MU-NLPC/Calc-aqua_rat huggingface dataset:
The two roots of the quadratic equation x2 - 85x + c = 0 are prime numbers. What is the
value of c? Options:  A) 84  B) 166  C) 332  D) 664  E) 1328

Solution: Assuming that two prime numbers x1 and x2 are the solutions, then x1 + x2 = 85.   Since 85 is an odd number, either x1 or x2 must be an even number. The only even prime   number is 2. Therefore, one number must be 2 and the other 83. Hence c = 2 *83= 
2 *83 = 166
166.   correct answer 166
Answer: B
A person was asked to state his age in years. His reply was, "Take my age three years hence, multiply it by 3 and then subtract three times my age three years ago and you will know how old I am." What was the age of the person?	Choose the correct choice from the following: A) 18 B) 19 C) 71 D) 16 E) 17

Solution: Let the present age of the person be x years.   Then, 3(x + 3) - 3(x - 3) = x   3x + 9 - 3x + 9 = x => x = 18   18nswer:18
Answer: A
A credit union customer borrowed $15,000, but received y dollars less than this due to discounting. If there was a separate $20 service charge, then, in terms of y, the service charge was what fraction of the amount that the customer received?
Choose one
A) 20/(15,000 + y)	B) 25/(10,000 - y)	C) 20/(15,000 - y)	D) 20y/(15,000 - y)	E) 20(y-1)

Solution: The amount of money the customer received was (15,000 - y) dollars. The $20 service charge as a fraction of the amount received was, therefore, 20/(15,000 - y).   20/(15,000 + y)nswer: 20/(15,000 + y).
Answer: A
If a cards are drawn from apack of 82 cards. The probability of getting a queen of club or a king of heart is Choose the correct choice from the following choices:
A) 1/31 B) 1/24 C) 1/31 D) 1/45 E) 1/41

Solution: Here, n(S) = 52.   Let E = event of getting a queen of club or a king of heart.   Then, n(E) = 2.   P(E) =	n(E)	=	2/82	=	1/41	.   n(S)   1/41
Answer: E
5 years ago Kate was 5 times as old as her Son. 5 years hence her age will be 8 less than three times the corresponding age of her Son. Find the age of son?  Select:
A) 7	B) 8	C) 9	D) 10	E) 11

Solution: let x be the mother's age and y be the son's age   x-5=5(y-5)   x+5=3(y+5)-8   by solving this we get x=35 and y=11   ANSW11R:11
Answer: E
If the selling price of 50 articles is equal to the cost price of 30 articles, then the loss or gain percent is: Choose the correct option:	A) 10%	B) 40%	C) 30%	D) 25%	E) 35%

Solution: Let C.P. of each article be Re. 1.   Then, C.P. of 50 articles = Rs. 50;   S.P. of 50 articles = Rs. 30.   Loss % = 20/50 * 100= 
20/50 * 100 = 40
40%   ANSWER:40%
Answer: B
P alone can complete a job in 12 days. The work done by Q alone in one day is equal to one-half of the work done by P alone in one day. In how many days can the work be completed if P and Q work together?	Choose one:
A) 5 B) 6 C) 7 D) 8 E) 9

Solution: P's rate is 1/12   Q's rate is 1/24   The combined rate is 1/12 + 1/24 = 1/8   If they work together, the job will take 8 days.   The answer is 8.
Answer: D
Jane makes toy bears. When she works with an assistant, she makes 70 percent more bears per week and works 10 percent fewer hours each week. Having an assistant increases Jane’s output of toy bears per hour by what percent?  Choose the most appropriate option: A) 20% B) 80% C) 100% D) 180% E) 200%

