MU-NLPC/Calc-aqua_rat huggingface dataset:
When Greenville State University decided to move its fine arts collection to a new library, it had to package the collection in 20-inch by 20-inch by 15-inch boxes. If the university pays $0.90 for every box, and if the university needs 3.06 million cubic inches to package the collection, what is the minimum amount the university must spend on boxes?  Pick one:
A) $255
B) $275
C) $459
D) $1,250
E) $2,550

Solution: Total no. Of boxes = 3060000/(20×20×15) = 510   Total cost = 510×$0.9=$459   Answer $459
Answer: C
The sequence x1, x2, x3,..., is such that Xn = 1/n - (1/(n+1)). What is the sum of the first 5 terms of the sequence? Pick one
A) 201/100
B) 99/100
C) 100/101
D) 1/10000
E) 5/6

Solution: Easy task and accomplish   X1=1-1/2   x2=1/2-1/3   x3=1/3-1/4   .....   x5=1/5-1/6   sum=X1+X2+X3+....X5=1-1/2+1/2-1/3+.......1/5-1/6=5/6   5/6 is the answer
Answer: E
162 students represent x percent of the boys at a school. If the boys at the school make up 50% of the total school population of x students, what is x?	Options.
A) 120
B) 150
C) 180
D) 250
E) 440

Solution: Let B be the number of boys in the school.   162 = xB/100   B = 0.5x   16200=0.5x^2   x^2 = 32400   x = 180   The answer is 180.
Answer: C
A, B and C can complete a piece of work in 24, 6 and 12 days respectively. Working together, they will complete the same work in:	Choose the correct choice.
A) 33/7  B) 43/7  C) 24/7  D) 19/7  E) None

Solution: If A can do a piece of work in n days, then A's 1 day's work = 1/n   (A + B + 24/7)'s 1 day's work =1/24+1/6+1/12=7/24   So, all the three together will complete the job in = 24/7 days   Answer: 24/7
Answer: C
At what time between 4 and 5 o’clock will the hands of a watch point in opposite directions?  Choose the correct choice from the following choices.
A) 54 6/11 min. past 4
B) 50 min. past 4
C) 45 min past 4
D) 40 min past 4
E) None

Solution: Sol.   At 4 o’clock, the hands of the watch are 20 min. spaces apart.   To be in opposite directions, they must be 30 min. spaces apart.   ∴ Minute hand will have to gain 50 min. spaces.   55 min. spaces are gined in 60 min.   50 min. spaces are gained in [60/55 * 50] min. or 54 6/11 min.   ∴ Required time = 54 6/11 min. past 4   54 6/11 min. past 4nswer 54 6/11 min. past 4
Answer: A
Difference between the length &breadth of a rectangle is 25 m. If its perimeter is 206 m, then its area is?  Choose one:
A) 2400 m^2  B) 2500 m^2  C) 2520 m^2  D) 2560 m^2  E) 3000 m^2

Solution: Solving the two equations, we get: l = 75 and b = 40.   Area = (l x b) = (75 x 40) m2 = 3000 m^2   3000 m^2
Answer: E
Each person who attended a company meeting was either a stockholder in the company, an employee of the company, or both. If 55 percent of those who attended the meeting were stockholders and 61 percent were employees, what percent were stockholders who were not employees?
Choose the most appropriate option.
A) 37  B) 38  C) 39  D) 40  E) 41

Solution: 55+61= 
55+61 = 116
116 so 16% were both stockholders and employees.   The percent who were stockholders but not employees is  55-16= 
 55-16 = 39
39%   The answer is 39.
Answer: C
In what time will a train 200 m long cross an electric pole, it its speed be 144 km/hr?
Choices.
A) 2.5 sec  B) 2.8 sec  C) 5 sec  D) 2.2 sec  E) 4.5 sec

Solution: Speed = 144 * 5/18= 
144 * 5/18 = 40
40 m/sec   Time taken= 200/40= 
200/40 = 5
5 sec.   Answer:5 sec
Answer: C
Machine P and Machine Q are each used to manufacture 550 sprockets. It takes Machine P 10 hours longer to produce 550 sprockets than Machine Q. Machine Q produces 10% more sprockets per hour than Machine A. How many sprockets per hour does Machine A produce?	Choose the correct answer:
A) 5 B) 15 C) 55 D) 95 E) 125

