MU-NLPC/Calc-aqua_rat huggingface dataset:
Heinz produces tomato puree by boiling tomato juice. The tomato puree has only 20% water while the tomato juice has 90% water. How many liters of tomato puree will be obtained from 50 litres of tomato juice?  Choose the correct choice from the following answers:
A) 2.8 liters.  B) 2.5 liters.  C) 8.5 liters.  D) 6.25 liters.  E) 2.1 liters.

Solution: Answer:   Explanation:   In each of the solutions, there is a pure tomato component and some water. So while boiling, water evaporates but tomato not. So we equate tomato part in the both equations.   â‡’â‡’ 10%(50) = 80%(x)   â‡’â‡’ x = 6.25 liters.   Answer:6.25 liters.
Answer: D
Out of 15 students in a class, 8 are wearing blue shirts, 4 are wearing green shirts, and 3 are wearing red shirts. Four students are to be selected at random. What is the probability that at least one is wearing a green shirt?  Choose the most appropriate option:
A) 39/61	B) 49/71	C) 59/81	D) 69/91	E) 79/101

Solution: Total possible ways to choose 4 students out of 15 = 15C4 = 1365   The number of ways to choose 4 students with no green shirts = 11C4 = 330   P(no green shirts) = 330/1365 = 22/91   P(at least 1 green shirt) = 1 - 22/91 = 69/91   The answer is 69/91.
Answer: D
A baseball team played 10 games and won 5. What is the ratio of the number of games played to the number of losses? Pick one
A) 5:1 B) 1:1 C) 20:4 D) 10:3 E) 2:1

Solution: The number of games played is 10. The number of games won is 5, so  10 - 5= 
 10 - 5 = 5
5= number of game losses.   Answer = !0:5 = 2:1   Answer is 2:1
Answer: E
A computer can perform z calculations in s seconds. How many minutes will it take the computer to perform k calculations?
Choose the correct answer:
A) ks/60z  B) ks/z  C) 60ks/z  D) 60z/ks  E) k/60zs

Solution: As 'thick' as this question might look, it's actually a fairly straight-forward Rate question and can be solved by TESTing VALUES.   We're told that a computer can perform z calculations in S seconds.   Let's TEST....   z = 2   S = 3   2 calculations every 3 seconds =   40 calculations every 1 minute   We're asked how many MINUTES it will take to perform K calculations.   Since we already know that the computer can perform 40 calculations in 1 minute, let's TEST...   K = 80   So we're looking for an answer that = 2 when z = 2, S = 3 and K = 80   Answer A:KS/60z = (80)(3)/(60)(2) = 2 This IS a match   Answer B: KS/z = (80)(3)/2 = 120 This is NOT a match   Answer C: 60KS/z = 60(80)(3)/2 = 7200 This is NOT a match   Answer D: 60z/KS = 60(2)/(80)(3) = 1/2 This is NOT a match   Answer E: K/60zS = 80/(60)(2)(3) = a fraction. This is NOT a match   ks/60z
Answer: A
In an election between the two candidates, the candidates who gets 70% of votes polled is winned by 360 vote’s majority. What is the total number of votes polled? Choose the correct choice from the following options:
A) 750
B) 700
C) 900
D) 850
E) None of these

Solution: Explanation:   Note: majority (40 %) = difference in votes polled to win (70 %) & defeated candidates (30 %)   40 % = 70 % - 30 %   40% -----> 360 (40*9 = 360)   100% -----> 900 (100*9 = 900)   Answer: Option 900
Answer: C
Mariah has decided to hire three workers. To determine whom she will hire, she has selected a group of 12 candidates. She plans to have one working interview with 3 of the 12 candidates every day to see how well they work together. How many days will it take her to have working interviews with all the different combinations of job candidates?  Choose the correct answer
A) 720
B) 120
C) 300
D) 30
E) 333

Solution: 300.   Answer 300
Answer: C
David covered a distance of 50 miles on his first trip. On a later trip he traveled 50 miles while going three times as fast. His new time compared with the old time was:	Select the correct option:
A) twice as much
B) three times as much
C) the same
D) half as much
E) a third as much

Solution: Let t be the time of the first trip.   On the later trip, David can travel 150 miles in time t.   The trip of 50 miles takes t/3.   The answer is a third as much.
Answer: E
A room is 25 meters long, 20 meters wide 10 meters in height. The longest possible rod which can be placed in the room is Choices:
A) 30.54 meters
B) 32.54 meters
C) 34.54 meters
D) 33.54 meters
E) 35.54 meters