Solution: We can use fractional equivalents here to solve the problem   80% = 4/5; this means that in 1st case if she prepares 5 bears, in 2nd case she prepares 9 bears   10% = 1/10; this means that in 1st case if she needs 10 hours, in 2nd case she needs 9 hours   Now we come to productivity   Based on above fractional values the productivity in 1st case is 0.5 bears / hour and in the 2nd case it is 1 bear / hour   Hence the productivity is double with the assistant i.e. the increase in productivity is 80%   80%
Answer: B
Maya purchase 15 jars in a store then she returned 5 jars to store .Now how many jars she had?	Choose the correct choice:	A) A)5	B) B)11	C) C)19	D) D)10	E) E)4

Solution: 15-5= 
15-5 = 10
10. Answer is 10
Answer: D
The principal that amounts to Rs. 4893 in 3 years at 6 1/4 % per annum C.I. compounded annually, is?  Choose one.
A) s. 3096 B) s. 4076 C) s. 4085 D) s. 4096 E) s. 5096

Solution: Principal = [4913 / (1 + 25/(4 * 100))3]   = 4893 * 16/17 * 16/17 * 16/17 = Rs. 4085.   ANSWER:s. 4085
Answer: C
Look at this series: 15, 15, 27, 27, 39, 39, 51, 51, ... What number should fill the blank? Choose the correct choice.
A) 51  B) 39  C) 63  D) 15  E) None

Solution: Explanation: In this simple addition with repetition series, each number in the series repeats itself, and then increases by 12 to arrive at the next number.   Answer: Option 63
Answer: C
Increasing the original price of an article by 6 percent and then increasing the new price by 6 percent is equivalent to increasing the original price by Choose the correct choice from the following.
A) 12.1%
B) 12.36%
C) 12.94%
D) 13.65%
E) 14.56%

Solution: 1.06*1.06*x = 1.1236*x   The answer is 12.36%.
Answer: B
A and B together can do a work in 7 days. If A alone can do it in 56 days. In how many days can B alone do it? Choose the correct choice from the following answers:
A) 11	B) 8	C) 21	D) 20	E) 25

Solution: 8   8   1/7 â€“ 1/56 = 1/8 => 8
Answer: B
Pipes A and B can fill a cistern in 8 and 56 minutes respectively. They are opened an alternate minutes. Find how many minutes, the cistern shall be full?
Choose the correct option:
A) 13 B) 14 C) 16 D) 18 E) 19

Solution: :   1/8 + 1/56 = 1/7   7 * 2= 
7 * 2 = 14
14.Answer:14
Answer: B
A coin is tossed 4 times. What is the probability that the number of Heads is equal to the number of Tails? Choose the correct choice:
A) 1/8 B) 1/4 C) 3/8 D) 1/2 E) 9/16

Solution: We have to find the probability that we get 2 heads and 2 tails in 4 tosses of the coin.   Using the binary formula and defining a head as a success,   P(2 heads in 4 tosses) = 43/82* (1/2)^2 * (1/2)^2   = 6/16   = 3/8   The answer is therefore (3/8)
Answer: C
The salary of all officers is increased twice successively by 20%. What is the net percentage increase in their salaries?
Answers:	A) 20%	B) 40%	C) 21%	D) 44%	E) 48%

Solution: M . F = 120/100*120/100 = 36/25   Net % increase = ( M . F -1 ) *100 =( 36/25-1) * 100   11/25 *100= 
11/25 *100 = 44
44 %   ANSWER:44%
Answer: D
A sum of money invested at C.I. amounts to Rs. 800 in 3 years to Rs. 860 in 4 years. The rate of interest per annum is? Choose one:	A) 2 1/2 %	B) 4%	C) 5%	D) 6 2/3 %	E) 7 1/2%

Solution: S.I. on Rs. 800 for 1 year = (860 - 800) = Rs. 60 Rate = (100 * 60)/(800 * 1) = 7 1/2%   ANSW7 1/2%R:7 1/2%
Answer: E
The area of a sector of a circle of radius 5 cm formed by an arc of length 3.5 cm is? Choose the correct choice from the following options:
A) 0.35 cm2
B) 17.5 cm2
C) 8.75 cm2
D) 55 cm2
E) 65 cm2

