MU-NLPC/Calc-aqua_rat huggingface dataset:
fill in ht blank:(a) the point with ___ (0,0) is called origin of a rectangular coordinate system,(b) to find the y-intercept of a line, we let ___ equal 0 and solve for ___; to find x- intercept , we let ____ equal 0 and solve for___  Select
A) (a) the point with line (0,0) is called origin of a rectangular coordinate system, (b) to find the y-intercept of a line, we let x equal 0 and solve for y ; to find x- intercept , we let y equal 0 and solve for y
B) (a) the point with coordinates (0,0) is called origin of a rectangular coordinate system, (b) to find the y-intercept of a line, we let x equal 0 and solve for y ; to find x- intercept , we let y equal 0 and solve for x
C) (a) the point with axis (0,0) is called origin of a rectangular coordinate system, (b) to find the y-intercept of a line, we let z equal 0 and solve for x ; to find x- intercept , we let x equal 0 and solve for y
D) (a) the point with xyz (0,0) is called origin of a rectangular coordinate system, (b) to find the y-intercept of a line, we let x equal 0 and solve for y ; to find x- intercept , we let y equal 0 and solve for x
E) none of the above

Solution: (a) the point with coordinates (0,0) is called origin of a rectangular coordinate system, (b) to find the y-intercept of a line, we let x equal 0 and solve for y ; to find x- intercept , we let y equal 0 and solve for xcorrect answer ((a) the point with coordinates (0,0) is called origin of a rectangular coordinate system, (b) to find the y-intercept of a line, we let x equal 0 and solve for y ; to find x- intercept , we let y equal 0 and solve for x)
Answer: B
Six years ago, the ratio of the ages of Kunal and Sagar was 6:5, Four years hence, the ratio of their ages will be 11:10. What is Sagar age at present	Select the correct option: A) 22 B) 17 C) 15 D) 16 E) 12

Solution: Let six years ago the age of Kunal and Sagar are 6x and 5x resp.   then,   =>(6x+6)+4(5x+6)+4=1110   =>(6x+6)+4(5x+6)+4=1110   <=>10(6x+10)=11(5x+10)   <=>10(6x+10)=11(5x+10)   <=>5x=10=>x=2   <=>5x=10=>x=2   So Sagar age is (5x+6) = 16   Answer: 16
Answer: D
A can complete a project in 20 days and B can complete the same project in 20 days. If A and B start working on the project together and A quits 10 days before the project is completed, in how many days will the project be completed?	Pick one.
A) 18 days B) 27 days C) 26.67 days D) 16 days E) 15 days

Solution: Let X = the number of days taken to complete the project.   The amount of work done by A is (x-10) * (1/20).   The amount of work done by B is (x) * (1/30).   (1/20)*(x-10) + (1/20)*(x) = 1   (x/20) + (x/20) - (10/20) = 1   x/10 = 3/2   x = 15   Therefore, the answer is 15 days: 15.
Answer: E
The positive numbers w, x, y, and z are such that x is 40 percent greater than y, y is 20 percent greater than z, and w is 20 percent less than x. What percent greater than z is w ? Pick:	A) 15.2%	B) 16.0%	C) 20.0%	D) 23.2%	E) 24.8%

Solution: My strategy is same as theDobermanbut instead take z=100, which makes life a bit easy. As:   z=100   y=120 (20% greater than z)   z=144(20% greater than y)   Now calculate w 20% less than z = 144*80/100= 
144*80/100 = 576/5 = around 115.2
115.2   Now by just looking, relation between w and z:   w-z/z*100= 23.2 - Answer 23.2%
Answer: D
Ashok secured average of 72 marks in 6 subjects. If the average of marks in 5 subjects is 74, how many marks did he secure in the 6th subject?  Choose the most appropriate option
A) 62  B) 74  C) 78  D) 80  E) None of these

Solution: Explanation:   Number of subjects = 6   Average of marks in 6 subjects = 72   Therefore total marks in 6 subjects = 72 * 6= 
72 * 6 = 432
432   Now, No. of subjects= 5   Total marks in 5 subjects = 74 * 5= 
74 * 5 = 370
370   Therefore marks in 6th subject= 432 – 370 = 62   62NSWER 62
Answer: A
A cube has a volume of 64 cubic feet. If a similar cube is twice as long, twice as wide, and twice as high, then the volume, in cubic feet of such cube is? Choose the correct option:
A) 24
B) 48
C) 64
D) 80
E) 512

