divelab/Sys2Bench huggingface dataset:
Question: There are 437 doctors and nurses in a hospital. If the ratio of the doctors to the nurses is 8 : 11, then how many nurses are there in the hospital?
Options:
A)152
B)253
C)57
D)171
E)181
Rationale: Given,
The ratio of the doctors to the nurses is 8 : 11
Number of nurses = 11/19 x 437 = 253
ANSWER:B
Answer: B
Question: In how many ways can live boys and three girls sit in a row such that all boys sit together?
Options:
A)3877
B)2778
C)2880
D)2987
E)1231
Rationale: Explanation:
Treat all boys as one unit. Now there are four students and they can be arranged in 4! ways. Again five boys can be arranged among themselves in 5! ways.
Required number of arrangements = 4! * 5! = 24 * 120 = 2880.
Answer: C
Answer: C
Question: What is the median of a set of consecutive integers if the sum of nth number from the beginning and nth number from the end is 150?
Options:
A)10
B)25
C)50
D)75
E)100
Rationale: Surprisingly no one answered this easy one.
property of a set of consecutive integerz.
mean=median=(first element+last element)/2 = (second element+last but one element)/2 =(third element+ third last element)/2 Etc. Etc.
So mean=median=150/2=75
Answer is D
Answer: D
Question: Kiran has 85 currency notes in all, some of which were of Rs. 100 denomination and the
remaining of Rs. 50 denomination. The total amount of all these currency notes was Rs.
5000. How much amount did she have in the denomination of Rs. 50?
A. B. C. None of these D.
Answer: Option B
Explanation:
Options:
A)1900
B)3500
C)4000
D)2000
E)2500
Rationale: Let the number of 50 – rupee notes be x.
Then, the number of 100-rupee notes = (85 – x)
50x + 100(85 – x) = 5000
x + 2 (85 – x) = 100 = x=70
So, required amount = Rs. (50 x 70) = Rs. 3500 ANSWER :B
Answer: B
Question: If 4 is the remainder when m is divided by 10, what is the remainder when 4m is divided by 10?
Options:
A)2
B)4
C)6
D)8
E)0
Rationale: We can put m=10*k+4.
So 4*m=40*k+16 ---> 40*k+16 = 10*(4*m+1) +6 ---> The remainder is 6.
The answer is, therefore, (C).
Answer: C
Question: If the area of circle O is 16π, what is the length of an arc on the circle formed by a central angle measuring 45 degrees?
Options:
A)π
B)3π/2
C)2π
D)5π/2
E)8π
Rationale: Area = 16π
Radius = 4
Circumference = 2 x 4 x π = 8π
Angle forming the arc = 45 degrees. 45/360 = 1/8.
Therefore length of arc = 1/8 * 8π = π - Answer choice A.
Answer: A
Question: A number when divided by 296 leaves 75 as remainder. When the same number is divided by 37, the remainder will be:
Options:
A)1
B)5
C)3
D)4
E)11
Rationale: Let x = 296q + 75
= (37 x 8q + 37 x 2) + 1
= 37 (8q + 2) + 1
Thus, when the number is divided by 37, the remainder is 1.
ANSWER A
Answer: A
Question: Find the fourth proportional to 2.4, 4.6 and 7.6?
Options:
A)14
B)14.56
C)15.14
D)15.17
E)15.26
Rationale: Formula = Fourth proportional = (b × c)/a
A = 2.4 , B = 4.6 and C = 7.6
(4.6 × 7.6)/2.4 = 14.56
B
Answer: B
Question: Two goods trains each 250 m long are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one?
Options:
A)24
B)45
C)48
D)51
E)44
Rationale: Relative speed = 45 + 30 = 75 km/hr.
75 * 5/18 = 125/6 m/sec.
Distance covered = 250 + 250 = 500 m.
Required time = 500 * 6/125 = 24 sec.
Answer: Option A
Answer: A
Question: Find the sum of all 2 digit numbers divisible by 3.
Options:
A)1565
B)1665
C)1300
D)1448
E)1465
Rationale: All 2 digit numbers divisible by 3 are 12,15,18,21,……….. 99
This is an A.P with a = 12, and d = 3, Let it contain n terms
Then, 12 + (n – 1 ) *3 = 99, or n = ( 99-12) /3 + 1 = 30
Required sum = 30/2*( 12 + 99 ) = 15*111 = 1665
ANSWER:B
Answer: B
Question: A restaurant serves 600 bowls of noodles for Rs. 12000 at a loss of Rs. 2 per bowl. Find the cost price for one bowl?
