MU-NLPC/Calc-aqua_rat huggingface dataset:
A train passes a station platform in 32 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?	Choose the correct choice from the following: A) 200 B) 220 C) 180 D) 250 E) 260

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 / 32= 15   x + 300 = 480   x = 180 m.   Answer: Option 180
Answer: C
Eighteen years ago, a father was three times as old as his son. Now the father is only twice as old his son. Then the sum of the present ages of the son and the father is? Select.
A) 109  B) 106  C) 104  D) 108  E) 101

Solution: Let the present ages of the father and son be 2x and x years respectively.   Then, (2x - 18) = 3(x - 18) => x = 36   Required sum = (2x + x) = 108 years.Answer: 108
Answer: D
In what time will a train 110 m long cross an electric pole, it its speed be 144 km/hr?	Choose one:
A) 2.35 sec  B) 2.85 sec  C) 7.5 sec  D) 2.75 sec  E) 1.5 sec

Solution: Speed = 144 * 5/18= 
144 * 5/18 = 40
40 m/sec   Time taken= 110/40= 
110/40 = 11/4 = around 2.75
2.75 sec.   Answer:2.75 sec
Answer: D
At what rate percent on simple interest will Rs.750 amount to Rs.900 in 5 years?	Choices:
A) 6
B) 5
C) 4
D) 78
E) 2

Solution: 150 = (750*5*R)/100   R = 4%.Answer: 4
Answer: C
Find out the wrong number in the series.
6, 12, 48, 102, 384, 768, 3072
Choices.
A) 768
B) 384
C) 102
D) 488
E) 12

Solution: Each even term of the series is obtained by multiplying the previous term by 2.   2nd term = (1st term) x 2 = 6 x 2 = 12   4th term = (3rd term) x 2 = 48 x 2 = 96.   6th term = (5th term) x 2 = 384 x 2 =768.   4th term should be 96 instead of 102.   ANSWER:102
Answer: C
Manet has to pay back her bank loan over 9 months following the below sequence.
$50, $55, $65, $80, $85, $95, $110, $115, ?
How much will she pay back on the ninth month?
Select the correct option:	A) $155	B) $145	C) $135	D) $125	E) $130

Solution: The sequence progresses +5, +10, +15 repeated; The amount to pay back on the 9th Month is $125   Ans $125
Answer: D
The difference between the local value and the face value of 7 in the numeral 32675149 is  Choose the correct option:
A) 69990  B) 69993  C) 70000  D) 77000  E) 78000

Solution: Explanation:   (Local value of 7) - (Face value of 7) = (70000 - 7)= 
(70000 - 7) = 69_993
69993   69993)
Answer: B
In a workshop there are 4 kinds of beds, 2 kinds of closets, 2 kinds of shelves and 7 kinds of chairs. In how many ways can a person decorate his room if he wants to buy in the workshop one shelf, one bed and one of the following: a chair or a closet?  Choose the correct choice
A) 72. B) 80. C) 56. D) 48. E) 16.

Solution: Bed = Select 1 out of 4 = 4C1 = 4   Shelf = Select 1 out of 2 = 2C1= 2   Chair (7)+ Closet (2) = Total 9 = Select 1 out of 9 = 9C1   Possible combinations to chooseBED*SHELF*(CH72.IR+CLOSET)=4*2*9= 
4*2*9 = 72
72 ways   72.NSWER IS 72.
Answer: A
Find the largest number of four digits exactly divisible by 12,15,18 and 27. Choose the correct choice from the following answers:
A) 9770	B) 9740	C) 9780	D) 9750	E) 9720

Solution: The Largest number of four digits is 9999.   Required number must be divisible by L.C.M. of 12,15,18,27 i.e. 540.   On dividing 9999 by 540,we get 279 as remainder .   Therefore, Required number = (9999-279)= 
(9999-279) = 9_720
9720.   Answer is 9720.
Answer: E
A started a business with an investment of Rs. 70000 and after 6 months B joined him investing Rs. 120000. If the profit at the end of a year is Rs. 52000, then the share of B is?  Choose the correct choice from the following answers.
A) 2888  B) 24000  C) 27777  D) 29997  E) 27712

