MU-NLPC/Calc-aqua_rat huggingface dataset:
Which of the options is a two-digit number, which has a unit's digit that exceeds its ten's digit by 4 and the product of the given number and the sum of its digits is equal to 208.
Choose the correct choice
A) 15 B) 37 C) 55 D) 26 E) 73

Solution: Using the elimination method the option that fits this description is 26   6-2= 
6-2 = 4
4 (unit's digit that exceeds its ten's digit by 3)   26*8= 
26*8 = 208
208 (the product of the given number and the sum of its digits is equal to 175)   answer :26
Answer: D
Which of the following equations has a root in common with x^2−4x+4=0 ?
Choose the correct choice from the following options.
A) x^2-1=0
B) x^2-2=0
C) x^2-3=0
D) x^2-4=0
E) x^2-5=0

Solution: If we carefully look at the given equation we can arrange it in the following manner:   (x-2)^2= 0   so the two root is 2.   Now put 2 in given equations. The equation in which one of them gives value 0, that will be our answer.   (A) putting 2: we get 3. Reject this option.   (B) putting 2: we get 2. Reject this option.   (C) putting 2: we get 1. Reject this option.   (D) putting 2: we get 0. This is the equation, no need to check other option.   x^2-4=0 is the answer.
Answer: D
A hungry child reaches into a candy jar filled with 5 different candies; red, green, yellow, black, and white colored candies. If the child randomly picks three candies, what is the probability the child will pick the red and green colored candies as two of the three candies?
Choose the correct choice from the following
A) 3/10	B) 1/10	C) 1/15	D) 3/15	E) 2/5

Solution: Combination Formula: nCr = n!/(r!(n - r)!), where n is the population/set, and r is the sample/subset.   Total number possible = 5C3 = 5!/(3!(5 - 3)!) = 10   Number red possible = 1C1 = 1   Number green possible = 1C1 = 1   Number other possible = 3C1 = 3   Probability Formula: P(3/10) = (Number Favorable Outcomes)/(Total Number Possible Outcomes)   P(RG) = (1C1)(1C1)(3C1)/5C3 = 3/10   3/10nswer: 3/10
Answer: A
If x and y are positive integers, and 4x^3=3y, then which of the following must be a multiple of 9?
I. x^2
II. y^2
III. xy Choose the correct answer
A) I only
B) II only
C) III only
D) I and II only
E) I, II and III

Solution: 4x^2 = 3y   since x,y are positive integers, x^2 = x*x is divisible by 3 -> x is divisible by 3 and y is divisible by x^2   -> x^2 and y is divisible by 9 -> y^2 is divisible by 9   (1),(2), and (3) must be true   Answer is I and II only
Answer: D
How many different positive integers are factors of 196 ?
Select.
A) 1 B) 2 C) 3 D) 49 E) 36

Solution: 15, 14×15, 14=7^2 × 2^2   So total factors = (6+1)(6+1) = 49   Answer: 49
Answer: D
It takes 10 days for digging a trench of 100 m long, 50 m broad and 10 m deep. What length of trench,25 m broad and 15 m deep can be dug in 30 days ?
Choose one.
A) 400 m B) 200 m C) 100 m D) 89 m E) 79 m

Solution: More days, more length (Direct)   Less breadth, more length (Indirect)   More depth, less length (Indirect   Days 10 : 30;   Breadth 25 : 50; : : 100 : x   Depth 15 : 10;   :. 10 * 25* 15 * x = 30 *50 * 10 *100   x= (30*50*10*100)/10*25*15 = 400   So the required length = 400m   400 mNSWER:400 m
Answer: A
If a/b=3/4 and 8a+5b=22,then find the value of a.
Select.
A) 3/2	B) 5/2	C) 1/2	D) 4/2	E) None of them

Solution: (a/b)=3/4 =>b=(4/3) a.   Therefore, 8a+5b=22 => 8a+5*(4/3) a=22 => 8a+(20/3) a=22   =>44a = 66 => a=(66/44)=3/2   3/2nswer is 3/2
Answer: A
Sid and Bonnie are opposing participants in an online auction. Each has a constant bidding strategy: Sid always bids up by raising $40 over any previous bid. Bonnie always bids up by doubling any previous bid. The auction begins with an initial bid by a third player, and progresses as follows: Sid bids up first, and Bonnie follows. Sid bids up again, and Bonnie follows and raises the bid to a final $600. What was the dollar value of the initial price?	Choose the correct choice from the following answers:	A) 46	B) 90	C) 68	D) 568	E) 464

