MU-NLPC/Calc-aqua_rat huggingface dataset:
There are three different pipes used to fill a pool: pipe x, pipe y, and pipe z. Pipe x can fill the pool in a days, pipe y in b days, and pipe z in c days, where a > b > c. When all three pipes are used together to fill a pool, it takes d days to fill the pool. Which of the following must be true?
I. d<c
II. d>b
III. c/3<d<a/3
Select
A) II B) I C) III D) I&II E) II &III

Solution: Name T = full pool   X fills a pool in a days ==> 1 day X fills: T/a   Y fills a pool in b days ==> 1 day Y fills: T/b   Z fills a pool in c days ==> 1 day Z fills: T/c   1 day (X+Y+Z) together fill: T(1/a + 1/b + 1/c)   d days (X+Y+Z) together fill: T   ==> d = Tx1 / T(1/a+1/b+1/c) = abc/(ab+bc+ca)   II   ==>d = abc/(ab+bc+ca)   d cannot be greater than c ; d is greater than b ; d is greater than c/3 but not less than a/3
Answer: A
The number of bacteria in a petri dish increased by 50 percent every 2 hours. If there were 108 million bacteria in the dish at 5: 00 p.m., at what time were there 32 million bacteria in the dish?
Answers
A) 11: 00 a.m.	B) 8: 00 p.m.	C) 6: 00 a.m.	D) 8: 00 a.m.	E) 10: 00 a.m.

Solution: Given:   The number of bacteria in a petri dish increased by 50 percent every 2 hours   There were 108 million bacteria in the dish at 2: 00 p.m   Since the bacteria is increasing by 50% every 2 hours, this means that the number is multiplied by 1.5 every 2 hours.   Required: At what time were there 32 million bacteria in the dish?   Assume that there were n intervals of 2 hours between 32 million and 108 million.   32 * (1.5)^n = 108   (3/2)^n = 108/32 = 27/8 = (3/2)^3   Hence n = 3 intervals.   Each interval was of 2 hours. Therefore, the number of hours = 6   Subtracting 6 hours from 5 PM, we get 11 AM as the answer.   Option 11: 00 a.m.
Answer: A
If 2 cards are selected at random from the deck of 52 cards then What is the probability of selected cards will be Queen?
A deck of cards has a total of 52 cards, consisting of 4 suits; (spades(Black), hearts(Red), diamond(Red)s, and clubs(Black)); and 13 cards including 1 king, 1 queen and 1 jack in each suit  Select the correct option
A) 12/2652 B) 14/2652 C) 2/2652 D) 4/2652 E) 8/2652

Solution: the total probability = (4/52 * 3/51) = 12/2652. 12/2652 is the correct answer.
Answer: A
A money lender lent a total of $1500 to two of his customers. He charged at the rate of 5%p.a. to one of them and 6% p.a. to the other. If he earned an average of 5.67% on $1500, how much did he lend to each of the two customers?
Answers.
A) 700; 1100 B) 1005; 495 C) 1000; 800 D) 1200; 800 E) None of the above

Solution: The method given above is the one given in the book.   However the method I used was   (1*x*5)/100 + (1500-x)*6/100 = 1500*5.67/100   Simplifying we get x=495   1005; 495
Answer: B
In a regular week, there are 5 working days and for each day, the working hours are 8. A man gets Rs. 2.40 per hour for regular work and Rs. 3.20 per hours for overtime. If he earns Rs. 432 in 4 weeks, then how many hours does he work for ?	Answers.
A) 175 B) 275 C) 375 D) 475 E) 575

