MU-NLPC/Calc-aqua_rat huggingface dataset:
Bon-Bean, a coffee shop, served a total of 460 cups of coffee and tea yesterday. 270 of these cups contained caffeine, and the number of decaffeinated tea cups was twice the total number of tea cups that contained caffeine. If Bon-Bean served 250 coffee cups yesterday, how many of them were decaffeinated?  Choose the correct choice from the following answers.
A) 50 B) 70 C) 140 D) 190 E) 210

Solution: Tc : Tea caffeine   Td : Tea No caffeine   Cc : Coffee Caffeine   Cd : Coffee No Caffeine   As per question, Tc + Td + Cc + Cd = 460 -- (1)   Also, Tc + Cc = 270 -- (2)   Td = 2 * Tc -- (3)   Cc + Cd = 250 -- (4)   Now, substituting (4) in (1), we will have Tc + Td + 250 = 460   or Tc + Td = 210. -- (5)   Substitute (3) in (5), we will get Tc = 70. Substitute Tc in (2), we will get Cc = 200   Now substitute Cc in (4), we will get Cd = 50. hence, 50
Answer: A
At a certain store, the price of a pair of shoes is twenty dollars more than three times the price of a pair of jeans and the price of a sweater is sixty percent more than the price of a pair of shoes. If the price of a pair of jeans is j dollars at this store, then what is the price, in dollars, of a pair of shoes, a sweater and a pair of jeans, in terms of j ?
Answers:	A) 1.5j + 10	B) 3j + 20	C) 4.5j + 30	D) 5.5j + 30	E) 8.6j + 52

Solution: Ans 8.6j + 52   Given   Price of Jeans = J   Price of shoes = 20+3J   Price of Sweater = 1.6(20+3J)   Total Price of all three items = J+20+3J+1.6(20+3J) = 52+8.6J
Answer: E
In an election contested by two parties, Party D secured 12% of the total votes more than Party R. If party R got 132,000 votes, by how many votes did it lose the election?
Choose the correct option
A) 240,000	B) 300,000	C) 168,000	D) 36,000	E) 24,000

Solution: Explanatory Answer   Let the percentage of the total votes secured by Party D be x%   Then the percentage of total votes secured by Party R = (x - 12)%   As there are only two parties contesting in the election, the sum total of the votes secured by the two parties should total up to 100%   i.e., x + x - 12 = 100   2x - 12 = 100   or 2x = 112 or x = 56%.   If Party D got 56% of the votes, then Party got  (56 - 12)= 
 (56 - 12) = 44
44% of the total votes.   44% of the total votes= 132,000   i.e., 44/100*T = 132,000   => T = 132000*100/44 = 300,000 votes.   The margin by which Party R lost the election = 12% of the total votes   = 12% of 300,000 = 36,000.   The correct choice is (36,000)
Answer: D
Each of the following numbers has a remainder of 4 when divided by 6 except:
Pick.
A) 4  B) 16  C) 64  D) 26  E) 46

Solution: It's 26   26 = 6*4+2
Answer: D
A man spends 10% of his income in house rent, 20% of the rest on his childrenâ€™s education, 25% of the rest miscellaneous causes. If he now posses Rs. 1944 then his income is?	Choose the correct answer: A) 3600 B) 4500 C) 5000 D) 2000 E) 2500

Solution: X * (90/100) * (80/100) * (75/100) = 1944   X * 0.9 * 0.8 * 0.75   X = 1944/0.54= 
1944/0.54 = 3_600
3600   3600NSWER 3600
Answer: A
In a party every person shakes hands with every other person. If there are 105 hands shakes, find the number of person in the party.
Choose the correct option
A) 13	B) 15	C) 12	D) 7	E) 9