Solution: Square root of 25^2+20^2+10^2...(Diognal) which is square root of 1125 that lies 33<√1125<34. Hence the answer should be 33.54 meters
Answer: D
6 people meet for a meeting. Each person shakes hands once with each other person present. How many handshakes take place?  Choices:  A) 30  B) 21  C) 18  D) 15  E) 10

Solution: Let's look at the logic.   Every person shakes hand with other '5'. So, 6 people shake hands with 6X5= 30 people   But in this 30 we have counted two times the total handshakes (e shakes hand with f and f shakes hand with e)   So just divide 30/2= 
30/2 = 15
15 total handshakes   Answer is 15
Answer: D
A train passes a station platform in 34 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?
Pick:
A) 276 m  B) 279 m  C) 210 m  D) 207 m  E) 202 m

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 / 34= 15   x + 300 = 510   x =210 m.   Answer: 210 m
Answer: C
Sam invested Rs. 12000 @ 10% per annum for one year. If the interest is compounded half-yearly, then the amount received by Sam at the end of the year will be? Choose the correct choice:
A) 13230.0
B) 12300.02
C) 16537.5
D) 15000.0
E) 16537.11

Solution: P = Rs. 12000 ; R = 10% p.a. = 5% per half-year; T = 1 year   = 2 half-year   13230.0mount = [12000 * (1 + 5/100)2]   = (12000 * 21/20 * 21/20)   = Rs.13230.00   13230.0nswer:13230.0
Answer: A
Half the people on a bus get off at each stop after the first, and no one gets on after the first stop. If only one person gets off at stop number 6, how many people got on at the first stop? Select:
A) 128 B) 64 C) 32 D) 16 E) 8

Solution: 7 - > 1   6 - > 2   5 - > 4   4 - > 8   3 - > 16   2 - > 32   1 - > 64   because people get off after the first stop   => the formula will be : 2^(n-1) where n is the stop number   in this case n =6   => 2^(6-1) = 2^5 = 32   => answer is 32
Answer: C
Raman mixed 48 kg of butter at Rs. 150 per kg with 36 kg butter at the rate of Rs. 125 per kg. At what price per kg should he sell the mixture to make a profit of 40% in the transaction?
Choose the correct choice from the following answers.
A) 129	B) 287	C) 195	D) 188	E) 112

Solution: Explanation:   CP per kg of mixture = [48(150) + 36(125)]/(48 + 36) = Rs. 139.28   SP = CP[(100 + profit%)/100]   = 139.28 * [(100 + 40)/100] = Rs. 195   Answer:195
Answer: C
The profit earned by selling an article for Rs 900 is double the loss incurred when the same article is sold for Rs.490. At what price should the article be sold to make 25% profit? Choose the correct choice from the following choices
A) 715  B) 469  C) 400  D) 750  E) 850

Solution: Explanation:   Let C.P be Rs. x   900 - x = 2(x - 450)   => x = Rs.600   C.P = 600 gain required is 25%   S.P = [(100 + 25) × 600]/100   = Rs.750   Answer: 750
Answer: D
6 men and 8 women can complete a work in 10 days. 26 men and 48 women can finish the same work in 2 days. 15 men and 20 women can do the same work in - days.  Choose the correct choice:
A) 4 days	B) 6 days	C) 8 days	D) 2 days	E) 10 days

Solution: Let work done by 1 man in 1 day = m and work done by 1 woman in 1 day = b   Work done by 6 men and 8 women in 1 day = 1/10   => 6m + 8b = 1/10   => 60m + 80b = 1 --- (1)   Work done by 26 men and 48 women in 1 day = 1/2   => 26m + 48b = ½   => 52m + 96b = 1--- (2)   Solving equation 1 and equation 2. We get m = 1/100 and b = 1/200   Work done by 15 men and 20 women in 1 day   = 15/100 + 20/200 =1/4   => Time taken by 15 men and 20 women in doing the work = 4 days   Option 4 days
Answer: A
Read the following three equations:
5 ~ 4 ~ 3 ~ 9 = 4215
6 ~ 9 ~ 2 ~ 6 = 3816
4 ~ 7 ~ 3 ~ 3 = 1122
Now based on the rule that has been used, solve the following equation:
3 ~ 2 ~ 7 ~ 4 = ____	Choose the correct choice from the following answers
A) 1412
B) 2910
C) 2940
D) 3749
E) 4470

