MU-NLPC/Calc-aqua_rat huggingface dataset:
In one year, the population, of a village increased by 5% and in the next year, it decreased by 5%. If at the end of 2nd year, the population was 9975, what was it in the beginning?	Choose the correct choice from the following options:
A) 7787  B) 10000  C) 1988  D) 1277  E) 2081

Solution: x*105/100 * 95/100 = 9975   X*0.9975=9975   X=9975/0.9975= 
9975/0.9975 = 10_000
> 10000   Answer:10000
Answer: B
If a and b are positive integers of C such that a/b=2.86, which of the following must be a divisor of a?
Choose the most appropriate option.
A) 10
B) B.13
C) 18
D) 26
E) 50

Solution: The prompt gives us a couple of facts to work with:   1) A and B are positive INTEGERS   2) A/B = 2.86   We can use these facts to figure out POSSIBLE values of A and B. The prompt asks us for what MUST be a divisor of A. Since we're dealing with a fraction, A and B could be an infinite number of different integers, so we have to make both as SMALL as possible; in doing so, we'll be able to find the divisors that ALWAYS divide in (and eliminate the divisors that only SOMETIMES divide in).   The simplest place to start is with...   A = 286   B = 100   286/100= 
286/100 = 143/50 = around 2.86
2.86   These values are NOT the smallest possible values though (since they're both even, we can divide both by 2)...   A= 143   B = 50   143/50= 
143/50 = 143/50 = around 2.86
2.86   There is no other way to reduce this fraction, so A must be a multiple of 143 and B must be an equivalent multiple of 50. At this point though, the value of B is irrelevant to the question. We're asked for what MUST divide into A....   Since A is a multiple of 143, we have to 'factor-down' 143. This gives us (11)(13). So BOTH of those integers MUST be factors of A. You'll find the match in the answer choices.   Final Answer:   B.13
Answer: B
The speed of a boat in still water is 60kmph and the speed of the current is 36kmph. Find the speed downstream and upstream?
A. 35, 25 kmph
Choose the correct choice from the following.
A) 76,24 kmph	B) 40,24 kmph	C) 96,24 kmph	D) 26,24 kmph	E) 12,36 kmph

Solution: Speed downstream = 60 + 36= 
60 + 36 = 96
96 kmph   Speed upstream= 60 - 36= 
60 - 36 = 24
24 kmph   Answer: 96,24 kmph
Answer: C
Anand and Deepak started a business investing Rs. 22,500 and Rs. 35,000 respectively. Out of a total profit of Rs. 14,950, Deepak's share is:? Choose the correct answer:
A) s.8467	B) s.9100	C) s.8400	D) s.8429	E) s.8420

Solution: Ratio of their shares   = 22500 : 35000   = 9:14   Deepak's share   = 14950 * 14/23   = Rs.9100.   Answer:s.9100
Answer: B
If the set S is composed of the following numbers {99, 100, 100, 105, 106, 114, 125}, which of the following is largest?
Choose one:	A) The average (arithmetic mean) of set S	B) The median of set S	C) The mode of set S	D) The range of set S	E) The standard deviation of set S

Solution: A) 99, 100, 100, 105, 106, 114, 125 = 749 and its mean is   749/7= 
  749/7 = 107
107.   B) The list is of 7 numbers and median is 105.   C) Mode is number of repetition of a number in the list , here it is 100.   D) Range= Max value - min value = 125 -99= 
125 -99 = 26
26.   E) SD= square root of (sum of ( mean of series - number)^2 ) / n =>< 100   IMO option The average (arithmetic mean) of set S is correct answer..
Answer: A
In X game of billiards, X can give Y 20 points in 60 and he can give Z 30 points in 60. How many points can Y give Z in X game of 120?  Choose the most appropriate option:  A) 30  B) 20  C) 25  D) 40  E) 50