Solution: Let n be the number of persons in the party. Number of hands shake = 105; Total number of hands shake is given by nC2.   Now, according to the question,   nC2 = 105;   Or, n!/[2!*(n-2)!] = 105;   Or, n*(n-1)/2 = 105;   Or, n^2-n = 210;   Or, n^2-n-210 = 0;   Or, n = 15, -14;   But, we cannot take negative value of n.   So, n = 15 i.e. number of persons in the party = 15.   Ans: 15
Answer: B
A man is 24 years older than his son. In two years, his age will be twice the age of his son. The present age of his son is: Pick:
A) 12 years B) 15 years C) 11years D) 22years E) 20 years

Solution: Let the son's present age be x years. Then, man's present age = (x + 24) years.   (x + 24) + 2 = 2(x + 2)   x + 26 = 2x + 4   x = 22.   Ans- 22years
Answer: D
A rectangular lawn of dimensions 80 m * 60 m has two roads each 15 m wide running in the middle of the lawn, one parallel to the length and the other parallel to the breadth. What is the cost of traveling the two roads at Rs.3 per sq m?	Select the correct option
A) A)3820 B) B)930 C) C)9309 D) D)3900 E) E)5625

Solution: 5625xplanation:   Area = (l + b – d) d   (80 + 60 – 15)15 => 1875 m2   1875 * 3 = Rs.5625   Answer: Option 5625
Answer: E
If Sand is coded as Brick, Brick as House, House as Temple, Temple as Palace then where do you worship?	Select the correct option.
A) Palace	B) Temple	C) Brick	D) House	E) none

Solution: palace because temple is coded as palace   PalaceNSWER:Palace
Answer: A
Today X is twice as old as Y and Y is 3 years younger than Z. If X, Y, and Z are all alive 4 years from today, which of the following must be true on that day. I. X is twice as old as Y II. Y is 3 years younger than Z III. X is older than Z
Choose the correct choice from the following options
A) I
B) II
C) I,II & III
D) III
E) II, III

Solution: Say Z age is 10   Y age is 7   X age is 14   After 4 years   Z age is 14   Y age is 11   X age is 28   i.e ) after 4 years   Y is 3 years younger than Z   X is twice as old as Y   X is older than Z   Answer : I,II & III
Answer: C
If a farmer wants to plough a farm field on time, he must plough 260 hectares a day. For technical reasons he ploughed only 85 hectares a day, hence he had to plough 2 more days than he planned and he still has 40 hectares left. What is the area of the farm field and how many days the farmer planned to work initially?	Select the correct option
A) 312	B) 490	C) 720	D) 435	E) 679

Solution: Let x be the number of days in the initial plan. Therefore, the whole field is 260â‹…x hectares. The farmer had to work for x+2 days, and he ploughed 85(x+2) hectares, leaving 40 hectares unploughed. Then we have the equation:   260x=85(x+2)+40   175x=210   x=1.2   So the farmer planned to have the work done in 6 days, and the area of the farm field is 260(1.2)=312 hectares   correct answer 312
Answer: A
Find the last digit of (1021^3921)+(3081^3921)  Pick one.
A) 0
B) 1
C) 2
D) 3
E) 4

Solution: last digit of 1st expression is 1 and second expression is also 1   as, 1 raised to any power will be 1 itself   so, 1+1 = 2   so the last digit will be 2   ANSWER:2
Answer: C
Three pipes A, B and C can fill a tank in 4 hours. After working at it together for 2 hours, C is closed and A and B can fill the remaining part in 5 hours. How many hours will take C alone to fill the tank?  Choose the correct choice from the following answers
A) 10/3  B) 15/4  C) 20/3  D) 25/4  E) 35/6

Solution: The rate of A+B+C is 1/4 of the tank per hour.   After 2 hours, the tank is half full.   The rate of A+B is 1/2 * 1/5 = 1/10 of a tank per hour.   The rate of C is 1/4 - 1/10 = 3/20   C can fill the tank in 20/3 hours.   The answer is 20/3.
Answer: C
A man invested Rs. 4455 in Rs. 10 shares quoted at Rs. 8.25. If the rate of dividend be 12%, his annual income is:  Choose the most appropriate option
A) 207
B) 530
C) 648
D) 600
E) 700

