MU-NLPC/Calc-aqua_rat huggingface dataset:
The price of lunch for 13 people was $207 including a 15% gratuity for service. What was the average price per person, EXCLUDING the gratuity?
Choose the correct choice from the following choices
A) 11.73  B) 12  C) 13.85  D) 14  E) 15.87

Solution: 13.85learly 13.85 is the answer   I used POE here   Lets consider option (13.85)   13*13.85= 180 now 180(115/100)=207   => possible ANSWER IMO 13.85
Answer: C
The daytime telephone rate between two cities is 50 cents for the first 3 minutes and c cents for each additional minute. The total charge is reduced 60 percent on calls made after 10:00 P.M. The cost, in dollars, of a 35-minute call made at 10:30 P.M. between these two cities is:
Choose one.
A) 0.4(0.60) + 35c  B) 0.4(0.50 + 0.32c)  C) 0.4(0.60 + 9c)  D) 0.6(0.60 + 32c)  E) 0.6(0.60 + 0.35c)

Solution: For first three minutes = 50 cents   Remaining minutes = 35 -3= 
35 -3 = 32
32   charge for 32 minutes= 32c   total cost (if the call was made in daytime) = 0.50 + 32c   60% chargereducedon night calls => 40% charge   =>0.4(0.50 + 32c)   Hence, Answer is 0.4(0.50 + 0.32c)
Answer: B
In Kiran's opinion, his weight is greater than 65 kg but less than 72 kg. His brother does not agree with Kiran and he thinks that Kiran's weight is greater than 60 kg but less than 70 kg. His mother's view is that his weight cannot be greater than 68 kg. If all are them are correct in their estimation, what is the average of different probable weights of Kiran?  Select the correct option:	A) 67	B) 68	C) 69	D) 70	E) 71

Solution: Let Kiran's weight = x. Then   According to Kiran, 65 < x < 72 ----(equation 1)   According to brother, 60 < x < 70 ----(equation 2)   According to mother, x ≤ 68 ----(equation 3)   Given that equation 1,equation 2 and equation 3 are correct. By combining these equations,we can write as   65<x≤68   i.e., x = 66 or 67 or 68   67verage of different probable weights of Kiran = (66+67+68)/3= 
(66+67+68)/3 = 67
67   67nswer is 67.
Answer: A
X and Y invest Rs.21000 and Rs.17500 respectively in a business. At the end of the year, they make a profit of Rs.26400. What is the share of X in the profit?
Choose the correct choice from the following:
A) 14400	B) 26400	C) 12000	D) 12500	E) 14500

Solution: Explanation:   Ratio of the investment   =21000:17500=210:175   =42:35=6:5   Share of X in the profit   =2400 x 6/11   =2400×6=14400   14400nswer: Option 14400
Answer: A
Working together, printer A and printer B would finish the task in 24 minutes. Printer A alone would finish the task in 60 minutes. How many pages does the task contain if printer B prints 10 pages a minute more than printer A ?  Choose the correct choice from the following answers
A) 600	B) 800	C) 1000	D) 1200	E) 1500

Solution: Answer: 1200.
Answer: D
Find the roots of quadratic equation: 2x2 + 5x + 2 = 0?  Pick
A) -2, -1/2
B) 4, -1
C) 4, 1
D) -2, 5/2
E) None of these

Solution: 2x2 + 4x + x + 2 = 0   2x(x + 2) + 1(x + 2) = 0   (x + 2)(2x + 1) = 0 => x = -2, -1/2   -2, -1/2NSWER:-2, -1/2
Answer: A
The difference between a positive proper fraction and its reciprocal is 9/20. The fraction is:
Select the correct option
A) 3/5	B) 3/10	C) 4/5	D) 5/4	E) 6/4

