MU-NLPC/Calc-aqua_rat huggingface dataset:
I have a few sweets to be distributed. If I keep 2, 3 or 4 in a pack, I am left with one sweet. If I keep 5 in a pack, I am left with none. What is the minimum number of sweets I have to pack and distribute ? Choose the correct choice from the following answers.
A) 25 B) 37 C) 54 D) 53 E) 65

Solution: when divided 2,3,4 leaves remainder 1 and leaves remainder 0 while dividing 5   25NSWER:25
Answer: A
The sequence of numbers a1, a2, a3, ..., an is defined by an = 1/n - 1/(n+2) for each integer n >= 1. What is the sum of the first 80 terms of this sequence? Select.
A) (1/81 +1/ 82)  B) (1+1/2) + (1/81 +1/ 82)  C) (1+1/2) / (1/81 +1/ 82)  D) (1+1/2) + (1/81 -1/ 82)  E) (1+1/2) – (1/81 +1/ 82)

Solution: The answer would most certainly be[E]. But the question needs a slight modification.n>=1, since the answer does consider a1 under the sum.   The sequence is :   a1 = 1-1/3   a2 = 1/2 - 1/4   a3 = 1/3 - 1/5....   We can observe that the third term in the sequence cancels the negative term in the first. A similar approach can be seen on all the terms and we would be left with 1 + 1/2 from a1 and a2 along with -1/82 and -1/81 from a80 and a79 term which could not be cancelled.   Hence the sum = (1+1/2) – (1/81 +1/ 82)   Answer : (1+1/2) – (1/81 +1/ 82)
Answer: E
A train 2500 m long is running at the speed of 30 km / hr. Find the time taken by it to pass a man standing near the railway line in seconds  Choose the correct option.
A) 15 sec B) 16 sec C) 17 sec D) 18 sec E) 19 sec

Solution: Explanation:   Speed of the train = (60 x 5/18m / sec = 50/3 m/ sec.   Distance moved in passing the standing man = 250 m.   Required time taken = 250/(50/3) = (250 Ã—(3/50)) sec =15 sec   15 secnswer: Option 15 sec
Answer: A
Which number doesn't belong to the following sequence? Choices:
A) 150
B) 180
C) 200
D) 210
E) 240

Solution: All of the numbers are multiples of 2, 3, 5 and 10.   3 of the numbers are multiples of 20, but 2 are not.   Only one number isn't divisible by 30: 200.   Answer: 200
Answer: C
If the average of ten numbers is 30, then which of the following could be the standard deviation of the ten numbers?
I. 0
II. 30
III. 20  Pick:
A) I  B) all three options  C) II  D) III  E) I&II

Solution: We know that we have 10 numbers (and they could be ANY values - including negatives and non-integers) and we know that the average of those numbers is 10. This is meant to say that there are an INFINITE number of possible sets of 10 numbers that fit this prompt.   IF all ten numbers were the same (meaning that we had ten 10s), then the SD would be 0. The more 'spread out' those ten numbers get, the higher the SD becomes. Since there's no limit to the 'spread', then there's no limit to what the SD could be either. Thus, it could be 10 or 20 or any other number.   all three options
Answer: B
The total age of A and B is 12 years more than the total age of B and C. C is how many years younger than A?
Choose the correct choice from the following:
A) 12	B) 24	C) C is elder than A	D) Data inadequate	E) None of these

Solution: (12 + B) - (B + C) = 12   12 - C = 12   12nswer: Option 12
Answer: A
A reduction of 15% in the price of wheat enables a house wife to obtain 3 kgs more for Rs.500, what is the reduced price for kg?  Options.
A) Rs.10	B) Rs.15	C) Rs.20	D) Rs.25	E) Rs.30

Solution: Explanation:   500*(15/100)= 
500*(15/100) = 75
75 ---- 3   ? ---- 1=> Rs.25   Answer: Rs.25
Answer: D
In a sample of associates at a law firm, 30 percent are second-year associates, and 60 percent are not first-year associates. What percentage of the associates at the law firm have been there for more than two years?  Select
A) 10
B) 20
C) 30
D) 40
E) 50

Solution: Let the sample be 100.   Given 60% are not first year i.e. there could be second year (x) and more than 2 years(y) possibility.   60% = (x) + y   Given 30% = second year (x)   club both , we get y = 30%.   Answer: option 30 is correct answer.
Answer: C
Alice is trying to plan her budget. She knows that she has $4000 to spend this month. She needs to budget equal amounts on rent, food, utilities, savings, and spending money. She also wants to divide her spending money into four equal categories: Books, Clothes, Gifts, and Restaurants. How much money should Alice budget for Books this month?	Choose the correct answer
A) $200	B) $150	C) $100	D) $75	E) $50