Solution: Suppose the man works overtime for x hours.   Now, working hours in 4 weeks = (5 x 8 x 4) = 160.   160 x 2.40 + x x 3.20 = 432   3.20x = 432 - 384= 
432 - 384 = 48
48   x= 15.   Hence, total hours of work = (160 + 15)= 
(160 + 15) = 175
175.   175nswer is 175.
Answer: A
If a farmer sells 15 of his chickens, his stock of feed will last for 4 more days than planned, but if he buys 25 more chickens, he will run out of feed 3 days earlier than planned. If no chickens are sold or bought, the farmer will be exactly on schedule. How many chickens does the farmer have?	Choose the most appropriate option
A) 12
B) 24
C) 48
D) 55
E) 49

Solution: Say farmer has n chicken and he is good for d days.:-   We have 3 equations given in question:-   (n-15) * d+4 =(n+25) *(d-3) = n * d   Solving these: (You can solve 1st and 3rd and 2nd and 3rd together)   We get:   25d-3n=75   4n-15d =60   => n~49   Ans 49 it is!
Answer: E
In a competitive examination in state Madhya Pradesh, 4% candidates got selected from the total appeared candidates. State Uttar Pradesh had an equal number of candidates appeared and 9% candidates got selected with 72 more candidates got selected than Madhya Pradesh. what was the number of candidates appeared from each state?	Choose the correct option
A) 1440	B) 1400	C) 1600	D) 720	E) 820

Solution: Explanation :   Solution: Let the number of candidates appeared from each state be x.   then, 9% of x - 4% of x =72.   =>5% of x =72   =>5x/100 =72 => x =72*100/5= 
72*100/5 = 1_440
1440   1440nswer : 1440
Answer: A
If after 700 grams of water were added to the 24%-solution of alcohol, the strength of the solution decreased by one-third, how much of the 24%-solution was used?
Choose the correct choice from the following answers:	A) 180 grams	B) 220 grams	C) 250 grams	D) 350 grams	E) 1400 grams

Solution: I too think 1400 grams should be the answer.   My reasoning is   The h20 content in 700 gms of water is 1   h20 content in 24% solution is 0.76   Resulting new solution's concentration decreases by one third means. Now it becomes 16% solution which means h20 content is 0.84   Let amount of solution be X   Then the equation can be set up   700*1 + 0.76X = 0.84 (X+700)   0.08X = 112   8X = 11200   X = 1400 (ANS 1400 grams)
Answer: E
The sum of ages of 5 children born at the intervals of 3 years each is 50 years. What is the age of the youngest child? Choose the correct choice from the following choices.
A) 4 years	B) 8 years	C) 10 years	D) None of these	E) CANNOT BE DETERMINED

Solution: EXPLANATION   Let the ages of children be x, (x + 3), (x + 6), (x + 9) and (x + 12) years.   Then, x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 50   5x = 20   x = 4.   Age of the youngest child = x = 4 years.   4 yearsnswer 4 years
Answer: A
The Sum of first N consecutive odd integers is N^2. What is the sum of all odd integers between 13 and 35 inclusive.  Answers
A) 288	B) 364	C) 410	D) 424	E) 450

Solution: We're dealing with a sequence of CONSECUTIVE ODD INTEGERS: 13 to 35, inclusive. We're asked for the SUM of this group.   1) Start with the sum of the smallest and the biggest:   13 + 35= 
  13 + 35 = 48
48   2) Now look at the 'next smallest' and the 'next biggest': 15 + 33= 
15 + 33 = 48
48   Now we have proof that there is no middle term. We have 6 bunches of 48.   6(48)= 288   288
Answer: A
One ball will drop from a certain height. The height it will reach after rebounding from the floor is 50 percent of the previous height. The total travel is 200cm when it touches the floor on third time. What is the value of the original height?  Choose the correct option
A) 80cm	B) 90cm	C) 100cm	D) 120cm	E) 130cm

