MU-NLPC/Calc-aqua_rat huggingface dataset:
A bag contains 5 red & 3 black balls and the second one 4 red and 5 black balls. One of is selected at random and a draw of two balls is made from it. What is the chances that one of them is red and the other is black?  Choose the correct choice from the following answers.
A) .5456 B) 1.5456 C) 2.5456 D) 3.5456 E) 4.5456

Solution: secet 1 bag from two=1/2   from 1 st bag=5c1*3c1/8c2=15/28   from 2nd bag=4c1*5c1/9c2=20/36   toatl p(s)=1/2(15/28 + 20/36)=.5456   .5456NSWER:.5456
Answer: A
n a race of 1000 m, A can beat by 100 m, in a race of 800m, B can beat C by 100m. By how many meters will A beat C in a race of 600 m?  Choose the correct choice from the following answers: A) 127.6 B) 127.5 C) 127.0 D) 127.2 E) 127.3

Solution: When A runs 1000 m, B runs 900 m and when B runs 800 m, C runs 700 m.   When B runs 900 m, distance that C runs = (900 * 700)/800 = 6300/8= 
6300/8 = 1_575/2 = around 787.5
787.5 m.   In a race of 1000 m, A beats C by   (1000 - 787.5)= 
  (1000 - 787.5) = 212.5
212.5 m to C.   In a race of 600 m, the number of meters by which A beats C= (600 * 212.5)/1000= 
(600 * 212.5)/1000 = 127.5
127.5 m.Answer: O127.5
Answer: B
The average of fifteen numbers is 0. In those 15, at the most, how many may be greater than zero?
Choose the correct answer
A) 0 B) 1 C) 10 D) 14 E) 17

Solution: Explanation :   Average of 15 numbers = 0   Sum of 15 numbers =(0 x 15) =0.   It is quite possible that 14 of these numbers may be positive and if there sum is a, then 15th number is (-a).   Answer : 14
Answer: D
If n is a natural number, then (6n^2+6n) is always divisible by? Answers.
A) 6 only  B) 6 and 12  C) 12 only  D) by 18 only  E) None of these

Solution: (6n^2+6n)=6n(n+1), which is always divisible by 6 and 12 both, since n(n+1) is always even.   Correct Option: 6 and 12
Answer: B
Jonathan can type a 40 page document in 40 minutes, Susan can type it in 30 minutes, and Jack can type it in 24 minutes. Working together, how much time will it take them to type the same document? Select
A) 5 minutes
B) 10 minutes
C) 15 minutes
D) 18 minutes
E) 20 minutes

Solution: You may set up common equation like this:   job/A+job/B+job/C=job/x   Memorize this universal formula, you will need it definitely for GMAT.   and find x from this equation   In this specific case, the equation will look like this:   40/40+40/30+40/24=40/x   If you solve this equation, you get the same answer 10 minutes (10)
Answer: B
A license plate in the country Kerrania consists of four digits followed by two letters. The letters A, B, and C are used only by government vehicles while the letters D through Z are used by non-government vehicles. Kerrania's intelligence agency has recently captured a message from the country Gonzalia indicating that an electronic transmitter has been installed in a Kerrania government vehicle with a license plate starting with 79. If it takes the police 9 minutes to inspect each vehicle, what is the probability that the police will find the transmitter within three hours? Choices.
A) 18/79	B) 1/6	C) 1/25	D) 19/900	E) 1/900

Solution: Everything is correct except that you assumed the letters can't be repeated. It can be repeated.   AA   BB   CC   AB, AC, BC, BA, CA, CB.   Thus; total government vehicles = (10)^2*(3)^2 = 100*9= 
100*9 = 900
900   Vehicles inspected within 3 hours= 60*3/9 = 19   P = 19/900   Ans:19/900
Answer: D
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 most appropriate option.
A) 2  B) 6  C) 8  D) 4  E) 10

Solution: Due to stoppages, it covers 9 km less.   Time taken to cover 9 km =(9/54x 60) min= 10 min.   ANSW10R 10
Answer: E
A batsman scores 26 runs and increases his average from 14 to 15. Find the runs to be made if he wants top increasing the average to 19 in the same match ?
Choose the correct option:  A) 12  B) 18  C) 25  D) 74  E) 88