Solution: 1412   1412   1412   The rule that is being followed here is   P ~ Q ~ R ~ S = [first digit of (P * S)] [last digit of (Q * R)] [first digit of (Q * R)] [last digit of (P * S)]   Using the same rule in the incomplete equation,   3 ~ 2 ~ 7 ~ 4 = [first digit of (3 * 4)] [last digit of (2 * 7)] [first digit of (2 * 7)] [last digit of (3 * 4)]   = 1412   Thus 1412 is the missing number.
Answer: A
During a certain season, a team won 65 percent of its first 100 games and 50 percent of its remaining games. If the team won 70 percent of its games for the entire season, what was the total number of games that the team played? Answers:
A) 80	B) 75	C) 56	D) 50	E) 105

Solution: We are first given that a team won 65 percent of its first 100 games. This means the team won 0.65 x 100 = 65 games out of its first 100 games.   We are next given that the team won 50 percent of its remaining games. If we use variable T to represent the total number of games in the season, then we can say T – 100 equals the number of remaining games in the season. Thus we can say:   0.5(T – 100) = number of wins for remaining games   0.5T – 50 = number of wins for remaining games   Lastly, we are given that team won 70 percent of all games played in the season. That is, they won 0.7T games in the entire season. With this we can set up the equation:   Number of first 100 games won + Number of games won for remaining games = Total Number of games won in the entire season   65 + 0.5T – 50 = 0.7T   15 = 0.2T   150 = 2T   75 = T   Answer is 75.
Answer: B
CMM, EOO, GQQ, _____, KUU Choose the correct option.
A) MSQ	B) IPS	C) IIS	D) ISS	E) POL

Solution: The first letters are in alphabetical order with a letter skipped in between each segment: C, E, G, I, K. The second and third letters are repeated; they are also in order with a skipped letter: M, O, Q, S, U.   ANSWER:ISS
Answer: D
At a certain diner, Joe ordered 3 doughnuts and a cup of coffee and was charged $ 2.25. Stella ordered 2 doughnuts and a cup of coffee and was charged $ 1.50. What is the price of 2 doughnuts?	Options:	A) $ 0.55	B) $ 1.00	C) $ 1.10	D) $ 1.30	E) $ 1.50

Solution: 3D + C = 2.25......(1)   2D + C = 1.5........(2)   (1) - (2) --> D = 0.75 --> 2D = 1.5   Answer: $ 1.50
Answer: E
Six children — A, B, C, D, E and F — are going to sit in six chairs in a row. The children C & F have to sit next to each other, and the others can sit in any order in any remaining chairs. How many possible configurations are there for the children?	Choose the correct option:	A) 240	B) 720	C) 1440	D) 4320	E) 4800

Solution: for such questions , we can treat both as one then total person=5..   these 5 can be arranged in 5! ways.. but within these 5 , one consists of two people who can be arranged in 2 ways CF or FC.. so ans =5!*2=240   ans 240
Answer: A
The value of x + x(x*x*(in x)) when x = 2 is:
Choose the correct choice:	A) 10	B) 16	C) 18	D) 36	E) 64

Solution: x + x(xx)   Put the value of x = 2 in the above expression we get,   2 + 2(22)   = 2 + 2(2 × 2)   = 2 + 2(4)   = 2 + 8= 
2 + 8 = 10
10   Correct 10nswer:10)10
Answer: A
In how many different number of ways 4 boys and 2 girls can sit on a bench?  Choose the correct choice from the following answers:
A) 720
B) 740
C) 760
D) 800
E) 810

Solution: npn = n!   6p6 = 6 × 5 × 4 × 3 × 2 × 1 = 720   720)
Answer: A
A cylinder of height h is 7/8 of water. When all of the water is poured into an empty cylinder whose radius is 25 percent larger than that of the original cylinder, the new cylinder is 3/5 full. The height of the new cylinder is what percent of h? Choose the correct choice from the following.
A) 25%  B) 50%  C) 69%  D) 80%  E) 100%

Solution: Basically we can disregard the radius is 25% information, as we are only asked about the height of the original and the new cylinder.   This is becausethe new cylinder is 3/5 fullmeans the same as that it's height is 3/5.   Original cylinder 7/8   New cylinder 3/5   So 3/5/7/8 = 3/5*8/7 = 0.69 or 69%.   Answer 69%
Answer: C
If the LCM and HCF of 4 and another number is 36 and 2 respectively. Find the other number ? Pick one:
A) 18 B) 16 C) 14 D) 13 E) 15