Solution: when Ball comes down, Then i have indicated the distance covered in green   when Ball goes up, Then i have indicated the distance covered in red   Distance travelled uptil the ball touches the floor 3rd time:h+0.5h+0.5 h+0.5*0.5 h+0.5*0.5 h   h + 2 * 0.5 * h + 2 * 0.25 * h = h (1+2*0.5+2* 0.25) = h (1+1+0.5) = 80   2.5 h = 80   h = 80.   80cm is the answer.
Answer: A
Three numbers are in the ratio of 2 : 3 : 4 and their L.C.M. is 264. What is their H.C.F.?	Options: A) 18 B) 22 C) 24 D) 28 E) 32

Solution: Let the numbers be 2x, 3x, and 4x.   LCM of 2x, 3x and 4x is 12x.   12x = 264   x = 22   HCF of 2x, 3x and 4x = x = 22   The answer is 22.
Answer: B
In a two-digit number, if it is known that its unit's digit exceeds its ten's digit by 4 and that the product of the given number and the sum of its digits is equal to 90, then the number is: Pick one:  A) 15  B) 27  C) 38  D) 46  E) 48

Solution: Let the ten's digit be x. Then, unit's digit = x + 4. Number = 10x + (x + 4) = 11x + 4   Sum of digits = x + (x + 4) = 2x + 4   (11x + 4)(2x + 4) = 90   22(x)(x) +52x - 74 = 0   (x - 1)(22x + 74) = 0   x = 1   Hence, required number = 11x + 4 = 15.   15NSWER:1511  + 4= 
11  + 4 = 15
15.   15NSWER:15
Answer: A
Andrew has a certain number of coins in his pocket. He has four times as many dimes as quarters and six times as many nickels as dimes. A nickel is worth $0.05, a dime is worth $0.10 and a quarter is worth $0.25. If he has a total of $10.15, then which of the following represents the number of dimes in Andrew’s pocket?	Choose the correct option.
A) 9
B) 10
C) 18
D) 20
E) 21

Solution: E.   Let number of quarters be q. Therefore , dimes are 3q and nickels are 18q.   Total value = 18q(.05) + 4q(0.1) + .25q =1.55q   Given total value = 10.15   therefore, 1.55q=10.15 or q=6   Number of dimes = 3q or 18   Answer : 18
Answer: C
If n is the product of the integers from 1 to 12, inclusive, how many different prime factors greater than 1 does n have?
Choose the correct answer:	A) Four	B) Five	C) Six	D) Seven	E) Eight

Solution: n = 1*2*3*4*5*6*7*8*9*10*11*12   The prime factors of n are 2, 3, 5, 7, and 11.   There are 5 prime factors.   The answer is Five.
Answer: B
A marketing survey of Anytown found that the ratio of trucks to sedans to motorcycles was 3:7:2, respectively. Given that there are 11,900 sedans in Anytown, how many motorcycles are there?
Pick one.
A) 1260 B) 2100 C) 3400 D) 4200 E) 5200

Solution: Let the total number of trucks = 3x   total number of sedans = 7x   total number of motorcycles = 2x   total number of sedans = 11900   => 7x = 11900   => x = 1700   total number of motorcycles =2x = 2*1700= 
2*1700 = 3_400
3400   Answer 3400
Answer: C
A thief is spotted by a policeman from a distance of 100metres. When the policeman starts the chase, the thief also starts running. If the speed of the thief be 8km/hr and that of the policeman 10km/hr, how far the thief will have run before he is overtaken ?
Choose the most appropriate option:  A) 400m  B) 1km  C) 500m  D) 450m  E) 650m

Solution: Relative speed of the policeman = 10-8= 
10-8 = 2
2 km/hr   time taken by policeman to cover 100m= (100/1000)*(1/2) = 1/20 hr   In 1/20 hr the thief covers a distance of 8/20 km = 2/5 km = 400m   400mnswer is 400m
Answer: A
A student scores 55% marks in 8 papers of 100 marks each. He scores 15% of his total marks in English. How much does he score in English?	Choose the correct choice from the following answers:
A) 55  B) 66  C) 77  D) 44  E) None of these

