MU-NLPC/Calc-aqua_rat huggingface dataset:
Aram’s car was fined when he gave Joe and Peter a ride, so they decided to help Aram pay the fine. Joe paid $3 more than 1/4 of the fine and Peter paid $3 less than 1/3 of the fine, leaving pay $4 less than 1/2 the fine to complete the payment. What fraction of the fine did Aram pay?  Select the correct option:	A) $13	B) $15	C) $20	D) $28	E) $48

Solution: As given Aram' payment is [1][/2]*Fine -4   i.e Total Fine = 2 * (Sam's payment + 4)   Now, as everything looks integer, Fine should be able to divide by 4 and 3 . Because Joe's contribution has 1/4 of the fine and Peter's contribution has 1/3 of the fine   So, that leads me to following :   Options , Aram's pay , Total Fine (F) , F/4 , F/3   A) , 13 , 34 , No i.e 34/4 , No i.e 34/3   B) , 14 , 38 , No , No   $20) , 20 , 48 , Yes Yes   ,   No need to further go on as we have got F/4 and F/3 correct, just for confirmation we go further   D) , 28 , 64 , Yes , No   E) , 48 , 104 , Yes , No   $20orrect answer is $20
Answer: C
The number of sailors on a ship is 82% more than the number of officers. The ratio of sailors to officers would be	Choose the correct option:	A) 33:25	B) 47:20	C) 47:25	D) 22:25	E) 91:50

Solution: Sailor = 1.82 * Officer   Sailor/Officer = 1.82/1 = 182/100 = 91/50   Answer will be 91:50
Answer: E
Two trains of equal length, running with the speeds of 60 and 40 kmph, take 40 seconds to cross each other while they are running in the same direction. What time will they take to cross each other if they are running in opposite directions?	Choose one.
A) 10 sec  B) 16 sec  C) 13 sec  D) 67 sec  E) 8 sec

Solution: RS = 60 -40= 
60 -40 = 20
20 * 5/18= 100/18   T = 40   D = 40 * 100/18 = 2000/9   RS = 60 + 40= 
60 + 40 = 100
100 * 5/18   T= 2000/9 * 18/500= 
2000/9 * 18/500 = 8
8 sec   Answer: 8 sec
Answer: E
When positive integer x is divided by 11, the quotient is y and the remainder is 4. When 2x is divided by 6, the quotient is 3y and the remainder is 5. What is the value of 7y – x ?  Choose the correct option:
A) 2 B) 1 C) 0 D) -1 E) -2

Solution: (1) x = 11y + 4   (2) 2x = 18y + 5   Let's subtract equation (1) from equation (2).   7y + 1 = x   7y - x = -1   The answer is -1.
Answer: D
Find the sum The difference between the compound and S.I. on a certain sum of money for 6 years at 10% per annum is Rs.80 of money?	Choose the correct choice.
A) 1000  B) 1200  C) 4800  D) 3600  E) 8400

Solution: P = 80(100/10)6 => P = 1500   Answer: 4800
Answer: C
A person crosses a 600 m long street in 5 minutes, What is his speed in km per hour?	Choices.
A) 4.3 B) 7.2 C) 2.3 D) 3.2 E) 1.1

Solution: Explanation:   Speed = {\color{7.2lue} \left ( \frac{600}{5\times 60} \right )m/ sec =2m/ sec=\left ( 2\times \frac{18}{5} \right )km/hr=7.2km/hr}   Answer: 7.2
Answer: B
A train passes a station platform in 36 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 choices:  A) 150 m  B) 350 m  C) 300 m  D) 240 m  E) none

Solution: Speed =(54 x5/18m/sec) = 15 m/sec.   Length of the train = (15 x 20)m =300 m.   Let the length of the platform be x metres.   Then,x + 300/36= 15   x + 300 = 540   x = 240 m   Answer: 240 m
Answer: D
Two trains, each 100 m long, moving in opposite directions, cross other in 6 sec. If one is moving twice as fast the other, then the speed of the faster train is?  Choose the correct choice from the following answers:
A) 26 km/hr  B) 17 km/hr  C) 90 km/hr  D) 77 km/hr  E) 46 km/hr