Solution: Ratio of investments of A and B is (70000 * 12) : (120000 * 6) = 7 : 6   Total profit = Rs. 52000   Share of B = 6/13 (52000) = Rs. 24000   Answer: 24000
Answer: B
The length of a train and that of a platform are equal. If with a speed of 90 k/hr, the train crosses the platform in one minute, then the length of the train (in meters) is?
Choose the correct choice from the following choices:
A) 299 B) 277 C) 112 D) 750 E) 123

Solution: Speed = [90 * 5/18] m/sec = 25 m/sec; Time   = 1 min. = 60 sec.   Let the length of the train and that of the platform be x meters.   Then, 2x/60 = 25 è x   = 25 * 60 / 2= 
25 * 60 / 2 = 750
750   Answer: 750
Answer: D
The perimeters of two squares are 40 cm and 24 cm. Find the perimeter of a third square whose area is equal to the difference of the areas of the two squares . Choose the correct choice from the following choices
A) 22 cm B) 24 cm C) 32 cm D) 28 cm E) 29 cm

Solution: Explanation:   We know perimeter of square = 4(side)   So Side of first square = 40/4= 
40/4 = 10
10 cm   Side of second square= 24/4= 
24/4 = 6
6 cm   Area of third Square= 10*10 - 6*6= 
10*10 - 6*6 = 64
64 cm   So side of third square= 8 [because area of square = side*side]   Perimeter = 4*Side = 4*8= 
4*8 = 32
32 cm   Answer: Option 32 cm
Answer: C
The C.P of 10 pens is equal to the S.P of 12 pens. Find his gain % or loss%?	Choose one:
A) 16 2/3% profit
B) 50/6% profit
C) 16 2/3% loss
D) 100/3% loss
E) 120/3% loss

Solution: Explanation:   10 16 2/3% lossP = 12 SP   12 --- 2 16 2/3% lossP loss   100 --- ? => 16 2/3%   ANSWER IS 16 2/3% loss
Answer: C
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:	A) 31/32	B) 31/35	C) 31/31	D) 31/36	E) 31/37

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 man can row a boat at 18 kmph in still water. If the speed of the stream is 6 kmph, what is the time taken to row a distance of 60 km downstream?	Choose the correct choice
A) 30/16 hours	B) 80/13 hours	C) 15/6 hours	D) 30/13 hours	E) 50/13 hours

Solution: Speed downstream = 18 + 6= 
18 + 6 = 24
24 kmph.   Time required to cover 60 km downstream= d/s = 60/24   = 15/6 hours.   Answer:15/6 hours
Answer: C
The ratio of the first and second class fares between two stations is 3 : 1 and that of the number of passengers travelling between the two stations by the first and the second class is 1 : 50. If in a day, Rs. 1, 325 are collected from the passengers travelling between the two stations, then the amount collected from the second class from the second class passengers is  Choose the most appropriate option:
A) 1,250
B) 1,000
C) 850
D) 750
E) 350

Solution: Explanation:   Let the fares be 3 x and x respectively for the first and second class.   Suppose in a day passengers travelling between the two stations be 1 and 50.   Then by given condition, 3 x × 1+x × 50=1,325 => x=25   The amount collected from second class = 25×50 = Rs. 1250   1,250nswer: 1,250
Answer: A
In a class, 5 people like baseball and football, 2 people only like baseball, 3 people only like football, and 6 people like neither. How many people are in the class?
Choose the correct answer.
A) 10	B) 14	C) 16	D) 20	E) 22

Solution: 16.   To get the answer, you can simply add the different types of students, as there are no overlaps in the categories: 5+2+3+6= 
5+2+3+6 = 16
16. As such, the correct answer is 16: 16.
Answer: C
Mr. Sam's car gets him 50 miles per gallons of gas. If Mr Sam get a full tank with 14 gallons of gas, How far can Mr Sam go?
Choose the correct choice from the following options:
A) 52 miles  B) 1400 miles  C) 700 miles  D) 1000 miles  E) 100 miles

Solution: Solution   Number of miles per gallon = 50 miles   Number of miles 14 gallons = x   x = 50 Ã— 14 = 700 miles.   So, Number of miles Sam gets with 14 gallons = 700 miles.   Option 700 miles
Answer: C
The least whole number which when subtracted from both the terms of the ratio 6 : 7 to give a ratio less than 16 : 21, is  Choose the most appropriate option:
A) 3 B) 4 C) 5 D) 6 E) 7

