mathewhe/aqua_rat huggingface dataset:
Question: The age of father 10 years ago was thrice the age of his son. Ten years hence, father's age was five times the age of the son. After 6 years, son's age will be:
(A) 5:2
(B) 7:3
(C) 9:2
(D) 13:4
(E) 3:4
Rationale: Let the age of father and son 10 years ago be 3x and x years respectively.
Then, (3x + 10) + 10 = 2[(x + 10) + 10]
3x + 20 = 2x + 40 => x = 20.
Required ratio = (3x + 10):(x + 10) = 70:30 = 7:3
ANSWER:B
Answer: (B) 7:3
Question: 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
(A) II
(B) I
(C) III
(D) I&II
(E) II &III
Rationale: 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)
A
==>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) II
Question: 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?
(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.
Rationale: 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 A
Answer: (A) 11: 00 a.m.
Question: 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
(A) 12/2652
(B) 14/2652
(C) 2/2652
(D) 4/2652
(E) 8/2652
Rationale: the total probability = (4/52 * 3/51) = 12/2652. A is the correct answer.
Answer: (A) 12/2652
Question: 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?
(A) 700; 1100
(B) 1005; 495
(C) 1000; 800
(D) 1200; 800
(E) None of the above
Rationale: 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
B
Answer: (B) 1005; 495
Question: 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 ?
(A) 175
(B) 275
(C) 375
(D) 475
(E) 575
Rationale: 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 = 48
x = 15.
Hence, total hours of work = (160 + 15) = 175.
Answer is A.
Answer: (A) 175
Question: 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?
(A) 12
(B) 24
(C) 48
(D) 55
(E) 49
Rationale: 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 E it is!
Answer: (E) 49
Question: 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?
(A) 1440
(B) 1400
(C) 1600
(D) 720
(E) 820
Rationale: 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 = 1440
Answer : A
Answer: (A) 1440
Question: 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?
(A) 180 grams
(B) 220 grams
(C) 250 grams
(D) 350 grams
(E) 1400 grams
Rationale: 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 E)
Answer: (E) 1400 grams
Question: 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?
(A) 4 years
(B) 8 years
(C) 10 years
(D) None of these
(E) CANNOT BE DETERMINED
Rationale: 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.
Answer A
Answer: (A) 4 years
Question: The Sum of first N consecutive odd integers is N^2. What is the sum of all odd integers between 13 and 35 inclusive.
(A) 288
(B) 364
(C) 410
(D) 424
(E) 450
Rationale: 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 = 48
2) Now look at the 'next smallest' and the 'next biggest': 15 + 33 = 48
Now we have proof that there is no middle term. We have 6 bunches of 48.
6(48) = 288
A
Answer: (A) 288
Question: 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?
(A) 80cm
(B) 90cm
(C) 100cm
(D) 120cm
(E) 130cm
Rationale: 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.
A is the answer.
Answer: (A) 80cm
Question: Three numbers are in the ratio of 2 : 3 : 4 and their L.C.M. is 264. What is their H.C.F.?
(A) 18
(B) 22
(C) 24
(D) 28
(E) 32
Rationale: 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 B.
Answer: (B) 22
Question: 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:
(A) 15
(B) 27
(C) 38
(D) 46
(E) 48
Rationale: 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.
ANSWER:A
Answer: (A) 15
Question: 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?
(A) 9
(B) 10
(C) 18
(D) 20
(E) 21
Rationale: 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 : C
Answer: (C) 18
Question: If n is the product of the integers from 1 to 12, inclusive, how many different prime factors greater than 1 does n have?
(A) Four
(B) Five
(C) Six
(D) Seven
(E) Eight
Rationale: 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 B.
Answer: (B) Five
Question: 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?
(A) 1260
(B) 2100
(C) 3400
(D) 4200
(E) 5200
Rationale: 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
=3400
Answer C
Answer: (C) 3400
Question: 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 ?