Solution: P makes x sprockets per hour.   Then Q makes 1.1x sprockets per hour.   550/x = 550/1.1x + 10   1.1(550) = 550 + 11x   11x = 55   x = 5   The answer is 5.
Answer: A
A car drives 40 miles on local roads at 20 mph, and 180 miles on the highway at 60 mph, what is the average speed of the entire trip? Choose the correct answer:
A) 36 mph
B) 40 mph
C) 44 mph
D) 52 mph
E) 58 mph

Solution: Explanations   1) In phase #1 of the trip, the car traveled 40 mi at 20 mph. That time of this phase was:   time = distance/rate = (40 mi)/(20 mph) = 2 hr   In phase #2 of the trip, the car traveled 180 mi at 60 mph. That time of this phase was:   time = distance/rate = (180 mi)/(60 mph) = 3 hr   The total distance of the trip = 40 mi + 180 mi = 220 mi   The total time of the trip = 2 hr + 3 hr = 5 hr   The average speed of trip is given by   speed = distance/time = (220 mi)/(5 hr) = 44 mph   Answer: 44 mph.
Answer: C
Tim and Jim enter into a partnership by investing $700 and $300 respectively. At the end of one year, they divided their profits such that a third of the profit is divided equally for the efforts they have put into the business and the remaining amount of profit is divided in the ratio of the investments they made in the business. If Tim received $800 more than Jim did, what was the profit made by their business in that year?
Choose the correct option:
A) 4565
B) 3000
C) 4654
D) 353464
E) 3465463

Solution: Say the profit was $x.   Tim share = x/6 (half of the third) + (x-x/3)*0.7   Jim share = x/6 (half of the third) + (x-x/3)*0.3   Thus (x-x/3)*0.7-(x-x/3)*0.3=800 --> x=3000.   answer is 3000
Answer: B
A certain characteristic in a large population has a distribution that is symmetric about the mean m. If 68% of the distribution lies one standard deviation g of the mean, what percent of the distribution is less than m+g? Choose the correct choice from the following.
A) 16%	B) 32%	C) 48%	D) 84%	E) 92%

Solution: 16%   ________________________________________________ m+g   34%   ________________________________________________ m   34%   ________________________________________________ m-g   16%   since 68% lies one standard deviation from mean m, => 50% of 68% lies on either side as it is symmetric about m.   thus 16% lie below m-g and 16% lie above m+g   now below m+g = 16+34+34= 
16+34+34 = 84
84%   hence 84%
Answer: D
If the arithmetic mean of p and q is 10 and the arithmetic mean of q and r is 20, what is the value of r-p? Choose the correct choice from the following answers
A) 20
B) 10
C) 30
D) 40
E) 5

Solution: 20rithmetic mean expression for p and q:   (p+q)/2=10 ; p+q=20 ----eq1   20rithmetic mean expression for q and r:   (q+r)/2=20 ; q+r=40 ----eq2   Subtracting eq1 from eq2 we get: r-p=20   Hence, the correct answer is 20
Answer: A
A coin is tossed live times. What is the probability that there is at the least one tail?	Choose the correct choice from the following options
A) 31/32	B) 31/36	C) 31/30	D) 31/36	E) 31/312

Solution: Let P(T) be the probability of getting least one tail when the coin is tossed five times.   = There is not even a single tail.   i.e. all the outcomes are heads.   = 1/32 ; P(T) = 1 - 1/32 = 31/32   31/32nswer:31/32
Answer: A
A department of ten people - five men and five women - needs to send a team of five to a conference. If they want to make sure that there are no more than three members of the team from any one gender, how many distinct groups are possible to send? Answers.
A) 100 B) 126 C) 200 D) 252 E) 288

Solution: We are given 5 men and 5 Women, out of which we need to select 5 People such that no more than 3 of any gender are selected.   So, We can have Either 3 Men + 2 Women Selected or 2 Men + 3 Women Selected.   Thus, Number of ways for selecting 3 Men + 2 Women = 5C3 * 5C2 = 10*10= 
10*10 = 100
100   AND Number of ways for selecting 2 Men + 3 Women= 5C2 * 5C3 = 10*10= 
10*10 = 100
100   Thus, total ways to get the distinct groups will be   100+100= 
  100+100 = 200
200.   Hence, Ans will be 200.
Answer: C
The different of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and 15 as remainder.What is the smaller number ?  Choose the correct choice from the following: A) 360 B) 320 C) 290 D) 240 E) 270