Solution: Explanation:   Let x is subtracted.   Then,   (6−x)/(7−x)< 16/21   21(6—x)<16(7—x)   =>5x>14=x>2.8   Least such number is 3   Option 3
Answer: A
In a kilometer race, A beats B by 50 meters or 10 seconds. What time does A take to complete the race? Choose the most appropriate option
A) 50 sec B) 190 sec C) 287 sec D) 74 sec E) 697 sec

Solution: Explanation:   Time taken by B run 1000 meters = (1000 * 10)/50= 
(1000 * 10)/50 = 200
200 sec.   Time taken by A= 200 - 10= 
200 - 10 = 190
190 sec.   ANSWER 190 sec
Answer: B
The length of a rectangle is increased by 35% and its breadth is decreased by 20%. What is the effect on its area? Pick:	A) 10800	B) 1299	C) 1000	D) 10000	E) 2887

Solution: 100 * 100= 
100 * 100 = 10_000
10000   135 * 80= 
135 * 80 = 10_800
10800   10800nswer: 10800
Answer: A
If the average cost of a house was $50,000 in 1965 and was x in 2000, what was the average increase in home prices per year over this period? Choose the correct choice from the following:
A) A)(x+50,000)/40 B) B)(x-50,000)/35 C) C)(50,000/40)+x D) D)(50,000-x)/40 E) E)x/40

Solution: Average house price in 2000: x   Average house price in 1965: 50,000   2000-1965= 
2000-1965 = 35
35   Average increase per year: (x-50,000)/35   Answer is (x-50,000)/35
Answer: B
To mail a package, the rate is 10 cents for the first pound and 5 cents for each additional pound. Two packages weighing 5 pounds and 10 pounds, respectively can be mailed seperately or combined as one package. Which method is cheaper and how much money is saved?
Pick:
A) Combined, with a saving of 10 cents B) Combined, with a saving of 15 cents C) Separately, with a saving of 5 cents D) Combined, with a saving of 5 cents E) Separately, with a saving of 15 cents

Solution: 5 pounds = 1*10+4*5= 
1*10+4*5 = 30
30   10 pounds= 1*10+9*5= 
1*10+9*5 = 55
55   total= 85   15 pound = 1*10+14*5= 
1*10+14*5 = 80
80   dif. 5   Answer : Combined, with a saving of 5 cents
Answer: D
A department of eight people - four men and four 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?	Choose the correct choice from the following:
A) 36 B) 48 C) 60 D) 72 E) 90

Solution: They can make a team of 3 men and 2 women.   The number of ways to do this is 4C3*4C2=4*6= 
4*6 = 24
24   They can make a team of 2 men and 3 women.   The number of ways to do this is 4C2*4C3=6*4= 
6*4 = 24
24   The total number of distinct groups is 48.   The answer is 48.
Answer: B
In how many different number of ways 4 boys and 3 girls can sit on a bench such that girls always sit together.
Choose the correct choice from the following answers:
A) 720
B) 730
C) 740
D) 780
E) 790

Solution: 720   Option '720'
Answer: A
A certain number of badges were distributed among a class of students. The student who got 1/6th of the total number of badges actually got 5 times the average number of badges the others got! How many students were there in the class?	Select
A) 30  B) 26  C) 11  D) 31  E) 32

Solution: DETAILED SOLUTION   Let the total students be (n + 1)   Let total badges be x   Let the average of ‘n’ students be y   The student who got 1/6th of x = 5y   Or y = x/30   Therefore ‘n’ students got 1/30th of total share each   Or n * x/30 + 1 * x/6 = x   nx + 5x = 30x   n + 5 = 30   Or n = 25   Total = n + 1 = 26   Correct Answer: 26
Answer: B
A certain company assigns employees to offices in such a way that some of the offices can be empty and more than one employee can be assigned to an office. In how many ways can the company assign 5 employees to 3 different offices?	Choose the correct choice from the following answers
A) 243	B) 245	C) 45	D) 121	E) 11

Solution: Each of three employee can be assigned to either of offices, meaning that each has 2 choices --> 3*3*3*3*3=3^5=243.   243nswer: 243.
Answer: A
Matt gets a $1,600 commission on a big sale. This commission alone raises his average commission by $150. If Matt's new average commission is $400, how many sales has Matt made?
Choose the correct choice from the following choices:
A) 9 B) 4 C) 5 D) 6 E) 7

