mathewhe/aqua_rat huggingface dataset:
Question: The Natural Woman, a women's health food store, offers its own blends of trail mix. If the store uses 4 different ingredients, how many bins will it need to hold every possible blend, assuming that each blend must have at least two ingredients? (Also assume that each bin can hold one and only one blend.)
(A) 1
(B) 4
(C) 7
(D) 11
(E) 10
Rationale: We're told that there are 4 ingredients (we'll call them A, B, C and D); we're told that each 'mix' must include AT LEAST 2 ingredients...
2 ingredient blends:
AB
AC
AD
BC
BD
CD
3 ingredient blends:
ABC
ABD
ACD
BCD
4 ingredient blends:
ABCD
Total blends = 6+4+1 = 11
Final Answer:D
Answer: (D) 11
Question: A cube of edge 17cm is immersed completely in a rectangular vessel containing water. If the dimensions of the base of vessel are 20cm * 15cm , find the rise in water level?
(A) 6cm
(B) 8.25cm
(C) 11.25cm
(D) 16.37cm
(E) 20.62cm
Rationale: Increase in volume = volume of the cube = 17*17*17 cm^3
Rise in water level = volume / area = 17*17*17/20*15 = 16.37cm
Answer is D
Answer: (D) 16.37cm
Question: A train 90 meters long is running with a speed of 54 kmph. The time taken by it to cross a tunnel 120 meters long is?
(A) 29
(B) 18
(C) 14
(D) 99
(E) 13
Rationale: D = 90 + 120 = 210
S = 54 * 5/18 = 15 mps
T = 210/15 = 14 sec
Answer: C
Answer: (C) 14
Question: A right circular cylinder has a height of 20 and a radius of 5. A rectangular solid with a height of 15 and a square base, is placed in the cylinder such that each of the corners of the solid is tangent to the cylinder wall. Liquid is then poured into the cylinder such that it reaches the rim. What is the volume of the liquid?
(A) 500(π – 3)
(B) 500(π – 2.5)
(C) 500(π – 2)
(D) 500(π – 1.5)
(E) 500(π – 1)
Rationale: The square base has sides of sqrt(50) due to the 45-45-90 triangle
20*25*pi - 15*sqrt(50)^2
=500(π – 1.5)
D. 500(π – 1.5)
Answer: (D) 500(π – 1.5)
Question: The sum of the present age of Henry and Jill is 33. What is their present ages if 6 years ago Henry was twice the age of Jill?
(A) and 20
(B) and 24
(C) and 22
(D) and 29
(E) of these
Rationale: Let the age of Jill 6 years ago be x, age of Henry be 2x
x+6 + 2x+6 = 33
x = 7
Present ages will be 13 and 20
Answer : A
Answer: (A) and 20
Question: The sum of the two numbers is 11 and their product is 35. What is the sum of the reciprocals of these numbers?
(A) 12/35
(B) 11/35
(C) 35/8
(D) 7/32
(E) None of these
Rationale: Let the numbers be a and b. Then, a+b=11 and ab =35.
a+b/ab=11/35; (1/b+1/a)=11/35
Sum of reciprocals of given numbers=11/35.
Correct Option: B
Answer: (B) 11/35
Question: A money lender lends Rs.2000 for six months at 20% p.a. rate. It the interest is reckoned quarterly than find the amount given after time limit.
(A) 2205
(B) 2877
(C) 2378
(D) 2988
(E) 2781
Rationale: A = 2000(21/20)2 = 2205.Answer:A
Answer: (A) 2205
Question: A library has an average of 660 visitors on Sundays and 240 on other days. The average number of visitors per day in a month of 30 days beginning with a Sunday is:
(A) 250
(B) 276
(C) 280
(D) 310
(E) None
Rationale: Since the month begins with sunday,to there will be five sundays in the month
Average required = (660x5 + 240x25) /30) = 310
Answer: Option D
Answer: (D) 310
Question: A train running at the speed of 60 km/hr crosses a pole in 9 seconds. Find the length of the train?
