MU-NLPC/Calc-aqua_rat huggingface dataset:
A vessel of capacity 90 litres is fully filled with pure oil. Nine litres of oil is removed from the vessel and replaced with water. Nine litres of the solution thus formed is removed and replaced with water. Find the quantity of pure oil in the final oil solution?  Choose one
A) 83.9 litres  B) 54.9 litres  C) 37.9 litres  D) 72.9 litres  E) 27.9 litres

Solution: D   72.9 litres   Let the initial quantity of oil in vessel be T litres.   Let us say y litres of the mixture is taken out and replaced by water for n times, alternatively.   Quantity of oil finally in the vessel is then given by [(T - y)/T]n * T   For the given problem, T = 90, y = 9 and n = 2.   Hence, quantity of oil finally in the vessel   = [(90 - 9)/90]2 (90) = 72.9 litres.
Answer: D
A set of football matches is to be organized in a "round-robin" fashion, i.e., every
participating team plays a match against every other team once and only once. If 21
matches are totally played, how many teams participated?
Choose one.
A) 4  B) 5  C) 6  D) 7  E) 8

Solution: 2 ways to solve this problem..   summation(x)=n(n-1)/2   n(n-1)/2=21;   n^2-n-42=0   factors : 7,-6   Ans : 7   ANSWER:7
Answer: D
If each letter in the English alphabet is assigned an even number such as A = 2, B = 4 and so on, then what will be the total value of the letters in the word LEAD?	Pick:
A) 42
B) 40
C) 46
D) 44
E) 48

Solution: GIven the Condition:   L=24,E=10, A=2 and 44=8   Hence the addition is 44   ANSWER:44
Answer: D
What is the unit digit in the product (3^65 x 6^59 x 7^71)?  Options:
A) 4 B) 8 C) 6 D) 2 E) 1

Solution: 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 7^3] = (1 x 3) = 3.   Required digit = Unit digit in (3 x 6 x 3) = 4.   4nswer 4)4.
Answer: A
Divide $300 among A,B in the ratio 1:2. How many $ that A get?
Answers: A) $50 B) $500 C) $150 D) $250 E) $100

Solution: Sum of ratio terms = 1+2= 
1+2 = 3
3   A= 300*1/3= 
300*1/3 = 100
$100   Answer is $100
Answer: E
A man can row
9 1/3
kmph in still water and finds that it takes him thrice as much time to row up than as to row, down the same distance in the river. The speed of the current is. Pick one.
A) 3 2/3kmph	B) 4 2/3kmph	C) 5 2/3kmph	D) 6 2/3kmph	E) None of these

Solution: Explanation:   Friends first we should analyse quickly that what we need to calculate and what values we require to get it.   So here we need to get speed of current, for that we will need speed downstream and speed upstream, because we know   Speed of current = 1/2(a-b) [important]   Let the speed upstream = x kmph   Then speed downstream is = 3x kmph [as per question]   speed in still water = 1/2(a+b)   =>1/2(3x+x)   =>2x as per question we know,   2x=9 1/3   =>2x=28/3   =>x=14/3   So,   Speed upstream = 14/3 km/hr, Speed downstream 14 km/hr.   Speed of the current   =1/2[14−14/3]   =14/3=4 2/3kmph   Option 4 2/3kmph
Answer: B
A rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered.If the area of the field is 800 sq.ft, how many feet of fencing will be required ? Choose the most appropriate option.
A) 100feet
B) 120feet
C) 150feet
D) 180feet
E) 186feet

Solution: Explanation:   We are given with length and area, so we can find the breadth.   as Length * Breadth = 100feetrea   => 20 * Breadth = 800   => Breadth = 40 feet   100feetrea to be fenced = 2B + L = 2*40 + 20= 
2*40 + 20 = 100
100 feet   100feetnswer: Option 100feet
Answer: A
A certain league has four divisions. The respective divisions had 9, 10, 11, and 12 teams qualify for the playoffs. Each division held its own double-elimination tournament -- where a team is eliminated from the tournament upon losing two games -- in order to determine its champion. The four division champions then played in a single-elimination tournament -- where a team is eliminated upon losing one game -- in order to determine the overall league champion. Assuming that there were no ties and no forfeits, what is the maximum number of games that could have been played in order to determine the overall league champion?  Choose the most appropriate option
A) 79  B) 83  C) 85  D) 87  E) 88