Solution: Let the speed of the slower train be x m/sec.   Then, speed of the train = 2x m/sec.   Relative speed = ( x + 2x) = 3x m/sec.   (100 + 100)/6 = 3x => x = 25/2.   So, speed of the faster train = 50/2 = 50/2 * 18/5= 
50/2 * 18/5 = 90
90 km/hr.   Answer:90 km/hr
Answer: C
The length of a rectangular floor is more than its breadth by 200%. If Rs.441 is required to paint the floor at the rate of Rs.3/sq m, what would be the length of the floor?	Choose the correct choice:	A) 12	B) 18	C) 20	D) 21	E) 24

Solution: Let the length and the breadth of the floor be l m and b m respectively.   l = b + 200% of b = l + 2b = 3b   Area of the floor = 441/3= 
441/3 = 147
147 sq m   l b= 147i.e., l * l/3 = 147   l^2 = 441 => l = 21.   21
Answer: D
Find the odd man out. 1, 8, 27, 64, 125, 196, 216, 343 Choose one.
A) 64	B) 196	C) 216	D) 1	E) 146

Solution: Explanation :   The pattern is 1^3, 2^3, 3^3, 4^3, 5^3, 6^3, 7^3.   196 is not a perfect cube   Answer : Option 196
Answer: B
The average age of a committee of 8 members is 40 years. A member aged 55 years retired and his place was taken by another member aged 39 years . The average age of
present committee is;  Pick.
A) 39 years	B) 38 years	C) 36 years	D) 35 years	E) 37 years

Solution: Total age of the committee = 40*8= 
40*8 = 320
320,   Total age when a member is retired   and a new one was joined= 320-55 +39, =304   Average age of present committee = 304/8= 
304/8 = 38
38.   ANSWER:38 years
Answer: B
What is the unit digit in the product (3^65 x 6^59 x 7^71)?  Choices.
A) 18  B) 12  C) 69  D) 32  E) 4

Solution: Explanation:   Unit digit in 3^4 = 1 Unit digit in (3^4)16 = 1   Unit digit in 3^65 = Unit digit in [ (3^4)16 x 3 ] = (1 x 3) = 3   Unit digit in 6^59 = 6   Unit digit in 7^4 Unit digit in (7^4)17 is 1.   Unit digit in 7^71 = Unit digit in [(7^4)17 x 73] = (1 x 3) = 3   Required digit = Unit digit in (3 x 6 x 3) = 4   4
Answer: E
__2A
x__B
____
CC
In the multiplication problem above, A, B, and C represent distinct digits. If the sum of A and B is equal to 3, what is the value of C?  Select the correct option.
A) 6
B) 5
C) 4
D) 3
E) 2

Solution: If A+B=3   assuming A and B are positive then A*B<10 (they could be either 1,2,)   therefore   A*B=C   2*B=C   A+B=3   Three simple equations - divide the 1st/2nd --> A=2 plug it the 3rd --> B=1 --> C=2 (ANSW2R 2)
Answer: E
An order was placed for the supply of a carpet whose breadth was 6 m and length was 1.44 times the breadth. What be the cost of a carpet whose length and breadth are 40% more and 25% more respectively than the first carpet. Given that the ratio of carpet is Rs. 45 per sq m? Pick:	A) 4082.42	B) 4082.38	C) 4082.78	D) 4082.4	E) 4082.94

Solution: Explanation:   Length of the first carpet = (1.44)(6) = 8.64 cm   Area of the second carpet = 8.64(1 + 40/100) 6 (1 + 25/100)   = 51.84(1.4)(5/4) sq m = (12.96)(7) sq m   Cost of the second carpet = (45)(12.96 * 7) = 315 (13 - 0.04) = 4095 - 12.6 = Rs. 4082.40   Answer: Option 4082.4
Answer: D
Father is 5 times faster than son. Father completes a work in 40 days before son. If both of them work together, when will the work get complete? Choose the correct option.
A) 8 1/0  B) 8 1/3  C) 8 1/8  D) 8 1/6  E) 8 1/5