Solution: A. Spending money is 1/5 of the total money. Books is 1/4 of the spending money. 1/4 of 1/5 is 1/20. 1/20 of $4000 is $200, so the answer is $200.
Answer: A
The amount of water (in ml) that should be added to reduce 9 ml. Lotion, containing 50% alcohol, to a lotion containing 20% alcohol, is?
Choose one
A) 13.5
B) 14.5
C) 15
D) 16
E) 17.5

Solution: 4.5 4.5   20% 80%   20% ----- 4.5   80% ------? => 18 - 4.5= 
18 - 4.5 = 13.5
13.5 ml   13.5NSWER:13.5
Answer: A
By selling 50 meters of cloth. I gain the selling price of 15 meters. Find the gain percent?
Choose the correct choice from the following answers:
A) 42 6/8%
B) 42 8/7%
C) 48 6/7%
D) 42 6/7%
E) 12 6/7%

Solution: SP = CP + g   50 SP = 50 CP + 15 SP   35 SP = 50 CP   35 --- 15 CP gain   100 --- ? => 42 6/7%   Answer:42 6/7%
Answer: D
A bag contains 7 green and 8 white balls. If two balls are drawn simultaneously, the probability that both are of the same colour iS?  Select:
A) 7/15 B) 7/16 C) 7/143 D) 7/18 E) 7/11

Solution: Drawing two balls of same color from seven green balls can be done in ⁷C₂ ways.   Similarly from eight white balls two can be drawn in ⁸C₂ ways.   P = 7C2/15C2 + 8C2/15C2 = 7/15   7/15nswer: 7/15
Answer: A
In a apartment, 30% of the people speak English, 20% speak Hindi and 10% speak both. If a people is selected at random, what is the probability that he has speak English or Hindi?  Answers
A) 1/3	B) 2/3	C) 2/5	D) 2/7	E) 3/7

Solution: P (E) = 30 / 100 = 3 / 10 , P (H) = 20 / 100 = 1 / 5 and P (E ∩ H) = 10 / 100 = 1 / 10   P (E or H) = P (E U H)   = P (E) + P (H) - P (E ∩ H)   = (3 / 10) + (1 / 5) - (1 / 10) = 4 / 10 = 2/5   2/5
Answer: C
Of the 200 students at University XYZ majoring in one or more of the engineering disciplines, 150 are majoring in electrical and 150 are majoring in mechanical. If at least 30 of the students are not majoring in either electrical or mechanical, then the number of students majoring in both electrical and mechanical could be any number from  Choose the correct choice from the following answers:
A) 30 to 70
B) 70 to 100
C) 110 to 130
D) 130 to 150
E) 150 to 170

Solution: if there are 150 students majoring in electrical then there must be 70 person not majoring electrical at all, since both of the student not majoring electrical and mechanical is at least 30, so the number of the student who are not majoring electrical but majoring mechanical will be at least 20.   if there are 150 students majoring in mechanical there must be 50 students who are not majoring mechanical at all, since the number of the student who are not majoring electrical but majoring mechanical will be at least 20, hence the number of students both majoring mechanical and electrical will be at least 70   so there must be at least 70 students who major in both   see the answers option the only possible answer is 70 to 100 !
Answer: B
Express a speed of 720 kmph in meters per second?	Choose the correct choice from the following answers
A) 120 mps  B) 200 mps  C) 181 mps  D) 190 mps  E) 125 mps

Solution: 720 * 5/18= 
720 * 5/18 = 200
200 mps   Answer: 200 mps
Answer: B
18 men can complete a piece of work in 20 days. In how many days can 12 men complete that piece of work?	Choose the correct choice from the following choices:
A) 23 days
B) 30 days
C) 22 days
D) 29 days
E) 20 days

Solution: 30 days   30 days   18 * 20 = 12 * x => x = 30 days
Answer: B
5 speakers gathered to deliver speeches on two topics. Even though 5 speeches were initially planned to be delivered, due to lack of time only 2 speeches were finally decided to be delivered. Topics are to be spoken in a specific order and the speeches differ with respect to speaker or topic. How many such two speeches are possible?  Choose the correct choice from the following options
A) 2
B) 20
C) 25
D) 100
E) 1024