Solution: Consider 4 teams.   Max possible games if a team is eliminated after 2 loses = 3 + 2= 
3 + 2 = 5
5   Similarly, if 5 teams are there,   Max possible games= 4 + 3= 
4 + 3 = 7
7.   So going forth we can play 15,17,19,21 max possible games for 9,10,11,12 teams respectively.   Adding them up gives 72. Now there are two teams left in each group still. So four more games to give a winner in each team.   So 72+ 4= 
72+ 4 = 76
76.   Now of the four teams we can have max 3 games if its a knock out round.   So 76 + 3= 
76 + 3 = 79
79.   79nswer 79= 79.
Answer: A
For the symbol, m”n=n^2−m for all values of m and n. What is the value of 6”3?  Select the correct option:
A) 5 B) 3 C) 2 D) 1 E) 0

Solution: 6”3= 9 - 6= 
9 - 6 = 3
3   Answer: 3
Answer: B
A brick measures 20 cm * 10 cm * 7.5 cm how many bricks will be required for a wall 25 m * 2 m * 0.75 m?
Choose the most appropriate option.
A) 33381
B) 27991
C) 92211
D) 25000
E) 27821

Solution: 25 * 2 * 0.75 = 20/100 * 10/100 * 7.5/100 * x   25 = 1/100 * x => x = 25000   Answer: 25000
Answer: D
Find the number of zeroes in the expression 15*32*25*22*40*75*98*112*125  Choose the correct choice from the following choices:
A) 12	B) 9	C) 14	D) 7	E) 8

Solution: (3*5)*(2*2*2*2*2)*(5*5)*(2*11)*(2*2*2*2*5)*(5*5*3)*(2*7*7)*(2*2*2*2*7)*(5*5*5)   there are 9 (5*2) pairs which gives zero   so.no of zeros 9   ANSWER:9
Answer: B
A fraudulent dairy guy declares to market his dairy at price range but he combined it with water and therefore benefits 25%. The percentage of water in the combination is:
Choose the correct choice from the following choices.
A) 20%
B) 30%
C) 50%
D) 35%
E) 60%

Solution: Explanation :   -> If Capability Price of 1 L of milk = Rs.1   And S.Price of 1 L of combination = Rs.1   Benefits = 20%   Capability Price of 1 L of combination =[ (100 / 100+25)*1 ]   = Rs. 100/125 = Rs. 4/5   -> From the rule of allegation   i. Capability Price of 1 L of water = 0   ii. Capability Price of 1 L of milk = 1   iii. (p) = 4/5   iv. d – m = 1 – 4/5 = 1/5   v. m – c = 4/5 – 0 = 4/5   Ratio of milk to water = 4/5 : 1/5 = 4:1   % of water in the combination = (1/5 x 100)% = 20%   20%nswer : 20%
Answer: A
On Monday Joshua sold 90 phones, Rob sold 30% more phones than Joshua, Prerna sold 11 more phones than Rob, and Declan sold 3/4 of what Prerna sold. How many phones did Declan sell?  Choose the correct choice from the following.
A) 111 B) 75 C) 29 D) 128 E) 96

Solution: E   96   Joshua sold 90 phones.   Rob sold 30 % more phones than Joshua   Rob = 90 + 90 × 30%   = 90 + 90 × 0.30   = 90 + 27= 
90 + 27 = 117
117   Prerna sold 11 more phones than Rob   Prerna= 117 + 11= 
117 + 11 = 128
128   Declan sold 3/4 of what Prerna sold.   Declan= 128 x 3/4   =96   Declan sold 96 phones.   The correct answer is 96.
Answer: E
Today John is twice as old as Sam and Sam is 3 years younger than Mike. If John, Sam, and Mike are all alive 4 years from today, which of the following must be true on that day. I. John is twice as old as Sam II. Sam is 3 years younger than Mike III. John is older than Mike Options:
A) I, III
B) I
C) II
D) I,II & III
E) III

Solution: Say Mike age is 10   Sam age is 7   John age is 14   After 4 years   Mike age is 14   Sam age is 11   John age is 28   i.e ) after 4 years   Sam is 3 years younger than Mike   John is twice as old as Sam   John is older than Mike   Answer : I,II & III
Answer: D
Kate and Danny each have $10. Together, they flip a fair coin 5 times. Every time the coin lands on heads, Kate gives Danny $1. Every time the coin lands on tails, Danny gives Kate $1. After the five coin flips, what is the probability W that Kate has more than $10 but less than $15?
Choose the correct choice from the following answers
A) 5/16  B) 1/2  C) 12/30  D) W=15/32  E) W=3/8