Solution: Explanation:   (5 * 3.5)/2= 
(5 * 3.5)/2 = 8.75
8.75   ANSWER IS 8.75 cm2
Answer: C
The angle between the minute hand and the hour hand of a clock when the time is 8.30, is:	Choose one
A) 75	B) 60	C) 35	D) 45	E) 50

Solution: hr hand in 17/2 hrs = (360/12 * 17/2)= 
(360/12 * 17/2) = 255
255   hr hand in 30 min= (360/60 * 30)= 
(360/60 * 30) = 180
180   req angle= (255-180)= 
(255-180) = 75
75d   75NSWER 75
Answer: A
A, B and C enter into a partnership. A invests 3 times as much as B invests and 2/3 of what C invests. At the end of the year, the profit earned is Rs. 12375. What is the share of C? Pick one
A) Rs. 2250	B) Rs. 3375	C) Rs. 6750	D) Rs. 5625	E) None of these

Solution: Explanation:   Let the investment of C be Rs. x.   The inverstment of B = Rs.(2x/3)   The inverstment of A = Rs. (3 × (2/3)x) = Rs. (2x)   Ratio of capitals of A, B and C = 2x : 2x/3 : x = 6 : 2 : 3   C's share = Rs. [(3/11) × 12375] = Rs. 3375   Answer: Option Rs. 3375
Answer: B
Ages of two coworkers differ by 26 years. If 8 years ago, the elder one was twice as old the younger one, find their present age
Select the correct option: A) 12,38 B) 14,40 C) 16,42 D) 28,54 E) 34,60

Solution: Explanation:   Let the age of younger person is x,   Then elder person's age is (x+26)   => 2(x-8) = (x+26-8) [8 years before]   => 2x-16 = x+18   => x = 34.   So elder person's age is x + 26 = 60   Answer: Option 34,60
Answer: E
The radius of a semi circle is 6.8 cm then its perimeter is?	Choose the correct choice from the following options.
A) 32.7 B) 32.4 C) 22.4 D) 34.9 E) 35.1

Solution: 36/7 r = 6.8 = 34.9   Answer:34.9
Answer: D
A train covers a distance of 11 km in 10 min. If it takes 6 sec to pass a telegraph post, then the length of the train is?
Choose the correct answer:
A) m
B) m
C) m
D) m
E) m

Solution: Speed = (11/10 * 60) km/hr   = (66 * 5/18) m/sec = 55/3 m/sec.   Length of the train = 55/3 * 6= 
55/3 * 6 = 110
110 m.   Answer:m
Answer: C
In a 1000 m race, A beats B by 90 m and B beats C by 100 m. In the same race, by how many meters does A beat C?
Options
A) 145 m	B) 176 m	C) 181 m	D) 159 m	E) 218 m

Solution: By the time A covers 1000 m, B covers  (1000 - 90)= 
 (1000 - 90) = 910
910 m.   By the time B covers 1000 m, C covers  (1000 - 100)= 
 (1000 - 100) = 900
900 m.   So, the ratio of speeds of A and C=   1000/910 * 1000/900 = 1000/819 So, by the time A covers 1000 m, C covers 819 m.   So in 1000 m race A beats C by 1000 - 819= 
1000 - 819 = 181
181 m.   Answer:181 m
Answer: C
A train 210 m long passed a pole in 21 sec. How long will it take to pass a platform 310 m long?	Choose the correct answer:
A) 19
B) 32
C) 52
D) 74
E) 83

Solution: Speed = 210/21= 
210/21 = 10
10 m/sec.   Required time= (210 + 310)/10= 
(210 + 310)/10 = 52
52 sec.   Answer: 52
Answer: C
Two trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 49 hours respectively. The ratio of their speeds is? Pick:
A) 4:5 B) 7:3 C) 4:4 D) 7:8 E) 7:1

Solution: Let us name the trains A and B.   Then, (A's speed) : (7:3's speed)   = √b : √a = √49 : √9   = 7:3   Answer: 7:3
Answer: B
What are the last three number of this series 11234783131?	Choose the correct choice from the following choices.
A) 191	B) 192	C) 193	D) 194	E) 195