(A) 150
(B) 272
(C) 278
(D) 277
(E) 112
Rationale: Speed = 60*(5/18) m/sec = 50/3 m/sec
Length of Train (Distance) = Speed * Time
(50/3) * 9
= 150 meter
Answer: A
Answer: (A) 150
Question: In a certain animal population, for each of the first 3 months of life, the probability that an animal will die during that month is 1/4. For a group of 200 newborn members of the population, approximately how many would be expected to survive the first 3 months of life?
(A) 40
(B) 46
(C) 52
(D) 62
(E) 85
Rationale: The probability of survival for each of the first 3 months of life is 1-1/4=3/4, so of 200 newborn 200*3/4 *3/4*3/4=~85 is expected to survive.
Answer: E.
Answer: (E) 85
Question: If the area of circle is 616 sq cm then its circumference?
(A) 22
(B) 88 cm
(C) 99
(D) 66
(E) 41
Rationale: 22/7 r2 = 616 => r = 14
2 * 22/7 * 14 = 88.Answer:B
Answer: (B) 88 cm
Question: A store sells 2 kinds of jelly beans mixes (A and B)both made up of red and yellow beans. if b contains 20% more red beans than A but 10% fewer yellow beans. and Jar A contains twice as many red beans as yellow by what percent is the number of beans in Jar B larger than the number in Jar A
(A) 5
(B) 6
(C) 8
(D) 9
(E) 10
Rationale: A has 10 yellows
20 reds
total=30
so B has 1.2 x 20 =24 reds
0.9 x 10 = 9 yellows
total=33
difference= 3/30= 10%
ANSWER:E
Answer: (E) 10
Question: 80 370 860 1550 2440 ?
(A) 900
(B) 840
(C) 750
(D) 860
(E) 3530
Rationale: 10^2 - 20 = 80
20^2 - 30 = 370
30^2 - 40 = 860
40^2 - 50 = 1550
50^2 - 60 = 2440
60^2 - 70 = 3530.
ANSWER:E
Answer: (E) 3530
Question: Which number should replace both the asterisks in (* /18) x (*/72) = 1 ?
(A) 24
(B) 30
(C) 36
(D) 42
(E) 48
Rationale: Let (y/18) x (y/72) = 1
y^2 = 18 x 72 = 18 x 18 x 4
y = (18 x 2) = 36
The answer is C.
Answer: (C) 36
Question: A part-time employee whose hourly wage was decreased by 20 percent decided to increase the number of hours worked per week so that the employee's total income did not change. By what percent Q should the number of hours worked be increased?
(A) 12.5%
(B) 20%
(C) 25%
(D) 50%
(E) 100%
Rationale: Correct Answer: C
Solution: C. We can set up equations for income before and after the wage reduction. Initially, the employee earns W wage and works H hours per week. After the reduction, the employee earns .8W wage and works X hours. By setting these equations equal to each other, we can determine the increase in hours worked: WH = .8WX (divide both sides by .8W) 1.25H = X We know that the new number of hours worked will be Q=25% greater than the original number. The answer is C.
Answer: (C) 25%
Question: Look at this series: 4, 7, 25, 10, __, 20, 16, 19, ... What number should fill the blank?
(A) 15
(B) 13
(C) 17
(D) 19
(E) 11
Rationale: B
13
Two series alternate here, with every third number following a different pattern. In the main series, 3 is added to each number to arrive at the next. In the alternating series, 5 is subtracted from each number to arrive at the next.
Answer: (B) 13
Question: Simplify 6235 * 99
(A) 256989
(B) 546892
(C) 567892
(D) 658793
(E) 617265
Rationale: Explanation:
Although it is a simple question, but the trick is to save time in solving this.
Rather than multiplying it we can do as follows:
6235 * (100 - 1) = 623500 - 6235 = 617265
Answer: Option E
Answer: (E) 617265
Question: A straight line is formed using two points A(3,3) and B(6,6). Another point P(x,y) lies between A and B such that AP/BP = 8. What are the coordinates of P?