Solution: For 21 heads Kate will end up with < $10 and we want her to win. Therefore, only possibilities W are 3 or 4 heads.   I made an educated guess and it worked fine.   Ans- 'D'   MGMAT's anagram helped here as well.   HHHHT = 5!/4!*1! = 5   HHHTT = 5!/3!*2! = 10   Total acceptable cases = 15   Total cases = 32   P = 15/32.W=15/32
Answer: D
The ratio by weight, measured in pounds, of books to clothes to electronics in a suitcase initially stands at 5:4:2. Someone removes 7 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 one: A) 6 B) 7 C) 8 D) 9 E) 10

Solution: The weights of the items in the suitcase are 5k, 4k, and 2k.   If removing 7 pounds of clothes doubles the ratio of books to clothes, then 7 pounds represents half the weight of the clothes.   2k = 7 pounds and then k = 3.5 pounds.   The electronics weigh 2(3.5) = 7 pounds.   The answer is 7.
Answer: B
A woman has two blouses of different colors, three skirts of different colors, and two different pairs of shoes. She refuses to wear her pink blouse with her green skirt. How many different blouseskirt-shoe combinations could she wear?  Select the correct option
A) 8	B) 10	C) 16	D) 17	E) 18

Solution: total ways = 2*3*2=12..   now its better to find the ways in which the pink blose and green skirty are together and subtract from total to get the answer..   the ways in which the pink blose and green skirty are together=1*1*2=2..   total ways =12-2=10..   10
Answer: B
A hollow iron pipe is 21 cm long and its external diameter is 8 cm. If the thickness of the pipe is 1 cm and iron weighs 8 g/cm^3, then the weight of the pipe is: Choose the correct choice from the following.
A) 3.6 kg B) 3.696 kg C) 36 kg D) 36.9 kg E) 3.06 kg

Solution: External radius = 4 cm,   Internal radius = 3 cm.   Volume of iron=(22/7	x [(4)^2 - (3)^2] x 21) cm^3   (22/7x 7 x 1 x 21)cm^3   462 cm^3.   Weight of iron = (462 x 8) gm = 3696 gm = 3.696 kg.   ANSWER 3.696 kg
Answer: B
A train passes a station platform in 34 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?  Pick:
A) 228
B) 210
C) 188
D) 266
E) 281

Solution: The speed of the train is 54 * 5/18 m/s = 15 m/s   The length of the train is 15 x 20 = 300 m   platform + 300 = 15 * 34= 
15 * 34 = 510
510 - 300= 
510 - 300 = 210
210   The answer is 210.
Answer: B
One computer can upload 120 megabytes worth of data in 6 seconds. Two computers, including this one, working together, can upload 1300 megabytes worth of data in 42 seconds. How long would it take for the second computer, working on its own, to upload 120 megabytes of data?
Select the correct option:
A) 6	B) 7	C) 9.13	D) 11	E) 13

Solution: Since the first computer can upload 120 megabytes worth of data in 6 seconds then in   6*7= 
  6*7 = 42
42 seconds it can upload   7*120= 
  7*120 = 840
840 megabytes worth of data, hence the second compute in 42 seconds uploads   1300-840= 
  1300-840 = 460
460 megabytes worth of data. The second computer can upload 120 megabytes of data in 9.13 seconds.   Answer: 9.13.
Answer: C
How many two-digit numbers yield a remainder of 1 when divided by both 6 and 15?	Choose the correct choice from the following answers:
A) 0  B) 1  C) 2  D) 3  E) 4

Solution: Easier to start with numbers that are of the form 15p+1 ---> 16,31,46,61,76,91.   Out of these 2 (31,61) are also of the form 6q+1. Thus 2 is the answer. 2 is the correct answer.
Answer: C
At a small company, 76 percent of the employees are women, and 60 percent of the employees are married. If 2/3 of the men are single, what fraction of the women are married? Choose the correct choice from the following answers
A) 13/19 B) 1/3 C) 9/20 D) 7/10 E) 5/7