Solution: 23-11= 
23-11 = 12
12   47-23= 
47-23 = 24
24   83-47= 
83-47 = 36
36   131-83= 
131-83 = 48
48   Thus all differences are multiple of 8.   so, 131+60=191   191NSWER:191
Answer: A
A mom and dad want to take thier 16 year old daughter, 14 year old son and 7 year old son on a trip to Six Flags. An adult ticket costs $25.50. A child under the age if 12 costs $20.50 and children under 5 are free. There is a promotion to get 15% off of two adult tickets when you buy two adult tickets at full price. How much will it cost the family total including the discount to purchase their tickets?	Choose the correct choice:  A) 122.5  B) 43.35  C) 114.85  D) 107.2  E) 94.35

Solution: 25.50*2= Y = 51.   Y*.15=7.65   Y-7.65=X = 43.35   Y= price of two adult tickets   X= price of two adult tickets after the discount   X+Y+20.50=114.85   The answer is 114.85.
Answer: C
If a certain sample of data has a mean of 18.0 and the value 26.0 is more than 2.5 standard deviations from the mean, which of the following could be the standard deviation of the sample
Choose the correct option
A) 3.75	B) 3.5	C) 3.15	D) 3.85	E) 2.75

Solution: 26.0 is more than 2.5 standard deviations from 18 --> 26 > 18 + 2.5*{SD} --> 2.5*{SD} < 8 --> {SD} < 3.2. Only option C offers the standard deviation less than 3.2.   Answer:3.15
Answer: C
A man saves Rs 100 at the end of each year and lends the money at 5% compound interest. How much will it become at the end of 3 years. Choose the most appropriate option:
A) Rs 331.01
B) Rs 362.01
C) Rs 362.02
D) Rs 362.03
E) None of these

Solution: Explanation:   =[100(21/20Ã—21/20Ã—21/20)+100(21/20Ã—21/20)+100(21/20)]=662.02   Option Rs 331.01
Answer: A
In how much time will a train of length 100 m, moving at 36 kmph cross an electric pole?  Choose the correct choice from the following choices:
A) 15 sec
B) 12 sec
C) 10 sec
D) 14 sec
E) 11 sec

Solution: C   10 sec   Convert kmph to mps. 36 kmph = 36 * 5/18= 
36 * 5/18 = 10
10 mps.   The distance to be covered is equal to the length of the train.   Required time t= d/s = 100/10= 
100/10 = 10
10 sec.
Answer: C
6persons enter a lift on the ground floor of a 9floor apartment. Assuming that each of them independently & with equal probability can leave the lift at any floor beginning with the first, what is the probability that all the 6persons are leaving the lift at different floors? Choose one.
A) 5P6/8^3 B) 7P6/8^2 C) 8P6/8^6 D) 9P6/8^5 E) 9P6/8^4

Solution: Apart from the ground floor, there are 8 floors   Let's find out the total number of ways in which all the six persons can leave the   lift at eight different floors   The 1st person can leave the lift in any of the 8 floors (8 ways)   The 2nd person can leave the lift in any of the remaining 7 floors (7 ways)   The 3nd person can leave the lift in any of the remaining 6 floors (6 ways)   ...   The 6th person can leave the lift in any of the remaining 3 floors (3 ways)   Total number of ways = 8 × 7 × 6 × 5 × 4 × 3 = 8P6   (In fact, from the definition of permutations itself,   we will be able to directly say that the number of ways in which all the six persons   can leave the lift at 8 different floors = 8P6)   n(E)= Total Number of ways in which all the six persons can leave the lift at eight   different floors = 8P6   Now we will find out the total number of ways in which each of the six persons   can leave the lift at any of the eight floors   The 1st person can leave the lift in any of the 8 floors (8 ways)   The 2nd person can leave the lift in any of the 8 floors (8 ways)   The 3nd person can leave the lift in any of the 8 floors (8 ways)   ...   The 6th person can leave the lift in any of the 8 floors (8 ways)   Total number of ways = 8 × 8 × 8 × 8 × 8 × 8 = 86   i.e., The total number of ways in which each the six persons can leave the lift   at any of the eight floors = n(S) = 86   P(E) = n(E)n(S)=8P6/8^6   8P6/8^6
Answer: C
By selling 12 pencils for a rupee a man loses 20%. How many for a rupee should he sell in order to gain 20%?	Select the correct option:  A) 9  B) 4  C) 8  D) 7  E) 65