Solution: X scores 60 while Y score 40 and Z scores 30.   The number of points that Z scores when Y scores 120 = (120 * 30)/40= 
(120 * 30)/40 = 90
90.   In X game of 100 points, Y gives (120 - 90)= 
(120 - 90) = 30
30 points to C.   30
Answer: A
The sum of the squares of the first 15 positive integers (1^2 + 2^2 + 3^2 + . . . + 15^2) is equal to 1260. What is the sum of the squares of the second 15 positive integers (16^2 + 17^2 + 18^2 + . . . + 30^2) ?
Choose the correct answer:
A) 2480  B) 3490  C) 6785  D) 8235  E) 9255

Solution: You'll never need a formula for the sums of squares on the actual GMAT. You don't need to use that formula here, though it's not all that straightforward to solve without one. Two different approaches:   16^2 + 17^2 + 18^2 + ... + 30^2 = (15 + 1)^2 + (15 + 2)^2 + (15 + 3)^2 + ... + (15 + 15)^2   Now we can expand each square; they are all in the (x + y)^2 = x^2 + 2xy + y^2 pattern.   = (15^2 + 2*15 + 1^2) + (15^2 + 4*15 + 2^2) + (15^2 + 6*15 + 3^2) + ... + (15^2 + 30*15 + 15^2)   Now we have fifteen 15^2 terms, so adding these gives 15*15^2 = 15^3 = 3375. We also have the entire sum 1^2 + 2^2 + ... + 15^2, which we know is equal to 1240. Finally adding the middle terms, we have:   2*15 + 4*15 + 6*15 + ... + 30*15 = 15(2 + 4 + 6 + .... + 30) = 15*2*(1 + 2 + 3 + ... + 15) = 15*2*8*15= 
15*2*8*15 = 3_600
3600   So the sum must be  3375 + 1240 + 3600= 
 3375 + 1240 + 3600 = 8_215
8215   Alternatively, we can use a different factoring pattern. We want to find the value of 30^2 + 29^2 + ... + 17^2 + 16^2. Well if we subtract 15^2 + 14^2 + .... + 2^2 + 1^2 from this, the answer will be 1240 less than what we want to find. So if we can find the value of   30^2 + 29^2 + ... + 17^2 + 16^2 - (15^2 + 14^2 + .... + 2^2 + 1^2)   then we can add 1240 to get the answer. Now grouping the terms above to get differences of squares, we have= (30^2 - 15^2) + (29^2 - 14^2) + ... + (16^2 - 1^2)   and factoring each of these using x^2 - y^2 = (x + y)(x - y), we have   = 45*15 + 43*15 + 41*15 + ... + 17*15 = 15(45 + 43 + 41 + ... + 17)   In brackets we have an equally spaced sum with fifteen terms, which we can evaluate using the familiar formula. So the above equals     15*15*62/2= 
  15*15*62/2 = 6_975
6975   and adding back the 1260, we get the answer of 8235. (ANS 8235)
Answer: D
14, 23, 32, 41, 50, 59, …
In the sequence above, each term is 9 more than the previous term. What is the 41st term T of the sequence? Choose the correct choice from the following choices.
A) 360	B) 365	C) 369	D) 374	E) 383

Solution: First term , a= 14   Common difference , d = 9   nth term , tn = a + (n-1)d   41st term T , t41 = a+ 40*d = 14 + 40*9= 
14 + 40*9 = 374
374   Answer 374
Answer: D
A decade is defined as a complete set of consecutive nonnegative integers that have identical digits in identical places, except for their units digits, with the first decade consisting of the smallest integers that meet the criteria, the second decade consisting of the next smallest integers, etc. A decade in which the prime numbers contain the same set of units digits as do the prime numbers in the second decade is the	Choose the correct option
A) fifth	B) seventh	C) eighth	D) ninth	E) eleventh