Solution: As efficiency is inversely proportional to days, If Father : son's efficiency is 5 : 1, then Days taken by them should be 1 : 5. Assume, the days taken by them are k, 5k.   Given that father takes 40 days less. So 5k - k = 40 ⇒⇒ k = 10   Father takes 10 days to complete the work. Total work is 10 x 5 = 50 units.   If both of them work together, they complete 5 + 1 units a day. 6/day. To complete 50 units, they take 50/6 = 8 1/3 days.   Ans: 8 1/3
Answer: B
Twenty four men can do a work in 42 days. How many men are required to complete the work in 21 days? Select.
A) 20  B) 10  C) 50  D) 40  E) 48

Solution: E   48   We have M1 D1 = M2 D2   So, 24 * 42 = M2 * 21 => M2 = 48.   Answer is 48
Answer: E
Siddharth wants to borrow Rs.5000 at rate of interest 6% p.a. at S.I and lend the same amount at C.I at same rate of interest for two years. What would be his income in the above transaction? Choose one
A) s.21.60 B) s.21.68 C) s.21.18 D) s.21.98 E) s.18

Solution: Amount of money Siddharth borrowed at S.I at 6% p.a. for two years = Rs.5,000   He lend the same amount for C.I at 6% p.a. for two years.   => Siddharth's income = C.I - S.I   = p[1 + r/ 100]n - p - pnr/100   = p{ [1 + r/ 100]2 - 1 - nr/100   = 5,000{ [1 + 6/100]2 - 1 - 12/100}   = 5,000 {(1.06)2- 1 - 0.12} = 5,000(1.1236 - 1 - 0.12)   = 5,000 (0.0036) = 5 * 3.6   = Rs.18   Answer: s.18
Answer: E
Solve x2 â€“ 7x = 0 Choose the correct choice:	A) 0,7	B) 1,7	C) 2,7	D) 3,7	E) 4,7

Solution: This quadratic factors easily: Copyright Â© Elizabeth Stapel 2002-2011 0,7ll Rights Reserved   x2 â€“ 7x = 0   x(x â€“ 7) = 0   x = 0 or x â€“ 7 = 0   x = 0 or x = 7   The solution is x = 0, 7   0,7NSWER 0,7
Answer: A
Pumps A, B, and C operate at their respective constant rates. Pumps A and B, operating simultaneously, can fill a certain tank in 2 hours; pumps A and C, operating simultaneously, can fill the tank in 3/2 hours; and pumps B and C, operating simultaneously, can fill the tank in 2 hours. How many hours does it take pumps A, B, and C, operating simultaneously, to fill the tank.
Choose the correct choice from the following options:
A) 1/3
B) 1/2
C) 1/4
D) 1
E) 5/6

Solution: A+B =2; A+1/4 =3/2 ,B+1/4 =2 ; ADD THEN 2*(A+B+1/4) = 4+3/2 = 11/2   A+B+1/4 = 11/4 HRS   1/4
Answer: C
Raffle tickets numbered consecutively from 1 through 250 are placed in a box. What is the probability that a ticket selected at random will have a number with a hundreds digit of 2 ?  Pick one:  A) 2/5  B) 1/5  C) 33/83  D) 99/250  E) 100/249

Solution: SOLUTION   The number of integers from 1 to 250, inclusive is 250, out of which 100 (from 200 to 299) will have a hundreds digit of 2. Thus the probability is 50/250=1/5.   Answer: 1/5
Answer: B
Income of a company doubles after every one year. If the initial income was Rs. 4 lakhs.What would be the income after 5 years? Choose the correct choice from the following options:
A) 6.78 crores	B) 1.28 crores	C) 2.98 crores	D) 3.78 crores	E) 4.29 crores

Solution: Income after 1 year=Rs. (4x2)lakhs   Income after 2 years= Rs. (4x2x2)lakhs   =Rs.4x4=16 lakhs   Income after 5years=Rs. (4x2^5)=Rs. 128 lakhs   =Rs. 1.28 crores   ANSWER: 1.28 crores
Answer: B
A cistern 6m long and 4 m wide contains water up to a depth of 1 m 25 cm. The total area of the wet surface is: Options:
A) 49
B) 87
C) 27
D) 66
E) 19