Solution: Number of runs scored more to increase the ratio by 1 is  26 - 14= 
 26 - 14 = 12
12   To raise the average by one (from 14 to 15), he scored 12 more than the existing average.   Therefore, to raise the average by five (from 14 to 19), he should score 12 x 5= 60 more than the existing average. Thus he should score  14 + 60= 
 14 + 60 = 74
74.   Answer 74
Answer: D
How many different three-digit multiples of 5 can be composed of digits 1, 3, 4, and 5 if none of the digits is repeated?  Choose the correct choice from the following options:  A) 3  B) 6  C) 10  D) 12  E) 18

Solution: = 3c2 x 2 = 6   can you explain your method. i solved it differently   XYZ, where Z must be 5. therefore 1 variation of digit in Z.   Y can be any of the 3 possible choices.   X can be any of the 2 possible choices.   2+3+1= 
2+3+1 = 6
6   6
Answer: B
If n is an integer greater than 6, which of the following must be divisible by 3?
Choose the correct option.
A) N(N+1)(N-4) B) N(N+2)(N-1) C) N(N+3)(N-5) D) N(N+4)(N-2) E) N(N+5)(N-6)

Solution: The product of 3 numbers to be divisible by 3 at least one of them must be divisible by 3. So, to ensure that the product of 3 integers shown is divisible by 3 all 3 numbers must have different remainders upon division by 3, meaning that one of them should have remainder of 1, another reminder of 2 and the last one remainder of 0, so be divisible by 3. We should have something like n(n+1)(n+2) (for example: if n divided by 3 yields remainder of 1, then n+1 yields remainder of 2 and n+2 yields remainder of 0, thus it's divisible by 3 OR if n divided by 3 yields remainder of 2, then n+2 yields remainder of 1 and n+1 yields remainder of 0, thus it's divisible by 3).   Only option A satisfies this, because n(n+1)(n−4)=n(n+1)(n−6+2) and n−6has the same remainder as nn upon division by 3 thus we can replace it by n.   N(N+1)(N-4)nswer: N(N+1)(N-4).
Answer: A
When x is divided by 3, the quotient is y and the remainder is 1. When x is divided by 5, the quotient is z and the remainder is 6. Which of the following is the value of y in terms of z? Choose the correct choice from the following answers.
A) 4z/7 + 5  B) (7z + 5) / 6  C) (6z + 7) / 4  D) (5z + 5) / 3  E) (4z + 6) / 7

Solution: When x is divided by 3, the quotient is y and the remainder is 1: x = 3y + 1.   When x is divided by 5, the quotient is z and the remainder is 6: x = 5z + 6.   Equate those two:   3y + 1 = 5z + 6;   y = (5z + 5)/3.   Answer: (5z + 5) / 3.
Answer: D
By selling 150 mangoes, a fruit-seller gains the selling price of 20 mangoes. Find the gain percent? Select the correct option:
A) 27%	B) 25%	C) 21%	D) 15%	E) 24%

Solution: SP = CP + g   150 SP = 150 CP + 20 SP   130 SP = 150 CP   130 --- 20 CP   100 --- ? => 15%   Answer:15%
Answer: D
What is the lowest possible common multiple of 2 distinct integers, each greater than 63?	Pick one.
A) 68 B) 69 C) 128 D) 68^2 E) 68·69

Solution: In order to get the lowest LCM, we have to take the first number as 64 and the next number as its multiple.   So, I can take 64 and 128 as two distinct numbers, such that Lowest LCM = 128.   Answer should be 128.
Answer: C
How many alphabets need to be there in a language if one were to make 1 million distinct 3 digit initials using the alphabets of the language?  Choose the correct choice from the following:
A) 100  B) 50  C) 26  D) 1000  E) None of these

Solution: Solution:   1 million distinct 3 digit initials are needed.   Let the number of required alphabets in the language be 'n'.   Therefore, using 'n' alphabets we can form n *n *n = n3 distinct 3 digit initials.   NOTE:   Distinct initials are different from initials where the digits are different. For instance, AAA and BBB are acceptable combinations in the case of distinct initials while they are not permitted when the digits of the initials need to be different.   This n3 different initials = 1 million.   i.e. n3 = 106 (1 million =106).   n3 = 1023.   => n = 102 = 100.   Hence, the language needs to have a minimum of 100 alphabets   100nswer: Option 100
Answer: A
If Finn was 17 months old one year ago, how old was he, in months, x months ago?
Choose the correct choice from the following choices.
A) x − 30	B) x − 12	C) 18 − x	D) 29 − x	E) 30 − x