Solution: 1)there are 5 speeches in ONE topic and 5 in OTHER..   2)there is a specific order for topics, so   a) both the topics are to be spoken on- so ONE from each   b) the order does not matter since there is ONLY one specific order..   so 5251∗5251=5∗5=25   ANSWER:25
Answer: C
Two kinds of Vodka are mixed in the ratio 1:2 and 2:1 and they are sold fetching the profit 10% and 25% respectively. If the vodkas are mixed in equal ratio and the individual profit percent on them are increased by 4/3 and 5/3 times respectively, then the mixture will fetch the profit of	Choose the correct choice from the following options:
A) 18%
B) 20%
C) 25%
D) 23%
E) Cannot be determined

Solution: Answer: 25%.
Answer: C
The ratio of the ages of Mini and Minakshi is 4 : 3. The sum of their ages is 28 years. The ratio of their ages after 8 years will be
Choices:
A) 4 : 3  B) 12 : 11  C) 7 : 4  D) 6 : 5  E) 6 : 11

Solution: Let Mini’s age = 4x and Minakshi’s age = 3x   Then 4x + 3x = 28   x = 4   Mini’s age = 16 years   And Minakshi’s age = 12 years   Ratio of their ages after 8 years = (16 + 8) : (12 + 8) = 24 : 20 = 6 : 5   ANSWER:6 : 5
Answer: D
The ratio of P's and Q's ages is 5 : 7. If the difference between the present age of Q and the age of P six years hence is 2 then what is the total of present ages of P and Q?  Choose the correct choice from the following answers:
A) 52 years  B) 48 years  C) 56 years  D) Data inadequate  E) None of these

Solution: P⁄Q = 5⁄7   or, Q = 7⁄5P   Case I : Q – (P + 6) = 2   or, Q = P + 8   ∴ 7⁄5P = P + 8   or, 7P = 5P + 40   ∴ P = 40⁄2 = 20 and Q = 7⁄5 × 20 = 28   P + Q = 20 + 28= 
20 + 28 = 48
48   Case II : (P + 6) – Q= 2   or, P + 6 – 7⁄5P = 2   or, P = –10 and Q = 14   ∴ P + Q = 10 + 14= 
10 + 14 = 24
24 years   Answer Data inadequate
Answer: D
David spends $320 buying his favorite dolls. If he buys only small Monkey dolls, which are $3 cheaper than the large Monkey dolls, he could buy 24 more dolls than if he were to buy only large Monkey dolls. How much does a large Monkey doll cost? Answers:
A) $8
B) $8.2
C) $9
D) $10
E) $11

Solution: If large doll costs $8, then he can buy   320/8= 
  320/8 = 40
40 large dolls and   320/5= 
  320/5 = 64
64 small dolls.   Difference is 24, which is we wanted.   $8nswer $8.
Answer: A
How many seconds will a 500 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?  Options
A) 20 B) 30 C) 40 D) 50 E) 60

Solution: Speed of train relative to man = 63 - 3= 
63 - 3 = 60
60 km/hr.= 60 * 5/18 = 50/3 m/sec.   Time taken to pass the man = 500 * 3/50= 
500 * 3/50 = 30
30 sec.   Answer: Option 30
Answer: B
The mean daily profit made by a shopkeeper in a month of 30 days was Rs. 350. If the mean profit for the first fifteen days was Rs. 265, then the mean profit for the last 15 days would be  Choose the correct choice from the following answers
A) Rs. 435	B) Rs. 350	C) Rs. 275	D) Rs. 425	E) None of these

Solution: Average would be : 350 = (265 + x)/2   On solving, x = 435.   Rs. 435nswer: Rs. 435
Answer: A
Michelle deposited a certain sum of money in a savings account on July 1st, 2007. She earns an 6.4% interest compounded semiannually. The sum of money in the account on December 31st, 2009 is approximately what percent of the initial deposit?
Choose one.
A) 117%	B) 120%	C) 121%	D) 135%	E) 140%

Solution: Since Michelle earns 6.4% interest compounded semiannually, then she earns 3.2% interest every 6 months.   Now, the simple interest earned in 5 periods (30 months = 5*6 months) would be 3.2%*5=16%. But, since the interest iscompoundedevery 6 months, then there would be interest earned on interest (very small amount) thus the actual interest earned would be a little bit more than 16%, only answer choice A fits.   117%nswer: 117% 3.2 *5= 
 3.2 *5 = 16
16%. But, since the interest iscompoundedevery 6 months, then there would be interest earned on interest (very small amount) thus the actual interest earned would be a little bit more than 16%, only answer choice A fits.   117%nswer: 117%
Answer: A
How many times in a day, are the hands of a clock in straight line but opposite in direction?  Choose one.
A) 22	B) 23	C) 24	D) 25	E) 26