Solution: Explanation:   49rea of the wet surface = [2(lb + bh + lh) - lb]   = 2(bh + lh) + lb   = [2 (4 x 1.25 + 6 x 1.25) + 6 x 4]   = 49   49nswer: 49) 49
Answer: A
X and Y began business with Rs.10000 and Rs.8000 after 6 months, X advances Rs.2000 and Y advances Rs.2000 more.
At the end of the year, their profits amounted to Rs.2000 find the share of X and Y respectively. Choose the correct choice from the following options.
A) 1000,1000	B) 900,1100	C) 1200,800	D) 800,1200	E) 1100, 900

Solution: (10*6 + 12*6):(8*6 + 10*6)   11:9   X share = 11/20 * 2000= 
11/20 * 2000 = 1_100
1100.   Y share= 9/20 * 2000= 
9/20 * 2000 = 900
900.   X and Y share respectively is 1100 , 900. Answer: 1100, 900
Answer: E
We bought 85 hats at the store. Blue hats cost $6 and green hats cost $7. The total price was $530. How many green hats did we buy?
Choices
A) A)36  B) B)20  C) C)40  D) D)42  E) E)44

Solution: Let B be the number of blue hats and let G be the number of green hats.   B+G=85.   B=85-G.   6B+7G=530.   6(85-G)+7G=530.   510-6G+7G=530.   G=530-510= 
530-510 = 20
20.   The answer is 20.
Answer: B
The greatest common factor of 16 and the positive integer n is 4, and the greatest common factor of n and 45 is 3. Which of the following could be the greatest common factor of n and 120? Choose the correct choice: A) 5 B) 8 C) 12 D) 24 E) 30

Solution: n includes the factors 2^2 (but not 2^3) and 3 (but not 3^2 or 5)   120 = 8*3*5   The GCF is   4*3= 
  4*3 = 12
12.   The answer is 12.
Answer: C
If M and N are positive integers that have remainders of 1 and 3, respectively, when divided by 4, which of the following could NOT be a possible value of M+N?	Answers.
A) 76 B) 52 C) 36 D) 28 E) 10

Solution: M=4p+1   N=4q+3   We need M+N=4p+1+4q+3=4(p+q)+4   Pick numbers for pq   Since it is an addition of pq and the answer to this expression should be an integer (because all the numbers being added are integers),   we just need to choose values so that we get integer multiples of 6 so   p+q=0 ; M+n = 4   p+q=1 ; M+N = 8   P+q=2 ; M+N = 12   and so on, so basically you get something like - 4,8,12,16,20,24,28,..... all the other options were turning up.   Then I directly tried p+q=2because it was closer to 10, i got 12,   So Answer 10.
Answer: E
In his pocket, a boy has 3 red marbles, 5 blue marbles, and 6 green marbles. How many will he have to take out of his pocket to ensure that he has taken out at least one of each color?  Pick one:	A) 10	B) 11	C) 12	D) 13	E) 14

Solution: The worst case scenario would be that he has taken 5 blue and 6 green, a total of 11 marbles, and still doesn't have 3 distinct colors. But the next draw, marble number 12, will surely be red as only the red marbles are left in his pocket.   The answer is 12.
Answer: C
A number consists of two digits. If the digits interchange places and the new number is added to the original number, then the resulting number will be divisible by :  Choose the correct answer:
A) 5	B) 7	C) 9	D) 11	E) 13

Solution: Sol.   Let the ten’s digit be x and unit’s digit be y. Then, number = 10x + y   Number obtained by interchanging the digits = 10y + x.   ∴ (10x+y) + (10y + x) = 11 (x + y), which is divisible by 11.   Answer 11
Answer: D
Two trains are moving in the same direction at 72 kmph and 36 kmph. The faster train crosses a man in the slower train in 27 seconds. Find the length of the faster train?  Pick one
A) 290 m	B) 270 m	C) 220 m	D) 260 m	E) 250 m