Solution: Volume = 64 = side^3   i.e. Side of Cube = 4   New Cube has dimensions 8, 8, and 8 as all sides are twice of teh side of first cube   Volume = 8*8*8= 
8*8*8 = 512
512 square feet   Answer: option 512
Answer: E
John traveled 80% of the way from Yellow-town to Green-fields by train at an average speed of 80 miles per hour. The rest of the way John traveled by car at an average speed of v miles per hour. If the average speed for the entire trip was 50 miles per hour, what is v in miles per hour?
Choose the correct choice from the following answers:
A) 20 B) 40 C) 50 D) 55 E) 70

Solution: HiBunuel   THe question seems incorrect. it should not be 80% at the speed of 80. However if it's 20% at the speed of 80, Answer comes out 55.   The question is correct. Here's the explanation:   Let distance be D. We can find the total timeequate it, which comes as:   0.8D / 80 + 0.2D / v = D / 50 => v = 20 (Option 20).
Answer: A
If a person moves 15km straight and turns right and moves 15km straight then how much distance he needs to walk to reach starting point?	Choose the correct answer:  A) 20.2  B) 21.2  C) 23.2  D) 24.2  E) 26.2

Solution: person will move along right angled traingle whose smaller sides are 15 km   & 15 km   reqd distance= hypotenuse of triangle = √(15^2+15^2)= 15√2 = 21.2 km   ANSWER:21.2
Answer: B
The profit earned by selling an article for $ 832 is equal to the loss incurred when the same article is sold for $ 448. What should be the sale price for making 30% profit? Select.
A) $480  B) $450  C) $960  D) $832  E) $660

Solution: Let C.P. = $ x.   Then, 832 - x = x - 448   2x = 1280 => x = 640   Required S.P. = 130% of $ 640 = $ 832.   $832
Answer: D
Tomeka is playing a dice game. If she rolls the same number on her second roll as she rolls on her first, she wins. Each roll is with two, fair, six-sided dice. If Tomeka rolled a seven on her first roll, what is the probability that she will win on her second roll? Choose the correct choice from the following choices.
A) 1/4 B) 1/5 C) 1/6 D) 1/9 E) 1/12

Solution: There are 6 ways to roll a seven: 1 and 6, 6 and 1, 2 and 5, 5 and 2, 3 and 4, 4 and 3.   There are  6*6= 
 6*6 = 36
36 ways to roll two six-sided dice.   Thus the probability of winning by rolling a seven on the second roll given a seven on the first roll is 6/36= 1/6   1/6
Answer: C
2/3rd of the boys and 3/4th of the girls of a school participate in a function. If the no.of participating students is 550, out of which 150 are girls, what is the total no.of students in the school?	Choose the correct choice from the following answers.
A) 300 B) 400 C) 800 D) 900 E) 1000

Solution: Let total number of boys be x and total number of girls be y. y=400=>x = 600and^= I50=>y = 200 Now, x + y = 800   800
Answer: C
If 8 persons meet at a reunion and each person shakes hands exactly once with each of the others, what is the total number of handshakes?  Choose the correct choice from the following choices
A) 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1	B) 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1	C) 8 × 9	D) 28	E) 45

Solution: 1st person will have 7 handshakes, 2nd will have 6, ....7th will have 1 and 8th will have 0   = 7+6+5+4+3+2+1= 
7+6+5+4+3+2+1 = 28
28   if we generalize this: if there are n people then there will be n(n-1)/2 handshakes.   Ans.28)
Answer: D
If x and y are positive integers such that x/y = 6.8, which of the following numbers could be y?	Pick one:
A) 1	B) 3	C) 2	D) 6	E) 10

Solution: With the given information, we are trying to find the value of y.   To achieve this we must convert the given decimal to a fraction and reduce it to it's lowest integer form.   Take the decimal x/y = 6.8 and because it's in the tens decimal place, put the given value (x/y = 6.8/1) and multiply it by 10.   Take the resulting fraction (x/y = 68/10) and reduce it to it's lowest form.   Both of the numbers are divisible by 2.   The result is x/y = 34/5.   Thus y = 5.   The correct answer is 2.
Answer: C
If two dice are thrown together, the probability of getting an even number on one die and an odd number on the other is?
Choose the correct choice from the following answers
A) 1/8	B) 1/2	C) 1/1	D) 1/6	E) 1/3