Solution: Given student scores 55% marks in english in 8 papers of 100 marks each.   so,his total marks are   (55*800)/100= 
  (55*800)/100 = 440
>440   15% of his 440 marks is  440*(15/100)= 
 440*(15/100) = 66
>66   so,he scored 66 marks in english.   ANSWER:66
Answer: B
A teacher grades students’ tests by subtracting twice the number of incorrect responses from the number of correct responses. If Student A answers each of the 100 questions on her test and receives a score of 64, how many questions did Student A answer correctly?
Choose the correct choice from the following answers.
A) 55
B) 60
C) 73
D) 82
E) 88

Solution: let the number of correct responses be x   then the number of incorrect responses =100-x   according to question   x-2(100-x)=64 (subtracting twice of incorrect from correct)   3x=264   x=88   ANSW88R:88
Answer: E
Joe is now 26 years older than Ella. If in 12 years Joe will be three times as old as Ella, how old will Joe be in 6 years? Choose the correct choice from the following choices
A) 31
B) 33
C) 35
D) 37
E) 39

Solution: J=E+26 so E=J-26.   J+12=3(E+12).   J+12=3(J-26+12).   J+12=3J-42.   2J=54.   J=27.   In 6 years, Joe will be 33 years old.   The answer is 33.
Answer: B
How many words, with or without meaning, can be formed using all letters of the word ORANGE using each letter exactly once?	Answers
A) 700  B) 720  C) 740  D) 760  E) 780

Solution: The Word ORANGE has exactly 6 letters which are all different.   Therefore the number of words that can be formed = Number of permutations of 6 letters taken all at a time.   = P (6, 6) = 6!   = 6 × 5 x 4 x 3 x 2 × 1   = 720   ANSWER:720
Answer: B
A, B and C invest in a partnership in the ratio: 7/2,4/3,6/5. After 4 months, A increases his share 50%. If the total profit at the end of one year is Rs.21,600, then what is B's share in the profit?	Choose the correct option: A) 2000 B) 3000 C) 5000 D) 4000 E) 6000

Solution: Ratio of the initial investment   =7/2:4/3:6/5=105:40:36   Therefore, let the initial investments of A, B and C be 105x,40x and 36x respectively   A increases his share 50% after 4 months. Hence the ratio of their investments   =((105x)×4)+((105x)×150/100×8) :(40x)×12:(36x)×12   =105+(105×32×2) :40×3:36×3   =105×4:40×3:36×3   =35×4:40:36   =35:10:9   B's share = total profit × 10/54   =21600×10/54=4000   Answer is 4000.
Answer: D
In a certain town, there are nine times as many people who were born in the town’s state as there are people who were born in another state or country. The ratio of those residents born in the town’s state to the town’s total population is  Choose the correct choice from the following:
A) 1 to 4
B) 1 to 3
C) 1 to 2
D) 3 to 4
E) 9 to 10

Solution: Town state: 9 times the whole town or country   then ratio will be 9 (times)/10 total(times)   So the answer is 9/10.   9 to 10
Answer: E
The total age of A and B is 18 years more than the total age of B and C. C is how many years younger than A.?	Select.
A) 16 B) 12 C) 15 D) 18 E) 10

Solution: (A+B)-(B-C)=18   A-C=18   Answer is 18
Answer: D
A sum of money is to be distributed among A, B, C, D in the proportion of 5:2:4:3. If C gets Rs. 10000 more than D, what is B's share?  Choose the correct choice from the following options:  A) A)82390  B) B)29000  C) C)20005  D) D)23930  E) E)20000

Solution: Let the shares of A, B, C and D be 5x, 2x, 4x and 3x Rs. respectively.   Then, 4x - 3x = 1000 => x = 10000.   B's share = Rs. 2x = 2 * 10000 = Rs. 20000.   Answer: 20000
Answer: E
what is the 10 th term in 1,3,9,15,25,35,-----?
Choices:
A) 66 B) 77 C) 88 D) 99 E) 95