Solution: Relative speed = (72 - 36) * 5/18 = 2 * 5= 
2 * 5 = 10
10 mps.   Distance covered in 27 sec= 25 * 10= 
25 * 10 = 250
250 m.   The length of the faster train= 250 m.   ANSW250 mR:250 m
Answer: E
If the sum of five consecutive even positive integers is A, then the sum of the next five even consecutive integers in terms of A is:	Choose the correct choice from the following: A) A+5 B) A+10 C) A+25 D) A+50 E) 2A + 5

Solution: In Case of Consecutive Integers or Integers in Arithmetic Progression Mean = Median   I.e. Median = A/5 = Mean = Third Integer   First Integer = A/5 - 4   Second Integer = A/5 - 2   Third Integer = A/5   Fourth Integer = A/5 + 2   Fifth Integer = A/5 + 4   i.e.   Sixth Integer = A/5 + 6   Seventh Integer = A/5 + 8   Eighth Integer = A/5 + 10   Ninth Integer = A/5 + 12   Tenth Integer = A/5 + 14   Now Mean of next 5 Integers = Median = A/5 + 5   i.e. Sum of Next 5 integers = (A/5 + 10)*5 = A+50   Answer: option A+50
Answer: D
Out of first 20 natural numbers, one number is selected at random. The probability that it is either an even number or a prime number is?	Choose the correct choice:
A) 17/27	B) 17/70	C) 17/90	D) 17/20	E) 17/23

Solution: n(S) = 20   n(Even no) = 10 = n(E)   n(Prime no) = 8 = n(P)   P(EᴜP) = 10/20 + 8/20 - 1/20 = 17/20   Answer: 17/20
Answer: D
Abby and Bobby type at constant rates of 70 words per minute and 60 words per minute, respectively. Bobby begins typing before Abby and has typed 600 words when Abby begins typing at 1:30 pm. If they continue typing at their respective rates, at what time will Abby have typed exactly 200 more words than Bobby?  Pick.
A) 1:40 PM B) 2:50 PM C) 2:00 PM D) 2:10 PM E) 2:20 PM

Solution: Say time needed for Abby to type 200 more words than Bobby is t. In that time she would type 70t words and Bobby would type 60t words.   Now, total words typed by Bobby would be 600+60t and we want that number to be 200 less than 70t: 600+60t=70t-200 --> t=80.   1:30 PM + 80 minutes = 2:50 PM.   Answer: 2:50 PM.
Answer: B
A man swims downstream 72 km and upstream 45 km taking 3 hours each time; what is the speed of the current?	Choose the most appropriate option:	A) 1.5	B) 3.5	C) 4.5	D) 2.5	E) 5.5

Solution: 72 --- 3 DS = 24   ? ---- 1   45 ---- 3 US = 15   ? ---- 1 S = ?   S = (24 - 15)/2= 
(24 - 15)/2 = 9/2 = around 4.5
4.5   Answer:4.5
Answer: C
A trader sells 85 meters of cloth for Rs. 8925 at the profit of Rs. 25 per metre of cloth. What is the cost price of one metre of cloth?
Answers:
A) 80
B) 28
C) 90
D) 26
E) 11

Solution: Explanation:   SP of 1m of cloth = 8925/85 = Rs. 105   CP of 1m of cloth = SP of 1m of cloth - profit on 1m of cloth   = Rs. 105 - Rs. 25 = Rs. 80.   80nswer: 80
Answer: A
If 1 > 1 - ab > 0, which of the following must be true?
I. a/b > 0
II. ab < 1
III. a/b < 2
Choose the correct choice from the following
A) I only  B) II only  C) III only  D) I and II only  E) I and III only