(A) 400m
(B) 1km
(C) 500m
(D) 450m
(E) 650m
Rationale: Relative speed of the policeman = 10-8 = 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
Answer is A
Answer: (A) 400m
Question: 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?
(A) 55
(B) 66
(C) 77
(D) 44
(E) None of these
Rationale: Given student scores 55% marks in english in 8 papers of 100 marks each.
so,his total marks are (55*800)/100 =>440
15% of his 440 marks is 440*(15/100)=>66
so,he scored 66 marks in english.
ANSWER:B
Answer: (B) 66
Question: 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?
(A) 55
(B) 60
(C) 73
(D) 82
(E) 88
Rationale: 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
ANSWER:E
Answer: (E) 88
Question: 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?
(A) 31
(B) 33
(C) 35
(D) 37
(E) 39
Rationale: 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 B.
Answer: (B) 33
Question: How many words, with or without meaning, can be formed using all letters of the word ORANGE using each letter exactly once?
(A) 700
(B) 720
(C) 740
(D) 760
(E) 780
Rationale: 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:B
Answer: (B) 720
Question: 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?
(A) 2000
(B) 3000
(C) 5000
(D) 4000
(E) 6000
Rationale: 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 D.
Answer: (D) 4000
Question: 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
(A) 1 to 4
(B) 1 to 3
(C) 1 to 2
(D) 3 to 4
(E) 9 to 10
Rationale: Town state: 9 times the whole town or country
then ratio will be 9 (times)/10 total(times)
So the answer is 9/10.
E
Answer: (E) 9 to 10
Question: 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.?
(A) 16
(B) 12
(C) 15
(D) 18
(E) 10
Rationale: (A+B)-(B-C)=18
A-C=18
Answer is D
Answer: (D) 18
Question: 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?
(A) A)82390
(B) B)29000
(C) C)20005
(D) D)23930
(E) E)20000
Rationale: 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: E
Answer: (E) E)20000
Question: what is the 10 th term in 1,3,9,15,25,35,-----?
(A) 66
(B) 77
(C) 88
(D) 99
(E) 95
Rationale: 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:D
Answer: (D) 99
Question: 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?
(A) 11
(B) 10
(C) 28
(D) 27
(E) 36
Rationale: 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: E
Answer: (E) 36
Question: 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?
(A) 1/6
(B) 1/5
(C) 1/3
(D) 1/4
(E) 1/6
Rationale: 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 : D
Answer: (D) 1/4
Question: 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 ?
(A) 5 seconds
(B) 6 seconds
(C) 9 seconds
(D) 8 seconds
(E) 7 seconds
Rationale: 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:C
Answer: (C) 9 seconds
Question: Evaluate 35% of 450 + 45% of 350
(A) 232
(B) 242
(C) 315
(D) 262
(E) 272
Rationale: Explanation:
= (35/100) * 450 + (45/100) * 350
= 315
Option C
Answer: (C) 315
Question: In how many ways letters of the word RESPECT be arranged?
(A) 2310
(B) 2536
(C) 3260
(D) 2520
(E) 1450
Rationale: RESPECT has 7 letters, out of which E repeated 2 times. Hence total ways = 7! / 2! = 2520 ways
D
Answer: (D) 2520
Question: 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)
(A) 6
(B) 8
(C) 10
(D) 20
(E) 40
Rationale: lXbXh= 15000
h= 15000/50*30= 8 cm
'C' is the answer.
Answer: (C) 10
Question: 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?
(A)  2.5%
(B)  5%
(C)  8%
(D)  10%
(E)  12%
Rationale: 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 = 2.5%
Answer: A
Answer: (A)  2.5%
Question: 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?
(A) 5,280(x/z)
(B) 5,280(y/x)
(C) 5,280(xy)
(D) 5,280/(xy)
(E) (xy)/5,280
Rationale: 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.
Answer: A.