Solution: Age Today = 17 months + 12 months (1year) = 29 months   X months ago- Today's Age - X = 29 - X   Ans- 29 − x
Answer: D
A cyclist bikes x distance at 8 miles per hour and returns over the same path at 812miles per hour. What is the cyclist's average rate for the round trip in miles per hour?  Answers
A) 8.1	B) 8.3	C) 8.6	D) 9.6	E) 9.0

Solution: Distance = d1 = x miles   Speed = s1 = 8 miles per hour   Time = t1 = Distance/ Speed = x/8   2. Going from B to A   Distance = d2 = x miles   Speed = s2 = 12 miles per hour   Time = t2 = Distance/ Speed = x/12   3. Average Speed = Total 9.6istance/Total Time   Total 9.6istance = x + x = 2x   Total Time = x/12 + x/8 = x (1/12 + 1/8) = =5x/24   Speed = 2x/(5x/24) = 48/5= 
48/5 = 48/5 = around 9.6
9.6   Answer : 9.6
Answer: D
If x = -6 and y = -3, what is the value of 4(x-y)^2 - xy ?	Choose the correct choice from the following options:  A) 20  B) 18  C) 17  D) 22  E) 23

Solution: x = -6 and y = -3   x-y = -6 - (-3) = -6+3 = -3   x*y = -6 * -3= 
-6 * -3 = 18
18   Now we apply it in the equation 4(x-y)^2 - xy=4 (-3)^2-18   ==>4*9 -18 = 36-18= 
36-18 = 18
18   Answer : 18
Answer: B
Eleven men and eleven women have to sit around a circular table so that no 2 women are together. In how many ways can that be done?
Choose the correct choice from the following answers:
A) 5!*6!
B) 7!*8!
C) 10!*11!
D) 10!*12!
E) 11!*12!

Solution: The number of arrangements of n distinct objects in a row is given by n!.   The number of arrangements of n distinct objects in a circle is given by (n-1)!.   The difference between placement in a row and that in a circle is following: if we shift all object by one position, we will get different arrangement in a row but the same relative arrangement in a circle. So, for the number of circular arrangements of n objects we have: n!/n=(n-1)!   Now, 11 men in a circle can be arranged in (11-1)! ways and if we place 11 women in empty slots between them then no two women will be together. The # of arrangement of these 11 women will be 11! and not 10! because if we shift them by one position we'll get different arrangement because of the neighboring men.   So the answer is indeed 10!*11!.   10!*11!
Answer: C
The average runs scored by a batsman in 30 matches is 40. In the next 10 matches the batsman scored an average of 13 runs. Find his average in all the 30 matches?	Choices
A) 24.3 B) 25.3 C) 26.3 D) 28.3 E) 34.5

Solution: Total score of the batsman in 30 matches = 600.   Total score of the batsman in the next 10 matches = 130.   Total score of the batsman in the 30 matches = 730.   Average score of the batsman = 730/30 = 24.3.   24.3NSWER:24.3
Answer: A
A rectangular with dimensions 25 inches by 35 inches is to be divided into squares of equal size. Which of the following could be a length of a side of the squares?  Choose the correct choice from the following answers.
A) a) 5 inches
B) b) 6 inches
C) c) 7 inches
D) d) 8 inches
E) e) 10 inches

Solution: you need to divide the width and length of the rectangular to equal pieces where L = W   you can solve this using GCF   25=5*5   35=5*7   GCF = 5   P.S you can make squares with side of 5   a) 5 inchesnswer : a) 5 inches
Answer: A
A courtyard is 20 meter long and 16 meter board is to be paved with bricks of dimensions 20 cm by 10 cm. The total number of bricks required is?  Choose the correct answer:
A) 16000  B) 27778  C) 20000  D) 27999  E) 17799

Solution: Number of bricks =Courtyard area/1 brick area   =(2000×1600/20×10)=16000   16000nswer: 16000
Answer: A
A, B, C together started a business. A invested Rs.6000 for 5 months B invested Rs.3600 for 6 months and C Rs.7500 for 3 months. If they get a total profit of Rs.9880. Find the share of B?	Choices:
A) 2880  B) 3000  C) 3018  D) 3019  E) 3012

Solution: 60*5:36*6:75*3   100: 72: 75   72/247 * 9880= 
72/247 * 9880 = 2_880
2880   2880nswer: 2880
Answer: A
How many pieces can a square pizza be cut into by making 4 linear cuts? Pick one: A) 10 B) 11 C) 12 D) 13 E) 14