Solution: Initial bid = p$   Sid = p+40   Bonnie = 2p   The sequence is R---> B ---> R -----> B ---> 600   Thus per the sequence we have: p+40, 2(p+40), 2p+80+40 , 2(2p+120)   Now given, 2(2p+120) = 600----> p =90$. Thus 90 is the correct answer.
Answer: B
A cyclist covers a distance of 750 meter in 2 minutes 10 seconds. What is the speed in km/hr of cyclist Choose the correct option
A) 20.88 km/hr
B) 17 km/hr
C) 18 km/hr
D) 19 km/hr
E) 20 km/hr

Solution: Explanation:   Speed=Distance/Time   Distance=750meter   Time=2 min 10sec=130sec   Speed=750/130=5.8m/sec   =>5.8âˆ—18/5km/hr=20.88km/hr   Option 20.88 km/hr
Answer: A
A company has two models of computers, model M and model N. Operating at a constant rate, a model M computer can complete a certain task in 24 minutes and a model N computer can complete the same task in 12 minutes. If the company used the same number of each model of computer to complete the task in 1 minute, how many model M computers were used?  Select
A) 3
B) 4
C) 5
D) 8
E) 6

Solution: Let's say 1 work is processing 24 gb of data.   Model M : 1 gb per min   Model N : 2 gb per min   Working together, 1 M and 1 N = 3 gb per min   So, 8 times as many computers would work at 18 gb per min.   So no. of M = 8   Answer is 8
Answer: D
six family members: 5 grandchildren (3 brothers and 2 sisters) and their 1 grandparents are to be seated around a circular table. How many different seating arrangements are possible so that 2 sisters are seated between any two of the three brothers?	Choose the correct choice from the following answers
A) 120  B) 48  C) 1440  D) 2880  E) 8640

Solution: Answer: 48.
Answer: B
If there are 50 red and blue marbles in a jar, and the ratio of red to blue marbles is 2:3, what is the probability that, drawing twice, you will select two red marbles if you return the marbles after each draw?	Choose the correct choice from the following options:
A) 1/25  B) 2/25  C) 3/25  D) 4/25  E) 21/25

Solution: 50 red and blue marbles in a jar, and the ratio of red to blue marbles is 2:3   So, 5x=50 ---> x=10   Red marbles = 2*x = 2*10= 
2*10 = 20
20   Blue marbles= 3*x = 3*10= 
3*10 = 30
30   Prob to select a red marble= 20/50 = 2/5   Prob to select 2 red marbles with replacement = 2/5*2*5= 
2/5*2*5 = 4
4/25   Hence, answer will be 4/25.
Answer: D
2y - 2x = 2xy and x ≠ 0. If x and y are integers, which of the following could equal y?  Pick
A) 2	B) 1	C) 0	D) -3	E) - 2

Solution: Plug in the answer choices in the equation from the question stem.   A) y = 2 >>> 4-x = 4x >>> No value of x will satisfy this, not even 0. POE   B) y = 1 >>> 2 - x = 2x >>> Same, POE   C) y = 0 >>> -x = 0 >>> x can not equal 0   D) y = -1 >>> -2 - 2x = -4x >>> Holds true for x = 1, no need to check E. This is the answer.   Answer -3
Answer: D
A bulldog received 1,600 votes in a bulldog competition, giving him 20 percent of the votes. What percent of the remaining votes would he have needed to receive in order to win 36 percent of the total votes?
Choices.
A) 10% B) 12.5% C) 15% D) 17.5% E) 20%

Solution: There were 80% of the votes remaining and he needed 16%/80% = 2/10 = 20%   The answer is 20%.
Answer: E
x is what percent of y percent of z, in terms of x, y and z? m be the value expressed in terms of x,y and z.	Choose the correct choice
A) xyz B) 1/xyz C) 10^2 x/yz D) 1000 x/yz E) 10,000x/yz

Solution: Algebraically, y% of z is just (y/100)*z, or yz/100. So we want to answer the question: x is what percent of yz/100? Say x is equal to m% of yz/100; then we have:   x = (m/100)*(yz/100)   10,000x/yz = m   10,000x/yz
Answer: E
The area of a circle is added to its diameter, and the circumference is then subtracted from this total, the result is 10. What is the radius of the circle?	Choose the correct choice from the following options
A) 2*pi	B) pi	C) 2	D) 4*pi	E) 4