(A) (7/3, 7/3)
(B) (17/3, 17/3)
(C) (8/9, 8/9)
(D) (8/3, 8/3)
(E) (7/8, 7/8)
Rationale: The equation of the straight line is y = x, so the x- and y-coordinates of P are the same.
The x, y coordinates are 8/9 of the distance from 3 to 6.
x = 3 + (6-3)*(8/9) = 3 + 8/3 = 17/3 = y
The answer is B.
Answer: (B) (17/3, 17/3)
Question: The average runs of a cricket player of 12 innings was 48. How many runs must he make in his next innings so as to increase his average of runs by 10?
(A) 12
(B) 142
(C) 164
(D) 178
(E) 84
Rationale: Explanation:
Average after 13 innings = 58
Required number of runs = (58 * 13) – (48 * 12)
= 754 – 576 = 178
ANSWER D
Answer: (D) 178
Question: Rebecca's annual income is $15 and Jimmy's annual income is $18. By how much must Rebecca's annual income increase so that it constitutes 55% of Rebecca and Jimmy's combined income?
(A) 8
(B) 7
(C) 9
(D) 10
(E) 11
Rationale: total rebecca = x+15; total = x+15+18
x+15/x+33 = 55/100 therefore x =7
B
Answer: (B) 7
Question: A motorist travel to a place 150 km away at an average speed of 70 km/hr and returns at 30 km/hr.His average speed for the whole journey in km/hr is
(A) 36 km/hr
(B) 37 km/hr
(C) 40 km/hr
(D) 42 km/hr
(E) None of these
Rationale: Explanation:
Average speed will be
2xy/x+y km/hr
= {2(70)(30)}/{70+30} km/hr
= 42 km/hr
Answer: Option D
Answer: (D) 42 km/hr
Question: Two trains 125 meters and 165 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?
(A) 7.2
(B) 7.17
(C) 7.19
(D) 7.15
(E) 7.11
Rationale: T = (125 + 165)/ (80 + 65) * 18/5
T = 7.2
Answer:A
Answer: (A) 7.2
Question: A person was asked to subtract 25% of a number from the original but he subtracted 25 from the number. His answer was 25 more than correct one. What was the original number?
(A) 297
(B) 187
(C) 278
(D) 200
(E) 267
Rationale: 25 + 25 = 50
25% ------ 50
100% ----- ? => 200
Answer:D
Answer: (D) 200
Question: Find the area of circle whose radius is 7m?
(A) 298
(B) 154
(C) 267
(D) 268
(E) 298
Rationale: 22/7 * 7 * 7 = 154
Answer: B
Answer: (B) 154
Question: A certain basketball team that has played 2/3 of its games has a record of 14 wins and 6 losses. What is the greatest number of the remaining games that the team can lose and still win at least 3/4 of all of its games?
(A)  1
(B)  6
(C)  5
(D)  4
(E)  3
Rationale: 14 wins, 6 losses - total 20 games played.
The team has played 2/3rd of all games so total number of games = 30
3/4th of 30 is 22.5 so the team must win 23 games and can afford to lose at most 7 total games. It has already lost 6 games so it can lose another 1 at most.
Answer (A)
Answer: (A)  1
Question: How many 5-letter words can be formed using the letters of the English alphabet that contain 3 different vowels and 2 different consonants?
(A) 4!*5c3
(B) 4!*5c3 *21c2
(C) 4!*21c2
(D) 3!*5c3 *21c2
(E) 5!*5c3 *21c2
Rationale: combination for 2 vowels out of 5 =5c3 ways
combination for 3 consonants of 21 = 21c2 ways
Additionally the arrangement can be = 5!
total arrangements =4!*5c3 *21c2
B
Answer: (B) 4!*5c3 *21c2
Question: A box contains 2 white balls, 3 black balls and 4 red balls. In how many ways can 3 balls be drawn from the box, if at least one black ball is to be included in the draw?
(A) 32
(B) 48
(C) 64
(D) 96
(E) None of these
Rationale: We may have 1 black and 2 non black or 2 black and 1 non black or 3 black
Required number of ways = (3C1 x 6C2) + (3C2 x 6C1) + 3C3
= [3 x (6x5)/(2x1)] + [(3x2)/(2x1) x 6] + 1 = 45 +18 + 1 = 64.