Solution: From question stem, we know that the first decade consists the smallest integers that meet the above definition   1st decade - 00,01,02,03,04,05,06,07,08,09   The second decade has the next smallest integers that meet the criteria   2nd decade - 10,11,12,13,14,15,16,17,18,19   We need to find the decade in which the prime numbers contain the same set of units digits as do the prime numbers in the second decade   2nd decade - 10,11,12,13,14,15,16,17,18,19   3rd decade - 20,21 --> 21 is not prime . So stop and let's move to the next decade   4th decade - 30,31,32,33 --> 33 is not prime. Stop !   5th decade - 40,41,42,43,44,45,46,47,48,49 -- > 49 is not prime   6th decade - 50,51 --> 51 is not prime . Stop !   7th decade - 60,61,62,63 --> 63 is not prime. Stop!   8th decade - 70,71,72,73,74,75,76,77 --> 77 is not prime. Stop!   9th decade - 80,81 --> 81 is not prime. Stop!   All options have been eliminated except one. So Answer should be (E)   10th decade - 90,91,92,93 -->93 is not prime. Stop!   11th decade - 100,101,102,103,104,105,106,107,108,109 - Match !   Therefore, Correct Answer is (eleventh) i.e eleventh decade
Answer: E
The down stream speed of a boat is 100km/hr and its up stream speed is 50km/hr, then find the speed of stream? Choose the correct choice from the following answers:
A) 20km/hr B) 50km/hr C) 100km/hr D) 25km/hr E) 15km/hr

Solution: speed of stream = (100-50)/2= 
(100-50)/2 = 25
25 km/hr   Answer is 25km/hr
Answer: D
A garden center sells a certain grass seed in 5-pound bags at $13.80 per bag, 10-pound bags at $20.43 per bag, and 25-pound bags $32.25	per bag. If a customer is to buy at least	65 pounds of the grass seed,	but no more than 80 pounds,	what is the least possible cost of the grass seed that the customer will buy?	Choose the correct answer.
A) $98.73	B) $96.75	C) $98.78	D) $102.07	E) $105.3

Solution: there can be 2 cases   1)25+25+10+5=$98.73 or   2)25+25+25=$96.75   $98.73
Answer: A
Machine G and machine B are each used to manufacture 660 sprockets. It takes machine G 10 hours longer to produce 660 sprockets than machine B. Machine B produces 10 percent more sprockets per hour than machine G. How many sprockets per hour does machine G produces?  Choose the correct choice from the following
A) 6
B) 6.6
C) 60
D) 100
E) 110

Solution: I think the correct answer is A.   Machine G produces at a speed of G sp/hour and B at a speed of B sp/hour.   so, 660/G=(660/B)+10 and B=1,1 G--->1,1*660=660+11G--->6=6, so answer 6 is correct
Answer: A
Without the use of calculation, can you find how many seconds are there in a year ?
Choose the correct choice from the following choices.
A) 42536000	B) 31536000	C) 24536000	D) 33536000	E) 71536000

Solution: 31536000   == Mathematical Answer ==   Mathematical Answer = number of seconds in a minute * number of minute in an hour * number hour in a day * number of day in year    60 * 60 * 24 * 365= 
 60 * 60 * 24 * 365 = 31_536_000
31536000   60 * 60 * 24 * 365.25= 
60 * 60 * 24 * 365.25 = 31_557_600
31557600 (if you want account for leap year)== We are looking for trick answer (which is 24) ==   Every month contains only 2 second like   A) 2nd January ("second" January)   31536000) 22nd January (twenty"second" January)   Therefore  2 * 12= 
 2 * 12 = 24
24.
Answer: B
if india=90 and france=146 then england equals to?
Select: A) 215 B) 216 C) 217 D) 218 E) 219

Solution: I=9 N=14 D=4 I=9 A=1   (9*1)+(14*2)+(4*3)+(9*4)+(1*5)= 
(9*1)+(14*2)+(4*3)+(9*4)+(1*5) = 90
90   Multiply code of each lettr wid 1 2 3 in dat order...   Similarly france wil b    (6*1)+(18*2)+(1*3)+(14*4)+(3*5)+(5*6)= 
 (6*1)+(18*2)+(1*3)+(14*4)+(3*5)+(5*6) = 146
146   In dat manner england will be 219   ANSW219R:219
Answer: E
There are 15 points in a given plane, no three of which are on the same line. If one of the points is represented as 'A', then how many triangles can be determined with the 15 points that contain the point A?  Select
A) 91	B) 105	C) 182	D) 210	E) 455

