the wall?  Answers:	A) 55/7	B) 1	C) 135/32	D) 222/37	E) 252/58

Solution: Solution:Let work done by man, women and girl per hour be m,w,g respectively.   Then, m+w = 1/5-->(1) , w + 2g = 1/5-->(2) and m + g =1/9-->(3).   No. of hours it would take forone woman, one man, and one girl, working together, to build the wall,n = 1/m+w+g   From (1) and (2), m=2g and from (3) g=1/27,m=2/27 and w=17/135.   So, n = 1/(32/135) = 135/32   Option, 135/32
Answer: C
Which of the following is not a leap year?
Choose the correct option:  A) 700  B) 800  C) 1000  D) 1200  E) 2000

Solution: The century divisible by 400 is a leap year.   The year 700 is not a leap year.   700nswer: Option 700
Answer: A
Excluding stoppages, the speed of a train is 45 kmph and including stoppages it is 30 kmph. Of how many minutes does the train stop per hour?  Answers.
A) A)5
B) B)10
C) C)20
D) D)30
E) E)40

Solution: Explanation:   T = 15/45 * 60= 
15/45 * 60 = 20
20   Answer: Option 20
Answer: C
Find the area of a parallelogram with base 20 cm and height 40 cm?  Select the correct option.
A) 100 cm2 B) 250 cm2 C) 800 cm2 D) 296 cm2 E) 456 cm2

Solution: Area of a parallelogram   = base * height   = 20 * 40= 
20 * 40 = 800
800 cm2   Answer: 800 cm2
Answer: C
A group of 10 representatives is to be selected out of 12 seniors and 10 juniors. In how many different ways can the group be selected if it should have at least one senior?  Choose one
A) ²²C₉  B) ²²C₁₀  C) ²²C₉ + ¹⁰C₁  D) ²²C₁₀ - 1  E) ¹⁰C₁

Solution: The total number of ways of forming the group of ten representatives is ²²C₁₀.   The total number of ways of forming the group that consists of no seniors is ¹⁰C₁₀ = 1 way   The required number of ways   = ²²C₁₀ - 1   Answer:²²C₁₀ - 1
Answer: D
A bucket full of nuts was discovered by the crow living in the basement. The crow eats a sixth of the total number of nuts in 8 hours. How many hours in total will it take the crow to finish a quarter of the nuts?	Options:
A) 10
B) 12
C) 14
D) 16
E) 18

Solution: In one hour, the crow eats 1/48 of the nuts.   (1/4) / (1/48)= 
(1/4) / (1/48) = 12
12 hours   The answer is 12.
Answer: B
Darcy lives 1.5 miles from work. She can walk to work at a constant rate of 3 miles per hour, or she can ride the train to work at a constant rate of 20 miles per hour. If she rides the train, there is an additional x minutes spent walking to the nearest train station, waiting for the train, and walking from the final train station to her work. If it takes Darcy a total of 15 more minutes to commute to work by walking than it takes her to commute to work by riding the train, what is the value of x? Choose the correct choice from the following.
A) 10.5	B) 15	C) 25.5	D) 30	E) 60

Solution: The time it takes Darcy to walk to work is (1.5/3)*60= 
(1.5/3)*60 = 30
30 minutes   The time it takes Darcy to take the train is (1.5/20)*60 + x= 4.5 + x minutes   It takes 15 minutes longer to walk, so 30 = 4.5 + x + 15   x=10.5 minutes   10.5nswer: 10.5
Answer: A
Mr Jacobs placed his folders on three chairs in a conference room comprising of 12 chairs, if Mrs Roberts walked in and also placed her folders on 3 chairs, what is the probability that she did no place any of her folders on a chair already containing Mr Jacobs folder?.	Choose one.
A) 3/9  B) 3/55  C) 9/12  D) 21/55  E) 3/12

Solution: Since Mr Jacob's folders are already on 3 chairs, the subset from which the 3 chairs on which Mrs Roberts placed her folders should be chosen are the 9 chairs not occupied by Mr Jacob's folders from the universe of 12.   The first chair can be one of the 9 from the 12 with probability 9/12.   The second chair can be one of the 8 from the 11 remaining with probability 8/11.   The third chair can be one of the 7 from the 10 remaining with probability 7/10.   The total probability will be 9/12 × 8/11 × 7/10. On cancellation, this comes to 21/55.   Thus, the answer is 21/55 - 21/55
Answer: D
Amar takes as much time in running 18 meters as a car takes in covering 48 meters. What will be the distance covered by Amar during the time the car covers 1.6 km? Choose the correct answer:	A) 189 m	B) 178 m	C) 172 m	D) 600 m	E) 186 m