Answer C.
Answer: (C) 64
Question: Ten percent of the women in a college class are science majors, and the non-science majors make up 80% of the class. What percentage of the men are science majors if 40% of the class are men?
(A) 15%
(B) 25%
(C) 35%
(D) 45%
(E) 50%
Rationale: Science majors make up 0.2 of the class.
60% of the class are women and 0.1*0.6 = 0.06 of the class are female science majors.
Then 0.14 of the class are male science majors.
0.4x = 0.14
x = 0.35 = 35%
The answer is C.
Answer: (C) 35%
Question: Among the employees of a certain company, 52 percent of the employees are male and 48 percent are female. In this company 70 percent of the male employees are married and 50 percent of the female employees are married. If one employee in the company is randomly selected, approximately what is the probability that he or she is NOT married?
(A) 0.3
(B) 0.4
(C) 0.5
(D) 0.6
(E) 0.7
Rationale: Total Males = 52
Total Female = 48
Total = 100
Not married Male = 30% = 15.6
Not marries Female = 50% = 24
Total = 39.6
Probability = 39.6/100 = .396 = approx .4
ANSWER:B
Answer: (B) 0.4
Question: In marathon Sam was faster than Jack. Denise beat Jim but lost to Jack. Who is the winner?
(A) Sam
(B) Jack
(C) Denise
(D) Jim
(E) none
Rationale: Denise beat Jim
Jack beat Jim
Sam beat Jack
So Sam is the winner
ANSWER:A
Answer: (A) Sam
Question: . The average of first ten prime numbers which are odd is?
(A) 22.9
(B) 28.1
(C) 12.9
(D) 15.8
(E) 11.2
Rationale: Explanation:
Sum of first 10 prime no. which are odd = 158
Average = 158/10 = 15.8
Answer:D
Answer: (D) 15.8
Question: A boat can travel with a speed of 13 km/hr in still water. If the speed of the stream is 6 km/hr, find the time taken by the boat to go 69 km downstream.
(A) 3.6 hr
(B) 5.25 hr
(C) 8.25 hr
(D) 2.25 hr
(E) 2.50 hr
Rationale: speed of boat in still water = 13 km/hr
speed of the stream = 6 km/hr
Speed downstream = (13+6) = 19 km/hr
Time taken to travel 69 km downstream = 69â„19 = 17â„4 = 3.6 hours
Answer is A
Answer: (A) 3.6 hr
Question: Without stoppages, a train travels certain distance with an average speed of 100 km/h, and with stoppages, it covers the same distance with an average speed of 95 km/h. How many minutes per hour the train stops ?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: Due to stoppages, it covers 5 km less .
Time taken to cover 5 km = 5â„100h = 1â„20h
= 1â„20 Ã— 60 min = 3 min
Answer C
Answer: (C) 3
Question: A man leaves a point P at 6 a.m. and reaches the point Q at 10 a.m. another man leaves the point give at 8 a.m. and reaches the point P at 12 noon. At what time do they meet?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 2
Rationale: 9 a.m.
Answer: C
Answer: (C) 8
Question: Two drivers began their journey with the same amount of petrol in their cars at the same time. The only difference is that the first driver�s car could drive 4 hours in that amount of petrol and the second one could drive 5 hours.
However, they only drove for some time and found that the amount of petrol that was left in one of the cars was four times the petrol left in the other one.
For how long had they driven at this point of time?
(A) 2.75 hours
(B) 3.75 hours
(C) 4.75 hours
(D) 5.75 hours
(E) None
Rationale: Solution:
3.75 hours
Explanation:
While you can solve it as you like, a simple mathematical equation can be used to find out.
Let M be the amount of petrol initially.
Let N be the time for which they drove.
According to the question, the amount of petrol used by first car in N hours = MN / 4
The amount of petrol used by second car in N hours = MN / 5
Hence, the amount of petrol left in the first car = (M - MN / 4)
The amount of petrol left in the second car = (M - MN / 5)
AS per the details given in the question, we can form the below equation:
M - MN / 5 = 4(M - MN / 4)
N = 15 / 4 or 3.75 hours.