Solution: Let, Average Commission = x   No. of items sold = y   Total Commission = xy   New Commission = xy+1600   New Average = (xy+1600) / (y+1) = 150+x   i.e. (xy+1600) = (y+1)* (150+x)   i.e. (xy+1600) = (xy+x+150y+150)   i.e. (1450) = (x+150y)   New Commission = 400 = 150+x   i.e. x=250   i.e. y = 8   New Sales = y+1 = 9   9nswer: option 9
Answer: A
Samantha's investment portfolio consists of three stocks: a railway, a bank, and a computer company. In the month of February, the price of the railway's stock rose by 10%, that of the bank decreased by 15% and that of the computer company also decreased by 15%, but the overall value of her portfolio increased. If Samantha owns equal amounts of all three stocks, which of the following could be the initial prices of the three stocks in the order railways, bank, and computer company respectively?	Choose the correct choice:
A) $55, $85, $40
B) $65, $60, $60
C) $65, $55, $90
D) $25, $60, $70
E) $85, $25, $20

Solution: Since Samantha owns equal amounts of stocks, the 10% increase alone should set off the 15% decrease in each of the other two stocks. i.e The stock which increased should have a substantially higher value than the two stocks which decreased. Between B and E, E is obviously the safer bet and is the right answer.   Answer is $85, $25, $20.
Answer: E
A professional janitor can clean a certain high school in 8 hours, working at a constant rate. A student sentenced to detention can clean that same high school in (10+10) hours, also working at a constant rate. If the student is paid $7 total per hour and the janitor is paid $21 per hour, how much more would it cost the school to pay the janitor to do the job himself than it would to pay the student and the janitor to do the job together?
Options: A) -$56 B) -$6 C) $0 D) $6 E) $8

Solution: A professional janitor can clean a certain high school in 8 hours   So (applying rule #1), the janitor can clean 1/8 of the school in ONE HOUR   A student sentenced to detention can clean that same high school in 20 hours   So (applying rule #1), the student can clean 1/(10+10) or 1/20 of the school in ONE HOUR   So, COMBINED, the student and janitor can clean (1/8 + 1/20) of the school in ONE HOUR   1/8 + 1/20 = 5/40 + 2/40 = 7/40   So, in ONE HOUR they can clean 7/40 of the school.   Applying rule #2, it will takethem40/7 hoursto clean the ENTIRE school.   The janitor earns $21/hour and the student earns $7/hour, so their combined rate is$28/hour.   Theircombined wages= (pay rate)(time) = ($28/hour)(40/7 hours) =$160   Working ALON$8, the janitor takes 8 hours and earns $21/hour   So, working alone, the janitor's earnings = (pay rate)(time) = ($21/hour)(8 hours) =$168   $168-$160= $8, so the answer is $8 168- 160= 
 168- 160 = 8
$8, so the answer is $8
Answer: E
When m is divided by 9, the remainder is 8. When m is divided by 13, the remainder is 1. If 1 < m < 200, what is the greatest possible value of m?  Choose the correct choice from the following.
A) 47  B) 65  C) 103  D) 117  E) 170

Solution: Looking at the choices, options BD can be eliminated as they are divisible by 13   Starting from the highest number 164;   170 = 162 + 8 (162 divisible by 9)   170 = 169 + 1 (169 divisible by 13)   it fits the result   Answer = 170
Answer: E
a coffee seller has two types of coffee Brand A costing 5 bits per pound and Brand B costing 3 bits
per pound. he mixes two brands to get a 40 pound mixture. he sold this at 6 bits per pound. the seller gets a profit of 33 1/2 percent. how much he has used Brand A in the mixture?
Choose the correct answer:
A) 10	B) 20	C) 30	D) 40	E) 50

Solution: cost price of mixture=(100*selling price of mixture)/(100+profit)=(100*6)/(100+33.5) =600/133.5=Rs 4.50(approximately),   Then ratio of A and B = (4.50-3):(5-4.50)=3:1,   Therefore Brand A in 40 pound mixture=40*3/4= 
40*3/4 = 30
30   ANSWER:30
Answer: C
Amanda goes to the toy store to buy 1 ball and 3 different board games. If the toy store is stocked with 3 types of balls and 6 types of board games, how many different selections R of the 4 items can Amanda make?  Choose one:
A) 9
B) 12
C) 14
D) 15
E) 60

