MU-NLPC/Calc-aqua_rat huggingface dataset:
A person purchased a TV set for Rs. 13000 and a DVD player for Rs. 6250. He sold both the items together for Rs. 31150. What percentage of profit did he make?
Choose one:
A) 16.82%
B) 87.82%
C) 61.82%
D) 17.82%
E) 18.82%

Solution: The total CP = Rs. 13000 + Rs. 6250 = Rs. 19250 and SP   = Rs. 31150   Profit(%) = (31150 - 19250)/19250 * 100   = 61.82%   Answer:61.82%
Answer: C
A cistern of capacity 40 litres has an inlet and an outlet pipe. When both the pipes are opened at once, it takes 8 minutes to fill the cistern. However, if the outflow rate is increased 1.5 times, the cistern never gets filled. Which of the following can be the outflow rate? Choose the correct choice from the following answers: A) 8 litres/minute B) 6 litres/minute C) 12 litres/minute D) 9 litres/minute E) 10 litres/minute

Solution: DETAILED SOLUTION   Initially, net flow in the tank = 40 litres/ 8 minutes = 5 litres/minute   Now, the increase in outflow should be greater than 5 litres/min for the tank to fill up   Increase in outflow = 1.5x – x = 0.5x   Only in option c) 0.5 X 12 = 6 litres/min > 5 litres/min   12 litres/minuteORRE12 litres/minuteT ANSWER 12 litres/minute
Answer: C
Of the 24 participants in a certain competition, half are male, and half of the males are younger than 18 years of age. If half of the female competitors are also younger than 18 years of age, into how many distinct groups of 4 competitors could the participants be divided if each group must contain two males under 18 years of age and 2 females over 18 years of age?	Choose the correct choice from the following:	A) 225	B) 45	C) 65	D) 95	E) 200

Solution: M under 18 - 6   F above 18 - 6   How many distinct groups can be formed now: 6c2 * 6c2 = 225   225nswer : 225
Answer: A
The speed of a boat in still water is 30kmph and the speed of the current is 20kmph. Find the speed downstream and upstream?
Select:  A) kmph  B) kmph  C) kmph  D) kmph  E) kmph

Solution: Speed downstream = 30+ 20= 
30+ 20 = 50
50 kmph   Speed upstream= 30 - 20= 
30 - 20 = 10
10 kmph   Answer:kmph
Answer: B
In how many different F ways can 4 ladies and 4 gentlemen be seated at a round table so that all ladies sit together? Answers:  A) 70  B) 288  C) 576  D) 10,080  E) 20,160

Solution: Treat the 4 ladies as one object, now you have 5 objects to arrange around a table (m1,m2,m3,m4,women). This can be done in (5-1)! ways   And there are 4! ways to arrange ladies among themselves   Answer F= (4!)^2 = 576 or 576
Answer: C
16384, 8192, 2048, 256, 16, ?
Answers:
A) 0.5
B) 1
C) 1.5
D) 2
E) 2.5

Solution: Terms are continuously divided by 2,4,8,16, and so on   16384   16384 ÷ 2 = 8192   8192 ÷ 4 = 2048   2048 ÷ 8 = 256   256 ÷ 16 = 16   16 ÷ 32 = 0.5   0.5nswer is 0.5.
Answer: A
George went to a fruit market with certain amount of money. With this money he can buy either 50 oranges or 40 mangoes. He retains 5% of the money for taxi fare and buys 25 mangoes. How many oranges can he buy?
Choose the most appropriate option:
A) 25
B) 30
C) 20
D) 22.5
E) 12

Solution: Let the amount of money be 200   Let cost of 1 Orange be 4   Let cost of 1 mango be 5   He decides to retain 5% of 200 = 10 for taxi fare, so he is left with 190   He buys 20 mangoes ( @ 5) so he spends 100   Money left is 90 (190 - 100)   No of oranges he can buy = 90/4 =>22,5   So, George can buy 20 Oranges.   22.5
Answer: D
A manufacturer sells a pair of glasses to a wholesale dealer at a profit of 18%. The wholesaler sells the same to retailer at a profit of 20%. The retailer in turn sells them to a customer for Rs. 30.09, there by earning a profit of 25%. The cost price for the manufacturer is?
Choose one.
A) 33 B) 29 C) 17 D) 10 E) 16