Hence, both the drivers have driven the car for 3.75 hours at that particular time.
Answer B
Answer: (B) 3.75 hours
Question: Three pipes A, B and C can fill a tank from empty to full in 30 minutes, 20 minutes, and 10 minutes respectively. When the tank is empty, all the three pipes are opened. A, B and C discharge chemical solutions P,Q and R respectively. What is the proportion of the solution R in the liquid in the tank after 3 minutes?
(A) 5/11
(B) 6/11
(C) 7/11
(D) 8/11
(E) 9/11
Rationale: PART filled (A+B+C) in 3 min = 3(1/30+1/20+1/10)=(3*11/60)=11/20
=>3/10
req ratio = 6/11
ANSWER B
Answer: (B) 6/11
Question: A,B,C subscribe Rs.50,000 for a business.A subscribes Rs.4000 more than B and B Rs.5000 more than C.Out of a total profit of Rs.35,000,A receives :
(A) Rs.8400
(B) Rs.11,900
(C) Rs.13,600
(D) Rs.14,700
(E) None of these
Rationale: Solution
Let C = x.Then, B = x + 5000 and A = x + 5000 + 4000 - x + 9000.
So, x + x + 5000 + x + 9000 - 50000 3x - 36000 x =12,000.
A : B : C = 21000 : 17000 : 12000 = 21 : 17 : 12.
∴ A’s share = Rs. (35000x21/50) = Rs. 14,700. Answer D
Answer: (D) Rs.14,700
Question: A 270 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds. What is the Length of the other train?
(A) 230 m
(B) 240 m
(C) 260 m
(D) 320 m
(E) None
Rationale: Solution
Relative Speed	= (120 + 80)km/hr
= (200 x 5/18)m/sec
= (500 / 9)m/sec
Let the length of the other train be x metres
Then, x + 270 / 9
x + 270 = 500
x = 230.
Answer A
Answer: (A) 230 m
Question: A photographer is to take group photographs of a class of students for the school magazine such that each photograph should have five students. If there are four girls and four boys in the class and each photograph must not have two girls or two boys standing together, how many different photographs can the photographer take?
(A) 80
(B) 288
(C) 4^4
(D) 576
(E) 288^2
Rationale: The condition that TWO boys or TWO girls cannot be together means they should be alternate..
Total five means 3 of one and 2 of other..
1) choose 3 girls and arrange them... 4C3*3! = 4!= 24
2 boys can be choosen in 4C2 and arrange them in 2! Ways... 4C2*2!= 12
Total ways = 24*12 = 288..
2) same as above.. 2 girls and 3 boys.. 288
Total 288*2=576
ANS:D
Answer: (D) 576
Question: Let R1 and R2 respectively denote the maximum and minimum possible remainders when (276)n is divided by 91 for any natural number n , n>= 144. Find R1+R2.
(A) 90
(B) 82
(C) 84
(D) 64
(E) None
Rationale: Explanation :
The remainder when 276 divided by 91 is 3 hence
remainder of (276)n/91 = remainder 3n/91
Taking n = 1,2,3,4,5
We get the possible remainders as 3, 9, 27, 81, 61, 1 respectively.
For n>5, the pattern repeats
Hence R1 = 81 and R2 = 1
R1+R2 = 81+1 = 82
Answer : B
Answer: (B) 82
Question: A person starting with Rs.64 and making 6 bets, wins 3times and loses 3times, the wins and loses occurring in random order. The chance for a win is equal to the chance for a loss. If each wager is for half the money remaining at the time of the bet, then the final result is?
(A) Rs.37
(B) Rs.45
(C) Rs.47
(D) Rs.53
(E) Rs.59
Rationale: As the win leads to multiplying the amount by 1.5 and loss leads to multiplying the amount by 0.5, we will multiply initial amount by 1.5 thrice and by 0.5 thrice (in any order).
The overall resultant will remain same.