Solution: Let the required fraction be x. Then,   1/x - x = 9/20   20x2 + 9x - 20 = 0   20x2 + 25x - 16x - 20 = 0   5x(4x + 5) -4(4x + 5) = 0   (4x + 5)(5x - 4) = 0   x = 4/5   ANSWER:4/5
Answer: C
If the mean of a data set is 75 and the standard deviation is 10, what is the range of scores that fall within one standard deviation of the mean?  Select:
A) 65, 80}
B) 65, 90}
C) 65, 70}
D) 65, 80}
E) 65, 85}

Solution: score ranges between 85 and 65, where 85 is within one Standard deviation above the mean and 65 is within one standard deviation below the mean   Answer is 65, 85}
Answer: E
What percent of 60 is 80?
Choices
A) 133 1⁄3 B) 75 C) 60 D) 33 1⁄3 E) 25

Solution: % of 60 is 80?   = 80/60 = 4/3 = 133.33%   Thus 133 1⁄3 is the correct answer.
Answer: A
A can do a piece of work in 30 days. He works at it for 5 days and then B finishes it in 20 days. In what time can A and B together it? Choose one
A) 13 1/8 days B) 13 1/3 days C) 83 1/3 days D) 13 8/3 days E) 19 1/3 days

Solution: 5/30 + 20/x = 1   x = 24   1/30 + 1/24 = 3/40   40/3 = 13 1/3 days   Answer: 13 1/3 days
Answer: B
Some man have some apples with him.He gave half of the apples and half an apple.This gets repeated for 4 time.After that he has no more apple with him.How many number of apples were there initially?  Choose the correct choice from the following answers:
A) 30 B) 31 C) 32 D) 33 E) 34

Solution: some apples=x   he gave half of an apples and half of an apple and reaming he have are x/2-1/2   It is repeated four times   2nd time x/4-1/2-1/2   3d time x/8-1/2-1/2-1/2   4th time x/16-1/2-1/2-1/2-1/2=0   x/16-2=0   x=32   ANSWER:32
Answer: C
If the cost price of 50 articles is equal to the selling price of 30 articles, then the gain or loss percent is?	Choices:  A) 22  B) 65  C) 78  D) 66.67  E) 25

Solution: Given that, cost price of 50 article is equal to selling price of 30 articles.   Let cost price of one article = Rs. 1   Selling price of 30 articles = Rs. 50   But Cost price of 30 articles = Rs. 30   Therefore, the trader made profit.\Percentage of profit = 20/30 * 100 = 66.67%   Answer:66.67
Answer: D
Pumps A, B, and C operate at their respective constant rates. Pumps A and B, operating simultaneously, can fill a certain tank in 1 hours; pumps A and C, operating simultaneously, can fill the tank in 1 hours; and pumps B and C, operating simultaneously, can fill the tank in 2 hours. How many hours does it take pumps A, B, and C, operating simultaneously, to fill the tank. Choose the correct option
A) 1/3	B) 1/2	C) 1/4	D) 1	E) 5/6

Solution: A+1/2 =1 ; A+C =1 ,1/2+C =2 ; ADD THEN 2*(A+1/2+C) = 4   A+1/2+C = 2 HRS   1/2
Answer: B
Kira's seafood restaurant gets a delivery of fresh seafood every day, 7 days per week, and her delivery company charges her dollars per delivery plus cents per item delivered. If lst week Sarah's seafood restaurant had an average of x items per day delivered, then which of the following is the total cost, in dollars, of last week's deliveries ?
Choose one.
A) 7cdx/100  B) d + 7cx/100  C) 7d + xc/100  D) 7d + 7xc/100  E) 7cdx

Solution: Answer is 7d + 7xc/100.
Answer: D
Torry has submitted 2/5 of his homework assignments, and he received an average grade of 75 for those assignments. If he wishes to receive an average grade of 120 for all his homework assignments, the average grade for Torry's remaining homework assignments must be what percent greater than the average grade for the assignments he has already submitted? Choose the correct choice:  A) 100%  B) 20%  C) 25%  D) 33 1/3%  E) 40%