Solution: Explanation:   Let the cost price for the manufacturer be Rs. x. Then, 125% of 120% of 118% of x = 30.09.   125/100 * 120/100 * 118/100 * x = 3009/100   177/100 x = 3009/100 => x = 17   Answer:17
Answer: C
A, B, C enter into a partnership investing Rs. 35,000, Rs. 45,000 and Rs. 55,000 respectively. The respective shares of A, B, C in annual profit of Rs. 40,500 are?	Choose the correct answer
A) Rs. 10,500, Rs. 13,500, Rs. 16,500
B) Rs. 10,500, Rs. 13,500, Rs. 16,509
C) Rs. 10,500, Rs. 13,500, Rs. 16,506
D) Rs. 10,500, Rs. 13,500, Rs. 16,588
E) Rs. 10,500, Rs. 13,500, Rs. 16,512

Solution: A:B:C = 35000 : 45000 : 55000 = 7:9:11   A's share = 40500 * 7/27 = Rs. 10500   B's share = 40500 * 9/27 = Rs. 13500   C's share = 40500 * 11/27 = Rs. 16500.Rs. 10,500, Rs. 13,500, Rs. 16,500nswer: a
Answer: A
If by selling an article for Rs.60, a person loses 1/7 of money, what would he have gained or lost % by selling it for Rs.77?  Answers:
A) 5% B) 10% C) 23% D) 25% E) 30%

Solution: Sol. CP - = EC7 = 70 1-7 6 77-70 % Profit = 100 = 10%   10%
Answer: B
In a class, if 50% of the boys were girls, then there would be 50% more girls than boys. What percentage of the overall class is girls?	Choose the correct choice from the following answers:
A) 25%
B) 33.33%
C) 40%
D) 20%
E) 10%

Solution: DETAILED SOLUTION   For questions of this type, it is best to go from the final step. In the final state, the number of girls should be 1.5 * the number of boys.   When 50% of the boys are taken as girls, let the number of boys = x   Number of girls = 1.5x   total number of students = 2.5x   Original number of boys = 2x (50% of boys = x)   Original number of girls = 0.5x   Girls form 20% of the overall class.   CORRECT ANSWER 20%.
Answer: D
The ratio of two quantities is 2 to 5. If each of the quantities is increased by 8, what is the ratio of these two new quantities?	Options
A) 2/5	B) 5/8	C) 7/13	D) 22/25	E) It cannot be determined from the information given.

Solution: Correct Answer: E   Let x and y be the two quantities such that x/y = 2/5. There is no algebraic operation that can be used to increase x and y each by 3 and determine what happens to the ratio 2/5.   For example, if x = 2 and y = 5, then (x+8)/(y+8) = (2+8)/(5+8) = 10/13. However, if x = 4 and y = 10 (which would still set x/y = 2/5), then (x+8)/(y+8) = (4+8)/(10+8) = 12/18 =6/9. The ratio of the two new quantities cannot be uniquely determined from the information given, and the correct answer is (It cannot be determined from the information given.).
Answer: E
A garrison of 400 men had a provision for 31 days. After 28 days 280 persons re-enforcement leave the garrison. Find the number of days for which the remaining ration will be sufficient?
Choose the correct choice from the following answers:
A) 65 days  B) 45 days  C) 10 days  D) 16 days  E) 18 days

Solution: 400 --- 31   400 --- 3   120 --- ?   400*3 = 120*x => x =10 days.Answer: 10 days
Answer: C
Tanks X and Y contain 500 and 200 gallons of water respectively. If water is being pumped out of tank X at a rate of K gallons per minute and water is being added to tank Y at a rate of M gallons per minute, how many hours will elapse before the two tanks contain equal amounts of water?  Choices:
A) 5/M+K hours
B) 6(M+K) hours
C) 300/M+K hours
D) 300/M−K hours
E) 60/M−K hours