Solution: Any 2 points out 14 points will create triangle with third point A, so the answer is C214=91.   91nswer: 91.
Answer: A
A man is 24 years older than his son. In two years, his age will be twice the age of his son. The present age of his son is Pick one:  A) 20  B) 21  C) 22  D) 23  E) 24

Solution: Explanation:   Let the son's present age be x years. Then, man's present age = (x + 24) years   => (x + 24) + 2 = 2(x + 2)   => x + 26 = 2x + 4   So, x = 22. Answer: 22
Answer: C
A, B and C enter into a partnership. They invest Rs. 60,000, Rs. 80,000 and Rs. 1,20,000 respectively. At the end of the first year, B withdraws Rs. 40,000, while at the end of the second year, C withdraws Rs. 80,000. In what ratio will the profit be shared at the end of 3 years ?	Choose the correct choice from the following choices
A) 9 : 14 : 8  B) 9 : 8 : 14  C) 9 : 4 : 2  D) 9 : 4 : 1  E) 9 : 4 : 5

Solution: A : B : C = (60000 x 36) : (80000 x 12 + 40000 x 24) : (120000 x 24 + 40000 x 12)   = 216 : 192 : 336   = 9 : 8 : 14.   Answer: 9 : 8 : 14
Answer: B
A woman purchased $100 of groceries which included $40 worth of vegetables and $60 worth of meat. What % of her total bill went toward purchasing meat?
Choose the correct choice from the following options: A) 25 % B) 30 % C) 60 % D) 50 % E) 80 %

Solution: Number of dollars spent on vegetables = 100 - (40)   = 100 - (40)= 
100 - (40) = 60
60   Now, we need to calculate 60 is what percent of 100.=> 60/100 * 100= 
60/100 * 100 = 60
60 %   60 %
Answer: C
A toy RC car goes 3 feet per second. A boy wants to add an updated part to his RC that will allow the RC car to travel at 6 feet per second. How far will the upgraded car travel in 1 minute? Round to the nearest hundredth.  Select
A) 200 feet  B) 250 feet  C) 300 feet  D) 360 feet  E) 400 feet

Solution: 6 feet per sec x 60= 360 feet   Answer 360 feet
Answer: D
There are n members in a certain department, including Michael. Two representatives are to be selected to attend a company conference. If there are 78 possible combinations in which Michael is not selected, what is the value of n?	Choose one.
A) 12  B) 13  C) 14  D) 15  E) 16

Solution: The combinations of two people, in which Michael was not selected = 28   The number of ways two people can be selected from m people = m*(m-1)/2   Let m be the number of people excluding Michael.   Then m*(m-1) = 156 = 13*12   Thus, n = m + 1(Michael) = 14   The answer is 14.
Answer: C
Three persons invested Rs.9000 in a joint business. The second person invested Rs.1000 more than the first and the third Rs.1000 more than second. After two years, they gained Rs.9000. How much third person will get?  Choose the correct choice from the following answers:	A) 2400	B) 4000	C) 2699	D) 2662	E) 1821

Solution: First persons investment = x   Second persons investment = x + 1000   Third persons investments = x + 2000   x + x + 1000 + x + 2000 = 9000   3x = 9000   x = 2000   Ratio = 2000 : 3000 : 4000   2:3:4   4/9 * 9000= 
4/9 * 9000 = 4_000
4000   Answer: 4000
Answer: B
A sum of Rs. 350 made up of 110 coins, which are of either Re.1 or Re.5 denomination. How many coins are of Re.1?	Choose the most appropriate option:  A) 60  B) 70  C) 80  D) 90  E) 100