Solution: Let the smaller number be x.Then larger number =(x+1365).   x+1365=6x+15   5x=1350   x=270   smaller number =270.   Answer is 270
Answer: E
An error 2% in excess is made while measuring the side of a square. The percentage of error in the calculated area of the square is
Select:
A) 2%
B) 2.02%
C) 4%
D) 4.04%
E) None of above

Solution: 100 cm is read as 102 cm.   A1 = (100 x 100) cm2 and A2 (102 x 102) cm2.   (A2 - A1) = [(102)2 - (100)2]   = (102 + 100) x (102 - 100)   = 404 cm2.   Percentage error = [(404/100x100)x 100]%   = 4.04%   Answer : 4.04%
Answer: D
A man decides to buy a nice horse. He pays $60 for it, and he is very content with the strong animal. After a year, the value of the horse has increased to $70 and he decides to sell the horse. However, already a few days later he regrets his decision to sell the beautiful horse, and he buys it again. Unfortunately, he has to pay $80 to get it back, so he loses $10. After another year of owning the horse, he finally decides to sell the horse for $90.
What is the overall profit the man makes?  Choose the correct choice from the following:
A) $70
B) $70
C) $20
D) $89
E) $68

Solution: C   $20   n the first trade, the man buys something for $60 and sells it again for $70, so he makes a profit of $10.   In the second trade, the man buys something for $80 and sells it again for $90, so he makes again a profit of $10.   Conclusion: The man makes an overall profit of $10 + $10 = $20.   You can also look at the problem as follows: the total expenses are $60 + $80 10 +  10= 
10 +  10 = 20
$20.   You can also look at the problem as follows: the total expenses are $60 + $80 = $140 and the total earnings are $70 + $90 60 +  80= 
60 +  80 = 140
$140 and the total earnings are $70 + $90 = $160. The overall profit is therefore $160 - $140   70 +  90= 
  70 +  90 = 160
$160. The overall profit is therefore $160 - $140 = $20. 160 -  140= 
 160 -  140 = 20
$20.
Answer: C
A company that ships boxes to a total of 12 distribution centers uses color coding to identify each center. If either a single color or a pair of two different colors is chosen to represent each center and if each center is uniquely represented by that choice of one or two colors, what is the minimum number of colors needed for the coding? (assume that the order of the colors in a pair does not matter)	Choose the correct answer.
A) 4 B) 5 C) 6 D) 12 E) 24

Solution: Back-solving is the best way to solve this problem.   You basically need 12 combinations (including single colors)   If we start from option 1->   1=> 4C2 + 4 = 10 (Not enough)   2=> 5C2 + 5 = 15 (Enough)   Since the minimum number is asked. It should be 5.   Answer - 5
Answer: B
A student's mark was wrongly entered as 83 instead of 63. Due to that the average marks for the class got increased by
1/2. What is the number of students in the class?  Choose the correct option:
A) 45
B) 40
C) 35
D) 30
E) 50

Solution: Explanation:   Let the total number of students = x   The average marks increased by 1/2 due to an increase of   83 - 63= 
  83 - 63 = 20
20 marks.   40ut total increase in the marks= 1/2×x=x/2   Hence we can write as   x/2=20   ⇒x=20 x 2=40   Answer: Option 40
Answer: B
A 300 m long train crosses a platform in 39 sec while it crosses a signal pole in 18 sec. What is the length of the platform?  Choose the most appropriate option: A) 286 m B) 350 m C) 277 m D) 278 m E) 267 m

Solution: Speed = 300/18 = 50/3 m/sec.   Let the length of the platform be x meters.   Then, (x + 300)/39 = 50/3   3x + 900 = 1950 => x = 350 m.   Answer:350 m
Answer: B
Anne traveled from City A to City B in 4 hours, and her speed was between 29 miles per hour and 61 miles per hour. John traveled from City A to City B along the same route in 2 hours, and his speed was between 50 miles per hour and 61 miles per hour. Which of the following could be the distance, in miles, from City A to City B?  Choose one:
A) 95
B) 115
C) 125
D) 120
E) 300