Solution: 600 mistance covered by Amar   = 18/4.8 (1.6km)   = 3/8(1600) = 600 m   Answer:600 m
Answer: D
A 110 cm long wire is to be cut into two pieces so that one piece will be 2/5th of the other, how many centimeters will the shorter piece be? Pick.
A) 35  B) 20  C) 47  D) 36  E) 31

Solution: 1: 2/5 = 5: 2   2/7 * 110 =31   Answer:31
Answer: E
A couple decides to have 6 children. If they succeed in having 6 children and each child is equally likely to be a boy or a girl, What is the probability that they will have exactly 3 girls and 3 boys?  Choose the correct choice from the following options:
A) 1  B) 9/64  C) 1/8  D) 3/16  E) 9/32

Solution: Sample space = 2^6 = 64.   Favourable events = {bbbggg}, {bgbgbg}, {bgbggb}, {bggbbg} {gggbbb}, {gbgbgb}, {gbbggb}.{gbgbbg}{gbbgbg}   Probability = 9/64 = 9/64   Ans (9/64).
Answer: B
The length of a rectangular landscape is 4times its breadth. There is a playground in it whose area is 1200 square mtr & which is 1/3rd of the total landscape. What is the length of the landscape?	Choose the correct choice from the following answers:
A) 80 B) 90 C) 120 D) 140 E) 160

Solution: Sol. x * 4x = 3 * 1200   x = 30   Length = 4 * 30= 
4 * 30 = 120
120   120
Answer: C
A man has some hens and cows. If the number of heads be 100 and the number of feet equals 240, then the number of cows will be: Choose the correct choice from the following choices
A) 22 B) 23 C) 24 D) 20 E) 28

Solution: Explanation:   Let the number of hens be x and the number of cows be y.   Then, x + y = 100 .... (i)   and 2x + 4y = 240 x + 2y = 120 .... (ii)   Solving (i) and (ii) we get: x = 26, y = 20.   The required answer = 20.   Answer: 20
Answer: D
If I walk at 2 kmph, I miss the train by 2 min, if however, I walk at 4 kmph. I reach the station 2 min before the arrival of the train. How far do I walk to reach the station?
Select.
A) 4/13 km  B) 4/15 km  C) 4/17 km  D) 1/15 km  E) 2/15 km

Solution: x/2 – x/4 = 4/60   x = 4/15 km   ANSWER:4/15 km
Answer: B
Two goods trains each 500 m long are running in opposite directions on parallel tracks. Their speeds are 50 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one?	Options:	A) 22	B) 27	C) 45	D) 99	E) 12

Solution: Relative speed = 50 + 30= 
50 + 30 = 80
80 km/hr.   80 * 5/18= 200/9 m/sec.   Distance covered = 500 + 500= 
500 + 500 = 1_000
1000 m.   Required time= 1000*9/200= 
1000*9/200 = 45
45 sec.   Answer: 45
Answer: C
6/9 of the population of the country of Venezia lives in Montague Province, while the rest lives in Capulet Province. In the upcoming election, 80% of Montague residents support Romeo, while 70% of Capulet residents support Juliet; each resident of Venezia supports exactly one of these two candidates. Rounded if necessary to the nearest percent, the probability that a Juliet supporter chosen at random resides in Capulet is Choose one.
A) 64%
B) 41%
C) 45%
D) 72%
E) 78%

Solution: Total population = 90 (assume).   6/9*90= 
6/9*90 = 60
60 people from Montague.   3/9*90= 
3/9*90 = 30
30 people from Capulet.   0.2*60= 
0.2*60 = 12
12 people from Montague support Juliet.   0.7*30= 
0.7*30 = 21
21 people from Capulet support Juliet.   The probability that a Juliet supporter chosen at random resides in Capulet is 21/(12+21)=~64.   64%nswer: 64%
Answer: A
What is the average (arithmetic mean) of all the multiples of ten from 10 to 250 inclusive?
Choose the most appropriate option:	A) 90	B) 95	C) 100	D) 130	E) 170

Solution: The multiples of ten from 10 to 250 inclusive would be an evenly spaced set with 25 terms - 10, 20, 30,.......250   So average = (First term + Last Term)/2 = (10 + 250)/2 = 260/2= 
260/2 = 130
130   Hence, the correct answer is 130.
Answer: D
If Jake loses 8 pounds, he will weigh twice as much as his sister Kendra. Together they now weigh 290 pounds. What is Jake’s present weight, in pounds?  Choose the correct option:  A) 180  B) 184  C) 188  D) 192  E) 196