Solution: The equation is; diameter + Area - Circumference = d + A - C = d + pi * r^2 - 2 * pi * r = 2r + pi * r(r - 2).   By plugging in the answers we can test the answers quickly; then, 4 is the only possible answer.   Answer: 4
Answer: E
Sandy buys an old scooter for $900 and spends $300 on its repairs. If Sandy sells the scooter for $1260, what is the gain percent?	Select the correct option:
A) 3%
B) 5%
C) 7%
D) 9%
E) 11%

Solution: selling price / total cost = 1260/1200= 
1260/1200 = 21/20 = around 1.05
1.05   The gain percent is 5%.   The answer is 5%.
Answer: B
Each of the 50 members in a high school class is required to sign up for a minimum of one and a maximum of three academic clubs. The three clubs to choose from are the poetry club, the history club, and the writing club. A total of 17 students sign up for the poetry club, 24 students for the history club, and 22 students for the writing club. If 3 students sign up for exactly two clubs, how many students sign up for all three clubs?  Select
A) 5 B) 6 C) 7 D) 8 E) 9

Solution: The total number in the three clubs is 17+24+22= 
17+24+22 = 63
63.   All 50 students signed up for at least one club.   3 of those students signed up for exactly one more club.   63 - 53= 
63 - 53 = 10
10 so 5 students must have signed up for exactly three clubs.   The answer is 5.
Answer: A
Working at a constant rate, P can finish a job in 3 hours. Q, also working at a constant rate, can finish the same job in 18 hours. If they work together for 2 hours, how many more minutes will it take P to finish the job, working alone at his constant rate?  Choose the correct answer:
A) 32
B) 36
C) 40
D) 44
E) 48

Solution: Each hour they complete 1/3 + 1/18 = 7/18 of the job.   In 2 hours, they complete 2(7/18) = 7/9 of the job.   The time for P to finish is (2/9) / (1/3) = (2/3) hour = 40 minutes   The answer is 40.
Answer: C
The average weight of A, B and C is 44 kg. If the average weight of A and B be 40 kg and that of B and C be 43 kg, then the weight of B is:	Choose the correct choice from the following options:	A) 17 kg	B) 28 kg	C) 26 kg	D) 31 kg	E) 35 kg

Solution: let d sum of a, b, c is 3*44= 
3*44 = 132
132   and sum of a and b s 2*40= 
2*40 = 80
80   sum of b and c is 2 *43= 
2 *43 = 86
86   hence 80+86-132=28   ans=28   ANSWER:28 kg
Answer: B
Which of the following is closest to (120!-119!)/(120!+119!)	Pick one.
A) 2	B) 2.5	C) 3	D) 1	E) 3.2

Solution: (120!-119!)/(120!+119!)   119! (120-1)/119! (120+1)   119/121 = 1 (approximately)   1 is the answer
Answer: D
In a jar there are balls in different colors: blue, red, green and yellow.
The probability of drawing a blue ball is 1/8.
The probability of drawing a red ball is 1/6.
The probability of drawing a green ball is 1/10.
If a jar cannot contain more than 250 balls, how many yellow balls are in the Jar? Choices.
A) 25.  B) 34.  C) 53.  D) 60.  E) 73.

Solution: We need to get some number which is less than 250 and exactly divisible by 8,6 and 10   Lets take LCM of three balls 8,6 and 10 = 120.   The probability of drawing a blue ball is 1/8...For every 8 balls we get 1 BLUE ball then out of 120 balls we get 15 BLUE balls.   The probability of drawing a red ball is 1/6...For every 5 balls we get 1 RED ball then out of 120 balls we get 12 REB balls.   The probability of drawing a green ball is 1/10. For every 10 balls we get 1 GREEN ball then out of 120 balls we get 20 GREEN BALLS.   Then out of 120 - ( 15 + 20 + 12 )= 
120 - ( 15 + 20 + 12 ) = 73
73 YELLOW balls.   IMO option 73. is correct.
Answer: E
There are 10 stations between Hyderabad and Bangalore. How many second class tickets have to be printed, so that a passenger can travel from any station to any other station?  Choose the most appropriate option.
A) 156	B) 167	C) 132	D) 352	E) 380

