MU-NLPC/Calc-aqua_rat huggingface dataset:
In flip of coin seven times in a row, what is the probability that the result will not be tails at any ?	Choose the correct choice from the following choices.
A) 1/128	B) 29/128	C) 35/128	D) 1/16	E) 1/4

Solution: In a flip of a coin seven times in a row, tails at no time means heads all the time   Heads = at least 7 heads   Atleast 7 heads in 7 flip.   The total outcome of flip is = 2^7 = 128   For any Coins problem write the ask in the shown format.   HHHHHHH   Once you have written in the above mentioned format the answer is pretty straight.   HHHHHHH = [7!]/[7!] = 1   Sum 7  / 7= 
7  / 7 = 1
1   Sum= 1 =   1/128nswer = 1/128   1/128nswer - 1/128
Answer: A
12 buckets of water fill a tank when the capacity of each bucket is 49 litres. How many buckets will be needed to fill the same tank, if the capacity of each bucket is 7 litres?
Select.
A) 39  B) 84  C) 80  D) 82  E) 86

Solution: Capacity of the tank = (12 Ã— 49) litre   Number of buckets required of capacity of each bucket is 17 litre = 12Ã—49/7=12Ã—7=84   Answer is 84
Answer: B
As they say, beggars can't be choosers, in fact begger take what they can get. A begger on the street can make one cigarette out of every 6 cigarette butts he finds. After one whole day of searching and checking public ashtrays the begger finds a total of 72 cigarette butts. How many cigarettes can he make and smoke from the butts he found?  Pick.
A) 14  B) 18  C) 15  D) 10  E) 13

Solution: A   14   If the beggar can make a whole cigarette from 6 butts then he can make 12 cigarettes from the 72 he found. Once he smokes those, he then will have another 12 butts, which gives him enough to make another 2 cigarettes. 14 total of 14.
Answer: A
Given that x and y are nonnegative integers, compute the number of pairs (x, y) such that
5x + y = 20.	Choices:  A) 2  B) 3  C) 5  D) 9  E) 8

Solution: For x = 0,1,2,3,4, there is a valid y, giving the answer 5 .   correct answer 5
Answer: C
A and B can finish a work in 16 days while A alone can do the same work in 24 days. In how many days B alone will complete the work?
Options:
A) 87 days
B) 48 days
C) 17 days
D) 87 days
E) 12 days

Solution: 48 days = 1/16 – 1/24   = 1/48   => 48 days   Answer: 48 days
Answer: B
Of 64 players on a cricket team, 37 are throwers. The rest of the team is divided so one third are left- handed and the rest are right handed. Assuming that all throwers are right handed, how many right- handed players are there total?  Choose the correct answer.
A) 54  B) 55  C) 59  D) 71  E) 92

Solution: Total = 64   Thrower = 37   Rest = 64 - 37= 
64 - 37 = 27
27   Left Handed= 27/3= 
27/3 = 9
9   Right handed= 18   If all Thrower are right handed then total right handed is   37 + 18= 
  37 + 18 = 55
55   so B. 55 is the right answer
Answer: B
Roger can read a book in k minutes. What part of the book can he read in 9 minutes? (k>8)	Choose the most appropriate option:
A) 8+k	B) 8/k	C) k/8	D) (k+ 8)/k	E) (k-8) / k

Solution: Let's sayk = 24   That is, it takes 24 minutes to read the entire book.   So, in 8 minutes, Roger can read1/3of the book   So, we're looking for the answer choice that yields an OUTPUT of1/3whenk = 24   A) 8+24=32ELIMINATE   B) 8/24=1/3KEEP   k/8)24/8 =3ELIMINATE   D) (24+ 8)/24=32/24 = 4/3ELIMINATE   E) (24-8) /24=16/24 = 2/3ELIMINATE   Answer: k/8
Answer: C
What is the dividend. divisor 14, the quotient is 9 and the remainder is 5?  Choose the correct answer:  A) A)130  B) B)131  C) C)148  D) D)158  E) E)160

Solution: D = d * Q + R   D = 14 * 9 + 5   D = 126 + 5= 
126 + 5 = 131
131   Answer 131
Answer: B
4 professors and 6 students are being considered for membership on a supervisory committee which must consist of 3 people. If the committee has to include at least 2 professor, how many ways can this committee be formed?	Choose the correct choice from the following.
A) 36 B) 64 C) 72 D) 80 E) 100

