MU-NLPC/Calc-aqua_rat huggingface dataset:
A luxury liner, Queen Marry II, is transporting several cats as well as the crew (sailors, a cook, and one-legged captain) to a nearby port. Altogether, these passengers have 14 heads and 41 legs. How many cats does the ship host?	Answers:
A) 5 B) 6 C) 7 D) 8 E) 9

Solution: sa's +co +ca +cats = 14. sa's + 1 +1 +cats =14 or sa's +cats =12.   sa's(2) +2 +1 +cats*4 =41 sa's*2 +cats*4 = 38 or sa's +cats*2 =19 or 12-cats +cat*2 =19   then cats =7   7
Answer: C
Two pipes A and B can fill a tank in 4 and 5 hours respectively. If they are turned up alternately for one hour each, the time taken to fill the tank is?  Pick
A) 4 hrs 54 min B) 4 hrs 24 min C) 4 hrs 14 min D) 4 hrs 34 min E) 4 hrs 04 min

Solution: 1/4 + 1/5 = 9/20   20/9 = 2 2/9   9/20 * 2 = 9/10 ---- 4 hours   WR = 1 - 9/10 = 1/10   1 h ---- 1/4   ? ----- 1/10   2/5 * 60= 
2/5 * 60 = 24
24= 4 hrs 24 min   Answer:4 hrs 24 min
Answer: B
What is the lowest possible common multiple of 2 distinct integers, each greater than 140?	Answers
A) 141
B) 142
C) 282
D) 141*141
E) 141*142

Solution: The least common multiple of two numbers greater than 140 is 2(141) = 282, where the two distinct integers are 141 and 282.   The answer is 282.
Answer: C
if i earn a profit 50$ in a day and I have 9 employees . After keeping 10 percent profit for me, and distribute remianing money equally among my employees then how much each employee would get? Choose the correct choice from the following
A) $3 B) $7 C) $1 D) $5 E) $9

Solution: Since I earned $50 sp 10 percent would be 5$ and 45$ would remain. $5ividing 45 by 9, each employee would get 5$ each and hince option $5 is correct.
Answer: D
A box contains six bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that atleast one bulb is good. Choose the correct choice from the following options:
A) 125/167
B) 14/15
C) 125/126
D) 125/186
E) 125/128

Solution: Required probability   = 1 - 1/15   = 14/15   Answer: 14/15
Answer: B
One day a car rental agency rented 3/4 of its cars, including 3/5 of its cars with CD players. If 3/5 of its cars have CD players, what percent of the cars that were not rented had CD players?  Answers
A) 29/30 B) 24/25 C) 19/20 D) 14/15 E) 9/10

Solution: The cars with CD players which were not rented is (2/5)(3/5) = 6/25 of all the cars.   The cars which were not rented is 1/4 of all the cars.   The percent of non-rented cars which had CD players is (6/25) / (1/4) = 24/25   The answer is 24/25.
Answer: B
In a certain sequence, the first term is 3, and each successive term is 1 more than the reciprocal of the term that immediately precedes it. What is the fifth term in this sequence?  Choose the correct choice from the following answers
A) 13/8	B) 21/13	C) 8/5	D) 5/8	E) 18/11

Solution: let five terms in the sequence be a,b,c,d,e   a=3   b= 1+1/3=4/3   c=1+3/4= 7/4   d= 1+4/7 = 11/7   e= 1+7/11 = 18/11   hence answer should be 18/11.
Answer: E
A sock drawer contains 6 socks, each one a different solid color. The colors of the socks are red, orange, yellow, green, indigo, and violet. If a person reaches into the drawer and pulls out two socks, how many different color combinations are possible in the selected pair of socks?  Choose one
A) 12
B) 15
C) 21
D) 36
E) 42

Solution: Since the order in which we select the socks does not matter, we can use combinations.   We can select 2 socks from 6 socks in 6C2 ways.   6C2 = 15   Answer : 15
Answer: B
Mrs. Napier has 23 stickers to give to 9 students for a reward. How many
stickers will each student get? Will there be any stickers left over? Choose the correct choice from the following answers
A) 2-5
B) 2-4
C) 2-6
D) 2-3
E) 2-8