Solution: Lets take total employees are 100.   Given that,Total Women= 76 and Total Married = 60.   Total Men = 100 - 76= 
100 - 76 = 24
24 and Single men= 2/3*24= 
2/3*24 = 16
16.   Married men= total men - single men = 24 - 16= 
24 - 16 = 8
8.   Married women= Total married - Married men = 60 - 8= 
60 - 8 = 52
52.   Fraction of women are married= Married women / Total Women = 52 / 76 = 13/19. 13/19NS 13/19
Answer: A
If CD represents a positive two digit number, where C and D are single digit integers, which of the following cannot be true?  Choices.
A) C+D =9  B) (C)(D)=9  C) C-D = 9  D) D-C= 9  E) C/D = 9

Solution: (A) CD = 45 or 63 or 27   (B) CD = 33 or 19   (C) 90   (D) impossible   (E) CD = 91   (D) is impossible because 09 is not a valid two digit number --- if there's a zero in the ten's place, that's just 9, a single digit number. Therefore, no valid two digit number would satisfy (D).   ans B)(C)(=9
Answer: D
8^100 is divisible by 17. Find the remainder for this?	Choose the correct option.
A) 10 B) 12 C) 16 D) 17 E) 19

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
The speed of a boat in upstream is 60 kmph and the speed of the boat downstream is 80 kmph. Find the speed of the boat in still water and the speed of the stream?	Choose the correct choice from the following answers.
A) 10 kmph
B) 22 kmph
C) 77 kmph
D) 66 kmph
E) 99 kmph

Solution: Speed of the boat in still water = (60+80)/2= 
(60+80)/2 = 70
70 kmph. Speed of the stream= (80-60)/2= 
(80-60)/2 = 10
10 kmph.   10 kmphnswer:10 kmph
Answer: A
A single letter is selected at random from the word 'SIM'. The probability that it is a vowel is..??	Choose the correct choice from the following:
A) 2/11
B) 3/11
C) 4/11
D) 1/3
E) 1

Solution: total vowels = 1, total number of letters = 3   so probability = 1/3   ANSWER:1/3
Answer: D
In year Y imported machine tools accounted for 25 percent of total machine - tool sales in the United States, and Japanese imports accounted for 55 percent of the sales of imported machine tools. If the total sales of machine tools imported Japan that year was x billion dollars, then the total sales of all machine tools in the United States was how many billion dollars?  Choose the correct choice from the following answers.
A) 9X/80	B) 13X/20	C) 80/9X	D) 20X/13	E) 80X/11

Solution: IMT = 0.25T   JI = 0.55 IMT   0.55 IMT = $x b   IMT = $x/(0.55) b   T = 4*IMT = 4x/0.55 = 4x*100/55 = 80x/11   Ans: "80X/11"
Answer: E
In 2000, a town had 1300 males and 1400 females. In 2015, the same town had 56500 males and 60000 females. By approximately what percent did the ratio of males to females increase from 2000 to 2015.  Choose the correct choice from the following answers:
A) 0.4%
B) 0.7%
C) 0.9%
D) 1.1%
E) 1.4%

Solution: 2000: males/females = 1300/1400 =3900/4200   2015: males/females = 56500/60000 =3955/4200   ASIDE: It's useful to write both ratios with the same denominator. This allows us to IGNORE the denominator and focus solely on the numerators.   So, our ratio went from 3900/4200 to 3955/4200   Ignoring the denominators, we went from 3900 to 3955   The percent change = 100(difference in values)/(original value)   = (100)(3955-3900)/3900   = (100)(55)/3900)   = (100)(0.0141)   ≈ 1.41...   Answer: 1.4%
Answer: E
A train 600 meters long is running with a speed of 50 kmph. The time taken by it to cross a tunnel 170 meters long is?
Choose the correct choice from the following options:	A) 287 sec	B) 288 sec	C) 55 sec	D) 16 sec	E) 17 sec

Solution: D = 600 + 170= 
600 + 170 = 770
770   S= 50 * 5/18 = 14 mps   T = 770/14= 
770/14 = 55
55 sec   Answer: 55 sec
Answer: C
Which one the following fractions has the smallest value?  Select
A) 123/847  B) 123/849  C) 123/874  D) 123/877  E) 246/1700