Solution: Sol.   Tha hands of a clock point in opposite directions (in the same straight line) 11 times in every 12 hours (Because between 5 and 7 they point in opposite directions at 6 o’clock only). So, in a day, the hands point in the opposite directions 22 times.   22nswer 22
Answer: A
A basketball team composed of 12 players scored 100 points in a particular contest. If none of the individual players scored fewer than 7 points, what is the greatest number of points E that an individual player might have scored? Choose the most appropriate option.
A) 7  B) 13  C) 16  D) 21  E) 23

Solution: General rule for such kind of problems:   to maximize one quantity, minimize the others;   to minimize one quantity, maximize the others.   Thus to maximize the number of points of one particular player minimize the number of points of all other 11 players.   Minimum number of points for a player is 7, so the minimum number of points of 11 players is 7*11= 
7*11 = 77
77.   Therefore, the maximum number of points E for 12th player is  100-77= 
 100-77 = 23
23.   Answer: 23.
Answer: E
If there are 664,579 prime numbers among the first 10 million positive integers, approximately what percent of the first 10 million positive integers are prime numbers? Choose the correct choice from the following choices
A) 0.0066%  B) 0.066%  C) 0.66%  D) 6.6%  E) 66%

Solution: 664,579 = (x/100) * 10^7;   664, 579 = x * 10^5   => x = 664, 579/10^5   = 6.64579 ~ 6.6%   Ans is (6.6%).
Answer: D
Twenty four men can do a work in 35 days. How many men are required to complete the work in 21 days?  Pick.
A) 39
B) 67
C) 44
D) 40
E) 20

Solution: 40   40   We have M1 401 = M2 402   So, 24 * 35 = M2 * 21 => M2 = 40.
Answer: D
An athlete runs 150 metres race in 24 seconds. What is his speed?
Choices
A) 27
B) 38
C) 37
D) 30
E) 28

Solution: Speed=Distance/Time = 150/20= 
150/20 = 15/2 = around 7.5
7.5 m/s= 7.5 * 18/5= 
7.5 * 18/5 = 27
27 km/hr   27nswer :27
Answer: A
The radius of a circular wheel is 1.75 m, how many revolutions will it make in traveling 1 km?	Choose one.
A) 1000  B) 817  C) 278  D) 268  E) 280

Solution: 2 * 22/7 * 1.75 * x   = 11000   x = 1000   1000nswer: 1000
Answer: A
Left shifting a number by 1 is always equivalent to multiplying it by 2.	Answers:
A) True  B) False  C) neither True nor a false  D) none of the above  E) Cannot be determined

Solution: Explanation :   0001 => 1   0010 => 2   0100 => 4   1000 => 8   Truenswer : True
Answer: A
An outlet pipe can empty 2/3 rd of a cistern in 12 minutes. In 8 minutes, what part of the cistern will be emptied?  Pick:
A) 4/9
B) 4/3
C) 4/1
D) 6/9
E) 2/9

Solution: 2/3 ---- 12   ? ----- 8 ==> 4/9   4/9nswer: 4/9
Answer: A
Isaac’s salary is reduced by 60% and then reduced salary is increased by 60%. Find ,how many percentage his present salary is less as compared to his previous salary?
Choose the correct choice from the following answers
A) 36%
B) 37%
C) 38%
D) 39%
E) 40%

Solution: 60*60   -------- = 36%   100   36%nswer: 36%
Answer: A
14 different biology books and 8 different chemistry books lie on a shelf. In how many ways can a student pick 2 books of each type?
Choose the correct option:
A) 80
B) 160
C) 720
D) 1100
E) 2548

Solution: No. of ways of picking 2 biology books(from 14 books) = 14c2 = (14*13)/2= 
(14*13)/2 = 91
91   No. of ways of picking 2 chemistry books(from 8 books)= 8c2 = (8*7)/2= 
(8*7)/2 = 28
28   Total ways of picking 2 books of each type= 91*28= 
91*28 = 2_548
2548   (Option 2548)
Answer: E
A car going at 40 miles per hour set out on an 60-mile trip at 9:00 A.M. Exactly 10 minutes later, a second car left from the same place and followed the same route. How fast, in miles per hour, was the second car going if it caught up with the first car at 10:30 A.M.?
Choose the correct choice from the following answers:  A) 45  B) 60  C) 53  D) 55  E) 50