Solution: 1^2 =1   2^2 -1 =3   3^2 =9   4^2 -1 =15   5^2 =25   6^2 -1 =35   7^2 =49   8^2 -1 =63   9^2 =81   10^2 -1=99   ANSWER:99
Answer: D
Two persons start running simultaneously around a circular track of length 400 m from the same point at speeds of 15 km/hr and 25 km/hr. When will they meet for the first time any where on the track if they are moving in opposite directions?	Choose the most appropriate option.
A) 11
B) 10
C) 28
D) 27
E) 36

Solution: Time taken to meet for the first time anywhere on the track   = length of the track / relative speed   = 400 / (15 + 25)5/18 = 400* 18 / 40 * 5 = 36 seconds.   Answer: 36
Answer: E
A fair coin is tossed repeatedly. If heads appears on first 3 tosses what is the probability that tail appears on the next two tosses?
Answers:	A) 1/6	B) 1/5	C) 1/3	D) 1/4	E) 1/6

Solution: Explanation :   Like mentioned in the question, the coin is fair. So chance of appearing of head and tail on each toss is same and each toss is independent from the previous one. So the chance of appearing tail on the next two tosses is still 1/2 each.   1/2 * 1/2 = 1/4   Answer : 1/4
Answer: D
A train 150 m long is running with a speed of 68 kmph. In what time will it pass a man who is running at 8 kmph in the same direction in which the train is going ?  Choose the correct choice from the following choices
A) 5 seconds B) 6 seconds C) 9 seconds D) 8 seconds E) 7 seconds

Solution: Relative speed of train and man=60kmph or 300/18m/s   Time taken by the train to pass the man:   Length of the train/relative speed   150/300/18=9 seconds.   ANSWER:9 seconds
Answer: C
In how many ways letters of the word RESPECT be arranged? Select the correct option.
A) 2310	B) 2536	C) 3260	D) 2520	E) 1450

Solution: RESPECT has 7 letters, out of which E repeated 2 times. Hence total ways = 7! / 2! = 2520 ways   2520
Answer: D
15 litres of water are poured into an aquarium of dimensions 50cm length, 30cm breadth, and 40cm height. How high (in cm) will the water rise?
(1 litre = 1000cm³)
Choose the correct answer:
A) 6
B) 8
C) 10
D) 20
E) 40

Solution: lXbXh= 15000   h= 15000/50*30= 8 cm   '10' is the answer.
Answer: C
For her customer feedback score, Jess wants to average at or above an 8.0 rating. For the month of June, she received the following scores: 9, 8, 8, 7, 9, 10, 6, 6, 8 and 7. By what percent did she fall short of her goal?  Choices: A) 2.5% B) 5% C) 8% D) 10% E) 12%

Solution: Expected minimum rating = 8   Deviation from the expected minimum rating = (1 + 0 + 0 - 1 + 1 + 2 - 2 - 2 + 0 - 1)/10 = -2/10 = -0.2   Current rating is 0.2 less than 8.   Percentage = (0.2/8)*100= 
(0.2/8)*100 = 2.5
2.5%   2.5%nswer: 2.5%
Answer: A
Ben is driving on the highway at x miles per hour. (One mile equals 5,280 feet.) Ben's tires have a circumference of z feet. Which of the following expressions gives the number of revolutions each wheel turns in one hour?  Options:
A) 5,280(x/z) B) 5,280(y/x) C) 5,280(xy) D) 5,280/(xy) E) (xy)/5,280

Solution: In one hour, at the rate of x miles per hour, Ben covers x miles, so 5,280x feet.   The number of revolutions = distance/circumference = 5,280x/z.   5,280(x/z)nswer: 5,280(x/z).
Answer: A
A man buys an article for 10% less than its value and sells it for 10% more than its value. His gain or loss percent is:	Choose the correct option:
A) no profit, no loss
B) 20% profit
C) less than 20% profit
D) more than 20% profit
E) None