Solution: HCF x LCM = Product of Numbers   2 x 36 = 4 x the other number   other number = (2 x 36) / 4   other number = 18   18NSWER : 18
Answer: A
How many different committees can be formed from a group of two women and four men if three people are on the committee and at least one member must be a woman?  Choose the correct choice from the following answers:
A) 6
B) 8
C) 10
D) 12
E) 16

Solution: 2 Women and 4 Men. Three people needed   It is always better to subtract the total from none in case of at least one problems.   Total ways = 6C3 = 20   Total ways without any women = 4C3 = 4   Hence ways in which at least one women will be present = 20 - 4= 
20 - 4 = 16
16   Correct option: 16
Answer: E
The surface area of a sphere is 4πR2, where R is the radius of the sphere. If the area of the base of a hemisphere is 3, what is the surface area R of that hemisphere?  Choose the correct choice
A) 6/π B) 9/π C) 6 D) 9 E) 12

Solution: Given Area of the base of a hemisphere is 3 = PI * R^2   Thus R = Sqrt ( 3 / PI ) .   Surface area of whole sphere = 4 *PI*R^2 .   = 4 * PI * 3 / PI   = 12 .   Since the hemisphere is half of a sphere the Surface area of the hemisphere = 12 / 2= 
12 / 2 = 6
6 ( curved part , not including the flat rounded base ) .   But the total surface area= 6 + Area of the base of a hemisphere .   = 6 + 3= 
6 + 3 = 9
9.   Answer is 9 !!
Answer: D
If 6log(4*5^2) = x, find x	Choose one.
A) 10  B) 11  C) 7  D) 12  E) 9

Solution: 6(log2^2*5^2)=x   6log(5*2)^2=x   6*2log(5*2)=x   12log10=x   log10 base 10=1   so   12*1=x   x=12   ANSWER:12
Answer: D
The edges of a cuboid are 2 cm, 5 cm and 3 cm. Find the volume of the cuboid?
Select the correct option
A) 20 B) 60 C) 80 D) 30 E) 45

Solution: 2*5*3= 
2*5*3 = 30
30   Answer: 30
Answer: D
In an examination, a pupil's average marks were 63 per paper. If he had obtained 20 more marks for his Geography paper and 2 more marks for his history paper, his average per paper would have been 65. How many papers were there in the examination?  Choose the correct choice from the following answers
A) 8  B) 9  C) 10  D) 11  E) 12

Solution: x(total marks)/y( no . of subjects)= 63;   x+20+2/y= 65;x+22/y=65   on solving :   y=11   ANSWER:11
Answer: D
In what ratio must water be mixed with milk costing Rs.12 per litre to obtain a mixture worth of Rs.8 per litre? Choose the correct choice
A) 1 : 2
B) 2 : 1
C) 4 : 3
D) 5 : 3
E) None

Solution: Ratio of water to milk = 4 : 8 = 1 : 2   1 : 2nswer 1 : 2
Answer: A
Two numbers are less than third number by 60% and 74% respectively. How much percent is the second number less than by the first ? Pick
A) 18% B) 29% C) 35% D) 41% E) None of these

Solution: Explanation :   Let the third number is x.   then first number = (100-60)= 
(100-60) = 40
40% of x= 4x/10   Second number is (26x/100)   Difference = 4x/10 - 26x/100 = 14x/10   So required percentage is, difference is what percent of first number   => (14x/100 * 10/4x * 100 )% = 35%   Answer : 35%(14 /100 * 10/4  * 100 )= 
(14 /100 * 10/4  * 100 ) = 35
35%   Answer : 35%
Answer: C
In how many ways the letters of the word LOOC be arranged?  Pick:
A) 8 B) 9 C) 12 D) 14 E) 17

Solution: In this four letters means 4! = 24 ways   But 'O' is repeated two times.   And thus we divide the final ways by 2. I.e. there are only  24/2= 
 24/2 = 12
12 ways of arranging the letters of this word.   LOOK, LOKO, LKOO, KOOL, KOLO, KLOO, OOLK, OOKL, OLOK, OKOL, OLKO, OKLO= 12 Ways   12
Answer: C
A and B’s salaries together amount to Rs. 2,000. A spends 95% of his salary and B spends 85% of his. If now their savings are the same, what is A’s salary?
Answers:
A) 338
B) 286
C) 266
D) 500
E) 128