Solution: MANHATTAN GMATOFFICIAL SOLUTION:   You can manipulate the original compound inequality as follows, making sure to perform each manipulation on every term:   1 > 1 - ab > 0   0 > -a b > -1 Subtract 1 from all three terms.   0 < ab < 1 Multiply all three terms by -1 and flip the inequality signs.   Therefore you know that 0 < ab < 1. This tells you that ab is positive, so a/b must be positive (a and b have the same sign). Therefore, I must be true. However, you do not know whether a/b < 1, so II is not necessarily true. But you do know that ab must be less than 1, so III must be true.   Therefore, the correct answer is (I and II only).
Answer: D
{-10, -6, -5, -4, -2.5, -1, 0, 2.5, 4, 6, 7, 10}
A number is to be selected at random from the set above. What is the probability that the number will be a solution to the equation (x-2)(x+1)(2X+5) = 0?  Choose the correct choice from the following choices.
A) 1/12 B) 1/6 C) 1/4 D) 1/3 E) 1/2

Solution: x = -1   Prob = 1/12   1/12nswer -1/12
Answer: A
If the average (arithmetic mean) of 5 positive temperatures is x degrees Fahrenheit, then the sum E of the 3 greatest of these temperatures, in degrees Fahrenheit, could be Choose the correct choice from the following answers:	A) 6x	B) 4x	C) 5x/3	D) 3x/2	E) 3x/5

Solution: Note that we have 5positivetemperatures.   Next, as the average is x then the sum of the temperatures is 5x and as all the temperatures are positive then the sum of the 3 greatest must be more than (or equal to) 3x (as the average of the 3 greatest must be at least x) and less than 5x: 3x<e<5x --=""> only option B fits.   Answer: 4x.</e<5x>
Answer: B
What will be the result of 12^4+ 3 +2^9 +3 - 8/2 ? Select:
A) 58
B) 14
C) 145
D) 69
E) 74

Solution: The multiplication(e.g. 12^4) and division(e.g. 8/2) is done first and then the sum(e.g. 48+3) and   subtraction (e.g.4-4), and the answer is 69, option 69.
Answer: D
A pet store holds cats and dogs. If the difference between the number of cats and the number of dogs is 7. What could be the ratio of Cats to dogs in the pet store? Choose the correct option.
A) 1:3	B) 1:4	C) 28:35	D) 2:5	E) 4:6

Solution: Say theratioof cats to dogs is a/b. Then thenumberof cats would be ax and thenumberof dogs bx, for some positive integer x.   We are told that ax - bx = 7 --> x(a - b) =7. Since 7 is a prime number it could be broken into the product of two positive multiples only in one way: x(a - b) = 1*7.   The above implies that either x = 1 and a - b = 7 or x = 7 and (a - b) = 1.   Therefore the correct answer should have the difference between numerator and denominator equal to 1 or 7.   For the original question only option which fits is E, 4:5. Cats = 7*4= 
7*4 = 28
28 and dogs= 7*5= 
7*5 = 35
35.   Answer: 28:35.
Answer: C
The average of 10 numbers is 40.2. Later it is found that two numbers have been wrongly copied. The first is 16 greater than the actual number and the second number added is 13 instead of 31. Find the correct average.  Choose the correct choice from the following
A) 40.2	B) 40.4	C) 40.6	D) 40.8	E) None of the above

Solution: Sum of 10 numbers = 402   Corrected sum of 10 numbers   = 402 – 13 + 31 – 16 = 404   Hence, new average = 404⁄10 = 40.4   Answer 40.4
Answer: B
When the positive integer A is divided by 9 and 5, the remainder is 3 and 4, respectively. When the positive integer B is divided by 9 and 5, the remainder is 3 and 4, respectively. Which of the following must be a factor of A-B?  Options.
A) 32  B) 36  C) 40  D) 45  E) 50

Solution: A = 9k+3 = 5j+4   B = 9m+3 5 +4= 
5 +4 = 9
9m+3= 5n+4   A-B = 9(k-m) = 5(j-n)   Thus A-B is a multiple of 9 and 5, so it is multiple of 45.   The answer is 45.
Answer: D
The 8 spokes of a custom circular bicycle wheel radiate from the central axle of the wheel and are arranged such that the sectors formed by adjacent spokes all have different central angles, which constitute an arithmetic series of numbers (that is, the difference between any angle and the next largest angle is constant). If the largest sector so formed has a central angle of 80°, what fraction of the wheel’s area is represented by the third smallest sector? Options: A) 1/72 B) 1/36 C) 1/18 D) 1/12 E) 1/9