Solution: 1 cut makes two pieces   a second cut can make 4 pieces by cutting through 2 of the pieces   a third cut can make 7 pieces by cutting through 3 of the pieces   a fourth cut can make 11 pieces by cutting through 4 of the pieces   11
Answer: B
The radius of a cylindrical water tank is reduced by 50%. However, the speed by which water is filled into the tank is also decreased by 50%. How much more or less time W will it take to fill the tank now? Select the correct option:	A) 50% less time	B) 50% more time	C) 75% less time	D) 75% more time	E) 100% more time

Solution: (VC)Volume of the cylinderical vessal is directly proportional to R^2.   So if radius is 50% less volume will be 1/4th of the original volume.(VC/4)   Now if with velocity V tank can be filled in T1 time of volume VC   So now Velocity is 50% less i..e V/2   So time taken to fill the capacity VC/4 by V/2 velocity is T2.   VT1 = VC   V/2*T2 = VC/4   So T1/T2 = 1/2   So Tank will be filled in less time. that W=is 50 % less.50% less time
Answer: A
What approximate value should come in the place of question mark (?) in the following equation?
1325√(17) + 508.24 of 20% – 85.39 of 3⁄4 = ? Choose the correct choice:
A) 5500	B) 5200	C) 5800	D) 4900	E) 5900

Solution: ? = 1325√(17) + 508.24 of 20% – 85.39 of 3⁄4   = 1325√(17) + 500 of 20% – 85 × 0.75   = 5460 + 100 – 60 = 5500   5500nswer 5500
Answer: A
Three numbers are in the ratio 5 : 6 : 7. The sum of its longest and smallest numbers equals the sum of the third number and 48. Find the third number?  Choose the correct choice from the following answers.
A) 18 B) 76 C) 48 D) 27 E) 12

Solution: Let the numbers be 5x, 6x, 7x.   Largest number = 7x.   Smallest number = 5x.   Third number = 6x.   7x + 5x = 6x + 48   6x = 48 => third number is 48.   Answer:48
Answer: C
A box contains five bulbs out of which 3 are defective. If three bulbs are chosen at random, find the probability that all the four bulbs are defective?	Choose the correct choice:
A) 1/12	B) 1/11	C) 1/10	D) 1/198	E) 1/126

Solution: Out of five, two are good and three are defective. Required probability   = 31/103/51/103   = 1/10   Answer: 1/10
Answer: C
hree seventh of a number is 12 more than 40% of that number. What will be the 60% of that number? Choose the correct choice from the following answers:  A) 238  B) 129  C) 126  D) 197  E) 112

Solution: Explanation:   3/7 x â€“ 40/100 x = 12   x = 35 * 12   35 * 12 * 60/100= 
35 * 12 * 60/100 = 252
252/2= 
252/2 = 126
126   Answer:126
Answer: C
Find the largest number of four digits which is exactly divisible by 25,18,12,15	Choose the correct choice:
A) 9900
B) 9710
C) 9720
D) 9730
E) 9740

Solution: Explanation:   LCM of 25-18-12-15 is 900.   After dividing 9999 by 900 we get 99 remainder.   So answer will be 9999-99= 
9999-99 = 9_900
9900   Option 9900
Answer: A
In expressing a length of 102.472 km as nearly as possible with the three significant digits, find the percentage error  Choose the correct choice from the following.
A) 0.38%	B) 0.27%	C) 0.027%	D) 0.038%	E) None of these

Solution: Explanation:   Error = (102.5 - 102.472)= 
(102.5 - 102.472) = 0.028
0.028   Required percentage=   0.028/ 102.472Ã—100=0.027   Option 0.027%
Answer: C
What is the remainder when 1273 * 1275 * 1277 *1285 is divided by 12?
Select:
A) 9  B) 1  C) 11  D) 0  E) 7

Solution: 1271*1275*1277*1285 = (1272 + 1)(1272 + 3)(1284 - 7)(1284 + 1) = (multiple of 12 - 1)(multiple of 12 + 3)(multiple of 12 - 7)(multiple of 12 + 1)   Now, if we expand this expression all terms but the last one will have a multiple of 12 in them, thus will leave no remainder upon division by 12, the last term will be (1)(3)(-7)(1) = 21. Thus the question becomes: what is the remainder upon division of 21 by 12? The answer to this question is 9.   9nswer: 9
Answer: A
In what time will a train 50 m long cross an electric pole, it its speed be 144 km/hr? Choose the correct answer:
A) 1.25 sec B) 2.75 sec C) 3.5 sec D) 2.39 sec E) 9.5 sec