Solution: The number of exhaustive outcomes is 36.   Let E be the event of getting an even number on one die and an odd number on the other. Let the event of getting either both even or both odd then = 18/36 = 1/2   P(E) = 1 - 1/2   = 1/2.   Answer:1/2
Answer: B
A shopkeeper sells a TV set for 16560 at 10 % discount on its marked price and earns 15 % profit. If no discount is offered, then what will be his present per cent profit? Choose the correct choice from the following options: A) 27 7⁄9 B) 22 7⁄9 C) 25 7⁄9 D) Data inadequate E) None of these

Solution: Original selling price of TV set   =16560×100/90 = 18400   Cost price of the TV = 16560×100/115 = 14400   at no discount, % profit will be   = (18400−14400)×100/14400 = 27 7/9   27 7⁄9nswer 27 7⁄9
Answer: A
Old women said no of days of my grand daughter = no of months my daughters is?
And my age in no of years is= no of weeks of my grand daughter . sum of their ages is 115. Find d old women age?	Choose the correct choice from the following answers:
A) 71.7 years
B) 72.7 years
C) 73.7 years
D) 74.7 years
E) 75.7 years

Solution: age of grand daughter is d days d/365 years   and age of daughter is d months d/12yrs   and age of old women is d/7 years   d/7 + d/12 + d/365 = 115years   4380d +2555d + 84d = 115*365*12*7   7019d = 3525900   d = 3525900/7019 = 502   age of old women is 502/7 =71.7 years   71.7 yearsNSWER:71.7 years
Answer: A
The ratio by weight, measured in pounds, of books to clothes to electronics in a suitcase initially stands at 7:4:3. Someone removes 8 pounds of clothing from the suitcase, thereby doubling the ratio of books to clothes. How many pounds do the electronics in the suitcase weigh? Choose the correct option:
A) 6	B) 8	C) 10	D) 12	E) 14

Solution: The weights of the items in the suitcase are 7k, 4k, and 3k.   If removing 8 pounds of clothes doubles the ratio of books to clothes, then 8 pounds represents half the weight of the clothes.   2k = 8 pounds and then k = 4 pounds.   The electronics weigh 3(4) = 12 pounds.   The answer is 12.
Answer: D
A and B can together complete a piece of work in 4 days. If A alone can complete the same work in 12
days, in how many days can B alone complete that work ?
Choose the correct choice from the following answers:
A) 4 days
B) 5 days
C) 6 days
D) 7 days
E) None of these

Solution: Explanation:   (A+B)'s 1 day work = 1/4   A's 1 day work = 1/12   B's 1 day work =   (14−112)=3−112=16   So B alone can complete the work in 6 days   Answer: 6 days
Answer: C
What is the rate percent when the simple interest on Rs.800 amount to Rs.160 in 5 Years?  Choose one: A) 5% B) 7% C) 9% D) 2% E) 4%

Solution: 160 = (800*5*R)/100   R = 4%   Answer: 4%
Answer: E
The difference of two numbers is 1415. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder. What is the smaller number ? Choose the correct choice from the following choices.
A) A)270  B) B)280  C) C)290  D) D)300  E) E)310

Solution: Let the smaller number be x. Then larger number = (x + 1415).   x + 1415 = 6x + 15   5x = 1400   x = 280   Smaller number = 280.   280)
Answer: B
A train traveled the first d miles of its journey it an average speed of 60 miles per hour, the next d miles of its journey at an average speed of y miles per hour, and the final d miles of its journey at an average speed of 160 miles per hour. If the train’s average speed over the total distance was 94 miles per hour, what is the value of y?
Choose the correct choice:
A) 98
B) 84
C) 90
D) 120
E) 135

Solution: 98verage speed=Total distance traveled /Total time taken   3d/d/60+d/y+d/160=94   Solving for d and y,   15y=11y+480   5y=480   y=98   98nswer 98
Answer: A
Four faces of a fair die are Yellow, two faces red and one blue.The die is tossed three
times. The probability that the colours, yellow, red and blue appear in the first, second and
third tosses respectively is	Choose the correct answer:
A) 1/36
B) 1/18
C) 1/32
D) 1/27
E) None of these