Solution: 23/9 = 2 R 5 Mrs. Napier will give each student 2 stickers and there   will be 5 left over.   correct answer 2-5
Answer: A
A rectangular garden is 12m by 5m, what is its area? Answers: A) 12 square meters B) 5 square meters C) 44 square meters D) 60 square meters E) 22 square meters

Solution: Area of a Rectangle: A = w × h   60 square meters) 60 square meters
Answer: D
How many ways are there to award a gold, silver and bronze medal to 11 contending teams?
Choose the correct choice from the following answers.
A) 11 x 10 × 9	B) 10!/(3!7!)	C) 10!/3!	D) 360	E) 300

Solution: we clearly know that there can be only one winning team which deserves the gold medal. we can do the selection in 11 ways   if gold medal is given to 1 of the teams then only possible 10 teams can be considered for silver medal. we can do selection in 10 ways   similarly if gold and silver medals are awarded then only remaining 9 teams can be considered for a bronze medal. we can do the selection in 9 ways   Total number of ways to select the 3 possible medal winners = 11*10 * 9   Correct answer - 11 x 10 × 9
Answer: A
If the true discount on s sum due 2 years hence at 14% per annum be Rs. 140, the sum due is:  Choose the correct choice from the following answers
A) s. 768	B) s. 640	C) s. 1960	D) s. 2400	E) s. 2800

Solution: td=pw*r*t/100 so 140=pw*14*2/100 so pw=500   sum=pw+td..   sum=500+140= 
500+140 = 640
640   ANSWER:s. 640
Answer: B
Souju's age is 131% of what it was 10 years ago, but 80 2/3% of what it will be after 10 years. What is her present age? Select the correct option:
A) 46 years B) 27 years C) 36 years D) 42 years E) 54 years

Solution: Let the age before 10 years =x. Then,   131x/100=x+10   â‡’131x=100x+1000   â‡’x=1000/31=32   Present age =x+10=32+10= 
32+10 = 42
42   ANSWER:42 years
Answer: D
By selling 175 apples, a shopkeeper gains the price of 25 apples. His gain per cent is  Choose the correct choice from the following options: A) 18.66% B) 17.66% C) 16.66% D) 15.66% E) 14.66%

Solution: Suppose S.P of 175 apples = Rs 175   Therefore, Gain = Rs 25 => 16.66%.P = Rs 150   Gain % = 25/150 x 100 = 16.66%   Gain = 16.66%   ANSWER:16.66%
Answer: C
Exactly 5% of the reporters for a certain wire service cover local politics in Country X. If 30% of the reporters who cover politics for the wire service do not cover local politics in Country X, what percent of the reporters for the wire service do not cover politics?	Pick one
A) 20%	B) 42%	C) 44%	D) 92%	E) 90%

Solution: You are correct. People who cover local politics are a subset of people who cover politics.   30% of reporters who cover politics do not cover local politics so 70% DO cover local politics.   Reporters covering local politics= 70% of reporters covering politics= 5% of all reporters   Reporters covering politics/All Reporters = 5/70 = 1/14   Reporters not covering politics/All Reporters = 13/14 = 92%=92%
Answer: D
If k is an integer and 2 < k < 7, for how many different values of k is there a triangle with sides of lengths 3, 6, and k?	Choose the correct answer:
A) 0	B) 1	C) 2	D) 3	E) 4

Solution: (6-3) < k < (6+3)   3 < k < 9   Thus k = 4, 5, 6, 7, 8   Since 2 < k < 7, then k can be 4, 5, or 6.   The answer is 3.
Answer: D
Worker A takes 8 hours to do a job. Worker B takes 10 hours to do the same job. How long it take both A & B, working together but independently, to do the same job? Choose the most appropriate option.
A) 40 days  B) 40/9 days  C) 39/9 days  D) 30/9 days  E) 60/9 days