Solution: 80% --- 12   120% --- ?     80/120 * 12= 
  80/120 * 12 = 8
8   9nswer: 9
Answer: A
Donovan took a math test and got 35 correct and 11 incorrect answers.
What was the percentage of correct answers? (Round to the nearest
hundredth)  Choose the most appropriate option:	A) 57.78%	B) 67.78%	C) 76.09%	D) 47.78%	E) 97.78%

Solution: 35 correct our of 46 total (35+11)   35/46   correct answer 76.09%
Answer: C
What distance (in meters) will be covered by a bus moving at 54 km/hr in 15 seconds?	Choose the correct choice from the following answers.
A) 175
B) 200
C) 225
D) 250
E) 275

Solution: 54 km/hr = 54 * 5/18= 
54 * 5/18 = 15
15 m/s   distance= 15 * 15= 
15 * 15 = 225
225 meters   The answer is 225.
Answer: C
Based on this year's costs, an orcharde grower budgets P dollars for planing N new trees next year. If the average cost of planting each tree were to increase 50% from this year's cost, then the greatest number of trees that the orchard grower could plant next year using P dollars would be  Choose the correct option
A) 33% less than N  B) 25% less than N  C) equal to N  D) 20% greater than N  E) 25% greater than

Solution: Correct answer is (A).   This year, the price of a tree is price1=P/N.   If this price increases by 50% it becomes price2=P/N*1.50   Then with P dollars, you can grow P/price2 tress i.e. P/(P/N*1.50) i.e. N/1.5 i.e. .67% less*   33% less than N
Answer: A
Out of three consecutive odd numbers nine times the first number is equal to addition of twice the third number and adding 9 to twice the second . What is the first number?
Answers:
A) 20/21
B) 23/25
C) 24/23
D) 22/5
E) 21/5

Solution: Description :   => 9x=2(x+2)+9+2(x+4)   => 9x=4x+21   => 5x=21   x=21/5   Answer 21/5
Answer: E
How many integers between 50 and 200 are there such that their unit digit is even?
Pick:
A) 50  B) 75  C) 100  D) 150  E) 200

Solution: 150 numbers between 50 and 200   Out of which half would be even, half would be odd.   Number of even unit digit number = 75.   The correct option is 75
Answer: B
An electric pump can fill a tank in 5 hours. Because of a leak in the tank, it took 10hours to fill the tank. If the tank is full, how much time will the leak take to empty it?  Choose one.
A) 10hours B) 12hours C) 8hours D) 5hours E) 15hours

Solution: Work done by the leak in 1 hour = 1/5 - 1/10 = 1/10   The leak will empty the tank in 10hours   10hoursnswer is 10hours
Answer: A
Let the second number be 3x, so that the first number is 6x and the third number is 2x.
Pick one:
A) 22	B) 77	C) 98	D) 27	E) 36

Solution: ∴ 6x + 3x + 2x = 132 ⇒ x = 12. Second number = 3x = 3×12 = 36.   Answer:36
Answer: E
In a garden, trees are planted in rows. In each row there are as many trees as the number of rows in the garden. If each tree bears as many fruits as the number of trees in each row and if the total number of fruits from the trees in that garden is n, then :
Choose the correct choice from the following.
A) n is a perfect square
B) n is an odd number
C) n is an even number
D) n is a perfect cube.
E) none