So final amount with the person will be (in all cases):
=64(1.5)(1.5)(1.5)(0.5)(0.5)(0.5)==64(1.5)(1.5)(1.5)(0.5)(0.5)(0.5)= Rs 2727
Hence the final result is:
64−27=3764−27=37:
A loss of Rs.37
A
Answer: (A) Rs.37
Question: A train 420 m long is running at a speed of 48 km/hr. In what time will it pass a bridge 60 m long?
(A) 40 sec
(B) 36sec
(C) 60 sec
(D) 48 sec
(E) 18 sec
Rationale: total length= 420+60=480
speed=48km/h=(48*5)/18= 40/3 m/s
time=(480*3)/40=36 sec.
ANSWER:B
Answer: (B) 36sec
Question: If books bought at prices ranging from Rs 200 to Rs 350 are sold at prices ranging from Rs 300 to Rs 425, what is the greatest possibleprofit that might be made in selling eight books.
(A) 800
(B) 1200
(C) 1600
(D) 1800
(E) None of these
Rationale: Explanation:
least cost price = 200*8 = 1600
greatest sold price = 425 * 8 = 3400
profit required = 3400- 1600 = 1800. Answer: D
Answer: (D) 1800
Question: On his drive to work, Leo listens to one of three radio stations A, B or E. He first turns to A. If A is playing a song he likes, he listens to it; if not, he turns it to B. If B is playing a song he likes, he listens to it; if not, he turns it to E. If E is playing a song he likes, he listens to it; if not, he turns off the radio. For each station, the probability is 0.30 that at any given moment the station is playing a song Leo likes. On his drive to work, what is the probability that Leo will hear a song he likes?
(A) 0.027
(B) 0.09
(C) 0.417
(D) 0.657
(E) 0.9
Rationale: Probability he hears a song is like:
Tune to A and likes what he is hearing = 0.3
Tune to A, don't find he like what they are airing, then tune to B and likes what he finds there = 0.7 * 0.3 = 0.21
Tune to A, finds crap there, Tune to B, hears a similar crap, Tune to E and finally falls in love with the program = 0.7^2 * 0.3 = 0.147
Total = 0.657
Ans D
Answer: (D) 0.657
Question: If 8^x = 2^6, what is x?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: 2^3x= 2^6
3x=6, therefore x=2
Answer A
Answer: (A) 2
Question: There are 3 numbers A, B and C. If A:B = 3/4, B:C = 4/5, C:D = 5/6, then B:D will be?
(A) 1 : 2
(B) 3 : 5
(C) 2:3
(D) 6 : 11
(E) 5 : 3
Rationale: Sol. A : B = 3 : 4, B : C = 4 : 5, C : D = 5 : 6
∴A∶B∶C∶D= 3 : 4 : 5 : 6.
Thus, B : D = 4 : 6 or, 2:3
C
Answer: (C) 2:3
Question: A collection of books went on sale, and 2/3 of them were sold for $5 each. If none of the 50 remaining books were sold, what was the total amount received for the books that were sold?
(A) $550
(B) $600
(C) $500
(D) $400
(E) $450
Rationale: If 50 books constitute 1/3rd of the total, then 2/3rd of the total = 100 books
Amount received for sold books = 100 * 5 = $500
Answer :C
Answer: (C) $500
Question: A train can travel 50% faster than a car. Both start from point A at the same time and reach point B 75 kms away from A at the same time. On the way, however, the train lost about 12.5 minutes while stopping at the stations. The speed of the car is:
(A) 100 kmph
(B) 110 kmph
(C) 120 kmph
(D) 130 kmph
(E) 140 kmph
Rationale: Let speed of the car be x kmph.
Then, speed of the train=(150/100)*x=(3/2)*x kmph
(75/x)-(75/(3/2x))=125/(10*60)
(75/x)-(50/x)=5/24
x = 25x24/5 = 120kmph.
Answer : C.
Answer: (C) 120 kmph
Question: In a pack of playing cards a card is drawn at random. What is the probability that the card selected is a red king card?