Solution: Among (A) , (B) , (C) & (D)   (D) is the smallest...   Now compare (123/877) Vs (E)   (123/877) 123/877 ~ 14%   (E) 246/1700 ~ 14.47%   So (123/877) < (E)   Hence correct answer must be (123/877)
Answer: D
If a is a positive integer, then 5^a+1^a =?
Pick one:  A) Cannot be determined  B) 1+(5^a)  C) 2a  D) 2a^(a + 1)  E) None

Solution: 5^a+1^a=5^a+1   Answer is option 1+(5^a)
Answer: B
If P gets 25% more than Q, then by what percent does Q get less than P?  Choose the correct choice from the following answers.
A) 60%  B) 22%  C) 12%  D) 20%  E) 13%

Solution: Let Q get 1 unit.   25% of 1 unit = 1/4= 
1/4 = 1/4 = around 0.25
0.25   P gets (1 + 0.25) i.e., 1.25 units.   Difference= (1.25 - 1)= 
(1.25 - 1) = 0.25
0.25   Required percentage= 0.25/1.25 * 100 = 1/5 * 100= 
1/5 * 100 = 20
20%   Answer: 12%
Answer: C
The present population of a town is 2000. Population increase rate is 20% p.a. Find the population of town after 1 years?  Choose the correct choice from the following
A) 1000  B) 2400  C) 1500  D) 1600  E) 1250

Solution: P = 2000   R = 20%   Required population of town = P(1 + R/100)^T   = 2000(1 + 20/100)   = 2000(6/5)   = 2400   Answer is 2400
Answer: B
A straight fence is to be constructed from posts 6 inches wide and separated by lengths of chain 5 feet long. If a certain fence begins and ends with a post, which of the following could be the length of the fence in feet? (12 inches = 1 foot).  Pick:
A) 17
B) 88
C) 266
D) 2777
E) 88

Solution: Explanation:   The fence will consist of one more post than there are chains. (e.g. P-c-P-c-P).   Therefore, a total length has to be a multiple of the length of the chain plus one post (5.5) plus one post extra.We have length = (5.5n + 0.5), where n can be any positive whole number. If n= 3, length =17   17nswer: 17) 17
Answer: A
The toll T, in dollars, for a truck using a certain bridge is given by the formula T =3.50 + 0.50( x − 2), where x is the number of axles on the truck. What is the toll for an 18-wheel truck that has 2 wheels on its front axle and 4 wheels on each of its other axles? Choose the correct choice from the following answers
A) $ 2.50 B) $ 3.00 C) $ 3.50 D) $ 4.00 E) $ 5.00

Solution: Number of wheels in truck = 18   Number of wheels on its front axle =2   number of wheels remaining = 16   number of axles remaining axles = 16/4= 
16/4 = 4
4   Total number of axles= 5   T = 3.50 + 0.50( x − 2)   = 3.50 + .5*3   = 3.5 +1.5= 
3.5 +1.5 = 5
5 $   Answer $ 5.00
Answer: E
If Yury has been writing programming code for 15 hours at a rate of 5 lines of code per 20 seconds, how many lines of code has he written?  Answers:
A) 126(10^2)  B) 135(10^2)  C) 12.6(10^5)  D) 1.26(10^7)  E) .126(10^9)

Solution: 5 LINES IN 20 SECONDS   SO FOR 1 MINUTE ( 5 X 3 = 15 LINES )   I HOUR = 60 MINUTES   15 X 60 = 900 LINES IN AN HOUR   15 HOURS = 900 X 15 = 135(10^2)   ANSWER 135(10^2)
Answer: B
A sum of money at simple interest amounts ti $2240 in 2 years and to $ 2600 in 5 years. What is the principal amount?
Select the correct option
A) $1520  B) $1880  C) $2120  D) $2000  E) $1980

Solution: S.I for 3 years = $ (2600-2240)= 
(2600-2240) = 360
$ 360   S.I for 2 years= $ ((360/3) x 2) = $ 240   Principal =$ (2240-240)= 
(2240-240) = 2_000
$ 2000   Answer is $2000
Answer: D
A no. when divided by the sum of 555 and 445 gives 2times their difference as quotient & 30 as remainder. Find the no. is?
Select the correct option:  A) 124345  B) 234545  C) 165767  D) 144656  E) 220030

Solution: (555 + 445) * 2 * 110 + 30 = 220000 + 30= 
220000 + 30 = 220_030
220030   220030
Answer: E
By selling an shirt for $300, a shop keeper gains 20%. During a clearance sale, the shopkeeper allows a discount of 10% on the marked price. His gain percent during the sale is:	Select:
A) 2	B) 14	C) 8%	D) 12	E) 10