Solution: Let the article be worth Rs. x.   C.P. 90% of Rs. x = Rs. 9x/10   S.P. = 110% of Rs. x = Rs. 11x/10   Gain = (11x/10 - 9x/10) = Rs. x/5   Gain % = x/5 * 10/9x * 100 = 22 2/9 % > 20%   ANSWER:more than 20% profit
Answer: D
if integer N has p factors ; how many factors will 3N have ?  Select:
A) p
B) 2p
C) P+1
D) 2p+1
E) Cannot be determined

Solution: Case 1:   Let N = 6 => 2 x 3 (prime factorization) => p = 4;   3N = 18 => 3^2 x 2 (prime factorization) => no. of factors = 6; (p+2)   Case 2:   Let N = 9 => 3^2 (prime factorization) => p = 3;   3N = 27 => 3^2 x 3(prime factorization) => no of factors = 4; (p+1)   For different N different results are observed. So, shouldn't Cannot be determined be the right answer?   Cannot be determined
Answer: E
A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 38 years now, the son's age five years back was  Pick:
A) 11 years B) 12 years C) 14 years D) 15 years E) 16 years

Solution: Let the son's present age be x years. Then, (38 - x) = x   2x = 38.   x = 19.   Son's age 5 years back (19 - 5)= 
(19 - 5) = 14
14 years.   14 years)
Answer: C
By selling 10 pens for a rupee a woman loses 18%. How many for a rupee should he sell in order to gain 30%?  Choose the correct choice from the following options.
A) 12	B) 14	C) 45	D) 6	E) 7

Solution: 6   82% --- 10   130% --- ?   82/130 * 10 = 6
Answer: D
Working together, Jose and Jane can complete an assigned task in 20 days. However, if Jose worked alone and completed half the work and then Jane takes over and completes the second half, the task will be completed in 45 days. How long will Jose take to complete the task if he worked alone? Assume that Jane is more efficient than Jose. Choose the correct choice from the following:
A) 25 days B) 30 days C) 60 days D) 65 days E) 36 days

Solution: Explanatory Answer   Step 1: Assign Variables and Frame Equations   Let Jose take 'x' days to complete the task if he worked alone.   Let Jane take 'y' days to complete the task if she worked alone.   Statement 1 of the question: They will complete the task in 20 days, if they worked together.   In 1 day, Jose will complete 1/x of the task.   In 1 day, Jane will complete 1/yof the task.   Together, in 1 day they will complete 1/20 of the task.   Therefore,1/x+ 1/y= 1/20.... (1)   Statement 2 of the question: If Jose worked alone and completed half the work and then Jane takes over and completes the second half, the task will be completed in 45 days.   Jose will complete half the task in x/2 days.   Jane will complete half the task in y/2 days.   ∴ x/2 + y/2= 45   Or, x + y = 90 or x = 90 - y .... (2)   Step 2: Solve the two equations and find x and y   Substitute the value of x as (90 - y) in the first equation   1/90−y + 1/y = 1/20   Or y2 - 90 + 1800 = 0.   The quadratic equation factorizes as (y - 60)(y - 30) = 0   So, y = 60 or y = 30.   If y = 60, then x = 90 - y = 90 - 60= 
90 - 60 = 30
30 and   If y= 30, then x = 90 - y = 90 - 30= 
90 - 30 = 60
60.   The question clearly states that Jane is more efficient than Jose. Therefore, Jane will take lesser time than Jose.   Hence, Jose will take 60 days to complete the task if he worked alone and Jane will take 30 days to complete the same task.   60 dayshoice 60 days
Answer: C
In a 100 m race, A runs at 8km per hour. If A gives B a start of 7 m and still him by 15 seconds, what is the speed of B ?	Choose the correct choice from the following choices
A) 5.58 km/hr.	B) 5.06 km/hr.	C) 5.76 km/hr.	D) 6.76 km/hr.	E) 5.72 km/hr.