Solution: 0.4*75 + 0.6x = 120   30 + 0.6x=120   0.6x = 90   x= 150   150/75= 
150/75 = 2
2   100%ns:100%
Answer: A
The average of 15 result is 60. Average of the first 10 of them is 10 and that of the last 10 is 80. Find the 8th result? Pick one: A) 35 B) 200 C) 150 D) 250 E) 300

Solution: Sum of all the 13 results = 15 * 60= 
15 * 60 = 900
900   Sum of the first 7 of them= 10 * 10= 
10 * 10 = 100
100   Sum of the last 7 of them= 10 * 80= 
10 * 80 = 800
800   So, the 8th number= 900 + 100 - 800= 
900 + 100 - 800 = 200
200.   200
Answer: B
Lilly has 10 fish and Rosy has 11 fish. In total, how many fish do they have in all?	Select the correct option.
A) 19  B) 20  C) 21  D) 22  E) 23

Solution: 10+11= 
10+11 = 21
21   The answer is 21.
Answer: C
Ten years ago, P was half of Q's age. If the ratio of their present ages is
3:4, what will be the total of their present ages?
Choices.
A) 45
B) 40
C) 35
D) 30
E) 38

Solution: Let present age P and Q be 3x 4x respectively   Ten years ago, P was half of Q's age   (3x-10) = 1/2 (4x-10)   2x = 10   x=5   Total of their present ages = 3x+4x = 7x 3 +4= 
3 +4 = 7
7x= 7 * 5= 
7 * 5 = 35
35   ANSWER 35
Answer: C
The effective annual rate of interest corresponding to a nominal rate of 12% per annum payable half-yearly is?  Choose the most appropriate option
A) 16.06%
B) 16.07%
C) 12.36%
D) 6.09%
E) 6.19%

Solution: Amount of Rs. 100 for 1 year when compounded half-yearly = [100 * (1 + 6/100)2] = Rs. 112.36 Effective rate = (112.36 - 100)= 
(112.36 - 100) = 12.36
12.36%   ANSWER:12.36%
Answer: C
The average age of husband, wife and their child 3 years ago was 26 years and that of wife and the child 5 years ago was 20 years. The present age of the husband is
Options:
A) 22 B) 40 C) 38 D) 21 E) 37

Solution: Explanation:   Sum of the present ages of husband, wife and child = (26 x 3 + 3 x 3) years = 87 years.   Sum of the present ages of wife and child (20 x 2 + 5 x 2) years = 50 years.   Husband's present age = (87 - 50)= 
(87 - 50) = 37
37 years.   Answer: 37
Answer: E
The percentage increase in the area of a rectangle, if each of its sides is increased by 20% is	Choose the correct choice from the following answers:
A) 38%  B) 40%  C) 44%  D) 48%  E) 50%

Solution: Let original length = x metres and original breadth = y metres.   Original area = (xy) m2.   New length = 120 x m = 6 x m.   100 5   New breadth = 120 y m = 6 y m.   100 5   New Area = 6 x x 6 y m2 = 36 xy m2.   5 5 25   The difference between the original area = xy and new-area 36/25 xy is   = (36/25)xy - xy   = xy(36/25 - 1)   = xy(11/25) or (11/25)xy   Increase % = 11 xy x 1 x 100 % = 44%.   25 xy   44%)
Answer: C
The average (arithmetic mean) of the even integers from 0 to 40 inclusive is how much greater than the average (arithmetic mean) of the even integers from 0 to 20 inclusive?
Pick:	A) 10	B) 20	C) 5	D) 30	E) 15

Solution: So, according to 10 mean of a set of even numbers from 0 to 40 =(0+40)/2= 
(0+40)/2 = 20
20 and mean of a set of even numbers from 0 to 20=(0+20)/2= 
(0+20)/2 = 10
10   Difference=20-10= 
20-10 = 10
10   10nswer: 10.
Answer: A
A can do a piece of work in 4 hours; B and C together can do it in 3 hours, which A and C together can do it in 2 hours. How long will B alone take to do it?
Select the correct option: A) 15 hours B) 14 hours C) 12 hours D) 74 hours E) 79 hours