Solution: Let Car A = car that starts at 9 AM   Car 60 = car that starts at 9:10 AM   Time for which car A travels at speed of 40 m per hour = 1.5 hours   Distance travelled by Car A = 40 *1.5= 
40 *1.5 = 60
60 miles   Since Car 60 catches up Car A at 10:30 , time= 60 mins =1 hour   Speed of Car 60 = 60/(1)= 
60/(1) = 60
60 miles per hour   Answer 60
Answer: B
A man sells two articles for Rs.3600 each and he gains 30% on the first and loses 30% on the next. Find his total gain or loss?	Choose the correct choice from the following answers: A) 9% loss B) 400 C) 4000 D) 324 E) 200

Solution: (30*30)/100= 
(30*30)/100 = 9
9%loss   9% lossnswer: 9% loss
Answer: A
Each of the following numbers has a remainder of 1 when divided by 7 except:  Choose the most appropriate option:
A) 1
B) 8
C) 15
D) 23
E) 43

Solution: It's 23   23 = 7*3+2
Answer: D
What is the smallest integer R greater than 1 that leaves a remainder of 1 when divided by any of the integers 6, 8, and 10?  Choose the correct answer.
A) 21  B) 41  C) R=121  D) 241  E) 481

Solution: Or u can just use the answer choices here. Since the answers are already arranged in ascending order, the first number which gives remainder R as 1 for all three is the correct answer. In the given question, the first number which gives a remainder of 1 for 6,8 and 10 is 121.R=121
Answer: C
If the length of the longest chord of a certain circle is 20, what is the radius of that certain circle? Choose the correct choice:
A) 2.5	B) 5	C) 10	D) 15	E) 20

Solution: Longest chord of a circle is the diameter of the circle   diameter = 2 * radius   If diameter of the circle is given as 20 = 2 * 10   so radius of the circle =10   correct answer - 10
Answer: C
Assume that 20 cows and 40 goats can be kept for 10 days for Rs.460. If the cost of keeping 5 goats is the same as the cost of keeping 1 cow, what will be the cost for keeping 50 cows and 30 goats for 12 days?	Choose the correct choice from the following answers.
A) Rs.1104  B) Rs.1000  C) Rs.934  D) Rs.1210  E) Rs.1410

Solution: Explanation :   Rs.1104ssume that cost of keeping a cow for 1 day = c ,   cost of keeping a goat for 1 day = g   Cost of keeping 20 cows and 40 goats for 10 days = 460   Cost of keeping 20 cows and 40 goats for 1 day = 460/10= 
460/10 = 46
46=> 20c + 40g = 46   => 10c + 20g = 23 ---(1)   Given that 5g = c   Hence equation (1) can be written as 10c + 4c = 23 => 14c =23   => c=23/14   cost of keeping 50 cows and 30 goats for 1 day   = 50c + 30g   = 50c + 6c (substituted 5g = c)   = 56 c = 56×23/14   = 92   Cost of keeping 50 cows and 30 goats for 12 days = 12×92 = 1104   Rs.1104nswer : Option Rs.1104
Answer: A
Two observations were made of a clock at different time:
1st observation:
The hour hand is exactly at a minute mark and the minute hand is six minutes ahead of it.
2nd observation:
The hour hand is exactly on a dissimilar minute mark and the minute hand is seven minutes ahead of it.
Can you find out how much time has passed between the above two observations? Choose the correct choice:
A) 1 hours and 12 minutes
B) 3 hours and 12 minutes
C) 2 hours and 12 minutes
D) 4 hours and 12 minutes
E) 5 hours and 12 minutes

Solution: Solution:   The time at first observation:   1:12   The time at second observation:   3:24   Thus, two hours and twelve minutes have passed between the two observations.   Answer 2 hours and 12 minutes
Answer: C
Two taps can separately fill a cistern 10 minutes and 15 minutes respectively and when the waste pipe is open, they can together fill it in 18 minutes. The waste pipe can empty the full cistern in?  Choose the most appropriate option:	A) 2	B) 7	C) 6	D) 9	E) 2

Solution: 1/10 + 1/15 - 1/x = 1/18   x = 9   Answer: 9
Answer: D
A man can row a boat at 20 kmph in still water. If the speed of the stream is 6 kmph, what is the time taken to row a distance of 60 km downstream?
Choose the correct choice from the following.
A) 30/83 hours  B) 33/13 hours  C) 31/13 hours  D) 30/13 hours  E) 30/14 hours