Solution: 1x+5y= 350   x+y=110   solving the two quations we get x= 50, y= 60 coins.   60NSWER:60
Answer: A
If two numbers are in the ratio 2:3. If 10 is added to both of the numbers then the ratio becomes 3:4 then find the smallest number?
Answers:  A) 10  B) 20  C) 25  D) 30  E) 35

Solution: 2:3   2x + 10 : 3x + 10 = 3 : 4   4[2x + 10] = 3[3x + 10]   8x + 40 = 9x + 30   9x - 8x = 40 - 30= 
40 - 30 = 10
10   Then smallest number is= 2   2x = 20   20)
Answer: B
At what rate percent per annum will a sum of money double in 16 years  Select:
A) 6 ¼ % p.a
B) 6 % p.a
C) 8¼ % p.a
D) 3 ¼ % p.a
E) 7 ¼ % p.a

Solution: Let principal = P. Then, S.l. = P and T = 16 yrs.   Rate = (100 x P)/(P*16)% = 6 ¼ % p.a   Answer is 6 % p.a.
Answer: B
If 4 girls can color 48 m long cloth in 2 days, then 6 girls can color 36 m long cloth in  Choose the correct answer
A) 1 1/5 days	B) 1/5 day	C) 1 day	D) 2 days	E) 3 days

Solution: The length of cloth painted by one girl in one day = 48 / 4 × 2 = 6 m   No. of days required to paint 36 m cloth by 6 girls = 36/ 6 × 6 = 1 day.   1 day
Answer: C
m and n are the x and y coordinates, respectively, of a point in the coordinate plane. If the points (m, n) and (m + p, n + 12) both lie on the line defined by the equation x = (y/4) - (2/5), what is the value of p?  Choices: A) 1 B) 2 C) 3 D) 4 E) 5

Solution: x = (y/4) - (2/5), and so y = 4x + 8/5. The slope is 4.   (n+12-n) / (m+p-m) = 3   p = 3   The answer is 3.
Answer: C
In a box of 10 pencils, a total of 2 are defective. If a customer buys 3 pencils selected at random from the box, what is the probability that neither pencils will be defective? Choose the most appropriate option:
A) 1/12
B) 7/15
C) 2/13
D) 2/15
E) 1/17

Solution: First, there are 8C3 ways you can select 3 good pencils from 4 good ones.   Second, there are 10C3 ways you select 3 pencils from 6 ones in the box.   Then, the probability that neither pen will be defective is: 8C3/10C3=56/120 =7/15   Answer is 7/15
Answer: B
A class consists of 15 biology students and 10 chemistry students. If you pick two students at the same time, what's the probability that one is maths and one is chemistry ?  Select the correct option:
A) 2/7  B) 5/7  C) 1/2  D) 3/7  E) 1/2

Solution: P(1st b, 2nd c) = 15/25*10/24 = 150/600 = 1/4;   P(1st c, 2nd b ) = 10/25*15/24 = 150/600 = 1/4.   P = 1/4 + 1/4 = 1/2.   Answer: 1/2.
Answer: C
The top of a 15 m. high tower makes an angle of elevation of 60 degree with the bottom of an electric pole and an angle of 30 degree with the top of the pole. What is the height of the pole?	Choose the correct choice from the following choices
A) 12 m.
B) 10 m.
C) 11 m.
D) 5 m.
E) 15 m.