Solution: A's 1 hour work = 1/4;   (B + C)'s 1 hour work = 1/3;   (A + C)'s 1 hour work = 1/2   (A + B + C)'s 1 hour work = (1/4 + 1/3) = 7/12   B's 1 hour work = (7/12 + 1/2) = 1/12   B alone will take 12 hours to do the work.   Answer:12 hours
Answer: C
A tyre has two punctures. The first puncture alone would have made the tyre flat in 9 minutes and the second alone would have done it in 4 minutes. If air leaks out at a constant rate, how long does it take both the punctures together to make it flat ?
Choose the correct choice from the following.
A) 3 1/5min	B) 2 10/13min	C) 3 3/5min	D) 3 4/5min	E) 3 min

Solution: Explanation:   Do not be confused, Take this question same as that of work done question's. Like work done by 1st puncture in 1 minute and by second in 1 minute.   Lets Solve it:   1 minute work done by both the punctures =   (1/9+1/4)=(13/36)   So both punctures will make the type flat in   (36/13)mins=2 10/13mins   Option 2 10/13min
Answer: B
A man can swim in still water at 9 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is?  Choose the correct choice
A) 1.7 B) 1.4 C) 3 D) 1.5 E) 1.9

Solution: M = 9   S = x   DS = 9+ x   US = 9 + x   9 + x = (9 - x)2   9+ x = 18 -2x   3x = 9   x = 3   Answer:3
Answer: C
If 5x^2 has two different prime factors, at most how many different prime factors does x have?  Choose one
A) 1  B) 2  C) 3  D) 4  E) 5

Solution: x cannot have more than 2 prime factors, because in this case 5x^2 would also have more than 2 prime factors.   Can x have 2 prime factors? Yes, consider x=2*5= 
2*5 = 10
10 (in this case 5x^2 still has 2 prime factors).   Answer: 2.
Answer: B
How many different ways can you select a pilot and a co pilot if you have 30 people to choose from?	Choose the most appropriate option:
A) 199	B) 200	C) 398	D) 4950	E) 870

Solution: You are not just choosing two from 30. Each of the two people chosen fills a particular slot. The first filling the pilot slot and the second filling the copilot slot is different from the first filling the copilot slot and the second filling the pilot slot.   So the answer is in a sense (30C2) x 2 = 870870
Answer: E
A big container is 30% full with water. If 27 liters of water is added, the container becomes 3/4 full. What is the capacity of the big container? Options
A) 36 liters	B) 40 liters	C) 45 liters	D) 54 liters	E) 60 liters

Solution: A big container is 30% full with water and after 27 liters of water is added, the container becomes 75% full. Hence these 27 liters account for 45% of the container, which means that the capacity of it is  27/0.45= 
 27/0.45 = 60
60 liters.   OR: if the capacity of the container is x liters then: 0.3x+27=0.75x --> x=60 liters.   Answer: 60 liters.
Answer: E
A person bought a certain quantity of rice at the rate of Rs. 150/quintal. 10% of the rice was spoiled. At what rate(per quintal) should he sell the remaining rice to earn 20% profit.
Choose the correct choice.
A) Rs. 180 B) Rs. 200 C) Rs. 210 D) Rs. 220 E) NONE

Solution: Solution: Suppose he buy 1 quintal of Rice in Rs.150.   10% is spoiled so he now have to sell of 90 kg remaining)   .But he has to make a profit of 20%,so he will sell   90kg for Rs. 180   This means his selling price is Rs. 200 per quintal.   Answer: Option Rs. 200
Answer: B
By selling an article at Rs.800, a shopkeeper makes a profit of 25%. At what price should he sell the article so as to make a loss of 30%? Choose one:
A) 448
B) 480
C) 267
D) 288
E) 276