Solution: No of shares = 4455/8.25= 
4455/8.25 = 540
540   face value= 540*10= 
540*10 = 5_400
5400   annual income= 12/100*5400= 
12/100*5400 = 648
648   ANSWER 648
Answer: C
Given that 0 < a < b < c < d, which of the following the largest ?
Pick one.
A) (c+d) / (a+b) B) (a+d) / (b+c) C) (b+c) / (a+d) D) (b+d) / (a+c) E) None

Solution: Explanation :   For the fraction to be largest, denominator should be minimum and numerator should be maximium.   Here a and b is minimum which is in denominator of option 1. and c and d is maximum which is also in the numerator of option 1.   Hence 1.) (c+d) / (a+b)   (c+d) / (a+b)nswer : (c+d) / (a+b)
Answer: A
The price of 2 sarees and 4 shirts is Rs. 1600. With the same money one can buy 1 saree and 6 shirts. If one wants to buy 12 shirts, how much shall he have to pay ?
Choices:  A) Rs. 2000  B) Rs. 2200  C) Rs. 2300  D) Rs. 2400  E) Rs. 2500

Solution: Let the price of a saree and a shirt be Rs. x and Rs. y respectively.   Then, 2x + 4y = 1600 .... (i)   and x + 6y = 1600 .... (ii)   Divide equation (i) by 2, we get the below equation.   => x + 2y = 800. --- (iii)   Now subtract (iii) from (ii)   x + 6y = 1600 (-)   x + 2y = 800   ----------------   4y = 800   ----------------   Therefore, y = 200.   Now apply value of y in (iii)   => x + 2 x 200 = 800   => x + 400 = 800   Therefore x = 400   Solving (i) and (ii) we get x = 400, y = 200.   Cost of 12 shirts = Rs. (12 x 200) = Rs. 2400.   Rs. 2400
Answer: D
In a Fish tank there are 8 fishes are there. In how many possibilities to choose 6 fishes from the tank?	Pick one: A) 20 B) 21 C) 28 D) 8 E) 30

Solution: The possible way to select 6 fishes out of 10 fishes in the tank is 8C6.   8286=8!/2!*6!=8*7*6!/6!*2*1   8286=28   There are 28 ways to select a 6 fishes from the tank.
Answer: C
John and Peter are among the nine players a volleyball coach can choose from to field a six-player team. If all six players are chosen at random, what is the probability of choosing a team that includes John and Peter?
Pick one
A) 3/10	B) 4/11	C) 5/12	D) 6/13	E) 7/15

Solution: The total possible ways of selecting a 6-member team is 95/126 = 84   The possible ways which include John and Peter is 75/124 = 35   The probability of choosing both John and Peter is 35/84 = 5/12   The answer is 5/12.
Answer: C
A no.when divided by 220 gives a remainder 43, what remainder will beobtained by dividingthe same no.17?	Choose the correct choice
A) 2	B) 8	C) 9	D) 11	E) 15

Solution: 220 + 43= 
220 + 43 = 263
263/17= 8 (Remainder)   8
Answer: B
The difference between the length and breadth of a rectangle is 23 m. If its perimeter is 206 m, then its area is: Choices.
A) 2520	B) 2376	C) 3235	D) 3569	E) 6323

Solution: We have: (l - b) = 23 and 2(l + b) = 206 or (l + b) = 103.   Solving the two equations, we get: l = 63 and b = 40.   2520rea = (l x b) = (63 x 40) m2 = 2520 m2   2520nswer:2520
Answer: A
A boat can travel with a speed of 42 km/hr in still water. If the speed of the stream is 10 km/hr, find the time taken by the boat to go 84 km downstream Answers:
A) 1 hour 40 min
B) 2 hour 40 min
C) 1 hour 20 min
D) 1 hour 30 min
E) 1 hour 50 min