(A) 1/26
(B) 1/13
(C) 3/26
(D) 2/13
(E) 5/26
Rationale: Total cards=52. Number of red king cards=2. Probability of selecting a red king card=2/52=1/26.
Correct Answer: A
Answer: (A) 1/26
Question: A certain car dealership sells economy cars, luxury cars, and sport utility vehicles. The ratio of economy to luxury cars is 5:2. The ratio of economy cars to sport utility vehicles is 4:3. What is the ratio of luxury cars to sport utility vehicles?
(A) 9:8
(B) 8:15
(C) 3:2
(D) 2:3
(E) 1:2
Rationale: The ratio of economy to luxury cars is 5:2 --> E:L = 5:2 = 20:8.
The ratio of economy cars to sport utility vehicles is 4:3 --> E:S = 4:3 = 20:15.
Thus, L:S = 8:15.
Answer: B.
Answer: (B) 8:15
Question: A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If four marbles are picked at random, what is the probability that none is blue?
(A) 33/96
(B) 33/91
(C) 33/18
(D) 33/87
(E) 33/17
Rationale: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles. When four marbles are picked at random, then the probability that none is blue is = ¹²C₄/¹⁵C₄
= (12 * 11 * 10 * 9)/(15 * 14 * 13 * 12)
= 33/91
Answer:B
Answer: (B) 33/91
Question: The sum of Two Numbers X, Y is 54. The Difference is 28 what is the square value of Y?
(A) 169
(B) 225
(C) 144
(D) 256
(E) 81
Rationale: X + Y = 54
X - Y = 28
2X = 82
X = 41
Y = 54 - 41 = 13. The square of 13 is 169
so the answer is option A.
Answer: (A) 169
Question: A pipe can empty 2/3rd of a cistern in 12mins. In 8 mins, what part of the cistern will be empty?
(A) 2/3
(B) 3/7
(C) 4/9
(D) 3/8
(E) 4/7
Rationale: 2/3 ---- 12
? ----- 8 ==> 4/9
C
Answer: (C) 4/9
Question: Two electronic musical instruments were purchased for Rs. 8000. The first was sold at a profit of 40% and the second at a loss of 40%. If the sale price was the same in both the cases, what was the cost price of the electronic musical instruments?
(A) 1400,5600
(B) 3400,5600
(C) 2400,5600
(D) 2400,4600
(E) 2400,3600
Rationale: let cost prices be x and 8000-x
s.p1=s.p2
(140/100)*x=(60/100)*(8000-x)
x=2400
cost prices are 2400,5600
ANSWER:C
Answer: (C) 2400,5600
Question: The sum of ages of 4 children born 1 years different each is 38 years. What is the age of the Elder child?
(A) 8
(B) 11
(C) 10
(D) 16
(E) 17
Rationale: Let the ages of children be x, (x + 1), (x + 2), (x + 3) years.
Then, x + (x + 1) + (x + 2) + (x + 3) = 38
4x = 32
x = 8.
x+3= 8+3=11
Answer : B
Answer: (B) 11
Question: In how many ways a committee, Consisting of 4 men and 6 women can be formed from 8 men and 10 women?
(A) 266
(B) 86400
(C) 11760
(D) 14700
(E) 15720
Rationale: To choose Required number of ways to form a committee:
Select 4 men out of 8 men and 6 women out of 10 women.
That is 8C4 * 10C6.
8C4=8!/4!*4!
=70
10C6=10!/6!*4!
=210
The Required number of ways=210*70=14700
D
Answer: (D) 14700
Question: Two pipes A and B can fill a tank in 2 and 6 minutes respectively. If both the pipes are used together, then how long will it take to fill the tank?
(A) 2.5 min
(B) 1.8 min
(C) 1.5 min
(D) 3.5 min
(E) 2 min
Rationale: Part filled by the first pipe in 1 minute = 1/2
Part filled by the second pipe in 1 minute = 1/6
Net part filled by pipe A and pipe B in 1 minute = (1/2)+(1/6)=2/3
i.e, pipe A and B together can fill the tank in 3/2 minutes = 1.5 minutes
Answer is C
Answer: (C) 1.5 min