Solution: SP = 800   Profit = 25%   CP = (SP)*[100/(100+P)]   = 800 * [100/125]   = 640   Loss 800 *  100/125= 
800 *  100/125 = 640
640   Loss= 25% = 25% of 640 = Rs.192   SP = CP - Loss = 640 - 192 = Rs.448   448nswer: 448
Answer: A
There is 2/5 chance it will rain today.
There is a probability of 1/2 I will find the love of my life today.
What is the probability I will find the love of my life in the rain today? Choose the correct choice from the following
A) 2/5	B) 3/5	C) 3/10	D) 1/5	E) 7/10

Solution: In order to find the answer we need to multiply the probabilities - 2/5*1/2=1/5   Answer:1/5
Answer: D
The speed of a boat in still water is 20 km/hr and the rate of current is 5 km/hr. The distance travelled downstream in 27 minutes is:
Choose one
A) 9.25 B) 5.25 C) 7.25 D) 6.25 E) 11.25

Solution: Explanation:   Speed downstream = (20+5)= 
(20+5) = 25
25 kmph   Distance travelled= (25*(27/60))= 
(25*(27/60)) = 45/4 = around 11.25
11.25 km.   ANSW11.25R:11.25
Answer: E
A particular library has 75 books in a special collection, all of which were in the library at the beginning of the month. These book are occasionally loaned out through an inter-library program. If, by the end of the month, 65 percent of books that were loaned out are returned and there are 61 books in the special collection at that time, how many books of the special collection were loaned out during that month?
Pick one:
A) 20  B) 30  C) 35  D) 40  E) 55

Solution: The total number of books is 75.   Let x be the number of books which were loaned out.   65% of books that were loaned out are returned.   35% of books that were loaned out are NOT returned.   Now, there are 61 books, thus the number of un-returned books is 75-61= 
75-61 = 14
14 books.   0.35x= 14   x = 40   The answer is 40.
Answer: D
Which of the following CANNOT be weighed using a balance scale and these unit weights: 1, 4, 7, and 10  Choose the correct choice from the following answers:  A) 14  B) 15  C) 17  D) 21  E) 20

Solution: A. 13 (can be weighed by keeping weights of 10 and 4)   B. 15 (can be weighed by keeping weights of 10,4 and 1 kg)   C. 17 (can be weighed by keeping weights of 10 and 7 kg)   D. 21 (can be weighed by keeping weights of 10, 7 and 4 kg)   E. 19(cannot be weighed)   20
Answer: E
The distance from City A to City B is 180 miles. While driving from City A to City B, Cara drives at a constant speed of 30 miles per hour. Dan leaves City A 60 minutes after Cara. What is the minimum constant speed in miles per hour that Dan must exceed in order to arrive in City B before Cara?	Choose the correct choice from the following choices:
A) 42
B) 44
C) 46
D) 36
E) 50

Solution: The time it takes Cara to drive to City B is 180 / 30= 
180 / 30 = 6
6 hours.   Dan needs to take less than 5 hours for the trip.   Dan needs to exceed a constant speed of  180 / 5= 
 180 / 5 = 36
36 miles per hour.   The answer is 36.
Answer: D
At a school dance, 40% of the students had a date, 70% of the remaining students arrived at the dance with a group. What percentage of the students arrived alone?  Choose the correct option.
A) 40% of the students arrived alone.  B) 10% of the students arrived alone.  C) 42% of the students arrived alone.  D) 18% of the students arrived alone.  E) None of these.

Solution: Explanation:Let total number of students be 100,Then, number of students with a date = 40.Number of students arriving with a group= 70% of 60 = 42.Total number of students arriving alone = 100 – (40 + 42) = 18.Thus, 18% of the students are arriving alone.Answer: Option 18% of the students arrived alone..
Answer: D
With both inlets open, a water tank will be filled with water in 24 minutes. The first inlet alone would fill the tank in 2 hours. If in every minutes the second inlet admits 50 cubic meters of water than the first, what is the capacity of the tank ?
Choices
A) 2,000
B) 10,500
C) 11,750
D) 12,000
E) 13,000