Solution: Speed of the boat in still water = 42 km/hr   speed of the stream = 10 km/hr   Speed downstream = (42+10)= 
(42+10) = 52
52 km/hr   Distance travelled downstream= 84 km   Time taken =distance/speed   =84/52   = 1.66 hours   = 1 hour 40 min.   1 hour 40 minNSWER:1 hour 40 min
Answer: A
Excluding stoppages, the speed of a bus is 54 kmph and including stoppages, it is 45 kmph. For how many minutes does the bus stop per hour ?
Choose the correct choice from the following options:
A) 8 minutes	B) 10 minutes	C) 12 minutes	D) 14 minutes	E) 16 minutes

Solution: Explanation:   Due to stoppages, it covers 9 km less.   Time taken to cover 9 km = (9/54) hour   = (1/6)*60= 
(1/6)*60 = 10
10 minutes   Option 10 minutes
Answer: B
I bought two books; for Rs.450. I sold one at a loss of 15% and other at a gain of 19% and then I found each book was sold at the same price. Find the cost of the book sold at a loss?
Pick
A) 337
B) 262.5
C) 299.5
D) 266.5
E) 299

Solution: x*(85/100) = (450 - x)119/100   x = 262.5   Answer: 262.5
Answer: B
A man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. What is the total distance traveled by the man? Choose one
A) 6.24 km  B) 6 km  C) 5.76 km  D) 5.66 km  E) 7 km

Solution: M = 6   S = 1.2   DS = 7.2   US = 4.8   x/7.2 + x/4.8 = 1   x = 2.88   D = 2.88 * 2= 
2.88 * 2 = 5.76
5.76   ANSWER:5.76 km
Answer: C
Two dice are tossed once. What is the probability of getting an even number on the first die or a total sum of 7 on the two dice?  Choose the correct option.
A) 7/12 B) 5/12 C) 11/36 D) 7/36 E) 5/36

Solution: There are 36 possible outcomes for two dice.   The number of outcomes with an even number on the first die is 3*6= 
3*6 = 18
18.   The number of outcomes with a sum of 7 is 6.   We need to subtract the outcomes that have both an even number on the first die and a sum of 7 because we have counted those outcomes twice. This number of outcomes is 3.   The number of outcomes with either an even number on the first die or a sum of 7 is  18+6-3= 
 18+6-3 = 21
21.   The probability is 21/36=7/12.   The answer is 7/12.
Answer: A
Submarine P and Submarine Q are equipped with sonar devices that can operate within a 5,000 yard range. Submarine P remains in place while Submarine Q moves 4,700 yards south from Submarine P. Submarine Q then changes course and moves due east, stopping at the maximum range of the sonar devices. In which of the following directions can Submarine Q continue to move and still be within the sonar range of Submarine P? I. North II. South III. West Choose the correct choice
A) I only	B) I and III only	C) II only	D) III only	E) I,II only

Solution: It's evident if we make a diagram for the Movement of Q respect to P.   From its South position to the east position, it has covered the maximum radius for the south direction. Similarly, it's east movement further will also make it out of range.   Thus it can only move north or west or anything in that curve.   Answer : I and III only
Answer: B
The diagonal of the floor of a rectangular closet is 7 feet. The shorter side of the closet is 4 feet. What is the area of the closet in square feet?	Choose the most appropriate option: A) 20 sq. ft B) 27 sq. ft C) 37 sq. ft D) 47 sq. ft E) 57 sq. ft

Solution: Other side	=   15 2	- 9 2   2	2   ft   =   225	-	81   4	4   ft   =   144   4   ft   =	6 ft.   Area of closet = (6 x 4.5) sq. ft = 27 sq. ft.   27 sq. ft)
Answer: B
A card is drawn from a pack of 52 cards. The probability of getting a face card?  Answers:
A) 2/15 B) 2/13 C) 1/15 D) 4/13 E) 5/7

Solution: Clearly in the 52 cards out of which there are 16 face cards.   probability of getting a face card = 16/52 = 4/13   correct option is 4/13
Answer: D
A cube of edge 6 cm is cut into cubes each of edge 3 cm. The ratio of the total surface area of one of the small cubes to that of the large cube is equal to:
Answers:
A) 1:4
B) 1:25
C) 1:52
D) 1:522
E) None