Solution: Consider k=1,m=2   Then per the question,   500 - 1x = 200 + 2x   x=100   Check answer options for No. of hours (x)=100 for k=1 and m=2   ANSWER:300/M+K hours
Answer: C
In how many different number of ways 4 boys and 3 girls can sit on a bench such that girls always sit together?  Answers:
A) 720 B) 740 C) 760 D) 790 E) 800

Solution: Option '720'
Answer: A
The probability of a lottery ticket being a prized ticket is 0.2. When 4 tickets are purchased, the probability of winning a prize on atleast one ticket is?	Select
A) 0.5919 B) 0.5904 C) 0.5929 D) 0.5928 E) 0.594

Solution: P(winning prize atleast on one ticket)   = 1 - P("Losing on all tickets")   = 1 - (0.8)4 = (1 + (0.8)2)(1 - (0.8)2)   = (1.64)(0.36) = 0.5904   Answer: 0.5904
Answer: B
2x + y = 13
|y| <= 13
For how many ordered pairs (x , y) that are solutions of the system above are x and y both integers?
Select.
A) 7 B) 10 C) 12 D) 13 E) 14

Solution: Hi - The questions says |y| <=13 so the values of y will range from 0 to 13. So the values of y will be 0,1,2,3,4,5,6,7,8,9,10,11,12,13. So 14 (E) is the answer. remember sign doesn't matter for y as y will always be positive.
Answer: E
Find the cost of fencing around a circular field of diameter 12 m at the rate of Rs.3.50 a meter?	Choose the correct choice:	A) 131.95	B) 132.9	C) 140.33	D) 123.4	E) 190.4

Solution: 2 * 22/7 * 6 = 37.7   37.7 * 3 1/2 = Rs.131.95   131.95nswer: 131.95
Answer: A
A palindrome is a number that reads the same forward and backward, such as 242. How many even nine-digit numbers are palindromes?	Pick:
A) 40
B) 40000
C) 500
D) 5,000
E) 100,000

Solution: if the palindrome must be even, it must begin and end in 2,4 6 and 8 ( 4 ways) e.g 222212222,444414444.   The middle number in the nine-digit could be 0-9 ( 10 ways), e.g 22522, 22822   The 2nd and fourth numbers   , the 3rd and 5th and 4th and 6th could must also be same i.e 0-9( 10 ways) e.g 242343242, 648565846   we thus have, 4 *10*10*10*10=40000 40000
Answer: B
The population of a bacteria colony doubles every day. If it was started 6 days ago with 2 bacteria and each bacteria lives for 12 days, how large is the colony today? Select:
A) 512
B) 768
C) 1024
D) 2048
E) 128

Solution: 2^6(2) = 2^7 = 128   The answer is 128.
Answer: E
The least number of complete years in which a sum of money put out at 20% C.I. will be more than doubled is?	Choose the correct choice from the following choices
A) 3	B) 4	C) 9	D) 3	E) 5

Solution: Explanation:   P(1 + 20/100)n > 2P or (6/5)n > 2   Now, (6/5 * 6/5 * 6/5 * 6/5) > 2. So, n = 4 years.   Answer: Option 4
Answer: B
A 270 m long train running at the speed of 120 km/hr crosses another train running in opposite direction at the speed of 80 km/hr in 9 sec. What is the length of the other train? Choose the correct choice
A) 230
B) 200
C) 250
D) 300
E) 500

Solution: Answer: Option A   Explanation:   Relative speed = 120 + 80= 
120 + 80 = 200
200 km/hr.= 200 * 5/18 = 500/9 m/sec.   Let the length of the other train be x m.   Then, (x + 270)/9 = 500/9 => x = 230.   230NSWER 230
Answer: A
What is the total number of integers between 20 and 100 that are divisible by 9? Choose the correct choice from the following options
A) 5	B) 15	C) 12	D) 7	E) 9