Solution: you count up combinations twice.   4*9*8... and let me name 6 with students A,B,C,..,F   after choosing a professor, when you choose Student A and B, you can choose A first, then B. Or B first, then A. Both combination are same.   I don't think that's the only mistake.   64 is a factor of = 2^2*4^2   144 is a factor of = 2^4*3^2.   These are very different numbers and you cannot divide 144 with something to get to 64.
Answer: B
How many three letter words are formed using the letters of the word LUNCH?  Pick.
A) A)15 B) B)150 C) C)12 D) D)120 E) E)18

Solution: The number of letters in the given word is fIVE.   The number of three letter words that can be formed using these five letters is 5P4   = 5 * 4 * 3*2= 
5 * 4 * 3*2 = 120
120.   Answer:120
Answer: D
A person covered one-fourth of the total distance at 15 kmph and remaining distance at 24 kmph. What is the average speed for the total distance?	Choose the correct choice from the following choices: A) 20 (1/8)kmph B) 20 (20/23)kmph C) 20 (17/23)kmph D) 27 (1/23)kmph E) 21 (1/8)kmph

Solution: Let the total distance be x km   total time taken = (x/4)/15 + (3x/4)/24 = x/60 + x/32 = 23x/480   Average speed = x/(23x/480) = 480/23kmph   = 20 (20/23)kmph.   Answer:20 (20/23)kmph
Answer: B
Car A runs at the speed of 65km/hr & reaches its destination in 8hr. Car B runs at the speed of 70 km/h & reaches its destination in 4h. What is the respective ratio of distances covered by Car A & Car B? Choose the correct answer:
A) 11 : 6
B) 12 : 7
C) 13 : 7
D) 15 : 6
E) 13 : 6

Solution: Sol. Distance travelled by 13 : 7ar A = 65 × 8 = 520 km   Distance travelled by 13 : 7ar B = 70 × 4 = 280 km   Ratio = 520/280 = 13 : 7   13 : 7
Answer: C
If I walk at 3 kmph, I miss the train by 2 min, if however, I walk at 4 kmph. I reach the station 2 min before the arrival of the train. How far do I walk to reach the station? Choose the correct answer: A) 4/5 B) 4/6 C) 4/0 D) 4/2 E) 4/1

Solution: x/3 – x/4 = 4/60   x = 4/5 km   4/5nswer: 4/5
Answer: A
On the number line, the number p is twice as many units from -2 as -2 is from 4. If p is less than –2, what is the value of p ?  Choose the correct choice from the following:
A) –14  B) –10  C) –6  D) 10  E) 14

Solution: Distance between -2 and 4 = 6   Since number p is twice as many units from -2 as -2 is from 4   , therefore p can be -14 Since , p is less than -2 ,   the value of p = -14   –14nswer –14
Answer: A
In a bag containing only blue, red and green marbles, all but 15 are blue, all but
13 are red and all but 12 are green. How many are red?
Choose the correct choice from the following options
A) 13	B) 7	C) 25	D) 20	E) 10

Solution: All but blue means number of marbles except blue..hence, let x be the red marble,y   be the green marble,z be the blue marble...   x+y=15   y+z=13   x+z=12   solving this eqns, we get x=7 y=8 z=5 hence number of red marbles are 7   ANSWER:7
Answer: B
A first grade teacher uses ten playing cards, each numbered from 1 to 10, to teach her students to order numbers correctly. She has students choose four flash cards randomly, then arrange the cards in ascending order. One day, she removes the cards '2' and '4' from the deck. On that day, how many different correct arrangements of four randomly selected cards are possible?	Options.
A) 70  B) 60  C) 50  D) 40  E) 30

Solution: proble of combination 8C4 = 8!/4!*(8-4)! = 8*7*6*5*4!/4!*4! 8 /4 *(8-4)= 
8 /4 *(8-4) = 8
8*7*6*5*4!/4!*4!=70   70
Answer: A
In the sequence 1, 2, 4, 8, 16, 32, …, each term after the first is twice the previous term. What is the sum of the 16th, 17th, and 19th terms in the sequence?
Choose the correct option
A) 2^18  B) 3(2^17)  C) 7(2^16)  D) 3(2^16)  E) 11(2^15)