Solution: B   40/9 days   A's one hour work = 1/8.   B's one hour work = 1/10.   (A+B)'s one hour work = 1/8+1/10 = 9/40.   40/9 daysoth A & 40/9 days can finish the work in 40/9 days
Answer: B
A grocer has a sale of Rs. 4435, Rs. 4927, Rs. 4855, Rs. 5230 and Rs. 4562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 4500?
Choose the correct choice: A) s. 1991 B) s. 2991 C) s. 3991 D) s. 4991 E) s. 5991

Solution: Explanation:   Total sale for 5 months = Rs. (4435 + 4927 + 4855 + 5230 + 4562) = Rs. 24009.   Required sale = Rs. [ (4500 x 6) â€“ 24009 ]   = Rs. (27000 â€“ 24009)   = Rs. 2991.   Answer s. 2991
Answer: B
A straight line in the xy-plane has a slope of 2 and a y-intercept of 2. On this line, what is the x-coordinate of the point whose y-coordinate is 480 ?
Choose the correct choice from the following answers:
A) 249 B) 498 C) 239 D) 823 E) 1,002

Solution: slope of 2 and a y-intercept of 2   y-coordinate is 480   y = 2x + 2   478 = 2x   x = 239   Answer:   C. 239
Answer: C
3^4+3^4+3^4=?	Choose the most appropriate option.
A) a) 3^3	B) b) 3^4	C) c) 3^5	D) d) 3^6	E) e) 3^15

Solution: The correct answer is c) 3^5 3^5   3^5 = 3^4+3^4+3^4
Answer: C
A man can row a boat at 20 kmph in still water. If the speed of the stream is 8 kmph, what is the time taken to row a distance of 60 km downstream?
Pick one:
A) 30/16 hours
B) 80/13 hours
C) 30/73 hours
D) 15/7 hours
E) 50/13 hours

Solution: Speed downstream = 20 + 8= 
20 + 8 = 28
28 kmph.   Time required to cover 60 km downstream= d/s = 60/28   = 15/7 hours.   Answer:15/7 hours
Answer: D
There are 25 Kids in a classroom. 12 Kids are wearing socks and 8 are wearing Shoes. 6 Kids are wearing both.
How many are Bare Feet ?  Choices
A) 10  B) 20  C) 40  D) 50  E) 11

Solution: 12 kids wear socks   8 kids wear shoes   6 wear both.   12 â€“ 6 = 6 (wear only socks)   8 â€“ 6 = 2 (wear only shoes)   6 (wear both)   hence, 25 -14 = 11   11 kids are with bare feet.   11
Answer: E
A train 108 m long moving at a speed of 50 km/hr crosses a train 112 m long coming from opposite direction in 6 seconds. The speed of the second train is:	Choose the correct choice from the following:
A) 48 km/hr
B) 54 km/hr
C) 66 km/hr
D) 82 km/hr
E) 85 km/hr

Solution: Explanation:   Let the speed of the second train be x km/hr.   Relative speed	= (x + 50) km/hr   =(x + 50) x 5/18 m/sec   =250 + 5x	/18 m/sec   Distance covered = (108 + 112)= 
(108 + 112) = 220
220 m.   220/ [(250+5x)	/18]=6   250 + 5x = 660   x = 82 km/hr.   ANSWER IS 82 km/hr
Answer: D
A trained covered x km at 30 kmph and another 2x km at 20 kmph. Find the average speed of the train in covering the entire 3x km.	Choose the correct choice
A) 20kmph B) 22.5kmph C) 25kmph D) 30kmph E) 35kmph

Solution: Total time taken = x/30 + 2x/20 hours   = 8x/60 = 2x/15 hours   Average speed = 3x/(2x/15)   = 22.5 kmph   Answer:22.5kmph3 /(2 /15)= 
3 /(2 /15) = 45/2 = around 22.5
22.5 kmph   Answer:22.5kmph
Answer: B
If each side of a square is increased by 25%, find the percentage change in its area. Choose the correct option:
A) 26.5%  B) 36.25%  C) 46.25%  D) 56.25%  E) 66.25%