Solution: The total number of stations = 12   From 12 stations we have to choose any two stations and the direction of travel (i.e., Hyderabad to Bangalore is different from Bangalore to Hyderabad) in 12P₂ ways.   ²⁰P₂ = 12 * 11= 
12 * 11 = 132
132.   Answer: 132
Answer: C
After running a series of television advertisements, a leading beverage producer saw its sales increase by 25% to $6 million dollars per month. Prior to the advertising campaign, about how many dollars in sales did the company average per day?  Choose the correct answer:	A) $1.25 million	B) $800,000	C) $750,000	D) $27,000	E) $160,000

Solution: Let sales in previous month = X   1.25 X=6,000,000   5/4 X= 6,000,000 ..........> X=4,800,000   sales per day= 4,800,000/30= less than 160,000   Answer: $160,000
Answer: E
John bought 15 apples for Rs.10 and sold them at the rate of 12 apples for Rs.12. What is the percentage of profit made by him?
Choose one:
A) 50 %  B) 60 %  C) 65 %  D) 100 %  E) None

Solution: Profit % = 15/10 * 12/12= 
15/10 * 12/12 = 3/2 = around 1.5
1.5 ⇒ 50%.   50 %nswer 50 %
Answer: A
An equilateral triangle T2 is formed by joining the mid points of the sides of another equilateral triangle T1. A third equilateral triangle T3 is formed by joining the mid-points of T2 and this process is continued indefinitely. If each side of T1 is 80 cm, find the sum of the perimeters of all the triangles.  Choose the correct option:  A) 180 cm  B) 220 cm  C) 240 cm  D) 270 cm  E) 480 cm

Solution: We have 80 for first triangle, when we join mid-points of first triangle we get the second equilateral triangle then the length of second one is 40 and continues.   So we have 80,40,20,...   We have ratio = 1/2, and it is GP type.   Sum of infinite triangle is a/1-r = 80/1-(1/2) = 160   Equilateral triangle perimeter is 3a = 3*160= 
3*160 = 480
480.   So option 480 cm.
Answer: E
A train passes a station platform in 30 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?	Choose one
A) 150  B) 166  C) 240  D) 157  E) 198

Solution: Speed = [54 * 5/18] m/sec = 15 m/sec.   Length of the train = (15 * 20)= 
(15 * 20) = 300
300 m.   Let the length of the platform be x meters.   Then, x + 300 / 30= 15   x + 300 = 450   x = 150 m.   150nswer: 150
Answer: A
In an office, totally there are 2800 employees and 25% of the total employees are males. 30% of the males in the office are at-least 50 years old. Find the number of males aged below 50 years? Select.
A) 390	B) 490	C) 400	D) 460	E) None of these

Solution: Number of male employees = 2800* 25/100= 
2800* 25/100 = 700
700   Required number of male employees who are less than 50 years old= 700* (100 - 30)%   = 700* 70/100= 
700* 70/100 = 490
490.   ANSWER:490
Answer: B
A number is increased by 60% and then decreased by 60%, the final value of the number is ?
Choose the correct choice from the following:	A) decrease by 36%	B) decrease by 30%	C) decrease by 32%	D) decrease by 34%	E) decrease by 35%

Solution: Here, x = 60 and y = - 60   Therefore, the net % change in value   = ( x + y + xy/100)%   = [60 - 60 + (60 * -60)/100]% or - 36%   Since the sign is negative, there is a decrease in value by 36%.   decrease by 36%NSWER: decrease by 36%
Answer: A
How many seconds will a 500 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?	Options:  A) 12 sec  B) 30 sec  C) 86 sec  D) 16 sec  E) 18 sec

Solution: Speed of train relative to man = 63 - 3= 
63 - 3 = 60
60 km/hr.= 60 * 5/18 = 50/3 m/sec.   Time taken to pass the man = 500 * 3/50= 
500 * 3/50 = 30
30 sec.   Answer: 30 sec
Answer: B
The sequence S is defined as Sn = (n + 1)! for all integers n >= 1. For example, S3 = 4! = (4)(3)(2)(1). Which of the following is equivalent to the difference between S100 and S99?	Options.
A) 101! B) 100! C) 99^2(98!) D) 100^2(99!) E) (100!)2

Solution: According to this Symbolism question, we're asked to figure out S100 - S99. According to the description of the symbol in the question, we're asked to figure out:   101! - 100!   Both these terms have something in common: 100! so we can factor that out of each piece...   101! - 100!   100!(101 - 1)   Simplifying the parentheses, we get...   100!(100)   Unfortunately, THAT answer isn't listed. We've done the math correctly though, so all we can do is try to convert "our" answer into the format that appears in the answer choices...   100! = (100)(99!) so our answer can be rewritten as...   (100)(99!)(100)   Or....   (100^2)(99!)   ANSWER:100^2(99!)
Answer: D
If books bought at prices ranging from Rs. 150 to Rs. 300 are sold at prices ranging from Rs. 250 to Rs 350, what is the greatest possible profit that might be made in selling 15 books ?  Choose the correct choice from the following options
A) Rs. 2500
B) Rs. 3000
C) Rs. 3500
D) Rs. 3200
E) Rs. 3600