Solution: Speed = 144 * 5/18= 
144 * 5/18 = 40
40 m/sec   Time taken= 50/40= 
50/40 = 5/4 = around 1.25
1.25 sec.   1.25 secnswer: 1.25 sec
Answer: A
judith is practicing her dance steps along with her friends. In a particular sequence, all of them form a row. At that point, judithis standing on the 4th position from either end of the row.
Can you find out how many girls are practicing together?
Choose the most appropriate option:
A) 4 B) 9 C) 7 D) 6 E) 8

Solution: As judith is 4th from either end of the row, it means that 3 girls are on one of her sides and 3 are present on the other.   3 + 3 + 1(judith herself) = 7.   Hence, 7 girls are practicing the dance together.   correct answer is 7)7
Answer: C
A man complete a journey in 10 hrs. He travels first half of the journey at the rate of 21 km/hr and second half at the rate of 24 km/hr. Find the total journey in km?  Select the correct option:	A) 228	B) 224	C) 288	D) 266	E) 121

Solution: Let the total distance be x km.   Then, [(1/2 x) / 21 + (1/2 x) / 24] = 10   15x = 168 * 20 => x = 224 km.   Answer: 224
Answer: B
For each 6-month period during a light bulb's life span, the odds of it not burning out from over-use are half what they were in the previous 6-month period. If the odds of a light bulb burning out during the first 6-month period following its purchase are 1/3, what are the odds of it burning out during the period from 6months to 1 year following its purchase? Choose the most appropriate option: A) 5/27 B) 2/9 C) 1/3 D) 4/9 E) 2/3

Solution: Probability of not burning out during the first 6 months 1-1/3=2/3   Probability of not burning out during the next 6 months 2/3/2=1/3, hence probability of burning out 1-1/3=2/3.   Probability of burning out during the period from 6 months to 1 year = Probability of not burning out in first 6 months * Probability of burning out in next 6 months = 2/3 * 2/3 =4/9   Answer: 4/9.
Answer: D
A thief steels a car at 6a.m. and drives it at 40kmph. The theft is discovered at 7a.m. and the owner sets off in another car at 60 kmph. When will he overtake the thief?
Options
A) 9a.m.	B) 9.30a.m.	C) 10a.m.	D) 11.45a.m.	E) 10.15a.m.

Solution: Suppose the thief overtakes x hours after 6a.m.   Distance covered by the thief in x hrs = distance covered by the owner in (x-1 hours)   40x = 60(x-1)   20x = 60   x = 3 hrs   Thief is overtaken at 9 a.m.   9a.m.nswer is 9a.m.
Answer: A
Two trains 110 meters and 180 meters in length respectively are running in opposite directions, one at the rate of 80 km and the other at the rate of 65 kmph. In what time will they be completely clear of each other from the moment they meet?	Choose the correct choice from the following answers
A) 7.2 B) 7.85 C) 6.85 D) 5.85 E) 6.15

Solution: T = (110+ 180)/ (80 + 65) * 18/5= 
(110+ 180)/ (80 + 65) * 18/5 = 36/5 = around 7.2
7.20   7.2NSWER:7.2
Answer: A
Find the invalid no.from the following series 2,3,12,37,86,166,288	Choose the correct option.
A) 123	B) 145	C) 166	D) 170	E) 180

Solution: 3-2= 
3-2 = 1
1   12-3= 
12-3 = 9
9   37-12= 
37-12 = 25
25   86-37= 
86-37 = 49
49   166-86= 
166-86 = 80
80(this must be 81=167-86= 
167-86 = 81
81)   so wrong number in the sequence is 166   difference between two sucessive numbers sequence would be   1,9,25,49,81,121(square of 1,3,5,7,9,11)   166
Answer: C
50 men took a dip in water tank 40 m long and 20 m broad on a religious day. If the average displacements of water by a man is 4 m3, then the rise in the water level in the tank will be Choose the correct answer
A) 20 cm  B) 25 cm  C) 35 cm  D) 50 cm  E) None