Solution: Let each side of the square be a. Then, area = a2.   New side =(125a/100) =(5a/4). New area = (5a/4) 2=(25a2)/16.   Increase in area = ((25 a2)/16)-a2=(9a2)/16.   Increase% = [((9a2)/16)*(1/a2)*100] % = 56.25%.   ANSWER 56.25% 56.25%
Answer: D
In a camp, there is a meal for 120 men or 200 children. If 150 children have taken the meal, how many men will be catered to with remaining meal? Choose the correct choice:
A) 20	B) 30	C) 40	D) 50	E) 60

Solution: Here given 120 men = 200 children   therefore 1 child = 3/5 of Man------ step I   Now given that the food was consumed by 150 children   From step I we get 150 children =90 Men ( 1 child = 3/5 Man ie , 150 X 3/5 = 90)   So the food is for  (120-90)= 
 (120-90) = 30
30 Men   ANSWER:30
Answer: B
A rectangular circuit board is designed to have a width of W inches, a length of L inches, a perimeter of P inches, and an area of D square inches. Which of the following equations must be true?	Pick.
A) 2W^2 + PW + 2D = 0  B) 2W^2 − PW − 2D = 0  C) 2W^2 − PW + 2D = 0  D) W^2 + PW + D = 0  E) W^2 − PW + 2D = 0

Solution: P = 2(L+W)-----------------1)   A= LW------------------------2)   option A is not possible why ?? because all the terms are positive.   lets try option B , put value of P and A from 1 and 2 we have,   2W^2-2(L+W)W + 2(LW)   2W^2 - 2LW - 2W^2 + 2LW=0.   hence answer is 2W^2 − PW + 2D = 0.
Answer: C
Rs.2500 is divided into two parts such that if one part be put out at 5% simple interest and the other at 6%, the yearly annual income may be Rs.140. How much was lent at 5%?
Choose the correct choice from the following choices:
A) 2888  B) 2999  C) 2799  D) 1000  E) 2881

Solution: (x*5*1)/100 + [(2500 - x)*6*1]/100 = 140   X = 1000   Answer: 1000
Answer: D
When a cylindrical tank is filled with water at a rate of 22 cubic meters per hour, the level of water in the tank rises at a rate of 0.7 meters per hour. Which of the following best approximates the radius of the tank in meters?  Choose the correct choice from the following choices: A) √10/2 B) √10 C) 4 D) 5 E) 10

Solution: V = pi(R^2)(H)   We have the Volume (22 cubic meters) and the Height (0.7 meters)...   22 = pi(R^2)(0.7)   pi = about 3.14   .7(pi) = about 2.2   22 = 2.2(R^2)   10 = R^2   \sqrt{10} = R   Final Answer:   √10
Answer: B
On a bright morning, Ashley and Cecilia decided to take out their old cars from the garage and check their speeds. Just to make things for interesting, they decided to race and find out whose car was fast. So they halted their car at the starting point and began with full throttle till the finish line.
When both the car crossed the finishing line, they realized that Ashley's car was 1.2 times faster than Cecelia. Also, Cecelia had reached the finishing line 1 minutes 30 seconds later than Ashley. Ashley's car had reached the finishing line at an average speed of 60 Km/h.
With all this data given, can you find out the total distance between the starting and the finishing lines?  Pick
A) 6.5Km	B) 8.5Km	C) 7.4Km	D) 7.5Km	E) 7.7Km