Solution: The work Done by Inlet A and B together in 1 min = 1/24   The work Done by Inlet A (First Inlet) in 1 min = 1/120   The work Done by Inlet B (Second Inlet) in 1 min = (1/24)- (1/120) = 1/30   DIfference of Work done by B and A = B - A = 50 Cubic meter   i.e. (1/30)- (1/120) = 50 Cubic meter   i.e. Tank = 40*50= 
40*50 = 2_000
2000 Cubic Meter   2,000nswer: option 2,000
Answer: A
By selling 8 pencils for a rupee a man loses 10%. How many for a rupee should he sell in order to gain 10%?	Choose the correct answer:
A) 6.54	B) 9.45	C) 7.34	D) 6.67	E) 5.09

Solution: 90% --- 8   110% --- ?   90/110 * 8 = 6.54   6.54nswer: 6.54
Answer: A
The credit card and a global payment processing companies have been suffering losses for some time now. A well known company recently announced its quarterly results. According to the results, the revenue fell to $48.0 billion from $69.0 billion, a year ago. By what percent did the revenue fall?
Options:
A) 20.8
B) 30.4
C) 31.8
D) 32.5
E) 33.8

Solution: $69-$48=21$   (21/69)*10069- 48= 
69- 48 = 21
21$   (21/69)*100=30.434%   ANSWER:30.4
Answer: B
If x+1/x=5 then find out the value of x^5+1/x^5=?  Choose one
A) 2515 B) 2525 C) 2535 D) 2545 E) 2555

Solution: given,(x+ 1/x) = 5   x^2 + 1/x^2 = (x+ 1/x)^2 - 2*x*1/x = 5^2 - 2 = 23 -------(1)   x^3 + 1/x^3 = (x+ 1/x)^3 - 3*x*1/x*(x+ 1/x) = 5^3 - 3*5 = 110 -------(2)   multiplying (1)& (2), we get   =>(x^2+ 1/x^2)*(x^3+ 1/x^3) = 23*110   => x^5 + 1/x + x + 1/x^5 = 2530   => x^5 + 1/x^5 + (x+ 1/x)= 2530   => x^5 + 1/x^5 + 5 = 2530   => (x^5+ 1/x^5)= 2525   ANSWER:2525
Answer: B
A basketball team scored x points per game in its first n games of the season, and in all the following games it scored an average (arithmetic mean) of y points per game. What was the average number of points per game in its first n + 4 games? Choose the correct choice from the following choices
A) x + 3y/(n + 3)	B) x + y/(n + 3)	C) (x + 3y)/(n + 3)	D) (nx + 3y)/(n + 4)	E) (3x + ny)/(n + 3)

Solution: Total points in first n games = nx   Total marks in next 3 games is 3y   So, Average marks in n + 4 games = (nx+3y)/(n+4)   Hence, correct answer will be ((nx + 3y)/(n + 4))
Answer: D
Carol and Jordan draw rectangles of equal area. If Carol's rectangle measures 15 inches by 24 inches and Jordan's rectangle is 8 inches long, how wide is Jordan's rectangle, in inches?	Choose the correct choice from the following choices
A) 30	B) 35	C) 40	D) 45	E) 50

Solution: Area of first rectangle is 15*24= 
15*24 = 360
360 hence area of second would be 8x=360x   x=45   answer is 45
Answer: D
What is the unit digit in 14^100?
Choose the most appropriate option:
A) 0  B) 5  C) 2  D) 3  E) 6

Solution: Unit digit in 14^100 = unit digit in [(14^4)^25 ]But unit digit in 14^4=6unit digit 14^100= 6Answer is 6
Answer: E
Sandy invested a certain sum of money at 12% p.a. simple interest for 'n' years. At the end of 'n' years, Sandy got back 7 times the original investment. What is the value of n?
Choose the correct choice from the following choices.
A) 30
B) 35
C) 40
D) 45
E) 50