Solution: the sequence comes out to be 2^0,2^1,2^2,2^3 and so on...   so 16th term will be 2^15   17th term 2^16   19th term 2^18   adding all three   we get   2^15+(2^15)*2+(2^15)*8   so answer is 2^15(1+2+8)=>11(2^15)   answer 11(2^15)
Answer: E
In an xy-coordinate plane, a line is defined by y = kx + 1. If (1, b), (a, 4), and (a, b+1) are three points on the line, where a and b are unknown, then k = ?
Choose one:
A) 1/2
B) 1
C) 3/2
D) 2
E) 5/2

Solution: b=k+1...(1)   b+1=ak+1...(2)   4=ak+1...(3)   Taking (2) and (3)   4=b+1   b=3   Taking (1)   3=k+1   k=2   Answer : 2
Answer: D
If the height of a cone is increased by 190% then its volume is increased by?	Select the correct option:
A) 100  B) 777  C) 998  D) 190  E) 2879

Solution: 100%   Answer:190
Answer: D
A set of numbers has the property that for any number t in the set,t+3 is in the set. If -2 is in the set, which of the following must also be in the set? I. -3 II. 1 III. 4	Pick one.
A) I,III only
B) III only
C) II only
D) II,III only
E) I only

Solution: question is asking for must be there elements.   According to the question if t is there t+3 must be there.   if -2 is the starting element the sequence is as follows.   S ={-2,1,4,7,10....}   if -2 is not the starting element the sequence is as follows   S = {...-5,-2,1,4,7,10...}   By observing the above two sequences we can say that 1,4 must be there in set S.   Answer : II,III only
Answer: D
If a:b = 2:3 and b:c = 4:3, then find a:b:c
Choose the correct choice from the following answers:
A) 8:12:9 B) 2:3:8 C) 2:3:9 D) 2:3:12 E) None of these

Solution: Explanation:   a:b=2:3   b:c=4:3=(4∗3/4:3∗3/4)   =3:9/4   a:b:c=2:3:9/4   =8:12:9   Option 8:12:9
Answer: A
If the L.C.M of two numbers is 660 and their product is 18480, find the H.C.F of the numbers.
Options:
A) 50
B) 30
C) 125
D) 25
E) None of these

Solution: H.C.F = (Product of the numbers) / (Their L.C.M) = 18480/660= 
18480/660 = 28
28.   ANSWNone of theseR:None of these
Answer: E
The current of a stream runs at the rate of 4 kmph. A boat goes 6 km and back to the starting point in 2 hours, then find the speed of the boat in still water?	Choices:
A) 4
B) 5
C) 8
D) 9
E) 6

Solution: S = 4   M = x   DS = x + 4   US = x - 4   6/(x + 4) + 6/(x - 4) = 2   x = 8   Answer: 8
Answer: C
The average of 6 no.'s is 5.40. The average of 2 of them is 5.2, while the average of the other 2 is 5.80. What is the average of the remaining 2 no's?  Choose the correct choice from the following answers:
A) 5.2
B) 2.6
C) 3.6
D) 4.5
E) 4.6

Solution: Sum of the remaining two numbers = (5.40 * 6) - [(5.2 * 2) + (5.8 * 2)]   = 32.40 - (10.4+ 11.6) = 32.40 - 22.0 = 10.40.   Required average = (10.4 / 2)= 
(10.4 / 2) = 5.2
5.2   5.2nswer : 5.2
Answer: A
The simple Interest on a certain sum of money at the rate of 4% p.a. for 5 years is Rs. 1680. At what rate of interest the same amount of interest can be received on the same sum after 4 years ?	Choices
A) 5%	B) 6%	C) 8%	D) 4%	E) 7%

Solution: S.I. = 1680, R = 4% T = 5 years   Principal = (100 *1680)/ (5*4)= 
(100 *1680)/ (5*4) = 8_400
8400   So P= 8400   Rate = (100 *1680)/ (8400 * 4)= 
(100 *1680)/ (8400 * 4) = 5
5%   5%NSWER:5%
Answer: A
The average of first 20 prime numbers is? Choose one
A) 9.5 B) 8.6 C) 9.3 D) 9.6 E) 9.8