Solution: 7.5Km   7.5Km   Explanation:   7.5Kmenoting Ashley with A and Cecelia with C   Speed A = 60 km/hr = 1.2 x Speed C [km/hr] = 1 km/ min   Hence Speed C = 60/1.2 [km/hr] = 50 [km/hr] = 5/6 km/ min   Time C = 7.5Km [km] /Speed C [km/min] = 7.5Km/Speed C [min] = 7.5Km/(5/6) min = 67.5Km/5 min = 1.2 7.5Km min   Time A = 7.5Km [km] /Speed A [km/min] = 7.5Km/Speed A [min] = 7.5Km/(1) min = 7.5Km min   Since Time C � Time A 7.5  /(1)= 
7.5  /(1) = 7.5
7.5Km min   Since Time C � Time A= 1.5 min   Then (1.2 � 1)7.5Km min = 0.27.5Km min = 1.5 min   Hence 7.5Km = 1.5/0.2 km = 1.5*5= 
1.5*5 = 7.5
7.5 km   The total distance as calculated above is 7.5 Km.
Answer: D
What is greatest positive integer n such that 2^n is a factor of 12^14?  Choose the correct choice from the following choices:
A) a)10  B) b)12  C) c)16  D) d)20  E) e)28

Solution: The given number is 12^14   =(2*2*3)^14   =(2^28)*(3^14)   So the greatest possible value for n such that 2^n can be factor of given number is 28.   Answer e)28
Answer: E
On a certain plane, 2/5 of the passengers speak French and 3/4 speak Hebrew. If all of the passengers on the plane speak at least one of these languages, what is the smallest number of passengers that could be on the plane?
Choose the correct choice.
A) 12	B) 15	C) 40	D) 54	E) 60

Solution: Assume the total members = x   French = .4x   Hebrew = .75x   French + Hebrew = 1.15x, but this is not possible hence 15 people speak both languages.   Only French = .25x, Only Hebrew = .6x, both = .15x   Since these are all people, all of these should be whole numbers.   Checking the options:   A. 12. Only Hebrew = 12*0.6= 
12*0.6 = 7.2
7.2 We do not get the people as whole numbers. INCORRECT   B. 15. Only French= 0.25*15 Again we do not get the people as whole numbers. INCORRECT   C. 40 Only Farsi = .25*40= 
.25*40 = 10
10, Only Hebrew= .6*40= 
.6*40 = 24
24, both= .15*40= 
.15*40 = 6
6. We have the people as whole numbers. CORRECT   D. 54   E. 60   Since we have to find the lowest number, no need to calculate for the rest of the options.   40orrect Option: 40
Answer: C
If there are 6 seats and 3 students, in how many ways can they be seated?	Choose the correct choice from the following answers:
A) 120
B) 124
C) 128
D) 132
E) 136

Solution: The first student has 6 choices, the second student has 5 choices, and the third student has 4 choices. The number of ways to sit is 6*5*4= 
6*5*4 = 120
120.   The answer is 120.
Answer: A
Can N and can В are both right circular cylinders. The radius of can N is twice the radius of can B, while the height of can N is half the height of can B. If it costs $4.00 to fill half of can B with a certain brand of gasoline, how much would it cost to completely fill can N with the same brand of gasoline?	Choose the correct choice from the following choices:  A) $1  B) $2  C) $4  D) $8  E) $16

Solution: Let x be the radius of b and 2h be the height of B. Therefore, radius of N = 2x and height = h   Vol of b = 3.14*x^2*2h   Vol of a = 3.14*4x^2*h   cost to fill half of B = $4 --> cost to fill full B = $8   --> 3.14*x^2*2h = 8 --> 3.14*x^2*h = 4 --> 4*(3.14*x^2*h) = $16   Ans $16
Answer: E
If the wheel is 14 cm then the number of revolutions to cover a distance of 880 cm is?
Choose the correct answer:	A) A)15	B) B)10	C) C)14	D) D)12	E) E)11

Solution: 2 * 22/7 * 14 * x = 880 => x = 10   ANSWER:10
Answer: B
A desalination process is able to remove 2/3 of salt in each cycle. If we have 1 liter of sea water that has 5% salt (i.e. 5 g in a liter), how much salt would have been removed from the liter of water after 3 cycles of the desalination process?  Choose the correct choice from the following options
A) 4.15	B) 4.21	C) 4.52	D) 4.81	E) 4.93