Solution: (5/100) A = (15/100) B   A = 3B   A + B = 2000   4B = 2000 => B = 500   A = 1500   Answer: 500
Answer: D
A sum of Rs. 2665 is lent into two parts so that the interest on the first part for 8 years at 3% per annum may be equal to the interest on the second part for 3 years at 5% per annum. Find the second sum?  Choose the most appropriate option
A) 2888
B) 1640
C) 2782
D) 833
E) 2772

Solution: (x*8*3)/100 = ((2665 - x)*3*5)/100   24x/100 = 39975/100 - 15x/100   39x = 39975 => x = 1025   Second sum = 2665 – 1025 = 1640.Answer: 1640
Answer: B
What will be the cost of building to decorate which area equal to 225 sq ft, if the price per foot of building is Rs. 5?  Select the correct option
A) 300 B) 150 C) 600 D) 1200 E) 800

Solution: Let the side of the square plot be a ft.   a2 = 225 => a = 15   Length of the fence = Perimeter of the plot = 4a = 60 ft.   Cost of building the fence = 60 * 5   = Rs.300.   300nswer: 300
Answer: A
A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 sec. The speed of the train is?
Choose the correct choice from the following answers
A) 50 km/hr
B) 24 km/hr
C) 8 km/hr
D) 5 km/hr
E) 16 km/hr

Solution: Explanation:   Speed of the train relative to man = 125/10 = 25/2 m/sec.   = 25/2 * 18/5= 
25/2 * 18/5 = 45
45 km/hr   Let the speed of the train be x km/hr. Then, relative speed= (x - 5) km/hr.   x - 5 = 45 => x = 50 km/hr.   50 km/hrnswer: 50 km/hr
Answer: A
Look at this series: 375000,75000,25000, ... What number should come next?
Choose the correct answer:
A) 17
B) 10
C) 15
D) 5000
E) 8

Solution: 5000   This is a simple division series. Each number is divided by 5.   ANSWER 5000
Answer: D
$378 is divided among A, B, and C so that A receives half as much as B, and B receives half as much as C. How much money is C's share? Choose the correct choice from the following answers:	A) $200	B) $208	C) $216	D) $224	E) $232

Solution: Let the shares for A, B, and C be x, 2x, and 4x respectively.   7x = 378   x = 54   4x = 216   The answer is $216.
Answer: C
If on an item a company gives 25% discount and 25% profit it makes. if they now gives 10% discount then the profit %age made by the company will be... Pick
A) 40
B) 55
C) 35
D) 30
E) 50

Solution: Let the Marked Price of the item is x and the Cost Price be y.   For 25% discount the Selling price is 0.75x.   (0.75x-y)/y=0.25 which gives y=0.6x   next if the SP is 0.9x then   gain%=(0.9x-y)/y * 100 = (0.9x-0.6x)/0.6x * 100=50%   hence,profit% (0.9 -0.6 )/0.6  * 100= 
(0.9 -0.6 )/0.6  * 100 = 50
50%   hence,profit%= 50%.   ANSW50R:50
Answer: E
An automobile financier claims to be lending money at simple interest, but he includes the interest every six months for calculating the principal. If he is charging an interest of 10%, the effective rate of interest becomes :	Select the correct option.
A) 10%  B) 10.25%  C) 10.5%  D) None of these  E) Cannot be determined

Solution: Let the sum be Rs 100. Then,   S.I. for first 6 months = (100×10×1/100×2) = 5   S.I. for last 6 months = (105×10×1/100×2) = 5.25   So, amount at the end of 1 year = (100 + 5 + 5.25) = 110.25.   ∴ Effective rate = (110.25 – 100) = 10.25%.   Answer 10.25%
Answer: B
A number is mistakenly divided by 5 instead of being multiplied by 5. Find the percentage change in the result due t this mistake.  Select the correct option:
A) 96% B) 95% C) 2400% D) 200% E) 400%

Solution: lets take a number 20   20/5= 
20/5 = 4
4   20*5= 
20*5 = 100
100   diff= 100 - 4= 
100 - 4 = 96
96 %   96%NSWER:96%
Answer: A
Q is the set of all positive integers x such that x^2 is a multiple of both 27 and 375. Which of the following integers must be a divisor of every integer x in Q?
I. 9
II. 15
III. 27  Select:	A) I only	B) II only	C) I and II only	D) I and III only	E) I, II, and III