Solution: Sol.   Required ratio = 6 * 3 * 3 / 6 * 6 * 6 = 1/4= 1:4.   1:4nswer 1:4
Answer: A
If shares of two persons in profits are Rs.400 and Rs.600 then ratio of their capitals is  Choose the correct choice:	A) 3:4	B) 2:3	C) 4:3	D) 1:3	E) 1:5

Solution: total profit =1000   ratio=400/600   =2:3   ANSWER:2:3
Answer: B
385, 462, 572, 396, 427, 671, 264	Select the correct option: A) 385 B) 427 C) 671 D) 264 E) None of these

Solution: Solution   In each number except 427,the middle digit is the sum of the other two. Answer 427
Answer: B
Obra drove 200π meters along a circular track. If the area enclosed by the circular track on which she drove is 57,600π square meters, what percentage of the circular track did Obra drive?	Choices
A) 6.67%	B) 12.5%	C) 41.66%	D) 25%	E) 33.3%

Solution: area enclosed by the circular track on which she drove is 57,600π square meters   So, π(r^2) = 57,600π ---> (r^2)=57,600 ---> r=240   41.66%ircumference of the circular track = 2πr = 480π   Therefore, part of circumference covered = 200π/480π =41.66%   Hence, answer is 41.66%.
Answer: C
Can you find a number such that if we multiply that number by 1 or 2 or 3 or 4 or 5 or 6 , then the resultant number contains same all digits, different places
Select
A) 143857  B) 142857  C) 144857  D) 142853  E) 142854

Solution: Correct Answer : 142857   142857 * 1= 
142857 * 1 = 142_857
142857   142857 * 2= 
142857 * 2 = 285_714
285714   142857 * 3= 
142857 * 3 = 428_571
428571   142857 * 4= 
142857 * 4 = 571_428
571428   142857 * 5= 
142857 * 5 = 714_285
714285   142857 * 6= 
142857 * 6 = 857_142
857142
Answer: B
The avg weight of A,B & C is 80 kg. If D joins the group, the avg weight of the group becomes 82 kg.If another man E who weights is 3 kg more than D Replaces A, Then the avgof B,C,D&E becomes 81 kg. What is the weight of A?  Pick one:
A) 56 B) 65 C) 75 D) 89 E) 95

Solution: A + B + C = 3 *80= 
3 *80 = 240
240   A + B + C + D= 4 * 82= 
4 * 82 = 328
328 ---- (i)   So, D= 88& E = 88 + 3= 
88 + 3 = 91
91   B + C + D +E= 81 * 4= 
81 * 4 = 324
324 --- (ii)   From Eq. (i) & (ii)   A-95= 328 – 324 = 4   A = 95 +4 = 91 + 4= 
91 + 4 = 95
95   Answer : 95
Answer: E
Shaquan has 5 playing cards, each one is ordered by the number on it, but one card is flipped over.
They are numbered 8, 16, 24, x , 40. If X is the card flipped over, what number will be on the other side? Choices:
A) 22  B) 30  C) 32  D) 26  E) 28

Solution: The answer is C) 32 because the cards are numbered by multipliers of 8.   8x2 is 16,   8x3 is 24,   8x4 is 32,   and 8x5 is 40.
Answer: C
A pair of articles was bought for $810 at a discount of 10%. What must be the marked price of each of the article?  Choose the correct choice:	A) $300	B) $500	C) $350	D) $450	E) $600

Solution: S.P. of each of the article = 810/2= 
810/2 = 405
$405   Let M.P= $x   90% of x = 405   x = 405*100/90= 
405*100/90 = 450
$450   Answer is $450
Answer: D
What is the probability that a number selected from number 1 to 30 is prime number,when each of the given numbers is equally likely to be selected? Pick one
A) 10/30
B) 20/30
C) 1
D) 5/30
E) 15/30