Solution: Explanation:   Average = (2+3+5+7+11+13+17+19/8 = 77/8= 9.6(Approx)   Answer is 9.6
Answer: D
At 1:00 PM, Train X departed from Station A on the road to Station B. At 1:30 PM, Train Y departed Station B on the same road for Station A. If Station A and Station B are p miles apart, Train X’s speed is r miles per hour, and Train Y’s speed is s miles per hour, how many hours after 1:40 PM, in terms of p, r, and s, do the two trains pass each other?	Options:
A) 0.5 + (p - 0.5s)/(r + s) B) (p - 0.5s)/(r + s) C) 0.5 + (p - 0.5r)/r D) (p - 0.5r)/(r + s) E) 0.5 + (p - 0.5r)/(r + s)

Solution: The distance A is going to cover between 1:00 and 1:30   = .5r   now the distance between the two trains = (p-.5r)   the relative velocity = (r-(-s)) = r+s   From 1:30, time is going to take when they meet = (p-.5r)/(r+s)   so the ans is .5+((p-.5r)/(r+s)) [.5 is added for the time from 1:00 to 1:30]   ans is 0.5 + (p - 0.5r)/r
Answer: C
A work crew of 7 Men takes 10 days to complete one-half of a job. If 8 men are then added to the crew and the men continue to work at the same rate, how many days will it take the enlarged crew to do the rest of the job?	Options.
A) 2 B) 3 C) 3 1/3 D) 4 E) 4 2/3

Solution: Suppose 1 man can do work in X days..   so 7 men will do in ..   7/X=1/10*1/2 as half job is done   X=140   now 8 more are added then   15/140=1/2*1/d for remaining half job   d=4 2/3 Number of days   4 2/3
Answer: E
If the annual interest on a principal is 25%, how many years before the amount is double? Select the correct option: A) 2 B) 3 C) 7 D) 4 E) 5

Solution: P = (P*25*R)/100   R = 4%   Answer: 4
Answer: D
A 10-by-4 inch piece of paper is used to form the lateral surface of a cylinder. If the entire piece of paper is used to make the lateral surface, which of the following must be true of the two possible cylinders that can be formed?
Choose the correct choice
A) The volume of the cylinder with height 10 is 40/pi cubic inches greater than the volume of the cylinder with height 6.	B) The volume of the cylinder with height 4 is 40/pi cubic inches greater than the volume of the cylinder with height 10.	C) The volume of the cylinder with height 10 is 40pi cubic inches greater than the volume of the cylinder with height 6.	D) The volume of the cylinder with height 4 is 40pi cubic inches greater than the volume of the cylinder with height 10.	E) The volume of the cylinder with height 4 is 240/pi cubic inches greater than the volume of the cylinder with height 10.

Solution: Pretty straightforward. Plug in the values to compute the volume of the cylinder. Keep in mind 4 and 10 are the circumference of the base and not the radius. The volume of the cylinder with height 4 is 40/pi cubic inches greater than the volume of the cylinder with height 10. is the right answer.
Answer: B
How many positive integers less than 300 are there such that they are multiples of 17 or multiples of 16?
Choose the correct choice from the following answers: A) 31 B) 32 C) 33 D) 34 E) 35

Solution: 300/17 = 17 (plus remainder) so there are 17 multiples of 17   300/16 = 18 (plus remainder) so there are 18 multiples of 16   We need to subtract 1 because 17*16 is a multiple of both so it was counted twice.   The total is  17+18-1= 
 17+18-1 = 34
34   The answer is 34.
Answer: D
A certain experimental mathematics program was tried out in 2 classes in each of 38 elementary schools and involved 44 teachers. Each of the classes had 1 teacher and each of the teachers taught at least 1, but not more than 3, of the classes. If the number of teachers who taught 3 classes is n, then the least and greatest possible values of n, respectively, are
Choose the most appropriate option:
A) 0 and 13
B) 0 and 14
C) 0 and 16
D) 1 and 9
E) 2 and 8

Solution: One may notice that greatest possible values differ in each answer choice in contrast to the least values, which repeat.   To find out the greatest value you should count the total classes (38*2=76), then subtract the total #of teachers since we know from the question that each teacher taught at least one class (76-44=32). Thus we get a number of the available extra-classes for teachers, and all that we need is just to count how many teachers could take 2 more classes, which is  32/2= 
 32/2 = 16
16. So the greatest possible value of the # of teachers who had 3 classes is 16.   Only answer 0 and 16 has this option.
Answer: C
A student traveled 25 percent of the distance of the trip alone, continued another 40 miles with a friend, and then finished the last half of the trip alone. How many miles long was the trip?	Options
A) 120
B) 140
C) 160
D) 180
E) 200