Solution: The greatest profit is possible only if the cost price of the books are minimum and selling prices are maximum.   Let lowest cost price of the 15 books = 150*15 = Rs. 2,250   Maximum selling price of 15 books = 350 *15 = Rs. 5,250   So, maximum profit = 5250 - 2250 = Rs. 3,000   ANSWER : OPTION Rs. 3000
Answer: B
In how many different ways can the letters of the word 'OPTICAL' be arranged so that the vowels always come together?  Choose the correct choice from the following choices:
A) 238  B) 227  C) 720  D) 128  E) 191

Solution: The word 'OPTICAL' contains 7 different letters.   When the vowels OIA are always together, they can be supposed to form one letter.   Then, we have to arrange the letters PTCL (OIA).   Now, 5 letters can be arranged in 5! = 120 ways.   The vowels (OIA) can be arranged among themselves in 3! = 6 ways.   Required number of ways = (120 x 6) = 720.   Answer: 720
Answer: C
On dividing 23 by a number, the quotient is 4 and the remainder is 3. Find the divisor.
Choose the correct choice from the following answers.
A) 1  B) 2  C) 4  D) 5  E) 7

Solution: d = (5-R)/Q   = (23 - 3)/4   = 20/4= 
20/4 = 5
5   5
Answer: D
How many liters of water must be evaporated from 50 liters of a 3-percent sugar solution to get a 4-percent solution?	Select the correct option:
A) 35
B) 33 1/3
C) 21
D) 16 2/3
E) 15

Solution: How many liters of water must be evaporated from 50 liters of a 3-percent sugar solution to get a 4-percent solution?   3% of a 50 liter solution is 1.5L. So you are trying to determine how many liters must a solution be for the 1.5L to represent 4% of the solution. Set up an inequality and solve for x:   1.5/x = 1/4   x = 6   Since you need a 15L solution, you must evaporate 21 of the original 50L solution to get a 4% solution.   Answer is 21.
Answer: C
If CRY is coded as MRYC then how will GET be coded? Choose the correct choice from the following answers:	A) MTEG	B) MGET	C) MEGT	D) METG	E) METC

Solution: CRY=M+RYC   GET=M+ETG   METG   ANSWER:METG
Answer: D
A and B walk around a circular track. They start at 8 a.m from the same point in the opposite directions. A and B walk at a speed of 2 rounds per hour and 3 rounds per hour respectively. How many times shall they cross each other before 9 a.m
Choose the correct choice from the following answers.
A) 5	B) 6	C) 7	D) 8	E) 9

Solution: Explanation:   Relative speed = (2+3)= 
(2+3) = 5
5 rounds per hour   So, they cross each other 5 times in an hour hence, they cross 5 times before 9 a.m   5nswer: Option 5
Answer: A
Special codes are designated by either a 2-letter or a 3-letter code that is created by using the 26 letters of the alphabet. Which of the following gives the maximum number of different codes that can be designated with this system?
Choose the correct choice from the following answers.
A) 2(26)^3  B) 26(26)^2  C) 27(26)^2  D) 26(26)^3  E) 27(26)^3

Solution: 26^2+26^3 = 26^2(1+26)=27*26^2   The answer is 27(26)^2.
Answer: C
The price of a jacket is reduced by 25%. During a special sale the price of the jacket is reduced another 20%. By approximately what percent must the price of the jacket now be increased in order to restore it to its original amount?  Pick
A) 32.5
B) 35
C) 48
D) 65
E) 66.67

Solution: 1) Let the price of jacket initially be $100.   2) Then it is decreased by 25% , therefore bringing down the price to $75.   3) Again it is further discounted by 20%, therefore bringing down the price to $60.   4) Now 60 has to be added byX %in order to equal the original price.   60 + ( X% ) 60 = 100.   Solving this eq for X, we get X = 66.67   Ans is 66.67.
Answer: E
A train is 360 meter long is running at a speed of 72 km/hour. In what time will it pass a bridge of 140 meter length?	Select:  A) 27 seconds  B) 29 seconds  C) 25 seconds  D) 11 seconds  E) 12 seconds