Solution: Speed downstream = 20 + 6= 
20 + 6 = 26
26 kmph.   Time required to cover 60 km downstream= d/s = 60/26   = 30/13 hours.   Answer:30/13 hours
Answer: D
The average weight of 8 person's increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg. What is the weight of the new person? Select
A) 75 Kg	B) 50 Kg	C) 85 Kg	D) 80 Kg	E) 60 KG

Solution: Explanation:   Total increase in weight = 8 × 2.5 = 20   If x is the weight of the new person, total increase in weight = x−65   => 20 = x - 65   => x = 20 + 65= 
20 + 65 = 85
85   Answer: Option 85 Kg
Answer: C
Given distinct positive integers 1, 11, 5, x, 2, and 9, which of the following could be the median?  Choose the correct choice from the following answers.
A) 3	B) 5	C) 6	D) 8	E) 9

Solution: The median of a set with even number of terms is the average of two middle terms when arranged in ascending (or descending) order.   Arrange numbers in ascending order: 1, 2, 5, 9, 11, and x.   Now, x can not possibly be less than 3 as given that all integers are positive and distinct (and we already have 1, 2, and 5).   Next, if x is 5<x<9 then the median will be the average of 5 and x. As all answers for the median are integers, then try odd values for x:   If x=6, then median=(5+6)/2= 
(5+6)/2 = 11/2 = around 5.5
5.5 --> not among answer choices;   If x=7, then median=(5+7)/2= 
(5+7)/2 = 6
6 --> OK;   Answer: 6.
Answer: C
A and B can do a piece of work in 12 days and 24days. Both starts the work together for some time, but B leaves the job 6 days before the work is completed. Find the time in which work is finished.
Select
A) 10 days
B) 12 days
C) 14 days
D) 5 days
E) 6 days

Solution: Explanation:   A & 12 days completes the work in 12*24/12+24 = 12*24/36= 
12*24/36 = 8
8 days   2 days work= 2+1/8 = ¼ work   Remaining work = 1-1/4 = ¾   A completes ¾ work in ¾*16 = 12 days   Answer: Option 12 days
Answer: B
In what ratio should a variety of Rice costing Rs. 20 per kg be mixed with another variety of Rice costing Rs. 31.50 per kg to obtain a mixture costing Rs. 23.75 per kg?
Choose the correct choice from the following answers:
A) 16 : 30
B) 30 : 14
C) 16 : 31
D) 31 : 15
E) 15 : 31

Solution: Let us say the ratio of the quantities of cheaper and dearer varieties = x : y   By the rule of allegation, x/y = (31.50 - 23.75) / (23.75 - 20) = 31/15   ANSWER:31 : 15
Answer: D
The retirement plan for a company allows employees to invest in 10 different mutual funds. Six of the 10 funds grew by at least 10% over the last year. If Sam randomly selected 4 of the 10 funds, what is the probability X that 3 of Sam’s 4 funds grew by at least 10% over last year?
Choose the correct choice from the following answers:
A) 6C3 / 10C4 B) 6C3 * 4C1 / 10C4 C) 6C3 * 4C1 / 10P4 D) 6P3 * 4P1 / 10C4 E) 6P3 * 4P1 / 10P4

Solution: Look at the answers. B is the only answer choice that uses only combination formulas and takes into account all the factors.   We know this is a combination, not a permutation. This rules out choices C, DE.   A clearly isn't the answer because X 6C3 only accounts for 3 of the funds he chose. 10C4, the denominator, is correct, so the numerator must be wrong.   6C3 * 4C1 / 10C4 it is.
Answer: B
Mike, Jim and Bob are all professional fisherman. Mike can catch 21 fish in one hour, Jim can catch twice as much and Bob can catch 50% more than Jim. If the three started to fish together and after 40 minutes Mike and Bob left, how many fish did the three fishermen catch in one hour?	Choices.
A) 64. B) 72. C) 86 D) 98 E) 112

Solution: We are given   Rate of catching the fish for all three people   M - 21 fish/hour   J - 42 fish/hour   B - 63 fish/hour.   So in 1 hour, if they work together they can catch - 126 fish.   It is given they work together for first 40 min,   So by then they will have caught 2/3 * 128 = 84   Last 20 mins J will work alone and he can catch   1/3*42= 
  1/3*42 = 14
14 in the remaining 20 mins, thus the total fishes they will catch in one hour= 84+14= 
84+14 = 98
98   ANSWER:98
Answer: D