Solution: Let x be the total length of the trip.   0.25x + 40 miles + 0.5x = x   40 miles = 0.25x   x = 160 miles   The answer is 160.
Answer: C
X alone can do a piece of work in 15 days and Y alone can do it in 10 days. X and Y undertook to do it for Rs. 720. With the help of Z they finished it in 5 days. How much is paid to Z?	Choose the correct option.
A) Rs. 360
B) Rs. 120
C) Rs. 240
D) Rs. 300
E) None

Solution: Solution:   In one day X can finish 1/15th of the work.   In one day Y can finish 1/10th of the work.   Let us say that in one day Z can finish 1/Zth of the work.   When all the three work together in one day they can finish 1/15 + 1/10 + 1/Z = 1/5th of the work.   Therefore, 1/Z = 1/30.   Ratio of their efficiencies = 1/15: 1/10: 1/30 = 2: 3: 1.Therefore Z receives 1/6th of the total money.   According to their efficiencies money is divided as 240: 360: 120.   Hence, the share of Z = Rs. 120.   Answer Rs. 120
Answer: B
What is the are of an equilateral triangle of side 8 cm?  Choose the correct choice
A) 11√3	B) 12√3	C) 16√3	D) 15√3	E) 18√3

Solution: Area of an equilateral triangle = √3/4 S2   If S = 8, Area of triangle = √3/4 * 8 * 8   = 16√3 cm2;   Answer:16√3
Answer: C
In the xy-plane, a triangle has vertices (0,0), (4,0) and (4,8). If a point (a,b) is selected at random from the triangular region, What is the probability that a-b>0? Choose the correct choice:
A) 1/5  B) 1/3  C) 1/2  D) 2/3  E) 4/5

Solution: The area of the right triangle is (1/2)*4*8= 
(1/2)*4*8 = 16
16.   Only the points (a,b) below the line y=x satisfy a - b > 0.   The part of the triangle which is below the line y=x has an area of (1/2)(4)(4) = 8.   P(a - b > 0) = 8/16 = 1/2   The answer is 1/2.
Answer: C
If a trader sold two cars each at Rs. 325475 and gains 12% on the first and loses 12% on the second, then his profit or loss percent on the whole is? Choose the correct answer
A) 1.44%
B) 2.45%
C) 7.44%
D) 8.44%
E) 2.44%

Solution: Explanation:   SP of each car is Rs. 325475, he gains 12% on first car and losses 12% on second car.   In this case, there will be loss and percentage of loss is given by = [(profit%)(loss%)]/100 = (12)(12)/100 % = 1.44%   1.44%nswer: 1.44%
Answer: A
There are three places P, Q and R such that 3 roads connects P and Q and 4 roads connects Q and R. In how many ways can one travel from P to R?  Select the correct option.
A) 12  B) 23  C) 28  D) 80  E) 84

Solution: The number of ways in which one can travel from P to R = 3 × 4 = 12   12nswer is 12
Answer: A
If the average (arithmetic mean) of a and b is 40 and the average of b and c is 60, what is the value of c − a?  Options
A) 25  B) 40  C) 90  D) 140  E) It cannot be determined from the information given.

Solution: -(a + b = 80)   b + c=120   c-a=40   B. 40
Answer: B
A and B invests Rs.3000 and Rs.4000 respectively in a business. If A doubles his capital after 6 months. In what ratio should A and B divide that year's profit?
Choose the correct option:  A) 9:9  B) 9:8  C) 9:3  D) 9:1  E) 9:2

Solution: (3*6 + 6*6): (4*12)   54:48 => 9:8   Answer: 9:8
Answer: B
Calculate the speed of a boat in still water (in km/hr) if in one hour, the boat goes at 13 km/hr downstream and 4 km/hr upstream.  Select: A) 4.5 kmph B) 9.5 kmph C) 7.5 kmph D) 8.5 kmph E) 5.5 kmph

Solution: Speed in still water = (13 + 4)1/2 kmph = 8.5 kmph.   answer :8.5 kmph
Answer: D
a number divided by 84 leaves remainder 57 what is the remainder when same number divided by 12  Choose the correct option.
A) 7
B) 8
C) 9
D) 10
E) 11

Solution: add 84+57= 
84+57 = 141
141   now 141divided by 12 so we get 9 as reaminder   ANSWER:9
Answer: C
Rajan borrowed Rs.4000 at 5% p.a compound interest. After 2 years, he repaid Rs.2210 and after 2 more year, the balance with interest. What was the total amount that he paid as interest?	Pick one:
A) 635.5
B) 635.57
C) 635.51
D) 635.59
E) 635.54