Solution: say for example, there are 4 rows in d garden, then there will b 4 trees in each row and each tree wud bear 4 fruits..Then total no of fruits in d garden wud b (4*4)*4= 64...which is a cube of 4.   ANSWER:n is a perfect cube.
Answer: D
There are 3 pairs of socks and 2 socks are worn from that such that the pair of socks worn are not of the same pair. what is the number of pair that can be formed.  Pick one:
A) 5
B) 1
C) 3
D) 6
E) 7

Solution: First of all you should remember that there is a difference in left and right sock.   now no. of way to select any of the sock = 3   and for second = 2   so total methods = 3*2= 
3*2 = 6
6   ANSWER:6
Answer: D
Three partners A, B, C in a business invested money such that 4(Aâ€™s capital) = 2(Bâ€™s capital) = 8(Câ€™s capital) then, The ratio of their capitals is  Answers:	A) 63 : 45 : 34	B) 63 : 54 : 34	C) 36 : 54 : 28	D) 2 : 4 : 1	E) None of these

Solution: Explanation:   Let 4(Aâ€™s capital) = 2(Bâ€™s capital) = 8(Câ€™s capital) = Rs.x   Then, Aâ€™s capital = Rs x/4, Bâ€™s capital = Rs. x/2 and Câ€™s capital = Rs. x/8.   A : B : C = x/4 : x/2 : x/8   2 : 4 : 1   Answer: Option 2 : 4 : 1
Answer: D
A gardener grows cabbages in her garden that is in the shape of a square. Each cabbage takes 1 square feet of area in her garden. This year, she has increased her output by 199 cabbages as compared to last year. The shape of the area used for growing the cabbages has remained a square in both these years. How many cabbages did she produce this year? Choose the correct choice:	A) 10,000	B) 11,025	C) 14,400	D) 12,696	E) can not be determined

Solution: Let the side for growing cabbages this year be X ft. Thus the area is X^2.   Let the side for growing cabbages last year be Y ft. Thus, the area was Y^2.   The area would have increased by 199 sq ft as each cabbage takes 1 sq ft space.   X^2 - Y^2 = 199   (X + Y)(X - Y) = 199   199 is a prime number and thus it will be (100 + 99)*(100-99).   Thus X = 100 and Y = 99   X^2 = 100^2 = 10,000   The answer is 10,000.
Answer: A
A walks around a circular field at the rate of one round per hour while B runs around it at the rate of six rounds per hour. They start in the same direction from the same point at 7.30 a.m. They shall first cross each other at? Answers
A) 11 min
B) 12 min
C) 10 min
D) 15 min
E) 16 min

Solution: B   12 min   Since A and B move in the same direction along the circle, so they will first meet each other when there is a difference of one round between the two.   Relative speed of A and B = 6 - 1= 
6 - 1 = 5
5 rounds per hour.   Time taken to complete one round at this speed= 1/5 hr = 12 min.
Answer: B
In a certain company, a third of the workers do not have a retirement plan. 20% of the workers who do not have a retirement plan are women, and 40% of the workers who do have a retirement plan are men. If 160 of the workers of that company are men, how many of the workers are women?
Select:  A) 80  B) 95  C) 105  D) 120  E) 140

Solution: Set up equation:   x = total number of workers   160 = 0,4 * 2/3 * x + 0,8 * 1/3 * x   160 = 16/30 x   x = 300   300 - 160= 
300 - 160 = 140
140   Answer 140
Answer: E
A number is trebled and 10 is added. If the resultant is doubled, it becomes 96. What is that number?
Select the correct option:
A) 4
B) 6
C) 8
D) None of these
E) Cannot be determined

Solution: Solution   Let the number be x.   Then, 2(3x + 10) ‹=› 96   ‹=› 3x+10 = 48   ‹=› 3x= 38   x= 38/3.   Answer None of these
Answer: D
In a certain school , 55 percent of student are females and the rest are males . In school elections , If 60 percent of males and 80 percent of females are expected to vote for a candidate (A) , what percent of students are expected to vote for candidate (A) ? Select the correct option:
A) 58%
B) 65%
C) 69%
D) 71%
E) 73%