Solution: x={2,3,5,7,11,13,17,19,23,29}   n(x)=10   n(s)=30   Hence required probability=n(x)/n(s)=10/30   Option 10/30 is answer
Answer: A
Carol is four times Alice’s age but only twice as old as Betty. Alice is twelve years younger than Carol. How old is Betty?	Choose the most appropriate option
A) 6 B) 8 C) 12 D) 18 E) 24

Solution: ans 8..8   given that C=4A=28..AND A=C-12..=4A-12   substituting the values A=4, C=12 AND 8=8..
Answer: B
A certain manufacturer sells its products	to stores in 113 different	regions worldwide, with an average (arithmetic mean) of 182 stores per region. If last year these stores sold an	average of 51,752 units of the manufacturer’s product per store, which of the following is closest to the total number of units of manufacturer’s product	sold	worldwide last	year?	Choose one: A) 10^5 B) 10^6 C) 10^7 D) 10^8 E) 10^9

Solution: 51752*182*113 or   51000*180*113 or   50000*200*100   =10^9   10^9
Answer: E
Three numbers are in the ratio 3:5:7. The largest number value is 42. Find difference between Smallest & largest number is?	Choose one
A) 18  B) 20  C) 22  D) 24  E) 25

Solution: == 3:5:7   Total parts = 15   = The largest number value is 42   = The largest number is = 7   = Then 7 parts -----> 42 ( 7 * 6 = 42 )   = smallest number = 3 & Largest number = 7   = 24ifference between smallest number & largest number is = 7 - 3= 
7 - 3 = 4
4= Then 4 parts -----> 24 (4 * 6 = 24)   24
Answer: D
Find odd one among 2,3, 4, 4, 6, 8, 9,12, 16 ?	Choose one: A) 9 B) 8 C) 77 D) 65 E) 212

Solution: 9NSWER: 9
Answer: A
Mrs. Rodger got a weekly raise of $145. If she gets paid every other week, write an integer describing how the raise will affect her paycheck.  Answers
A) $140
B) $141
C) $142
D) $147
E) $145

Solution: Let the 1st paycheck be x (integer).   Mrs. Rodger got a weekly raise of $ 145.   So after completing the 1st week she will get $ (x+145).   Similarly after completing the 2nd week she will get $ (x + 145) + $ 145.   = $ (x + 145 + 145)   = $ (x + 290)   So in this way end of every week her salary will increase by $ 145.   correct answer $145)$145
Answer: E
A bus 15 m long is running with a speed of 40 km/hr. In what time will it pass a man who is skateboarding at 8 km/hr in the direction opposite to that in which the car is going?
Choose the correct choice from the following answers:
A) 1.125
B) 1.5
C) 1.75
D) 1.25
E) 1

Solution: Speed of bus relative to man = 40 + 8= 
40 + 8 = 48
48 km/hr.= 48 * 5/18 = 40/3 m/sec.   Time taken to pass the man = 5 * 3/40   = 1.125 sec.   1.125nswer: 1.125
Answer: A
The population of a town is 10000. It decreases annually at the rate of 10% p.a. What will be its population after 2 years?	Pick:
A) 4300	B) 4500	C) 8100	D) 5230	E) 5366

Solution: 10000 × 90/100 × 90/100 = 8100   Answer : 8100
Answer: C
A speaks truth in 75% of cases and B in 80% of cases. In what percentage of cases are they likely to contradict each other, narrating the same incident?  Choices:  A) 30/100  B) 32/100  C) 35/100  D) 41/100  E) None of these