Solution: X is the initial quantity of salt in the water.   After a cycle of desalination the quantity of salt left would be X1=X-2/3X i.e. X1=1/3X   Same thing for X2, X3 respectively representing the quantity of salt left after 2, 3 cycles of desalination.   So we have:   X1=1/3 X   X2=1/3 X1   X3=1/3 X2   By multiplying both ends of the equations we get:   X1*X2*X3 = (1/3)^3 X*X1*X2   Simplification leaves us with:   X3 = (1/3)^3 X   X3 is the quantity of salt left after three cycles. So the cumulative quantity of salt (Q3) which has been removed after 3 cycles is: Q3= X-X3=X-(1/3)^3 X i.e. Q3 = X (1-(1/3)^3)   In this case, given X was: X=5 g   So we have Q3=5 * (1-1/27) = 5 * 26/27 = 4.814 g rounded Q3=4.81   Answer: 4.81
Answer: D
The expression pq+p is odd when the p and q are integers. Which of the following expressions must be even?	Select.
A) p B) q C) p + q D) pq - p E) p + q^2

Solution: pq+p is odd   p and q are integers   If p were even pq+p would be even despite any value of q.   q can't be odd, so q must be even.   Ans : q
Answer: B
What will be the ratio of simple interest earned by certain amount at the same rate of interest for 12 years and that for 28 years? Choose the correct choice from the following answers
A) 5 : 7
B) 4 : 7
C) 3 : 7
D) Data inadequate
E) None of these

Solution: Let the principal be P and rate of interest be R%.   ∴ Required Ratio = [(P×R×12/100) /(P×R×28/100)]=12PR/28PR=12/28=3:7   Answer 3 : 7
Answer: C
Two trains are moving in opposite directions with speed of 110 km/hr and 90 km/hr respectively. Their lengths are 1.10 km and 0.9 km respectively. the slower train cross the faster train in --- seconds
Pick:
A) 26
B) 48
C) 47
D) 36
E) 25

Solution: Explanation:   Relative speed = 110+90= 
110+90 = 200
200 km/hr (Since both trains are moving in opposite directions)   Total distance= 1.1+.9= 
1.1+.9 = 2
2km   Time= 2/200 hr = 1/100 hr = 3600/100= 
3600/100 = 36
36 seconds   Answer: Option 36
Answer: D
There are 15 points in a given plane, no three of which are on the same line. If one of the points is represented as 'P, then how many triangles can be determined with the 15 points that contain the point P?
Pick:
A) 91 B) 105 C) 182 D) 210 E) 455

Solution: Fist point is P which is fixed so can be selected in 1 way   Second point can be selected in 14 ways   Third point can be selected in 13 ways   so total ways = 1x14x13 = 182   but answer is 91 which is 182/2=182
Answer: C
A father said to his son, "I was as old as you are at present at the time of your birth." If the father's age is 42 years now, the son's age 5 years back was?
Choose the correct choice from the following options:
A) 12yr
B) 15yr
C) 14yr
D) 16yr
E) 20yr

Solution: Let the son's present age be x years   Then, 42-x = x   x = 21   Son's age 5 years back = 21-5= 
21-5 = 16
16years   Answer is 16yr
Answer: D
How many odd prime numbers are there less than 50?  Choose the correct choice from the following options.
A) 15	B) 1	C) 2	D) 14	E) 17

Solution: Odd prime number less than 50 :3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47   There is 14 the odd prime number   Answer is 14
Answer: D
The sum of the present ages of two persons A and B is 60. If the age of A is twice that of B, find the sum of their ages 5 years hence?
Select the correct option:
A) 100
B) 80
C) 70
D) 20
E) 40

Solution: A + B = 60, A = 2B   2B + B = 60 => B = 20 then A = 40.   5 years, their ages will be 45 and 25.   Sum of their ages = 45 + 25= 
45 + 25 = 70
70.   answer is 70.
Answer: C
A person crosses a 600m long street in 4 minnutes. What is his speed in km per hour?	Pick one:
A) 5.8km/hr
B) 7.2km/hr
C) 9km/hr
D) 2.5km/hr
E) 3km/hr