Answer: (A) 5,280(x/z)
Question: 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:
(A) no profit, no loss
(B) 20% profit
(C) less than 20% profit
(D) more than 20% profit
(E) None
Rationale: 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:D
Answer: (D) more than 20% profit
Question: if integer N has p factors ; how many factors will 3N have ?
(A) p
(B) 2p
(C) P+1
(D) 2p+1
(E) Cannot be determined
Rationale: 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 E be the right answer?
E
Answer: (E) Cannot be determined
Question: 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
(A) 11 years
(B) 12 years
(C) 14 years
(D) 15 years
(E) 16 years
Rationale: 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) = 14 years.
C)
Answer: (C) 14 years
Question: By selling 10 pens for a rupee a woman loses 18%. How many for a rupee should he sell in order to gain 30%?
(A) 12
(B) 14
(C) 45
(D) 6
(E) 7
Rationale: D
82% --- 10
130% --- ?
82/130 * 10 = 6
Answer: (D) 6
Question: 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.
(A) 25 days
(B) 30 days
(C) 60 days
(D) 65 days
(E) 36 days
Rationale: 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 = 30 and
If y = 30, then x = 90 - y = 90 - 30 = 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.
Choice C
Answer: (C) 60 days
Question: 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 ?
(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.
Rationale: Time taken by A to cover 100 m =(60 X 60 / 8000)	x 100 sec = 45 sec.
B covers (100 - 7) m = 93 m in (45 + 15) sec = 60 sec.
B's speed = (93 x 60 x 60)/(60 x 1000)km/hr = 5.58 km/hr.
Answer is A
Answer: (A) 5.58 km/hr.
Question: 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?
(A) 1/12
(B) 1/16
(C) 1/19
(D) 1/14
(E) 1/13
Rationale: X * (120/100)
---------------- = 2/15
Y * (75/100)
X/Y = 1/12
Answer: A
Answer: (A) 1/12
Question: 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
(A) 12 sec
(B) 24 sec
(C) 48 sec
(D) 60 sec
(E) 65 sec
Rationale: only need length of slower train which is L=500m
relative sped (both are opposite direction)
s=45+30=75kmph
75*5/18=125/6 m/s
time =dist/speed
=(500*6)/125=24 sec
ANSWER:B
Answer: (B) 24 sec
Question: 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?
(A)  15
(B)  20
(C)  30
(D)  45
(E)  60
Rationale: 30% of students are assigned to Monday and Wednesday = 0.3*200 = 60
70% of students are assigned to Tuesday and Thursday = 0.7*200 = 140
60% of students prefer Monday and Wednesday = 0.6*200 = 120
40% of students prefer Tuesday and Thursday = 0.4*200 = 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.
Answer is A.
Answer: (A)  15
Question: 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
(A) 3/10
(B) 7/19
(C) 12/19
(D) 21/95
(E) None
Rationale: Solution
P( None is defective)
= 21C2 / 25C2
= 7/10
P( at least one is defective)
= (1- 7/10)
=3/10.
Answer A
Answer: (A) 3/10
Question: 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.)
(A) 34
(B) 38
(C) 42
(D) 46
(E) 50
Rationale: 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 = 46.
The answer is D.
Answer: (D) 46
Question: A biker covered half the distance between two towns in 2 hr 30 min. After that he increased his speed by 2 km/hr. He covered the second half of the distance in 2 hr 20 min. Find the distance between the two towns and the initial speed of the biker.
(A) 140
(B) 120
(C) 130
(D) 150
(E) 160
Rationale: Let x km/hr be the initial speed of the biker, then his speed during the second part of the trip is x + 2 km/hr. Half the distance between two cities equals 23060⋅x km and 22060⋅(x+2) km. From the equation: 23060⋅x=22060⋅(x+2) we get x=28 km/hr.
The intial speed of the biker is 28 km/h.
Half the distance between the two towns is
2h30min×28=2.5×28=70.
So the distance is 2×70=140 km.
Answer is A.
Answer: (A) 140