Solution: Amanda goes to the toy store to buy 1 ball and 3 different board games. If the toy store is stocked with 3 types of balls and 6 types of board games, how many different selections of the 4 items can Amanda make?   3! / 1!2! * 6! / 3!3!   R=3*20= 
3*20 = 60
60   E. 60
Answer: E
A and B walk around a circular track. They start at 8 a.m. from the same point in the opposite directions. A and B walk at a speed of 2 rounds per hour and 3 rounds per hour respectively. How many times shall they cross each other before 9.00 a.m. ?	Choose the correct option.
A) 7
B) 6
C) 5
D) 2
E) 8

Solution: C   5   Relative speed = 2 + 3= 
2 + 3 = 5
5 rounds per hour.   So, they cross each other 5 times in an hour and 2 times in half an hour.   Hence, they cross each other 5 times before 9.00 a.m.
Answer: C
The compound interest earned on a sum for the second and the third years are $1200 and $1260 respectively. What is the rate of interest?
Choose the correct option:
A) 5%
B) 8%
C) 11%
D) 14%
E) 18%

Solution: 1260 - 1200= 
1260 - 1200 = 60
60 is the rate of interest on $1200 for one year.   The rate of interest= (100 * 60) / (1200)= 
(100 * 60) / (1200) = 5
5%   The answer is 5%.
Answer: A
A clock shows the time as 9 a.m. If the minute hand gains 5 minutes every hour, how many minutes will the clock gain by 6 p.m.? Choose the correct choice from the following:
A) 30 min
B) 35 min
C) 45 min
D) 50 min
E) 55 min

Solution: there are 9 hours in between 9 a.m. to 6 p.m.   9*5= 
9*5 = 45
45 minutes.   ANSWER:45 min
Answer: C
A coin is tossed 7 times. Find the probability of getting more heads than tails in all 7 tosses? Options:  A) 1/2  B) 63/128  C) 4/7  D) 61/256  E) 63/64

Solution: Assuming the coin is fair - P(H)=P(T)=1/2   We can do as proposed by the explanation in your initial post:   Total outcomes: 2^7   Favorable outcomes:   4 heads --> combination of HHHHTTT --> 7!/(4!*3!)=35 (# of permutation of 7 letters out of which 4 H's and 3 T's are identical);   5 heads --> combination of HHHHHTT --> 7!/(5!*2!)=21;   6 heads --> combination of HHHHHHT --> 7!/(6!*1!)=7;   7 heads --> combination of HHHHHHH --> 1;   P(H>T)=Favorable outcomes/Total outcomes=(35+21+7+1)/2^7=1/2.   1/2nswer:1/2
Answer: A
Working together at their respective constant rates, Machine A and Machine B can produce 900 units in 8 hours. Working alone, Machine B would complete that same output in 50% more time. If Machine A were to work on its own for an 8-hour shift, what percent of the 900 unit total would it produce?
Choose the correct choice from the following:
A) 30 B) 33 C) 50 D) 67 E) 75

Solution: 1/A+1/B= 1/T   1/A +1/12= 1/8 (50% more of 8 is 12)   1/A= 1/24   Machine A can produce 900 units in 24 hrs, so it can produce  900*8/24= 
 900*8/24 = 300
300 units is 8 hrs.   300 is 30% of 900.   30 is the answer
Answer: A
Two stations P and Q are 110 km apart on a straight track. One train starts from P at 7 a.m. and travels towards Q at 20 kmph. Another train starts from Q at 8 a.m. and travels towards P at a speed of 25 kmph. At what time will they meet? Choose the correct option:	A) 10.30	B) 10	C) 8.45	D) 9.3	E) 11

Solution: Explanation:   Assume both trains meet after x hours after 7 am   Distance covered by train starting from P in x hours = 20x km   Distance covered by train starting from Q in (x-1) hours = 25(x-1)   Total distance = 110   => 20x + 25(x-1) = 110   => 45x = 135   => x= 3   Means, they meet after 3 hours after 7 am, ie, they meet at 10 am. Answer: 10
Answer: B
A welder received an order to make a 1 million liter cube-shaped tank. If he has only 3x2 meter sheets of metal that can be cut, how many metal sheets will be required for this order? (1 cubic meter = 1,000 liters)
Choose the correct choice from the following choices.
A) 100  B) 90  C) 82  D) 78  E) 75