Solution: Probability of getting yellow color = P(Y) = 4/6 = 2/3   Probability of getting red color = P(R) = 2/6 = 1/3   Probability of getting blue color = P(B) = 1/6   So, the probability that the colors yellow, red and blue appear in first, second and third toss respectively= P(Y ∩ R ∩ B) = P(Y) x P(R) x P(B) = 2/3 x 1/3 x 1/6 = 1/27   ANSWER:1/27
Answer: D
Country X imported approximately $1.44 billion of goods in 1996. If Country X imported $488 million of goods in the first two months of 1997 and continued to import goods at the same rate for the rest of the year, by how much would Country Xs 1997 imports exceed those of 1996?	Select:
A) $1124 million B) $1120 million C) $1144 million D) $1240 million E) $1488 million

Solution: Convert units to millions as answer is in millions   1996 Imports = $1.44 bill = $1440 mill   i.e. 1440/12 = $120 mill/month   1997 Imports = $488 mill/2 month   i.e. $244 mill/month   Difference/month = 244-120= 
244-120 = 124
124   Difference/year= $124 mill * 12 = $1488 mill   ANSW$1488 millionR: $1488 million
Answer: E
A certain sum amounts to Rs.1725 in 3 years and Rs.1875 in 5 years. Find the rate % per annum? Choose the correct choice from the following answers:
A) 6% B) 5% C) 3% D) 9% E) 2%

Solution: 3 --- 1725   5 --- 1875   --------------   2 --- 150   N = 1 I = 75 R = ?   P = 1725 - 225= 
1725 - 225 = 1_500
1500   75= (1500*1*R)/100   R = 5%   Answer: 5%
Answer: B
One pump drains one-half of a pond in 4 hours, and then a second pump starts draining the pond. The two pumps working together finish emptying the pond in one-half hour. How long would it take the second pump to drain the pond if it had to do the job alone? Pick.
A) 1 hour
B) 1.1 hour
C) 3 hours
D) 5 hours
E) 6 hours

Solution: First pump drains 1/2 of the tank in 4 hours   so 8 hours it will take to drain the full tank.   Let, 2nd pump drains the full tank in a hours   so both together can drain (1/8+1/a) part in 1 hour   son in 1/2 hour they drain 1/2*(1/8+1/a) part of the tank   given that in 1/2 hour they drain 1/2 of the tank   hence we can say   1/2*(1/8+1/a) = 1/2   solving u get a = 8/7=1.1   Hence answer is 1.1 hour
Answer: B
A solid yellow stripe is to be painted in the middle of a certain highway. If 1 gallon of paint covers an area of t square feet of highway, how many gallons of paint will be needed to paint a stripe of t inches wide on a stretch of highway m miles long? (1 mile = 5,280 feet and 1 foot = 12 inches)
Choose the correct choice from the following options:	A) (5,280 mt) / 12 t	B) (5,280 pt) / 12m	C) (5,280 pmt) /12	D) (5,280)(12m) / pt	E) (5,280)(12p) / mt

Solution: Given that: 1 gallon of paint covers an area oftsquare feet. Question:how many gallonsof paint will be needed ...   In any case you will have:(total area in square feet)/(gallons per feet)=(total area in square feet)/t, so t must be in the denominator: eliminate all but A and D.   Now, lets see where should be t: (area in square feet)=(width in feet)*(length in feet) --> width=tinchesas1 feet=12 inchesthent inches=t/12 feet, so (area in square feet)=(t/12) * (length in feet), so t must be in the nominator: only A is left.   (5,280 mt) / 12 tnswer: (5,280 mt) / 12 t.
Answer: A
8^100 is divisible by 17. Find the remainder? Choose the correct option:
A) 10
B) 12
C) 16
D) 21
E) 26

Solution: This is an extremely difficult problem to solve with out Fermat's little theorem. By applying Fermat's little theorem , We know that 816 when divided by 17, the remainder is 1.   So divide 100 by 16 and find the remainder. Remainder = 4   Therefore, 100 = (16 × 6) + 4   Now this problem can be written as 810017 = 816×6+417 = (816)6×8417   Now this problem simply boils down to (1)6×8417 = 8417   84 = 82×82, we need to find the remainder when 64 × 64 is divisible by 17. Or 13 × 13 = 169. When 169 is divided by 17, remainder is 16.   16
Answer: C
In the Biotechnology class of 2000, there were W graduates. 32 of the graduates found a job, 45 continued on to their second degree and 13 did both. If only 9 people didn't do both, What is W equal to?
Choose the correct choice from the following options:
A) 69.
B) 71.
C) 73.
D) 75.
E) 76.