Solution: Using the given options,   A.95. If distance=95 miles, and Anne takes 4 hours, then her speed=95/4=23.xx(Her speed is b/w 25 and 45 miles per hour) . So this is out   B 115. If distance=115 miles, and Anne takes 4 hours, then her speed=115/4= 
115/4 = 115/4 = around 28.75
28.75 (Her speed is b/w 25 and 45 miles per hour) . So this is out   C 125 if distance is 125 and anne takes 4 hours her speed is 125/4=31.5, ok. Bob travels 125/2 hours or 62.5 mph this is too high   D 120 if distance is 120 and anne takes 4 hours her speed is   120/4= 
  120/4 = 30
30, ok. Bob travels 120/2 hours or 60 mph this is also good.   120 is the answer
Answer: D
Present ages of Sameer and Anand are in the ratio of 5 : 4 respectively. Seven years hence, the ratio of their ages will become 11 : 9 respectively. What is Anand's present age in years?
Choose the correct answer
A) A)84
B) B)89
C) C)67
D) D)56
E) E)45

Solution: Let the present ages of Sameer and Anand be 5x years and 4x years respectively.   Then,	(5x + 7/4x + 7)=11/9   9(5x + 7) = 11(4x + 7)   45x + 63 = 44x + 77   45x - 44x = 77 - 63= 
77 - 63 = 14
14.   Anand's present age= 4x = 84 years.   84nswer:84
Answer: A
John walking at 4 Kmph reaches his office 8 minutes late. If he walks at 6 Kmph, he reaches there 8 minutes earlier. How far is the office from his house?	Choose the correct choice from the following answers:
A) 3 2/5 Km
B) 3 1/5 Km
C) 3 1/7 Km
D) 4 1/5 Km
E) 4 2/5 Km

Solution: Formula = S1*S2/S2-S1 * T1+T2/60   = 4*6/2 * 16/6   = 24/2 * 16/60   = 8 * 2/5   = 16/5 = 3 1/5 Km   3 1/5 Km)
Answer: B
John purchased 8kg of grapes at the rate of 70 per kg and 9 kg of mangoes at the rate of 55 per kg. How much amount did he pay to the shopkeeper?  Choose the correct choice from the following answers.
A) 1045	B) 1050	C) 1055	D) 1060	E) 1065

Solution: Cost of 8 kg grapes = 70 × 8 = 560.   Cost of 9 kg of mangoes = 55 × 9 = 490.   Total cost he has to pay = 560 + 490 = 1055   1055
Answer: C
Ram professes to sell his goods at the cost price but he made use of 800 grms instead of a kg, what is the gain percent?	Choose the correct option.
A) 25%	B) 11 1/8%	C) 11 9/9%	D) 11 5/9%	E) 11 1/5%

Solution: 800 --- 200   100 --- ? => 25%   25%nswer:25%
Answer: A
The speed of a train including stoppages is 90 kmph and excluding stoppages is 120 kmph. Of how many minutes does the train stop per hour?  Choose the correct choice from the following.
A) 9
B) 10
C) 12
D) 14
E) 15

Solution: 15xplanation:   T = 30/120 * 60= 
30/120 * 60 = 15
15   Answer: Option 15
Answer: E
Find the cost of fencing around a circular field of diameter 30 m at the rate of Rs.2 a meter?  Choose the correct choice from the following options: A) 100.5 B) 188.5 C) 190.5 D) 168.5 E) 175.5

Solution: 2 * 22/7 * 15 = 94.25   94.25 * 2 = Rs.188.5   Answer: 188.5
Answer: B
Jayant opened a shop investing Rs. 30,000. Madhu joined him 2 months later, investing Rs. 45,000. They earned a profit of Rs. 58,000 after completion of one year. What will be Madhu's share of profit?
Choose the correct choice:
A) Rs. 27,000	B) Rs. 24,000	C) Rs. 30,000	D) Rs. 29,000	E) None of these

Solution: 30,000 *12=45,000*8   1:1   Madhu's share=1/2*58,000   i.e. Rs. 29,000   ANSWER:Rs. 29,000
Answer: D
A can contains a mixture of liquids A and B is the ratio 7:5. When 9 litres of mixture are drawn off and the can is filled with B, the ratio of A and B becomes 7:9. How many liter of liquid A was contained by the can initially?
Choose the correct choice from the following choices
A) 10 B) 20 C) 21 D) 25 E) 27