Solution: say there are a total of 100 students in this school , 55 are females and 45 are males    55*0.8= 
 55*0.8 = 44
44 female are expected to vote    45*0.6= 
 45*0.6 = 27
27 males are expected to vote   Thus total of   44+27= 
  44+27 = 71
71 are expected to vote , which is 71 percent of students .   answer: 71%
Answer: D
A car gets 40 kilometers per gallon of gasoline. How many gallons of gasoline would the car need to travel 120 kilometers?	Choose the correct choice from the following answers:
A) 4.5	B) 5.5	C) 6.5	D) 3	E) 8.5

Solution: Each 40 kilometers, 1 gallon is needed. We need to know how many 40 kilometers are there in 120 kilometers?   120 ÷ 40 = 3 × 1 gallon = 3 gallons   correct answer 3
Answer: D
Nil and Ethan are brothers. They left their home
at the same time and drove to the same beach.
Nil drove at a speed of 70 miles per hour. Ethan
drove at a speed of 20 miles per hour. Nil
arrived at the beach 0.5 hour earlier than Ethan.
What is the distance between their home and the
beach? Select
A) 80 miles  B) 70 miles  C) 60 miles  D) 50 miles  E) 40 miles

Solution: Every hour, Nil gets ahead of Ethan  70 - 20= 
 70 - 20 = 50
50 miles. When Nil arrived at the beach, Ethan   is only 20 × 0.5= 10 miles behind. That tells us   they only drove 1 hour when Nil arrived at the   beach.   The distance between their home and the beach   is   Nil’s speed × Nil’s time   = 70 × 1 = 70 miles.   correct answer 70 miles
Answer: B
A certain manufacturer of cake, muffin, and bread mixes has 140 buyers, of whom 50 purchases cake mix, 40 purchase muffin mix, and 20 purchase both cake mix and muffin mix. If a buyer is to be selected at random from the 100 buyers, what is the probability that the buyer selected will be one who purchases neither cake mix nor muffin mix?
Answers.
A) a. 1/10 B) b. 3/10 C) c. 1/2 D) d. 7/10 E) e. 3/14

Solution: C+M+B-CM-MB-CB-2CMB = 140   C - cake buyers, M - muffin an0d B - Bread buyers. CM,MB,CB and CMB are intersecting regions.   the question asks for people who have bought only bread mixes = B-CB-MB-2CMB has to be found out.   50 + 40 + B-CB-MB-20-2CMB = 140   B-CB-MB-2CMB = 30   hence the probability = 30/140 = 3/14.   e. 3/14
Answer: E
At the beginning of 2010, 60% of the population of Town X lived in the south and the rest lived in the north. During 2010, the population of Town X grew by 5.5%. If the population in the south grew by 4.5%, by how much did the population in the north grow?
Choose the correct choice from the following options:
A) 1%
B) 3.5%
C) 6.5%
D) 7%
E) 13.75%

Solution: Ratio of population - South:North :: 60%:40% = 3:2   Mean growth = 5.5%   South Growth: 4.5%   North Growth = ??   South-------------Average--------------North   4.5% __(2n)_____5.5%_____(3n)_____??   Since:   4.5 + 2n = 5.5   n = 1/2 (this is the multiplier of the ratio)   Therefore:   North = 5.5 + 3n   North = 5.5 + 3(0.5) = 7%   ANSWER:7%
Answer: D
If x/(9p) is an odd prime number, where x is a positive integer and p is a prime number, what is the least value of x? Choose the correct choice from the following choices:
A) 54  B) 33  C) 44  D) 66  E) 99

Solution: x/(9p) = odd prime number   x = odd prime number * 9p   Least value of x = Lowest odd prime number * 9 * Lowest value of p   = 3 * 9* 2= 
3 * 9* 2 = 54
54   54nswer 54
Answer: A