Solution: Its an AP question .... it is given clearly in the question .   Let the smallest angle be a   and the circle has 8 sectors and hence 8 angle with a common difference d   hence all the angles can be written in AP form with Cd as d ,   a, a+d, a+2d, a+3d ,a+4d, a+5d, a+6d ,a+7d,   given that a+7d = 80 --------1   also   a + a+d + a+2d + a+3d +   a+4d + a+5d + a+6d + a+7d = 360 ( as sum of all the angle is 360)   which is 8a + 28d = 360 --------2   solving 1 and 2   we get a=10   We are almost done ,   now the question ask what fraction of the wheel’s area is represented by the smallest sector ?   (30/360)( pie r*r)/ (pie r*r) = 30/360= 1/12   1/12 ans ....
Answer: D
A quadratic function f(x) attains its minimum value of -15 at x=3. If f(0)=5, find the value of f(9). Options:	A) 65	B) 55	C) -25	D) 75	E) 25

Solution: Explanation :   65ny quadratic equation can be written as f(x) = α(x-k)2 - β   Given that minimum value of f(x) is -15 at x=3   f(x) is minimum when x=k => k=3   -15=-β => β= 15   65lso given that f(0) = 5   => 5 = α(0-3)2 - 15 => α= 20/9   Hence, f(9)=20/9(9-3)2 - 15 = 65   65nswer : 65
Answer: A
A circular garden is surrounded by a fence of negligible width along the boundary. If the length of the fence is 1/4 of th area of the garden. What is the radius of the circular garden? Choose the correct answer:
A) 1	B) 2	C) 4	D) 8	E) 16

Solution: as per the question-- width is negligible   now,   let L be the length of the fence =2pir   L=1/4(pir^2)   pir^2=8pir   r=8   Answer : 8
Answer: D
If the horse can run 10 miles/hour, how many days would it take for a horse to run from New York City to Washington. D.C.? (240 miles from NYC to D.C.)	Choose the correct choice from the following answers.
A) 0.6 B) 0.8 C) 1 D) 1.2 E) 1.4

Solution: The horse runs 10 miles/hour, thus it would take the horse 240 miles/10 miles/hour to = 24 hours to run from NYC to D.C. There are 24 hours in a day, so days it take would be 24hours/24hours/day = 1 day. 1orrect Option: 1
Answer: C
Anil can do a work in 15 days while Sunil can do it in 25 days. How long will they take if both work together?  Choose the most appropriate option
A) 4 3/8 days	B) 7 3/8 days	C) 9 3/8 days	D) 8 3/8 days	E) 11 3/8 days

Solution: 9 3/8 days   9 3/8 days   1/15 + 1/25 = 8/75   75/8 = 9 3/8 days
Answer: C
Trapezoid JKLM in the x-y plane has coordinates J = (–2, –4), K = (–2, 1), L = (6, 7), and M = (6, –4). What is its perimeter?	Answers
A) 34
B) 36
C) 38
D) 40
E) 42

Solution: This one may look challenging initially, but all kinds of simplifying tricks. First of all, J & K have the same x-coordinate, so that’s a vertical segment, and the length is JK = 1 – (–4) = 5. L & M also have the same x-coordinate, so that’s also a vertical segment, and the length is LM = 7 – (–4) = 11. J & M have the same y-coordinate, so that’s also a horizontal segment, and the length is JM = 6 – (–2) = 8. Right there, we have the lengths of three of the four sides.   The last side to find is KL. From K = (–2, 1), we have to go over 8 and up 6 to get to L = (6, 7), so 6 and 8 the legs of the right triangle, and KL is the hypotenuse. We recognize another common Pythagorean triplet — (6, 8, 10), which is a multiple of the (3, 4, 5) triplet. Thus, without further calculations, we immediately know KL = 10.   Perimeter = JK + KL + LM + JM = 5 + 10 + 11 + 8= 
5 + 10 + 11 + 8 = 34
34   34nswer= 34
Answer: A