Solution: 27, 36, 45, ..., 90,99   This is an equally spaced list; you can use the formula:   n = (largest - smallest) / ('space') + 1 = (99 - 27) / (9) + 1 = 8 + 1= 
8 + 1 = 9
9   Answer is 9
Answer: E
In shop there are 10 bulbs, a total of 4 are defective. If a customer buys 4 bulbs selected at random from the box, what is the probability that neither bulbs will be defective?	Choose the correct choice from the following:
A) 2/19
B) 3/29
C) 4/15
D) 1/15
E) 1/2

Solution: First, there are 6C4 ways you can select 6 good bulbs from 4 good ones.   Second, there are 10C4 ways you select 4 bulbs from 10 ones in the box.   Then, the probability that neither bulb will be defective is: 6C4/10C4=15/210 = 1/15   Answer is 1/15
Answer: D
A salesman's income consists of a commission and a base salary of $350 per week. Over the past 5 weeks, his weekly income totals have been $556, $413, $420, $436 and $395. What must his average (arithmetic mean) commission be per week over the next two weeks so that his average weekly income is $500 over the 7-week period?	Choose one
A) $150 B) $290 C) $365 D) $715 E) $730

Solution: Total weekly income over 5 weeks=$556+$413+$420+$436+$395=$2220   For avg weekly income to be $500 over 7 weeks, we need total weekly income over 7 weeks556+ 413+ 420+ 436+ 395= 
556+ 413+ 420+ 436+ 395 = 2_220
$2220   For avg weekly income to be $500 over 7 weeks, we need total weekly income over 7 weeks=$3500   Now, $3500-$2220=$1280   From this, we subtract base salary for 2 weeks i.e $350*2= 
350*2 = 700
$700   Therefore, commission=$1280-$700=$580 for 2 weeks   Avg weekly commission1280- 700= 
1280- 700 = 580
$580 for 2 weeks   Avg weekly commission=$290   Answer $290
Answer: B
The population of a town is 216400. If it increase at the rate of 4% per annum. What will be its population for 3years hence?	Choose the correct option:
A) 200000
B) 243420
C) 194582
D) 194481
E) 215460

Solution: population after 3years = 216400*(1+ 4/100)^3 = 243420   Answer is 243420
Answer: B
If u and v are positive integers, and 3 is not a factor of v, then v may be which of the following?  Pick one
A) (u−1)·u·(u+1)
B) (u−3)·(u−1)·(u+1)
C) (u−2)·u·(u+2)
D) (u−1)·u·(u+2)
E) (u−3)·(u+1)·(u+2)

Solution: Plugged in values :   let u=5   A. (u−1)·u·(u+1) --> divisible by 3   B. (u−3)·(u−1)·(u+1) --> divisible by 3   C. (u−2)·u·(u+2) --> divisible by 3   D. (u−1)·u·(u+2) --> not divisible. Hence the answer.
Answer: D
In how many different ways can 2 identical blue balls and 2 identical red balls be shared among 4 children such that each child receives a ball? Select the correct option:
A) 10  B) 24  C) 34  D) 20  E) 21

Solution: GGG RRR   Therefore total number of ways is   4! but there are two groups of 2 identical things.   Therefore total number of "different" ways is   4!/ (2!) (2!) = 24 ANS:24
Answer: B
If x^2 + y^2 = 20 and xy = 3, then (x − y)^2 =	Options
A) 8  B) 11  C) 14  D) 17  E) 20

Solution: but you cannot take xy+ 3 to mean xy=-3..   only if xy+3=0, it will mean xy=-3..   rest your solution is perfect and you will get your correct answer as 20-2*3=14..   Answer 14
Answer: C
If k, l, and m are distinct positive prime numbers, then (k^3)(l)(m) has how many different positive factors greater than 1?	Choose the most appropriate option:
A) a. 8	B) b. 9	C) c. 12	D) d. 10	E) e. 27