Solution: Using the values here might be the most straightforward way for this question.   As A:B::7:5 ---> only option C is a multiple of 7 and hence it is a good place to start. Also A:B::7:5 means that , A = (712)*Total and B = (5/12)*Total   If A = 21 , B = 15 ---> remove 9 litres ---> you remove (7/12)*9 of A ---> A remaining = 21-(7/12)*9 = 63/4   Similarly, for B, you remove (5/12)*9 ---> B remaining = 15 - (5/12)*9 = 45/4 and then add 9 more litres of B ---> 9+45/4 = 81/4   Thus A/B (final ratio) = (45/4)/(81/4) = 7:9 , the same as the final ratio mentioned in the question.   Hence C is the correct answer.   FYI, the algebraic equations will become:   A/B = 7/9 = (7x-(7/12)*9)/ (5x-(5/12)*9+9), where 7x and 5x are initial quantities of A and B respectively.   Thus, 7/9 = (7x-(7/12)*9)/ (5x-(5/12)*9+9) ---> giving you x=3. Thus A (original) = 7*3= 
7*3 = 21
21.   ANSWER:21
Answer: C
S is the infinite sequence S1 = 2, S2 = 22, S3 = 222,...Sk = Sk–1 + 2(10k–1). If p is the sum of the first 30 terms of S, what is the ninth digit of p, counting right to left from the units digit?
Select the correct option:
A) 1 B) 2 C) 4 D) 6 E) 9

Solution: C   Sum of unit digits of first 30 terms = 60   Sum of tens digits of first 30 terms = 58   Sum of thousands digits of first 30 terms = 56   and so on..   p1 = 0   p2 = (6+58) = 4   p3 = (6+56) = 2   p4 = (6+54) = 0   p5 = (6+52) = 8   p6 = (5+50) = 5   p7 = (5+48) = 3   p8 = (5+46) = 1   p9 = (5+44) = 9   ANSW9R: 9
Answer: E
Using all the letters of the word "THURSDAY", how many different words can be formed? Select the correct option.
A) 7	B) 8!	C) 8	D) 7!	E) 3

Solution: Explanation:   Total number of letters = 8   Using these letters the number of 8 letters words formed is ⁸P₈ = 8!.   Answer: Option 8!
Answer: B
What is the median of a set of consecutive integers if the sum of nth number from the beginning and nth number from the end is 200?
Choose the correct choice from the following choices: A) 10 B) 25 C) 50 D) 75 E) 100

Solution: Surprisingly no one answered this easy one.   property of a set of consecutive integerz.   mean=median=(first element+last element)/2 = (second element+last but one element)/2 =(third element+ third last element)/2 Etc. Etc.   So mean=median=200/2= 
200/2 = 100
100   Answer is 100
Answer: E
What is the probability of getting a number less than 4 when a die is rolled?  Choose the correct option:	A) 3/5	B) 1/6	C) 2/5	D) 4/7	E) 1/2

Solution: Total number of outcomes possible when a die is rolled = 6 (∵ any one face out of the 6 faces)   i.e., n(S) = 6   1/2 = Getting a number less than 4 = {1, 2, 3}   Hence, n(1/2) = 3   P(1/2) = n(1/2)/n(S)=3/6=1/2   Answer is 1/2.
Answer: E
John and Steve are speed walkers in a race. John is 12 meters behind Steve when he begins his final push. John blazes to the finish at a pace of 4.2 m/s, while Steve maintains a blistering 3.7 m/s speed. If John finishes the race 2 meters ahead of Steve, how long was John’s final push?  Choose the correct choice from the following answers: A) 13 seconds B) 17 seconds C) 26 seconds D) 34 seconds E) 28 seconds

Solution: Let t be the time that John spent for his final push.   Thus, per the question,   4.2t = 3.7t+12+2 ---> 0.5t = 14 ---> t = 28 seconds.   28 seconds is the correct answer.
Answer: E
38 69 22 73 31 47 13 52
Which of the following numbers is greater than three fourths of the numbers but less than one fourth of the numbers in the list above?	Pick one:	A) 41	B) 68	C) 67	D) 69	E) 73

Solution: Arrange the numbers in ascending order:   13, 22, 31, 38, 47, 52, 69, 73 (Just cross check the count to ensure that you didn't miss anything)   How many numbers do we see?   8, alright.   What's (1/4)8?   2.   What's (3/4)8?   6.   We're asked to find a number that are greater than 6 numbers in the list AND smaller than the remaining two.   13, 22, 31, 38, 47, 52, 69,73   13, 22, 31, 38, 47, 52: Find a number greater than any of these numbers.   69, 73: Find a number smaller than any of these numbers.   Only 67 fits the description.   Ans:67
Answer: C
Judges will select 4 finalists from the 8 contestants entered in a singing competition. The judges will then rank the contestants and award prizes to the 3 highest ranked contestants: a blue ribbon for first place, a red ribbon for second place, and a yellow ribbon for third place. How many different arrangements of prize-winners are possible?  Choose the correct answer.
A) 10
B) 21
C) 280
D) 420
E) 1,260