Solution: Time taken by A to cover 100 m =(60 X 60 / 8000)	x 100 sec = 45 sec.   B covers (100 - 7)= 
(100 - 7) = 93
93 m in (45 + 15)= 
(45 + 15) = 60
60 sec.   B's speed= (93 x 60 x 60)/(60 x 1000)km/hr = 5.58 km/hr.   5.58 km/hr.nswer is 5.58 km/hr.
Answer: A
If the numerator of a fraction is increased by 20% and its denominator is diminished by 25% value of the fraction is 2/15. Find the original fraction?
Choose the correct answer.
A) 1/12  B) 1/16  C) 1/19  D) 1/14  E) 1/13

Solution: X * (120/100)   ---------------- = 2/15   Y * (75/100)   X/Y = 1/12   1/12nswer: 1/12
Answer: A
Two goods train each 500 m long are running in opposite directions so parallel tracks.Their speeds are 45 kmph and 30 kmph respectively.Find the time taken by the slower train to pass the driver of the first one  Choose the correct choice from the following options
A) 12 sec  B) 24 sec  C) 48 sec  D) 60 sec  E) 65 sec

Solution: only need length of slower train which is L=500m   relative sped (both are opposite direction)   s=45+30= 
45+30 = 75
75kmph   75*5/18=125/6 m/s   time =dist/speed   =(500*6)/125= 
(500*6)/125 = 24
24 sec   ANSWER:24 sec
Answer: B
Of the 200 math majors at a certain university, 50 percent will be assigned to advanced calculus on Monday and Wednesday and the remaining 70 percent will be assigned to advanced calculus on Tuesday and Thursday. However, 40 percent of the math majors prefer Tuesday and Thursday and 60 percent prefer Monday and Wednesday. What is the lowest possible number of math majors who will NOT be assigned to the days they prefer?  Choose the correct choice from the following options.
A) 15	B) 20	C) 30	D) 45	E) 60

Solution: 30% of students are assigned to Monday and Wednesday = 0.3*200= 
0.3*200 = 60
60   70% of students are assigned to Tuesday and Thursday= 0.7*200= 
0.7*200 = 140
140   60% of students prefer Monday and Wednesday= 0.6*200= 
0.6*200 = 120
120   40% of students prefer Tuesday and Thursday= 0.4*200= 
0.4*200 = 80
80   Since we need theleastnumber of students who will not be assigned to their preferred days, we shall fit in themaximumpossible students as per their preference:   All of the 40% of students who prefer Tuesday and Thursday can be accommodated to their preferred days, whereas only 60 out of 120 students who prefer Monday and Wednesday can be accommodated to their preferred days.   The remaining 15 students who prefer Monday and Wednesday will be allocated to Tuesday and Thursday by default, which is not their choice.   15nswer is 15.
Answer: A
A box contains 25 electric bulbs, out of which 4 are defective. Two bulbs are chosen at random from this box. The probability that at least one of these is defective is Answers:  A) 3/10  B) 7/19  C) 12/19  D) 21/95  E) None

Solution: Solution   P( None is defective)   = 21C2 / 25C2   = 7/10   P( at least one is defective)   = (1- 7/10)   =3/10.   3/10nswer 3/10
Answer: A
A certain team consists of 3 professors and 5 teaching assistants. How many different teams of 3 can be formed in which at least one member of the group is a professor? (Two groups are considered different if at least one group member is different.)  Choose the correct option
A) 34 B) 38 C) 42 D) 46 E) 50

Solution: The total number of ways to form a group of 3 from 8 people is 8C3 = 56   The number of ways to form a group without a professor is 5C3 = 10   The total number of ways to form a valid group is   56 - 10= 
  56 - 10 = 46
46.   The answer is 46.
Answer: D