Solution: Let Number is (k^3)(l)(m) = (1^3)(4)(20) = 80   We can write 80 as product of two numbers in following ways   1*80   2*40   4*20   5*16   8*10   5 cases = 5*2 i.e. 10 factors (including 1)   Factors greater than 1 = 9   Answer: Option d. 10
Answer: D
A man can row a boat at 18 kmph in still water. If the speed of the stream is 12 kmph, what is the time taken to row a distance of 90 km downstream? Pick one
A) 6 hours  B) 4 hours  C) 3 hours  D) 5 hours  E) 6 hours

Solution: Speed downstream = 18 +12= 
18 +12 = 30
30 kmph.   Time required to cover 90 km downstream= d/s = 90/30= 
90/30 = 3
3 hours.Answer:3 hours
Answer: C
Ayisha's age is 1/6th of her father's age. Ayisha's father's age will be twice Shankar's age after 10 years. If Shankar's eight birthdays was celebrated two years before, then what is Ayisha's present age.
Choose the correct choice:	A) 5	B) 10	C) 7	D) 9	E) 4

Solution: Shankar's present age =8+2= 
8+2 = 10
10   5yisha's father's age after 10 years=2(10+10)=40   5yisha's father's present age =40−10=30   5yisha's present age =16×30=5   5nswer is 5.
Answer: A
3 years ago, the average age of P and Q was 20years. With R joining them, theiraverage age becomes 23years. What is the age of R?  Choose the correct option
A) 18 years	B) 20 years	C) 21years	D) 23 years	E) 30 years

Solution: Three years ago, the average age of P and Q was 20 years.   Three years ago, their sum of the ages was 2x20= 40 years   Present age of P+Q+R = 3 X23 =69   Present age of P+Q=40+( 2 x 3)= 46   Present age of R = ( P+Q+R)- (P+Q)= 69-46= 
69-46 = 23
23 years   23 years
Answer: D
For all integers x>1. <x>=2x+(2x-1)+(2x-2)+......2+1. What is the value of <2>*<3>? Select.
A) 210 B) 116 C) 212 D) 263 E) 478

Solution: Since <x></x>=2x+(2x-1)+(2x-2)+......2+1=1+2+..+(2x-2)+(2x-1)+2x then<x> is basically the sum of all integers from 1 to 2x, inclusive.   Hence <3> is the sum of all integers from 1 to  2*3</x>= 
 2*3 = 6
6 and <2> is the sum of all integers from 1 to  2*2= 
 2*2 = 4
4 --> <3>=21 and <2>=10 --> <3>*<2>=21*10= 
21*10 = 210
210.   210nswer: 210
Answer: A
Tea worth Rs.126 per kg are mixed with a third variety in the ratio 1: 1 : 2. If the mixture is worth Rs.173 per kg, the price of the third variety per kg will be Choices:  A) Rs.169.50  B) Rs.1700  C) Rs. 195.50  D) Rs. 180  E) None

Solution: Solution   Since first second varieties are mixed in equal proportions, so their average price = Rs.(126+135/2) = Rs.130.50   So, the mixture is formed by mixing two varieties, one at Rs. 130.50 per kg and the other at say, Rs. x per kg in the ratio 2 : 2, i.e., 1 : 1. We have to find x.   x-173/22.50 = 1 =â€º x - 173 = 22.50 =â€º x=195.50.   Hence, price of the third variety = Rs.195.50 per kg.   Answer Rs. 195.50
Answer: C
A man rows his boat 78 km downstream and 56 km upstream, taking 4 hours each time. Find the speed of the stream? Choose the correct choice from the following options:
A) 6
B) 5
C) 7
D) 8
E) 3

Solution: Speed downstream = d/t = 78/(4) = 20 kmph   Speed upstream = d/t = 56/(4)= 
56/(4) = 14
14 kmph   The speed of the stream= (20 - 14)/2= 
(20 - 14)/2 = 3
3 kmph   Answer:3
Answer: E
A person can row at 10 kmph in still water. If the velocity of the current is 2 kmph and it takes him 10 hour to row to a place and come back, how far is the place?	Choose one:  A) 24km  B) 30km  C) 48km  D) 12km  E) 48km