Solution: J + K = 290 and so K = 290 - J   J - 8 = 2K   J - 8 = 2(290-J)   3J = 588   J = 196   The answer is 196.
Answer: E
Two numbers A and B are such that the sum of 6% of A and 4% of B is two-third of the sum of 6% of A and 8% of B. Find the ratio of A : B. Select.
A) 2 : 3  B) 1 : 2  C) 4 : 3  D) 1 : 1  E) 3 : 2

Solution: Explanation:   6% of 2 : 3 + 4% of B = 2/3(6% of 2 : 3 + 8% of B)   62 : 3/100 + 4B/100 = 2/3(62 : 3/100+8B/100)   ⇒62 : 3 + 4B = 2/3(62 : 3 + 8B)   ⇒182 : 3 + 12B = 122 : 3 + 16B   ⇒ 62 : 3 = 4B   ⇒ 2 : 3B = 4/6=2/3   ⇒ 2 : 3:B=2:3   2 : 3nswer: Option 2 : 3
Answer: A
Imagine a disk spinning like a record player turn table. Half of the disk is black and the other is white. Assume you have an unlimited number of color sensors. How many sensors would you have to place around the disk to determine the direction the disk is spinning? Where would they be placed?	Choose the correct choice.
A) 1
B) 2
C) 3
D) 4
E) 5

Solution: 1 sensor between the black and white border on the edge of disk   1 is enough to determine the drection   1NSWER:1
Answer: A
Sum of two number is 1000 and the sum of their recipocal is 2/255.Let the smallest of 2 number be L, so which of the following is correct value range for L?
Choose the most appropriate option:
A) 100  B) 150  C) 180  D) 200  E) 220

Solution: As per the question , let the smaller number be L and larger number be H.   So, L+H = 1000..........eqn 1   And   1/L+1/H= 2/255   (L+H)/LH = 2/255   LH = (L+H)*255/2   LH= 127500.................eqn 2   Now,   (H-L)^2 =(H+L)^2 - 4HL   (H-L)^2 = 1000000-4*127500   = 1000000-510000= 
1000000-510000 = 490_000
490000   Now,   (H-L)=sqrt(490000)   = 700   H-L=700...............................eqn 3   From eqn 1 and 3   L=150   ANSWER:150
Answer: B
If a book is sold at 10% profit instead of 10% loss, it would have brought Rs 14 more. Find out the cost price of the book Choose the correct option: A) 75 B) 72 C) 60 D) 70 E) 80

Solution: Let C.P. of the book be Rs. ’X’   Given, 1.10 X - 0.90X = 14   => 0.2 X = 14 = 14/0.2= 
14/0.2 = 70
Rs 70   ANSWER:70
Answer: D
Thomas's age and Matt's age are in the ratio 6:7. Four years ago the ratio of their ages was 5:6. Find the ratio of their ages 10 years before?	Pick one
A) 3:5 B) 5:7 C) 7:9 D) 9:11 E) 11:13

Solution: Let ages of Thomas and Matt be x and y respectively.   x/y = 6/7 => x = 6/7 y   (x-4)/(y -4) = 5/6   => 6x - 24 = 5y - 20 => 6x = 5y + 4   But x = 6/7 y   6 * 6/7 y = 5y + 4   36y = 35y +28 => y = 28 years   => x = 6*28/7= 
6*28/7 = 24
>24 years   Ratio of their ages four years hence, (24-10)/(28-10)= 14/18. => 7:9   Answer: 7:9
Answer: C
A company has a job to prepare certain number of cans and there are three machines A, B and C for this job. A can complete the job in 5 days, B can complete the job in 25 days and C can complete the job in 2 days. How many days the company will it take to complete the job if all the machines are used simultaneously?
Choose the correct choice.
A) 4 days B) 5/3 days C) 50/37 days D) 37/50 days E) 14 days

Solution: Let the total number of cans to be prepared be 50.   The number of cans prepared by A in 1 day = 10.   The number of cans prepared by B in 1 day = 2.   The number of cans prepared by C in 1 day = 25.   Thus, the total number of cans that can be prepared by all the machines working simultaneously in a single day = 37.   Therefore, the number of days taken to complete the whole work = 50/37 days.   ANSWER:50/37 days
Answer: C
The parameter of a square is equal to the perimeter of a rectangle of length 22 cm and breadth 20 cm. Find the circumference of a semicircle whose diameter is equal to the side of the square.	Choose the correct answer
A) 23.56	B) 33.0	C) 23.55	D) 23.53	E) 23.57