Solution: Explanation :   Let A = Event that A speaks the truthB = Event that B speaks the truthThen P(A) = 75/100 = 3/4P(B) = 80/100 = 4/5P(A-lie) = 1-3/4 = 1/4P(B-lie) = 1-4/5 = 1/5Now ,A and B contradict each other =[A lies and B true] or [B true and B lies]= P(A).P(B-lie) + P(A-lie).P(B)= (3/5*1/5) + (1/4*4/5) = 7/20= (7/20 * 100)= 
(7/20 * 100) = 35
35%   Answer : 35/100
Answer: C
The consumption of diesel per hour of a bus varies directly as square of its speed. When the bus is travelling at 50 kmph its consumption is 1 litre per hour. if each litre costs $50 and other expenses per hous is $ 50, then what would be the minimum expenditure required to cover a distance of 500 Km?	Answers
A) 800
B) 950
C) 900
D) 1000
E) 1250

Solution: 50 kmph consumption is 1 lt/hr   so 500 km will take 10 hrs and the consumption is 10 lt for entire distance.   1 lt costs $50   so 10 lt costs $500   extra expenses for 1 hr - $50   10 hrs - $500   total expense - $500 + $500 = $1000   Answer : 1000
Answer: D
here are 5 Rock songs, 6 Karnatic songs and 3 Hindi pop songs. How many different albums can be formed using the above should contain at least 1 Rock song and 1 karnatic song? Choose the correct choice from the following:  A) 45133  B) 15384  C) 63215  D) 15624  E) 45123

Solution: There are 2n ways of choosing ‘n’ objects. For e.g. if n = 3, then the three objects can be chosen in the following 23 ways - 3C0 ways of choosing none of the three, 3C1 ways of choosing one out of the three, 3C2 ways of choosing two out of the three and 3C3 ways of choosing all three.   In the given problem, there are 5 Rock songs. We can choose them in 25 ways. However, as the problem states that the case where you do not choose a Rock song does not exist (at least one rock song has to be selected), it can be done in 25 - 1 = 32 - 1= 
32 - 1 = 31
31 ways.   Similarly, the 6 Carnatic songs, choosing at least one, can be selected in 26 - 1= 64 - 1= 
64 - 1 = 63
63 ways.   And the 3 Indi pop can be selected in 23= 8 ways. Here the option of not selecting even one Indi Pop is allowed.   Therefore, the total number of combinations = 31 * 63 * 8= 
31 * 63 * 8 = 15_624
15624   Ans: 15624
Answer: D
A person took some amount with some interest for 8 years, but increase the interest for 1%, he paid Rs.640/- extra, then how much amount he took? Choose the correct choice from the following: A) Rs.5500/- B) Rs.8000/- C) Rs.4000/- D) Rs.7000/- E) None of these

Solution: Explanation:8 years = Rs.640/-year = 640/8Rate of Interest = 1%100/1% × 640/8 = Rs.8000/-P = Rs.8000/- Answer: Option Rs.8000/-
Answer: B
Machine A working alone can complete a job in 10 hours. Machine B working alone can do the same job in 12 hours. How long will it take both machines working together at their respective constant rates to complete the job? Choose the correct choice from the following
A) 50/11 B) 60/11 C) 40/11 D) 47/11 E) 57/15

Solution: Machines ( A ) ( 60/11 ) (A+60/11)   ---Time - 10 - ( 12 ) -   ---Rate 12--- 10-- 22   --Work 120 --120 -120   A+60/11 = (120/22) = 60/11   60/11
Answer: B
The average of five natural numbers is 150. A particular number among the five exceeds another by 100. The rest three numbers lie between these two numbers and they are equal. How many different values can the largest number among the five take? Choose the correct choice from the following answers.
A) 59  B) 19  C) 21  D) 18  E) 42

Solution: We basically have 5 positive numbers - x, y, y, y, x+100 with sum = 750   so 2x + 3y = 650 and x<y<x+100.   Take extreme cases of inequality and we get for x=y case, 5x=650 so x = 130.   Another case, y=x+100, 5x+300 = 650. x=70.   BOTH THESE CASES are not allowed since y lies between x and x+100. But these are the bounds.   Once we have that, it is only a matter of finding the allowed values of x. (650-2x) should be divisible by 3, so changes allowed in x should be only in factors of 3. Start writing numbers from 73, 76....upto 127 and we get 19!   Answer is 19,
Answer: B