Solution: let distance between tower and pole be x & height of pole be y.   x=15/tan60 & (15-y)/x = tan 30   thus solving two equation gives y= 10m   ANSWER:10 m.
Answer: B
A farm used two harvesting machines, H and K, to harvest 100 acres of wheat. Harvesting machine H, working alone at its constant rate, harvested 40 acres of wheat in 8 hours. Then harvesting machine K was brought in, and harvesting machines H and K, working together at their respective constant rates, harvested the remaining acres of wheat in 4 hours. Harvesting machine K harvested how many acres of wheat per hour? Choose the correct choice:  A) 7  B) 8  C) 11  D) 13  E) 15

Solution: Rate of H = 4 acres/hr   Remaining land to be harvested = 100 - 40= 
100 - 40 = 60
60   Rate of H and K= 60/4= 
60/4 = 15
15 acres/hr   Rate of K= 15- 4= 
15- 4 = 11
11   Answer: 11
Answer: C
In the new budget the price of wheat rose by 8%. By how much percent must a person reduce his consumption so that his expenditure on it does not increase?  Choose the most appropriate option:	A) 7.5%	B) 7.41%	C) 10.9%	D) 12.6%	E) 15%

Solution: Reduce in consumption = R/(100+R) *100% = 8/108 *100 = 7.41%   Answer is 7.41%
Answer: B
Of the books standing in a row on a shelf, an atlas is the 30th book from the left and the 33rd book from the right. If 2 books to the left of the atlas and 7 books to the right of the atlas are removed from the shelf, how many books will be left on the shelf?	Choose the correct answer.
A) 53	B) 57	C) 58	D) 61	E) 63

Solution: 100%. There are total of   30+33-1= 
  30+33-1 = 62
62 books and   2+7= 
  2+7 = 9
9 books are removed, thus 62-9= 
62-9 = 53
53 books are left.   53nswer: 53.
Answer: A
For which of the following functions is f(e+b)=f(e)+f(b) for all positive numbers e and b?  Choose the correct choice from the following answers.
A) a) f(x)=x^2  B) b) f(x)=x+1  C) c) f(x)=root x  D) d) f(x)=2/x  E) e) f(x)= -3x

Solution: f(e+b)=f(e)+f(b) Its e) f(x)= -3x
Answer: E
Evaluate:55- 12*3*2 =?	Select:  A) 42  B) 47  C) 62  D) 72  E) 82

Solution: According to order of operations, 12?3?2 (division and multiplication) is done first from left to right   12**2 = 4* 2= 
4* 2 = 8
8   Hence   55 - 12*3*2= 55- 8= 
55- 8 = 47
47   correct answer 47
Answer: B
You forgot the three digit code of your safe. But you have written some hints to calculate the code if you forgot the code.
Below are the hints that you have written
Hint-1 : One of the numbers is correct and is placed in its correct position
5 4 7
Hint-2: Nothing is correct
5 3 0
Hint-3: Two numbers are correct but not placed at its correct position.
2 5 9
Hint-4: One number is correct but not placed at its correct position.
7 0 6
Hint-5: One number is correct but not placed at its correct position.
6 4 9
What's is the code.	Choose one:
A) 827 B) 728 C) 923 D) 323 E) 927

Solution: 927   927   1) 5 4 7 : 7 is placed correctly   2) 5 3 0 : None of the numbers is in the code   3) 2 5 9 : 2 & 9 are correct number of code but placed at wrong position   4) 7 0 6: Number 7 is there but placed at wrong position   5) 6 4 9: Number 9 is there but placed at wrong position
Answer: E
If x/y=4 and y is not '0' what % of x is 2x-y	Select.
A) 150%
B) 175%
C) 200%
D) 250%
E) 350%

Solution: let z be the percentt   x*z/100=2x-y   zx=7y*100   z=700y/4y   z7 *100= 
7 *100 = 700
700y/4y   z=350/2= 
350/2 = 175
175%   ANSWER:175%
Answer: B
If x/y=4 and y is not '0' what % of x is 2x-y
Choose the correct choice from the following choices.
A) 150%  B) 175percent  C) 200%  D) 250%  E) 350%

Solution: let z be the percent   x*z/100= 2x-y   zx=7y* 100   z=700y/4y   z7 * 100= 
7 * 100 = 700
700y/4y   z=350/2= 
350/2 = 175
175%   ANSWER:175percent
Answer: B
Find the middle one when The sum of three consecutive even numbers is 21?  Pick one.
A) 7  B) 10  C) 8  D) 6  E) 11