Solution: First Select 5 from 7 contestants and then select top 3 from those 5 =   82804*42803 = 70 * 4= 
70 * 4 = 280
280   ANS:280
Answer: C
Jack has two dice, one has six equally probable sides, labeled 1, 2, 3, 4, 5, 6, and the other has seven equally probable sides, labeled 1, 2, 3, 4, 5, 6, 7. If Jack rolls both dice what is the probability that both of the numbers will be 3? Choose the correct choice from the following.
A) 3/14 B) 2/7 C) 1/3 D) 1/42 E) 12/21

Solution: METHO1/42-1   Probability that the number on first die is 3 = 1/6   Probability that the number on Second die is 3 = 1/7   Probability that Both 1/42ice result in odd numbers = (1/6)*(1/7) = 1/42   Answer: Option 1/42
Answer: D
5 men are equal to as many women as are equal to 8 boys. All of them earn Rs.120 only. Menâ€™s wages are?	Choose the correct choice from the following answers
A) 6Rs	B) 7Rs	C) 8Rs	D) 4Rs	E) 1Rs

Solution: 5M = xW = 8B   5M + xW + 8B ----- 120 Rs.   5M + 5M + 5M ----- 120 Rs.   15M ------ 120 Rs. => 1M = 8Rs.   Answer:8Rs
Answer: C
Three 6 faced dice are thrown together. The probability that all the three show the same number on them is ?  Choose the correct choice from the following choices:
A) 1/37  B) 1/36  C) 1/38  D) 1/11  E) 1/33

Solution: It all 3 numbers have to be same basically we want triplets. 111, 222, 333, 444, 555 and 666. Those are six in number. Further the three dice can fall in 6 * 6 * 6= 
6 * 6 * 6 = 216
216 ways.   Hence the probability is 6/216= 1/36   Answer:1/36
Answer: B
The value of a machine depreciates at 20% per annum. If its present value is Rs. 1,50,000, at what price should it be sold after two years such that a profit of Rs. 24,000 is made? Choose the correct choice from the following options:	A) Rs.1,20,050	B) Rs.1,20,000	C) Rs.1,20,008	D) Rs.1,22,000	E) Rs.1,20,085

Solution: The value of the machine after two years   = 0.8 * 0.8 * 1,50,000   = Rs. 96,000   SP such that a profit of Rs. 24,000 is made   96,000 + 24,000   = Rs.1,20,000   Answer: Rs.1,20,000
Answer: B
Excluding stoppages, the speed of a bus is 54 kmph and including stoppages, it is 45 kmph. For how many minutes does the bus stop per hour?
Choose the correct choice
A) 9 B) 10 C) 12 D) 20 E) 8

Solution: Due to stoppages, it covers 9 km less.   Time taken to cover 9 km =(9/54x 60)min	= 10 min.   Answer :10
Answer: B
If x is an odd negative integer and y is an even integer, which of the following statements must be true? I. (3x + 2y) is positive integer II. (xy)^2 is positive integer III. (y^2 - x) is negative integer	Answers:	A) I only	B) II only	C) III only	D) I,II only	E) II,III only

Solution: I. It is true if 3x < 2y   II. It is always positive   III. It is not true   Answer : II only
Answer: B
9 basketball players are trying out to be on a newly formed basketball team. Of these players, 5 will be chosen for the team. If 6 of the players are guards and 3 of the players are forwards, how many different teams of 3 guards and 2 forwards can be chosen?	Choose the correct choice from the following options
A) 23  B) 30  C) 42  D) 60  E) 126

Solution: Out of 6 gaurds we have to select 3 -> selection means we use C -> so 6C3   Out of 3 forwards we have to select 2 -> selection means we use C -> so 3C2   Total ways = 6C3 x 3C2 = 60   ANSWER:60
Answer: D
If a certain coin is flipped, the probability that the coin will land heads is 1/2. If the coin is flipped 5 times, what is the probability that it will land heads up on the first 2 flips but not on the last 3 flips?	Choose the correct choice:
A) 1/2
B) 1/4
C) 1/8
D) 1/16
E) 1/32

Solution: P(HHTTT) = 1/2*1/2*1/2*1/2*1/2 = 1/32   The answer is 1/32.
Answer: E