Solution: Speed of down stream = 10+2= 
10+2 = 12
12kmph   speed of upstream= 10-2= 
10-2 = 8
8kmph   Let the required distance be xkm   x/12 + x/8= 10   2x+3x = 240   x = 48 km   Answer is 48km
Answer: E
If f(x) = k(x - k) and k is a constant, what is the value of f(6) - f(2), in terms of k? Choose the correct choice from the following choices: A) 1 B) 4k C) 7k - 1 D) k^2 + k E) k^2 - k

Solution: First, distribute f(x). k(x - k) = kx - k^2. Now evaluate f(6) and f(2):   f(6) = k(6) - k^2 = 6k - k^2   f(2) = 2k - k^2   Answer 4k
Answer: B
Insert the missing number.
2, 6, 12, 20, 30, 42, 56, (....)
Choose the most appropriate option: A) 22 B) 38 C) 72 D) 66 E) 19

Solution: Explanation:   The pattern is 1 x 2, 2 x 3, 3 x 4, 4 x 5, 5 x 6, 6 x 7, 7 x 8.   So, the next number is 8 x 9 = 72.   Answer: 72) 72
Answer: C
If each day a tree loses half its remaining leaves, what fraction of its leaves will it have lost after 5 days ? Choose the correct choice from the following answers
A) 1/32
B) 1/16
C) 9/10
D) 15/16
E) 31/32

Solution: At the end of each day, the tree has 1212 it's remaining leaves.   If initially the tree has x leaves.   After day 1: 1/2x   After day 2: 1/2x∗1/2=1/^2 x and so on ....   After day 5: 1/2^5x=1/32x   So leaves lost = Initial amount of leaves - Leaves remaining = x−1/32x=31/32x   Answer:31/32
Answer: E
In the junior basketball league there are 15 teams, 2/3 of them are bad and ½ are rich. What can't be the number of teams that are rich and bad?  Choose the correct choice from the following:
A) 4.
B) 6.
C) 7.
D) 9.
E) 5.

Solution: total teams =16   bad teams=(2/3)*15= 
(2/3)*15 = 10
10   rich teams=8   so maximum value that the both rich and bad can take will be 8. so E= 9 can not be that value.   ans 9..
Answer: D
How much tea worth $0.93 per pound must be mixed with tea worth $0.75 per pound to produce 10 pounds worth $0.85 per pound?  Choose the most appropriate option:  A) 2 2⁄9  B) 3 1⁄2  C) 4 4⁄9  D) 5 5⁄9  E) 9 1⁄2

Solution: Let weight of tea worth .75 $ = w1   and weight of tea worth .93 $ = w2   w1 + w2 = 10 --- equation 1   .85 = ( w1*.75 + w2* .93 )/(w1+ w2 )   => .85 w1 + .85 w2 = .75 w1 + .93 w2   => .10 w1 -.08 w2 = 0   => 10 w1 - 8 w2 = 0 --- equation 2   From 1 ,   8 w1 + 8 w2 = 80 --- equation 3   From equations 2 and 3 , we get   18 w1 = 80   => w1 = 40/9   and w2 = 50/9   Answer 5 5⁄9
Answer: D
Four of the five parts numbered (a), (b), (c), (d) and (e) in the following equation are exactly equal. You have to find out the part that is not equal to the other four. The number of that part is the answer.
Pick one
A) 7529.0 – 6(1110.555) B) 93.27 – 167.20 + 439.60 C) 490.92 + 439.65 – 64.9 D) (7189.3 – 2860.93) + 5 E) 2(269.40 + 163.435)

Solution: Others are equal to 865.67.   Answer (7189.3 – 2860.93) + 5
Answer: D
The angles of a triangle are in the ratio 4:6:8. Find the measurement of the largest of three angles of triangle.	Choose the correct choice from the following answers:
A) 80° B) 100° C) 120° D) 140° E) 160°

Solution: If the ratio of the three angles is 4:6:8, then the measures of these angles can be written as 4x, 6x and 8x. Also the sum of the three interior angles of a triangle is equal to 180°. Hence   4x + 6x + 8x = 180   Solve for x   18x = 180   x = 10   The measures of the three angles are   4x = 4 x 10° =40   6x = 6 × 10 = 60°   8x = 8 × 10 = 80°   80°
Answer: A
In store B there are 10 pairs of pants for every 40 store A has. The price ratio between the pants in store A and the pants in store B is 3:4. If all the pants were sold in both places until the stock ran out, what is the ratio between the total amount stores B earned to the total amount store A earned?	Select the correct option
A) 3:16.	B) 3:1.	C) 1:3.	D) 3:4.	E) 2:5.