Solution: Total = 32 +45 -13 + 9= 
32 +45 -13 + 9 = 73
73 .... My first post on the forum... I hope I am correct   73. is correct choice.
Answer: C
On an order of 5 dozen boxes of a consumer product, a retailer receives an extra dozen free. This is equivalent to allowing him a discount of: Pick: A) 26 2/3%. B) 18 2/8%. C) 16 2/3%. D) 18 2/3%. E) 19 2/3%.

Solution: Explanation:   Clearly, the retailer gets 1 dozen out of 6 dozens free.   Equivalent discount = 1/6 * 100 = 16 2/3%.   Answer: 16 2/3%.
Answer: C
The rate of a certain chemical reaction is directly proportional to the square of the concentration of chemical A present and inversely proportional to the concentration of chemical W present. If the concentration of chemical W is increased by 100 percent, which of the following is closest to the percent change in the concentration of chemical A required to keep the reaction rate unchanged?  Answers
A) 100% decrease
B) 50% decrease
C) 40% decrease
D) 40% increase
E) 50% increase

Solution: Let A and W be the concentratrations of the individual chemicals.   Rate of chemical reaction = A^2/W   Since new B is increased by 100%   Rate = A^2/(2W)   For the rate to be constant, new value of A should be square root(2)   So new value of A = 1.414A   That means A is increased by 41.4%   Nearest solution is 40% increase
Answer: D
If 2 cards are selected at random from the deck of 52 cards then What is the probability of one of the selected cards will be Jack and other will be Queen?
A deck of cards has a total of 52 cards, consisting of 4 suits; (spades(Black), hearts(Red), diamond(Red)s, and clubs(Black)); and 13 cards including 1 king, 1 queen and 1 jack in each suit  Pick one:
A) 8/2652	B) 1/2652	C) 28/2652	D) 6/2652	E) 18/2652

Solution: 2 possible cases:   Jack - Queen or Queen - Jack (4 Jacks and 4 queens).   Either way,   the total probability = 2( Jack -Queen) = 2 (4/52 * 4/51) = 18/2652. 18/2652 is the correct answer.
Answer: E
At a certain college, 80 percent of the total number of students are freshmen. If 60 percent of the fresh-men are enrolled in the school of liberal arts and, of these, 50 percent are psychology majors, what percent of the students at the college are freshmen psychology majors enrolled in the school of liberal arts?  Select
A) 25%  B) 30%  C) 24%  D) 28%  E) 20%

Solution: Let's say there is a TOTAL of 100students at this college.   80 percent of the total number of students are freshmen.   # of freshmen = 80% of 100 =80   60 percent of the fresh-men are enrolled in the school of liberal arts...   Number of liberal arts freshmen = 60% of 80 = 48   ...and, of these, 50 percent are psychology majors...   Number of liberal arts freshmen who are psychology majors = 50% of 48=24   What percent of the students at the college are freshmen psychology majors enrolled in the school of liberal arts?   24/100= 24%   Answer:24%
Answer: C
If the least common multiple of two prime numbers x and y is 77, where x > y, then the value of 2x + y is	Pick.
A) 11 B) 17 C) 21 D) 29 E) 33

Solution: LCM (x,y) = 77 and both x an y are prime.   The only values of x and y can be 11 and 7 (x = 11 and y = 7)   2x + y = 2*11 + 7= 
2*11 + 7 = 29
29   Correct Option: 29
Answer: D
Working at their respective constant rates, machine A makes 100 copies in 12 minutes and machine B makes 150 copies in 15 minutes. If these machines work simultaneously at their respective rates for 30 minutes, what is the total number of copies that they will produce? Choose the correct choice.
A) 250  B) 425  C) 550  D) 700  E) 750

Solution: Machine A can produce 100 *30/12= 
100 *30/12 = 250
250 copies   And, Machine B can produce   150* 30/15= 
  150* 30/15 = 300
300 Copies   Total producing 550 Copies.   550 is the answer
Answer: C
How much time will it take for an amount of Rs. 400 to yield Rs. 60 as interest at 12% per annum of simple interest?  Choose one:  A) 2.35 years  B) 4.25 years  C) 7 years  D) 1.25 years  E) 2 years

Solution: Explanation:   Time = (100 x 60)/(400 x 12) years   = 1.25 years.   Answer: 1.25 years
Answer: D
For every positive even integer n, the function h(n) is defined to be the product of all the even integers from 2 to n, inclusive. If p is the smallest prime factor of h(100) +2, then p is?	Choose the correct choice from the following answers.
A) between 2 and 20
B) between 10 and 20
C) between 20 and 30
D) between 30 and 40
E) 2