Solution: Speed = 72 Km/hr = 72*(5/18) m/sec = 20 m/sec   Total distance = 360+140= 
360+140 = 500
500 meter   Time= Distance/speed   = 500 * (1/20)= 
500 * (1/20) = 25
25 seconds   Answer:25 seconds
Answer: C
A and B together can do a work In 3 days. A alone can do it in 12 days. What time B will take to do the work alone?  Answers
A) 4 days
B) 8 days
C) 12 days
D) 10 days
E) 5 days

Solution: Explanation:   4 days and B 1day's work = 1/3   4 days alone can do 1day's work = 1/12   what time B will take to do the work alone?   B = (4 days+B) - 4 days = (1/3 - (1/12) = 4 Days   4 daysnswer: Option 4 days
Answer: A
If 10 crates have 95 apples each and how many apples more is required in order to make 100 apples in each crate?
Choose the most appropriate option:
A) 5
B) 10
C) 15
D) 50
E) 0

Solution: Each crate requires 5 apples and totally there are 10 crates so required apples = 10 * 5= 
10 * 5 = 50
50   Answer: 50
Answer: D
A certain theater has 100 balcony seats. For every $2 increase in the price of a balcony seat above $10, 5 fewer seats will be sold. If all the balcony seats are sold when the price of each seat is $10, which of the following could be the price of a balcony seat if the revenue from the sale of balcony seats is $1,160 ?  Choose the correct answer.
A) $12	B) $14	C) $11.5	D) $17	E) $18

Solution: I solved it as follows:   10+2(x) = 100 -5(x)   x= 12   Equation should be (10+$2*x)(100-5x)=1,160, where x is the # of times we increased the price by $2. (10+$2*x)(100-5x)=1,160 --> (5+x)(20-x)=116 --> x=0.75 or x=14.25 --> price=10+$2*0.75=$11.5 or price10+ 2*0.75= 
10+ 2*0.75 = 11.5
$11.5 or price=10+$2*14.25=$38.5.   Answer: $11.5.
Answer: C
The sum of ages of 5 children born 1 years different each is 30 years. What is the age of the Elder child?
Choose one
A) 8 B) 9 C) 10 D) 16 E) 17

Solution: Let the ages of children be x, (x + 1), (x + 2), (x + 3) and (x + 4) years.   Then, x + (x + 1) + (x + 2) + (x + 3) + (x + 4) = 30   5x = 20   x = 4.   x +4= 
 +4 = 4
4+4= 
4+4 = 8
8   8nswer : 8
Answer: A
The ratio between the present ages of P and Q is 6:8. If Q is 4 years old than P, what will be the ratio of the ages of P and Q after 4 years? Choose the correct choice from the following options:
A) A)8:9
B) B)3:5
C) C)4:3
D) inadequate
E) of these

Solution: Let P's age and Q's age be 6x and 8x years respectively.   Then, 8x - 6x = 4 => x =2   Required ratio = (6x + 4) : (7x + 4)   16 : 18 = 8:9   8:9NSWER:8:9
Answer: A
A bag contains 2 yellow, 3 green and 2 blue balls. Two balls are drawn at random. What is the probability that none of the balls drawn is blue? Choose the correct choice from the following:
A) 1/2	B) 10/21	C) 9/11	D) 7/11	E) 5/2

Solution: Total number of balls = 2 + 3 + 2= 
2 + 3 + 2 = 7
7   Let S be the sample space.   n(S)= Total number of ways of drawing 2 balls out of 7 = 7C2   Let E = Event of drawing 2 balls , none of them is blue.   n(E) = Number of ways of drawing 2 balls , none of them is blue   = Number of ways of drawing 2 balls from the total 5 (=7-2) balls = 5C2   (∵ There are two blue balls in the total 7 balls. Total number of non-blue balls = 7 - 2= 
7 - 2 = 5
5)   P(E)= n(E)/n(S)=5C2/7C2=(5×42×1)/(7×62×1)=5×4/7×6=10/21   Answer is 10/21
Answer: B
The probability that a convenience store has no iced tea is 40%. If Karl is stopping by 2 convenience stores on his way to work, what is the probability that at least one of the stores will not have a can of iced tea?	Choose the correct choice:
A) 1/8  B) 1/4  C) 1/2  D) 3/4  E) 21/25

Solution: p=1-2/5^2(all stores have iced tea)=21/25   21/25
Answer: E