Solution: C   8%   Marked price = $300   C.P. = 100/120 * 300= 
100/120 * 300 = 250
$250   Sale price= 90% of $300 = $270   Required gain % = 20/250 * 100= 
20/250 * 100 = 8
8%.
Answer: C
An author received $0.80 in royalties for each of the first 100,000 copies of her book sold, and $0.50 in royalties for each additional copy sold. If she received a total of $260,000 in royalties, how many copies of her book were sold?	Choose the correct choice from the following answers.
A) 130,000 B) 300,000 C) 380,000 D) 400,000 E) 460,000

Solution: Total royalties for first 100.000 books = .8*100,000= 80,000   Total royalties for the rest of the books = 260,000-80,000 = 180,000   Remaining books = 180,000/0.5 = 360,000   Total books = 360,000+100,000 = 460,000 Answer 460,000
Answer: E
All windows are doors. No door is wall
Conclusions:
1. No window is wall
2. No Wall is door	Choose the correct choice from the following options.
A) Both 1 and 4 follow	B) Both 1 and 3 follow	C) Both 4 and 1 follow	D) Both 1 and 2 follow	E) Both 1 and 6 follow

Solution: Explanation:   Since both the premises are universal and one premise is negative, the conclusion must be universal negative. Also, the conclusion should not contain the middle term. So, 1 follows.   However, 2 is the converse of the second premise and thus it also holds.   Answer: Both 1 and 2 follow
Answer: D
If 1 + 9 + 11 = 1, Then what is the value of
12 + 11 + 9 = ?
Choose one
A) one B) Ten C) six D) five E) foue

Solution: Solution:   10   Explanation:   Equation 1 + 9 + 11 = 1 can be derived from   One (o) + nine (n) + eleven (e) = one => 1   Similarly for equation,   12 + 11 + 9   Twelve (t) + eleven (e) + nine (n) => ten (10)   Answer Ten
Answer: B
A delegation of 5 members has to be formed from 3 ladies and 5 gentlemen. In how many ways the delegation can be formed, if 2 particular ladies are always included in the delegation?  Select the correct option:  A) 20  B) 34  C) 37  D) 27  E) 24

Solution: There are three ladies and five gentlemen and a committee of 5 members to be formed.   Number of ways such that two ladies are always included in the committee   = ⁶C₃ = (6 * 5 * 4)/6= 
(6 * 5 * 4)/6 = 20
20.   20nswer: 20
Answer: A
There are 3 states and 3 students representing each state. In how many ways can 5 students be chosen such that at Least one student is chosen from each state.
Pick one:  A) 108.  B) 118  C) 128  D) 138  E) 148

Solution: To choose 5 students so that atleast one student will represent each state can be done in two ways:   A. 3-1-1 (3 students from 1 state and 1 student from other two states)   3C1*3C3*3C1*3C1=27   3C1 - # of ways to choose 3-student state;   3C3 - # of ways to choose 3 students from 3-student state;   3C1 - # of ways to choose 1 student from the first 1-student state;   3C1 - # of ways to choose 1 student from the second 1-student state.   OR   B. 1-2-2 (1 student from 1 state and 2 students from other two states)   3C1*3C1*3C2*3C2=81   3C1 - # of ways to choose 1-student state;   3C1 - # of ways to choose 1 student from the 1-student state;   3C2 - # of ways to choose 2 students from the first 2-student state;   3C2 - # of ways to choose 2 students from the second 2-student state.   27+81= 
27+81 = 108
108.   108.nswer: 108 108.
Answer: A
2 oranges, 3 bananas and 4 apples cost Rs.15. 3 oranges, 2 bananas and 1 apple costs Rs 10. What is the cost of 3 oranges, 3 bananas and 3 apples
Answers
A) 22
B) 28
C) 15
D) 77
E) 10

Solution: Explanation:   2 O + 3 B + 4 A = 15 - - - - (1)   3 O + 2 B + 1 A = 10 - - - - (2)   Where A,B and O are number of apple, bananas, and oranges respectively.   Adding 1 and 2,   5 O + 5 B + 5 A = 25 ⇒ 1 O + 1 A + 1 B = 5   now,   3O + 3A + 3B = 5 × 3 = 15   Answer:15
Answer: C