Solution: 3 consecutive numbers can be a - 1, a, a + 1   So sum of numbers = 3a = 21.   Hence a = 7.   7
Answer: A
In a class, there are 21 boys who are over 160 cm tall. If these constitute three–fourth of the boys and the total number of boys is one–fourth of the total number of students in the class. What is the total number of girls in the class	Choose the correct choice from the following choices:
A) 22
B) 78
C) 267
D) 997
E) 722

Solution: 22nswer:22
Answer: A
Two stations P and Q are 245 km apart on a straight track. One train starts from P at 7 a.m. and travels towards Q at 20 kmph. Another train starts from Q at 8 a.m. and travels towards P at a speed of 25 kmph. At what time will they meet?	Choose the correct choice from the following answers
A) 10 am B) 12 am C) 10.30 am D) 12.30 am E) 1 pm

Solution: Assume both trains meet after x hours after 7 am   Distance covered by train starting from P in x hours = 20x km   Distance covered by train starting from Q in (x-1) hours = 25(x-1)   Total distance = 245   => 20x + 25(x-1) = 245   => 45x = 270   => x= 6   Means, they meet after 6 hours after 7 am, ie, they meet at 1pm   Answer is 1 pm.
Answer: E
A cricketer has a certain average for 10 innings. In the eleventh inning, he scored 108 runs, thereby increasing his average by 6 runs. His new average is	Choices: A) 42 runs B) 45 runs C) 48 runs D) 52 runs E) None

Solution: Sol.   Let the average for 10 innings be x. Then,   10x + 108 / 11 = x+6 ⇔ 11x + 66 = 10x + 108 ⇔ x = 42.   ∴ New average = (x+6) = 48 runs.   Answer 48 runs
Answer: C
A radio station has to choose three days of the seven in a week to broadcast a certain program, and that set will repeat each week. The program can be broadcast equally on any of the seven weekdays —- weekdays vs. weekends don’t matter at all —- nor does it matter whether the days the program airs are adjacent or not. Absolutely any three of the seven weekdays can be chosen. How many different three-day combinations of the seven weekdays can be constructed?	Answers:
A) 9	B) 15	C) 21	D) 35	E) 56

Solution: Behind the story, we are really being asked to evaluate 7C3. We could use the factorial formula, but above we conveniently happen to have Pascal’s Triangle written out to the seventh row. We see that 7C3, the third entry of the seventh row, is 35. Answer = 35.
Answer: D
At coffee factory, each employee working the second shift produced 2/3 as many widgets as each employee working the first shift. If the first shift has 3/4 as many employees, what fraction of the total widgets did the second shift produce? Choices
A) 8/17	B) 1/2	C) 8/9	D) 9/8	E) 17/8

Solution: At coffee factory, Let the first shift have 3 employee and each produce 3 widgets, so the total number of widgets produced by the first shift is 3*3= 
3*3 = 9
9;   Then the second shift would have 4 employees and each second shift employee would produce   3*2/3= 
  3*2/3 = 2
2 widgets, so the total number of widgets produced by the second shift employees would be   4*2= 
  4*2 = 8
8;   The ratio of the second shift production to the total is 8/(9+8)=8/17.   8/17nswer: 8/17.
Answer: A
Foodmart customers regularly buy at least one of the following products: milk, chicken, or apples. 60% of shoppers buy milk, 50% buy chicken, and 55% buy apples. If 10% of the customers buy all 3 products, what percentage of Foodmart customers purchase exactly 2 of the products listed above?  Choose the correct choice from the following answers:
A)  5%	B)  10%	C)  15%	D)  45%	E)  30%

Solution: Total = n(A) + n(B) - n(Exactly 2 products) -2 (AnBnC) + Neither.   Neither is zero.   Hence 100 = 60 + 50 + 55 - n (Exactly 2 products) - 2*10   100 = 145 - n (Exactly 2 products) => n (Exactly 2 products) = 45.   Answer:  45%
Answer: D