Solution: The question say:A welder received an order to make a 1 million liter cube-shaped tank. (1 cubic meter = 1,000 liters)   In other words, the tank is going to have a volume of 1000 cubic meters. That would equal 1 million liters.   A cube with a volume of 1000 cubic meters must be (10 meters) x (10 meters) x (10 meters).   The question doesn't specify whether this tank should have a closed top or an open top. (The real GMAT is good about specifying things like that.) Here, we are going to assume a closed top, only because if the top is open, we don't use enough metal --- we get an answer smaller than any of the answer choices. A closed-top cube, a full cube, has 6 sides, each of which is (10 meters) x (10 meters). That's a total surface area of 600 sq m.   The question tells us:he has only 3x2 meter sheets of metal that can be cut.   Each sheet has an area of 6 sq m. How many of these need to fill up 600 sq m?  600/6= 
 600/6 = 100
100. He needs 100 sheets.   100nswer=100
Answer: A
The area of a rectangular field is equal to 300 square meters. Its perimeter is equal to 70 meters. Find the length and width of this rectangle.  Select
A) W = 15 and L = 20 B) W = 25 and L = 30 C) W = 35 and L = 40 D) W = 45 and L = 50 E) W =55 and L = 60

Solution: L * W = 300 : area , L is the length and W is the width.   2 L + 2 W = 70 : perimeter   L = 35 - w : solve for L   (35 - W) * W = 300 : substitute in the area equation   W = 15 and L = 20 : solve for W and find L using L = 35 - w.   correct answer W = 15 and L = 20
Answer: A
In how many different number of ways 7 men and 2 women can sit on a shopa which can accommodate persons?
Choose the correct choice from the following answers:	A) 17000	B) 18000	C) 15120	D) 21000	E) 23000

Solution: 9p5 =9 x 8 x 7 Ã— 6 Ã— 5 = 15120   Answer : 15120
Answer: C
Following an increase in prices, the price of a candy box was 15 pounds and the price of a can of soda was 6 pounds. If the price of a candy box was raised by 25%, and the price of a can of soda was raised by 50%. What was the price of a box of candy plus a can of soda before prices were raised? Options:
A) 11. B) 12. C) 13. D) 14. E) 16

Solution: Price of candy before price increase= 15/1.25= 
15/1.25 = 12
12   Price of soda before price increase= 6/1.5= 
6/1.5 = 4
4   Total price= 12+4= 
12+4 = 16
16   16 is the answer
Answer: E
If 183 is divisible by 11, find the value of the smallest natural no. N?
Choose the correct answer:
A) 5	B) 7	C) 9	D) 10	E) 12

Solution: In aptitude tests , we get questions on divisibility by 11.   A number is divisible by 11, when the difference between the sum of digits at even places and at odd places is 0 or multiple of 11   The given number is N183.   (Sum of digits at EVEN places) – (sum of digits at ODD places)=0   (8 + N)- (3+1)= 0   (8 + N) - 4 = 0   Here the value of N must be 7   7
Answer: B
A’s speed is 20/12 times that of B. If A and B run a race, what part of the length of the race should A give B as a head start, so that the race ends in a dead heat?  Choose the correct choice from the following choices.
A) 1/17 B) 3/17 C) 1/10 D) 6/20 E) 3/10

Solution: We have the ratio of A’s speed and B’s speed. This means, we know how much distance A covers compared with B in the same time.   This is what the beginning of the race will look like:   (Start) A_________B______________________________   If A covers 20 meters, B covers 12 meters in that time. So if the race is 20 meters long, when A reaches the finish line, B would be 8 meters behind him. If we want the race to end in a dead heat, we want B to be at the finish line too at the same time. This means B should get a head start of 8 meters so that he doesn’t need to cover that. In that case, the time required by A (to cover 20 meters) would be the same as the time required by B (to cover 12 meters) to reach the finish line.   So B should get a head start of 8/20th of the race.   Answer (6/20)
Answer: D
If x is an odd integer, which of the following is an even integer? Pick:	A) 2x-x	B) x+1	C) 2x+3	D) x^3	E) 3x+2x

Solution: Plug in an odd integer; in this case 3   (2*3)-3= 
(2*3)-3 = 3
3 Odd    3+1= 
 3+1 = 4
4 Even     (2*3)+3= 
  (2*3)+3 = 9
9 Odd   3^3= 27 Odd   (3*3)+(2*3) = 9 + 6= 
9 + 6 = 15
15 Odd   Answer: x+1
Answer: B