Solution: n* 0.12 * principal + principal = 7 * principal   n * 0.12 = 6   n = 50 years   The answer is 50.
Answer: E
Prabhu purchased 30 kg of rice at the rate of 17.50 per kg and another 30 kg rice at a certain rate. He mixed the two and sold the entire quantity at the rate of 18.60 per kg and made 20 per cent overall profit. At what price per kg did he purchase the lot of another 30 kg rice?	Options.
A) 14.5  B) 12.5  C) 15.5  D) 13.5  E) None of these

Solution: Let he purchase of x/kg.   ∴ (525 + 30x) × 120⁄100 = 60 × 18.60   ⇒ x = 13.5/kg.   Answer 13.5
Answer: D
A BOWLER CAN TAKE MAX. 3WICKETS IN A OVER.IF HE BOWLS 6OVERS IN AN INNINGS, HOW MANY MAXIMUM WICKETS CAN HE TAKE?
Choose the most appropriate option: A) 8 B) 9 C) 11 D) 7 E) 10

Solution: 10 because after 10 wickets, the innings is complete.   ANSW10R:10
Answer: E
A and C can finish 100,000 piece of work in 15 days each. B can do 30% faster than A and B.Approximately how many days would it take to finish million piece of work with all three working simultaneously? Choose the correct choice from the following choices
A) 40	B) 46	C) 51	D) 42	E) 54

Solution: since B is 30% faster , thus it will finish130,000 piece of work in 15 days   in 15 days total piece of work finish by all three will be :   100,000+100,000+130,000 = 330,000   in 30 days:   330,000+330,000 = 660,000   in 45 days:   660,000+330,000 = 990,000   now only 10,000 more piece of work are required to finish , which will take 1 day   thus in all 46 days.   Ans:46
Answer: B
Find the missing in the series: 60, 54, 45, 41,___
Select the correct option:	A) 22	B) 287	C) 267	D) 2767	E) 2771

Solution: Answer:267
Answer: C
A bag contains 6 red, 5 blue and 2 green balls. If 2 ballsare picked at random, what is the probability that both are red?	Choose the correct choice.
A) 1/13  B) 2/23  C) 5/26  D) 4/27  E) 3/23

Solution: P(Both are red),   =65/262135/262=65/262135/262   =5/26   5/26
Answer: C
What is the total number of positive integers that are less than 500 and that have no positive factor in common with 500 other than 1? Choices.
A) 50
B) 100
C) 200
D) 300
E) 400

Solution: Since 500=2^2*5^3 then a number can not have 2 and/or 5 as a factor.   The odd numbers do not have 2 as a factor and there are 250 odd numbers from 1 to 500.   We then need to eliminate the 50 numbers that end with 5, that is 5, 15, 25,...,495.   There are a total of 250 - 50= 
250 - 50 = 200
200 such numbers between 1 and 500.   The answer is 200.
Answer: C
Two women started running simultaneously around a circular track of length 1800 m from the same point at speeds of 10 km/hr and 20 km/hr. When will they meet for the first time any where on the track if they are moving in opposite directions?
Choose the correct choice from the following answers
A) 72
B) 74
C) 76
D) 78
E) 80

Solution: Time taken to meet for the first time anywhere on the track   = length of the track / relative speed   = 1800 / (30 + 60)5/18 = 1800* 18 / 90 * 5 = 72 seconds.   72nswer:72
Answer: A
Three people have $28, $72, and $98, respectively. If they pool their money then redistribute it among them, what is the maximum value for the median amount of money? Choose the correct choice from the following.
A) $72 B) $85 C) $99 D) $101 E) $202

Solution: Solution -   Total money distributed is $198. In order to maximize median, one person has to accept $0 and remaining two people share $99 each. Hence median is $99.   ANS $99
Answer: C
Find the length of the altitude of an equilateral triangle of side 3√3 cm.	Choose the correct choice from the following options
A) 4.5cm
B) 7.2cm
C) 4.3cm
D) 5.6cm
E) 5.7cm

Solution: Area of the triangle = (√3/4) x (3√3)2 = 27√3. Let the height be h.   Then, (1/2) x 3√3 x h = (27√3/4) X(2/√3) = 4.5 cm.   4.5cmns: 4.5cm
Answer: A