Solution: Let the side of the square be a cm.   Parameter of the rectangle = 2(22 + 20) = 84 cm Parameter of the square = 84 cm   i.e. 4a = 84   A = 21   Diameter of the semicircle = 21 cm   Circimference of the semicircle   = 1/2(âˆ)21   = 1/2(22/7)(21) = 66/2= 
66/2 = 33
33 cm   Answer:33.0
Answer: B
A group of people were given 2 puzzles. 71% people solved puzzle X and 89% people solved puzzle Y. What is the maximum and minimum percentage of people who could have solved both the puzzles?
Select the correct option:
A) 71%, 60%
B) 49%, 33%
C) 68%, 57%
D) 79%, 68%
E) 89%, 79%

Solution: To solve this question, we don't need any formulas. Just read the question carefully. If 71% of the people solved puzzle X and 89% solved puzzle Y, then maximum % that can solve both correctly can only be 71%. From the given options, only D looks good   71%, 60%nswer 71%, 60%
Answer: A
40 persons like apple. 7 like orange and mango dislike apple. 10 like mango and apple and dislike orange. 5 like all. How many people like apple?  Options
A) 48  B) 46  C) 54  D) 58  E) 62

Solution: orange+mango-apple=7   mango+apple-orange=10   apple=40   orange+mango+apple=5   40+10+5-7= 
40+10+5-7 = 48
48 like apple   48NSWER:48
Answer: A
If the cost price of 12 pens is equal to the selling price of 6 pens, the gain percent is: Choose the correct choice from the following options
A) 80%	B) 90%	C) 100%	D) 40%	E) 10%

Solution: Explanation:   Let C.P. of each pen be Re. 1.   Then, C.P. of 6 pens = Rs. 6; S.P. of 6 pens = Rs. 12.   Gain % = 6/6 * 100= 
6/6 * 100 = 100
100%   Answer:100%
Answer: C
Divide Rs. 1500 among A, B and C so that A receives 1/3 as much as B and C together and B receives 2/3 as A and C together. A's share is? Choose the correct answer.
A) 711 B) 378 C) 375 D) 318 E) 319

Solution: A+B+375 = 1500   A = 1/3(B+375); B = 2/3(A+375)   A/(B+375) = 1/3   A = 1/4 * 1500= 
1/4 * 1500 = 375
> 375   Answer: 375
Answer: C
Free notebooks were distributed equally among children of a class. The number of notebooks each child got was one-eighth of the number of children. Had the number of children been half, each child would have got 16 notebooks. Total how many notebooks were distributed ?  Choose the correct choice from the following options
A) 512	B) 513	C) 514	D) 515	E) 516

Solution: Let total number of children be x.   Then, (x) x 1/8x = (x/2)x 16   = x = 64.   Number of notebooks = 1/8 x2 = (1/8	x 64 x 64)	= 512.   512nswer is 512.
Answer: A
Which of the following numbers is divisible by each one of 3, 7, 9 and 11?	Select
A) 639  B) 2079  C) 3791  D) 37911  E) None of these

Solution: 639 is not divisible by 7;   2079 is divisible by each one of 3, 7, 9, 11.   Correct Option: 2079
Answer: B
The owner of an electronic store charges his customer 14% more than the cost price. If a customer paid Rs.1,65300 for an LED TV, then what was the original price of the TV?	Choose the correct choice from the following choices:	A) Rs.140400	B) Rs.150500	C) Rs.145000	D) Rs.135200	E) None of these

Solution: Explanation:   14% more than CP means SP = 114% = Rs.165300.   :. CP = 165300x100/140 = Rs.145000.   Answer: Option Rs.145000
Answer: C
On Saturday, Kramer purchases exactly 3 new shirts, 2 new sweaters, and 4 new hats, On the following day and each subsequent day thereafter, Kramer wears one of his new shirts together with one of his new sweaters and one of his new hats. Kramer avoids wearing the exact same combination of shirt, sweater, and hat for as long as possible. On which day is this no longer possible?  Choose the correct option:
A) Tuesday	B) Wednesday	C) Thursday	D) Friday	E) Saturday

Solution: Shirt combinations = 3!/1*(3-1)! = 3*2*1/1*2*1 = 3   Sweater combinations = 2!/1*(2-1)! = 2*1/1*1 2 /1*(2-1)= 
2 /1*(2-1) = 2
2*1/1*1= 
2*1/1*1 = 2
2   Hat combinations= 4!/1!*(4-1)! = 4*3*2*1/1*3*2*1 = 4   Total Combinations = Shirt Combos*Sweater Combos*Hat Combos    3*2*4= 
 3*2*4 = 24
24 combinations   24 / 7 (days of the week)= remainder of 3   Purchased on Saturday, 3rd day is Tuesday. Next day, which he won't have a new combination for, is Wednesday. (Wednesday)
Answer: B