Solution: 4000   200 ---- I   200   10 ---- II   ---------------   4410   2210   --------   2000   110 ---- III   110   5.50 ---- IV   -----------   2425.50   2210   -----------   4635.50   4000   ----------   635.50   635.5nswer:635.5
Answer: A
A contractor undertakes to built a walls in 50 days. He employs 60 peoples for the same. However after 25 days he finds that only 40% of the work is complete. How many more man need to be employed to complete the work in time?
Answers: A) 25 B) 90 C) 35 D) 20 E) None of these

Solution: 60 men complete 0.4 work in 25 days.   Applying the work rule, m1 × d1 × w2 = m2 × d2 × w1   we have,   60 × 25 × 0.6 = m2 × 25 × 0.4   or m2 = 60×25×0.6/25×0.4 = 90 men   Answer90
Answer: B
Fox jeans regularly sell for $15 a pair and Pony jeans regularly sell for $18 a pair. During a sale these regular unit prices are discounted at different rates so that a total of $3 is saved by purchasing 5 pairs of jeans: 3 pairs of Fox jeans and 2 pairs of Pony jeans. If the sum of the two discounts rates is 18 percent, what is the discount rate on Pony jeans? Choose the correct choice from the following answers:
A) 9%	B) 56.6%	C) 11%	D) 12%	E) 15%

Solution: You know that Fox jeans costs $15, and Pony jeans costs $18, you also know that 3 pairs of Fox jeans and 2 pairs of Pony jeans were purchased. So   3(15) = 45 - Fox   2(18) = 36 - Pony   The total discount discount is $3 and you are asked to find the percent discount of pony jeans,   so 45(18 - X)/100 + 36(X)/100 = 3 or 45*18 -45*x + 36*x =3*100 or 9x = -3*100 +45*18= 
-3*100 +45*18 = 510
510/9= 56.6%   56.6%
Answer: B
Find the compound ratio of (2:5), (6:11) and (11:2) is Choose the correct choice from the following options.
A) 3:2  B) 2:1  C) 1:2  D) 6:5  E) 2:3

Solution: Required ratio = 2/5 * 6/11 * 11/2 = 2/1 = 6:5   Answer is 6:5
Answer: D
If two-third of a bucket is filled in 6 minute then the time taken to fill the bucket completely will be . Choose the correct answer:
A) 90 seconds B) 70 seconds C) 60 seconds D) 9 minutes E) 120 seconds

Solution: 2/3 filled in 6 mint   1/3 filled in 3 mint   thn 2/3+1/3=6 + 3= 
6 + 3 = 9
9 minutes   ANSWER:9 minutes
Answer: D
A jogger running at 9 km/hr along side a railway track is 240 m ahead of the engine of a 120 m long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger?  Answers
A) 88 B) 27 C) 36 D) 88 E) 12

Solution: Speed of train relative to jogger = 45 - 9= 
45 - 9 = 36
36 km/hr.= 36 * 5/18= 
36 * 5/18 = 10
10 m/sec.   Distance to be covered= 240 + 120= 
240 + 120 = 360
360 m.   Time taken= 360/10= 
360/10 = 36
36 sec.   Answer: 36
Answer: C
Two family reunions are happening at the same hotel, the Dates reunion and the Hall reunion. All 50 guests at the hotel attend at least one of the reunions. If 50 people attend the Dates reunion and 60 people attend the Hall reunion, how many people attend both reunions?  Choose the correct choice from the following answers.
A) 2 B) 5 C) 10 D) 16 E) 60

Solution: No of people in Dates reunion=50   No of people in Hall reunion=60   Attending both=x   All guests attend at least one.   Therefore, 50=50+60-(Both)   Both=60   Answer 60
Answer: E
What will be the cost of building a fence around a square plot with area equal to 81 sq ft, if the price per foot of building the fence is Rs. 58?	Choose the correct choice
A) 2088	B) 2882	C) 2999	D) 2667	E) 2121

Solution: Let the side of the square plot be a ft.   a2 = 81 => a = 9   Length of the fence = Perimeter of the plot = 4a = 36 ft.   Cost of building the fence = 36 * 58 = Rs. 2088.   2088nswer: 2088
Answer: A