Solution: 1st statement : ratio of pants   Store 3:1. : Store A   10x : 40x   X:4X   Price :   4y:3y   Total revenue   4xy : 12xy   3:1   Answer : 3:1.
Answer: B
Find the expenditure on digging a well 14m deep and of 3m diameter at Rs.19 per cubic meter?	Choose the correct choice from the following answers
A) 2998	B) 1881	C) 2890	D) 1485	E) 2780

Solution: 22/7 * 14 * 3/2 * 3/2= 
22/7 * 14 * 3/2 * 3/2 = 99
99 m2   99 * 19= 
99 * 19 = 1_881
1881   Answer:1881
Answer: B
Man bought 20 shares of Rs. 50 at 5 discount, the rate of dividend being 11 1/2. The rate of interest obtained is: Options:  A) 16%  B) 15%  C) 20%  D) 25%  E) 38.33%

Solution: Investment = 10*(40-10)= 
10*(40-10) = 300
300   Face value= 40*10= 
40*10 = 400
400   dividend= 23/2*1000/100   ==115   ===>115/300*100 = 38.33   ANSW38.33%R 38.33%
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? Choose the correct choice from the following options.
A) Rs.4082.67 B) Rs.4082.49 C) Rs.4082.48 D) Rs.4082.40 E) Rs.4082.13

Solution: 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: Rs.4082.40
Answer: D
Series F(n) is such that i*F(i) = j*F(j) for any pair of positive integers (i, j). If F(1) is a positive integer, which of the following is possible?
I. 2*F(100) = F(99) + F(98)
II. F(1) is the only integer in the series
III. The series does not contain negative numbers
Select the correct option:	A) I only	B) II only	C) IIII only	D) IIIII only	E) I, IIIII

Solution: First thing I want to understand is this relation: i*F(i) = j*F(j) for any pair of positive integers. I will take examples to understand it.   When i = 1 and j = 2, F(1) = 2*F(2)   So F(2) = F(1)/2   When i = 1 and j = 3, F(1) = 3*F(3)   So F(3) = F(1)/3   I see it now. The series is: F(1), F(1)/2, F(1)/3, F(1)/4 and so on...   II and III are easily possible. We can see that without any calculations.   II. F(1) is the only integer in the series   If F(1) = 1, then series becomes 1, 1/2, 1/3, 1/4 ... all fractions except F(1)   III. The series does not contain negative numbers   Again, same series as above applies. In fact, since F(1) is a positive integer, this must be true.   I. 2*F(100) = F(99) + F(98)   2*F(1)/100 = F(1)/99 + F(1)/98 (cancel F(1) from both sides)   2/100 = 1/99 + 1/98   Not true hence this is not possible   Answer (IIIII only)
Answer: D
For all numbers l and m, the operation @ is defined by l@m = l^2 - lm. If xy ≠ 0, then which of the following can be equal to zero?
I. x@y
II. (xy)@y
III. x@(x + y)  Choose the correct choice.
A) II  B) I and II  C) I and III  D) II and III  E) All of the above

Solution: l@m= l^2 - lm=l(l-m).... so l@m will be zero if l=m or l=0.. but a cannot be equal to 0.. as per Q, x and y can take any int value except 0...   now lets look at the choices..   when x=y, it will be 0... so ok...   when we put xy=y, it is possible when x=1 and y any integer... so ok again   when we put x=x+y.... only possibility when y=0 and it is given x and y cannot be 0....so not possible   only l and ll possible   answer: I and II
Answer: B