Solution: Solution   Total number of water displaced	= (4 ×50)m3   ‹=› 200m3   Rise in water level	= (200 / 40×20)m   = 0.25 m   ‹=› 25 cm   Answer 25 cm
Answer: B
A shopkeeper sold an article for 1000 after giving 20% discount on the labelled price and made 25% profit on the cost price. What would have been the percentage profit,had he not given the discount’? Choose one:
A) 25%
B) 56.25%
C) 23%
D) 28%
E) None of these

Solution: Cost price = 1000×100/125= 800   S.P. at no discount = 1000×100/80 = 1250   ∴ % profit = 450×100/800 = 56.25 %   Answer 56.25%
Answer: B
David obtained 70, 60, 78, 60 and 65 marks (out of 100) in English, Mathematics,Physics, Chemistry and Biology What are his average marks ?  Choose the correct choice.
A) 75
B) 27.6
C) 66.6
D) 16.5
E) 11

Solution: Explanation:   Average = (70+ 60+ 78+ 60+ 65 )/ 5 = 333/5 = 66.6.   Answer:66.6
Answer: C
Of the 19,210 employees of the anvil factory, 2/7 are journeymen. If half of the journeymen were laid off, what percentage of the total remaining employees would be journeymen? Choose the correct choice from the following.
A) 14.3%
B) 16.67%
C) 33%
D) 28.6%
E) 49.67%

Solution: The exam gives us a number that is easily divisible by 7 to pique our curiosity and tempt us into calculating actual numbers (also because otherwise the ratio would be incorrect). Since the question is about percentages, the actual numbers will be meaningless, as only the ratio of that number versus others will be meaningful. Nonetheless, for those who are curious, each 1/7 portion represents (14210/7) 2,030 employees. This in turn means that 4,060 employees are journeymen and the remaining 10,150 are full time workers.   If half the journeymen were laid off, that would mean 1/7 of the total current workforce would be removed. This statistic is what leads many students to think that since half the journeymen are left, the remaining journeymen would represent half of what they used to be, which means 1/7 of the total workforce. If 1/7 of the workforce is journeymen, and 1/7 is roughly 14.3%, then answer choice A should be the right answer. In this case, though, it is merely the tempting trap answer choice.   What changed between the initial statement and the final tally? Well, you let go of 1/7 of the workforce, so the total number of workers went down. The remaining workers are still 1/7 of the initial workers, but the group has changed. The new workforce is smaller than the original group, specifically 6/7 of it because 1/7 was eliminated. The remaining workers now account for 1/7 out of 6/7 of the force, which if we multiply by 7 gives us 1 out of 6. This number as a percentage is answer choice B, 33%.   Using the absolute numbers we calculated before, there were 4,060 journeymen employees out of 14,210 total. If 2,030 of them are laid off, then there are 2,030 journeyman employees left, but now out of a total of (14,210-2,030) 12,180 employees. 2,030/12,180 is exactly 1/6, or 16.67%. The answer will work with either percentages or absolute numbers, but the percentage calculation will be significantly faster and applicable to any similar situation.   The underlying principle of percentages (and, on a related note, ratios) can be summed up in the brainteaser I like to ask my students: If you’re running a race and you overtake the 2nd place runner just before the end, what position do you end up in?   The correct answer is 2nd place.   Percentages, like ratios and other concepts of relative math, depend entirely on the context. Whether 100% more of something is better than 50% more of something else depends on the context much more than the percentages quoted. When it comes to percentages on the GMAT, the goal is to understand them enough to instinctively not fall into the traps laid out for you.33%
Answer: C
Three friends A, Band C started a business by investing a sum of money in the ratio of 5 : 7 : 6. After 6 months C withdraws half of his capital. If the sum invested by ‘A’ is 40,000, out of a total annual profit of 33,000, C’s share will be Choices:
A) 9,000  B) 12,000  C) 11,000  D) 10,000  E) None of these

Solution: Sum invested by 9,000, B and C is   5 × 12 : 7 × 12 : 6 × 6 + 3 × 6   or, 60 : 84 : 54 or, 10 : 14 : 9   \Share of C = 9⁄33 × 33,000 = 9,000   9,000nswer 9,000
Answer: A
If a particular player is never chosen, in how many ways can 11 cricket players be chosen out of 14 players? Choose the most appropriate option: A) 45 B) 56 C) 64 D) 78 E) 90

Solution: A particular players is never chosen, it means that 11 players are selected out of 13 players.   => Required number of ways = 13C11   = 78   78
Answer: D