Solution: Speed = 600/4*60 = 2.5m/sec   =2.5*18/5= 
2.5*18/5 = 9
9km/hr   Answer is 9km/hr
Answer: C
P alone can complete a job in 7 days. The work done by Q alone in one day is equal to one-sixth of the work done by P alone in one day. In how many days can the work be completed if P and Q work together? Answers:
A) 2 B) 3 C) 4 D) 5 E) 6

Solution: P's rate is 1/7   Q's rate is 1/42   The combined rate is 1/7 + 1/42 = 1/6   If they work together, the job will take 6 days.   The answer is 6.
Answer: E
A man rows his boat 90 km downstream and 5` km upstream, taking 3 hours each time. Find the speed of the stream?  Choose the most appropriate option.
A) 7 kmph
B) 5 kmph
C) 2 kmph
D) 8 kmph
E) 1 kmph

Solution: Speed downstream = d/t = 90/(3)= 
90/(3) = 30
30 kmph   Speed upstream= d/t = 51/(3)= 
51/(3) = 17
17 kmph   The speed of the stream= (30 - 17)/2 = 7 kmph   7 kmphnswer:7 kmph
Answer: A
Two persons start running simultaneously around a circular track of length 200 m from the same point at speeds of 15 km/hr and 25 km/hr. When will they meet for the first time any where on the track if they are moving in opposite directions?
Choose the most appropriate option.
A) 11	B) 10	C) 18	D) 27	E) 12

Solution: Time taken to meet for the first time anywhere on the track   = length of the track / relative speed   = 200 / (15 + 25)5/18 = 200* 18 / 40 * 5 = 18 seconds.   Answer: 18
Answer: C
If you drew a dot on the edge of a wheel and traced the path of the dot as the wheel rolled one complete revolution along a line, then the path formed would be called a cycloid, combining both forward and circular motion. What is the length of the path formed by one complete revolution? Assume the wheel has a radius of r.	Choose the correct choice from the following answers:
A) 5r
B) 7r
C) 4r
D) 8r
E) 9r

Solution: Imagine the circle resting on coordinate (0,0) and moving east.   Also magine the point on the circle to start at (0,0).   Let t be the angle between the point on the circle and the center of the circle.   The position of the point on the circle, relative to t, is:   x = rt - r×sin(t)   y = r - r×cos(t)   Taking the derivatives:   dx/dt = r - r×cos(t)   dy/dt = r×sin(t)   The change in arc length can be defined as ( (dx/dt)2 + (dy/dt)2 ) 1/2.   So the total arc length is the integral from 0 to 2pi of ( (dx/dt)2 + (dy/dt)2 ) 1/2.   After a few steps this integral becomes:   r×21/2 × (1-cos(t))1/2.   Using the hint:   r×21/2 × 21/2 × integral of sin(t/2) dt from 0 to 2×pi   = 2×r × (-2×cos(t/w) from 2×pi to 0)   = 8r   Hint: (1-cos(t))0.5 = 20.5×sin(t/2)
Answer: D
Diane find 6 and a half cans of paint are just enough to paint one third of her room. How many more cans of paint will she need to finish her room and paint a second room of the same size?
Select the correct option
A) 5
B) 7 and a half
C) 10
D) 32 and a half
E) 35

Solution: She will need 13 cans to paint the rest of this room and 19 1/2 for the next room for a total of 32 1/2 cans.   32 and a half
Answer: D
A restaurant meal cost $31.50 and there was no tax. If the tip was more than 10 percent but less than 15 percent of the cost of the meal, then total amount paid must have been between:
Choices.
A) $40 and $42
B) $39 and $41
C) $38 and 40
D) $37 and $39
E) $35 and $37

Solution: let tip=t   meal cost=31.50   range of tip = from 10% of 31.5 to 15% of 35.5 = 3.55 to 5.325   hence range of amount paid= 31.5+T= 35.05 to 36.825   ANSW$35 and $37R:$35 and $37
Answer: E