Solution: Ans: C   Q->{x} where x^2 is a multiple of both 27 and 375 means 3^3 and (5^3)*3   means x must contain 3^2 and 5^2   so with these conditions we know that 9=3^2 and 15=3*5 both have required factors for the divisibility of lowest int for x which is 9*25   but 27 is not a divisor because it can't divide 9*25 fully.   so Ans : I and II only
Answer: C
In how many different ways can 3 girls and 3 boys be seated at a rectangular table that has 3 chairs on one side and 3 stools on the other side, if two girls or two boys can never sit side by side?	Select the correct option
A) 24 B) 36 C) 72 D) 84 E) 96

Solution: The prompt gives us the specific restriction that a boy can't sit next to another boy and a girl can't sit next to another girl. Since there are chairs on one side of the table and stools on the other side of the table, we have to account for 2 possible seating arrangements:   BGB   GBG   and   GBG   BGB   From here, we can use a simple permutation to get to the answer:   Moving from left-to-right....   For the firstspot, there are 3 different boys to choose from   For the secondspot, there are 3 different girls to choose from   For the thirdspot, there then 2 different boys to choose from   For the fourthspot, there are then 2 different girls to choose form   For the fifth and sixthspots, we have the 1 boy and 1 girl that are left   (3)(3)(2)(2)(1)(1) = 36 possible seating arrangements for each of the two options.   (36)(2) = 72   72
Answer: C
The average height of 35 boys in a class was calculated as 181cm. It has later found that the height of one of the boys in the class was wrongly written as 166 cm whereas his actual height was 106 cm. Find the actual average height of the boys in the class (Round off your answer to two decimal places?	Choose the correct choice from the following answers:
A) 187.89 cm B) 179.29 cm C) 123.98 cm D) 149.98 cm E) 146.89 cm

Solution: Calculated average height of 35 boys = 181 cm.   Wrong total height of 35 boys = 181 * 35 cm. This was as a result of an actual height of 106 cm being wrongly written as 166 cm. Correct total height of 35 boys = 181 cm - (166 cm - 106 cm)/35   = 181 cm - (166 cm - 106 cm)/35 = 181 cm - 60 /35 cm   = 181 cm - 1.71 cm = 179.29 cm.   Answer: 179.29 cm
Answer: B
If selling price is doubled, the profit triples. Find the profit percent: Choose the most appropriate option:
A) 200%	B) 500%	C) 100%	D) 450%	E) 800%

Solution: C   C.P. be Rs. x and S.P. be Rx. y.   Then, 3(y - x) = (2y - x) => y = 2x   Profit = (y - x) = Rs. (2x - x) = Rs. x   Profit % = x/x * 100 = 100%.
Answer: C
Ayesha's father was 34 years of age when she was born while her mother was 28 years old when her brother four years younger to her was born. What is the difference between the ages of her parents?
Choose the correct answer.
A) 16 B) 14 C) 15 D) 10 E) 12

Solution: Mother's age when Ayesha's brother was born = 28 years.   Father's age when Ayesha's brother was born = (34 + 4)= 
(34 + 4) = 38
38 years.   Required difference= (38 - 28)= 
(38 - 28) = 10
10 years.   Answer:10
Answer: D
Shane is playing a board game. For his first turn he moved ahead 3 spaces, for the second, 5
spaces and for the third, 1 space. For his next turn he had to go back 6 spaces. After that he got
a card that said he could move two times the biggest forward move he had done so far. Now how
many spaces from the beginning is Shane’s game piece?	Select: A) 3 B) 13 C) 23 D) 33 E) 43

Solution: You may want to draw this one.   biggest move is 5, so two times   biggest move is 10.   3 + 5 + 1= 
3 + 5 + 1 = 9
9   9 - 6= 
9 - 6 = 3
3   3 + 10= 
3 + 10 = 13
13, so he is 13 spaces   from the beginning.   correct answer 13
Answer: B
Find the greatest number which leaves the same remainder when it divides 25, 62 and 105. Pick one:
A) 1 B) 8 C) 12 D) 16 E) None of these

Solution: 105 - 62= 
105 - 62 = 43
43   62 - 25= 
62 - 25 = 37
37   105 - 25= 
105 - 25 = 80
80   The H.C.F of 37, 43 and 80 is 1.   1NSWER:1
Answer: A
Water is leaking out from a cylinder container at the rate of 0.31 m^3 per minute. After 10 minutes, the water level decreases 9 meters. What is value of the radius in meters?  Select the correct option: A) 1/2 B) 1/3 C) 1.5 D) 3 E) 6

Solution: 10*0.31= 
10*0.31 = 3.1
3.1= pi*R^2*h   R^2 = 3.1 / (pi*9) which is about 1/9   R = 1/3   The answer is 1/3.
Answer: B