Solution: h(100)+2=2∗4∗6∗...∗100+2h(100)+2=2∗4∗6∗...∗100+2 . Notice that we can factor out 2 from h(100)+2, thus the smallest prime factor of h(100)+2 is 2: h(100)+2=2∗(4∗6∗...∗100+1)h(100)+2=2∗(4∗6∗...∗100+1).   Answer: 2.
Answer: E
If a particular is never chosen, in how many ways can a cricketbe chosen out of 15 players?  Choose the most appropriate option:
A) 250 B) 320 C) 364 D) 390 E) 430

Solution: A particular players is never chosen, it means that 11 players are selected out of 14 players.   => Required number of ways = 1436411   = 14!/11!x3! = 364   364
Answer: C
The operation is defined for all integers a and b by the equation ab = (a - 1)(b - 1). If x9 = 160, what is the value of x ?	Choose one:
A) 18  B) 15  C) 17  D) 19  E) 21

Solution: ab = (a - 1)(b - 1)   x9 = (x-1)(9-1) = 160 --> x-1=20 --> x=21   Answer: 21
Answer: E
If money is invested at r percent interest, compounded annually, the amount of investment will double in approximately 70/r years. If Pat's parents invested $ 5000 in a long term bond that pays 4 percent interest, compounded annually, what will be the approximate total amount of investment 36 years later, when Pat is ready for college?  Select.
A) $20000
B) $15000
C) $12000
D) $10000
E) $9000

Solution: Since investment doubles in 70/r years then for r=4 it'll double in 70/4=~18 years (we are not asked about the exact amount so such an approximation will do). Thus in 36 years investment will double twice and become ($5,000*2)*2=$20,000 (after 18 years investment will become $5,000*2=$10,000 and in another 18 years it'll become $10,000*2=$20,000).   $20000nswer: $20000.
Answer: A
A train has a length of 150 meters . it is passing a man who is moving at 7 km/hr in the same direction of the train, in 3 seconds. Find out the speed of the train.  Choose the correct choice from the following choices.
A) 182 km/hr  B) 180 km/hr  C) 152 km/hr  D) 169 km/hr  E) 187 km/hr

Solution: 187 km/hrxplanation:   Length of the train, l = 150m   Speed of the man , Vm= 7 km/hr   Relative speed, Vr = total distance/time = (150/3) m/s = (150/3) × (18/5) = 180 km/hr   Relative Speed = Speed of train, Vt - Speed of man (As both are moving in the same direction)   => 180 = Vt - 7   => Vt = 180 + 7= 
180 + 7 = 187
187 km/hr   Answer: Option 187 km/hr
Answer: E
A man cycles at a rate of 4 kmph. He cycles for 45 minutes and then takes a 15 minute break. Determine the total time taken to cover 12 kms by him.	Select:
A) 3 hours 48 minutes	B) 3 hours 49 minutes	C) 3 hours 25 minutes	D) 3 hours 45 minutes	E) 8 hours 45 minutes

Solution: Explanation:   Speed of man = 4kmph   Time for which he cycled = 45 minutes.   Distance covered = speed*time   => 4*45/60= 
4*45/60 = 3
> 3km   Total time to cover 3 km= 45 minutes + 15 minutes = 60 minutes = 1 hour   Thus 3 km is covered in 1 hour   Required distance to be covered = 12 km   Beginning from origin point, he covers 9 km in 3 hours taking 15 minutes rest after every 45 minutes. To complete 12 kms he goes another 3 km in 45 minutes.   Thus, total time he takes is 3 hours 45 minutes.   ANSWER: 3 hours 45 minutes
Answer: D
The area of a square garden is A square feet and the perimeter is p feet. If a=2p+20, what is the perimeter of the garden, in feet?  Options:
A) 28 B) 36 C) 40 D) 56 E) 64

Solution: Perimeter of square = P   Side of square = P/4   Area of Square = (P^2)/16 =A   Given that A = 2P + 20   (P^2)/16 = 2P + 20   P^2 = 32P + 320   P^2 -32P -320 = 0   P^2 -40P +8P -320 = 0   P(P-40)+8(P+40) = 0   (P-40)(P+8) = 0   P = 40 or - 8   Discarding negative value , P = 40   Answer is 40
Answer: C