Options:
A)12
B)18
C)22
D)35
E)26
Rationale: SP per bowl = 12000/600 = Rs. 20 Loss per bowl = Rs. 2 CP per bowl = 20 + 2= Rs. 22Answer: C
Answer: C
Question: Entry fee is Re.1.there are 3 rides each is of Re.1. total boys entering are 3000.total income is Rs.7200. 800 students do all 3 rides. 1400 go for atleast 2 rides.none go the same ride twice. then no of students who do not go any ride is?
Options:
A)1328
B)1000
C)2378
D)8287
E)1872
Rationale: Total entries are 3000 So fee collected through entry fee = 3000 x 1 = Rs.3000
Income generated through rides = 7200 - 3000 = 4200
Now 800 went for 3 rides so total fee paid by these 800 = 800 x 3 = 2400
(1400 - 800) went for 2 rides so fee paid by these 600 = 600 x 2 = 1200
Assume K went for exactly 1 ride
Then K x 1 + 1200 + 2400 = 4200 ⇒⇒ K = 600
So number of boys who did not go for any ride = 3000 - (600 + 600 + 800 ) = 1000
Answer:B
Answer: B
Question: A can do a piece of work in 80 days. He works at it for 10 days & then B alone finishes the remaining work in 42 days. In how much time will A and B, working together, finish the work?
Options:
A)30 days
B)20 days
C)25 days
D)35 days
E)45 days
Rationale: Work done by A in 10 days = 10/80 = 1/8
Remaining work = (1 - (1/8)) = 7/8
Now, work will be done by B in 42 days.
Whole work will be done by B in (42 x 8/7) = 48 days
Therefore, A’s one day’s work = 1/80
B’s one day’s work = 1/48
(A+B)’s one day’s work = 1/80 + 1/48 = 8/240 = 1/30
Hence, both will finish the work in 30 days.
ANSWER:A
Answer: A
Question: The mean of 50 observations was 36. It was found later that an observation 48 was wrongly taken as 23. The corrected new mean is?
Options:
A)36.6
B)36.1
C)36.5
D)36.2
E)36.9
Rationale: Correct sum
= (36 * 50 + 48 - 23)
= 1825.
Correct mean
= 1825/50 = 36.5
Answer:C
Answer: C
Question: If Greg buys 3 shirts, 4 trousers and 2 ties, the total cost is $40. If Greg buys 7 shirts, 2 trousers and 2 ties, the total cost is $60. How much will it cost him to buy 3 trousers, 5 shirts and 2 ties?
Options:
A)$50
B)$64
C)$75
D)$96
E)Cannot be determined
Rationale: Solution: 3x+4y+2z=40 7x+2y+2z=60
adding both the equations= 10x+6y+4z=100
5x+3y+2z=50
ans A
Answer: A
Question: How many combinations of three letters taken from letters (a, b, b, c, c, d,d) are possible?
Options:
A)4C3+4
B)4C3+9
C)4C3+2
D)4C3
E)4C3+6
Rationale: So 4C3 for abcd - 4 choices
3 more for dd(b,c or a)
3 more for bb(a,c or d)
3 more for cc(a,b or d)
total 4C3+9
Ans : B
Answer: B
Question: In how many ways can you seat 6 people on a bench if one of them, Rohit, does not want to sit on the middle seat or at either end?
Options:
A)360
B)1720
C)2880
D)5040
E)10080
Rationale: Since Rohit does not want to sit on the middle seat or at either end (3 chairs), then he can choose 3 chairs to sit. The remaining 5 people can sit in 5! ways. Thus the # of arrangements is 3*5! = 360.
Answer: A.
Answer: A
Question: The area of a triangle is with base 8.4m and height 5.8m?
Options:
A)11.36 m2
B)10.36m2
C)18.36 m2
D)19.36 m2
E)24.36 m2
Rationale: 1/2 * 8.4 * 5.8
= 24.36 m2
Answer: E
Answer: E
Question: 8 fruits are tpo kept on a table. A pair of oranges and apples must be kept together. in how many arrangements can the fruits be arranged?
Options:
A)A.1296
B)B.1850
C)C.4200
D)D.3546
E)E.2880
Rationale: Glue pair of oranges and apples together: {AB}, {CD}.
6 units {AB}, {CD}, {E}, {F}, {G}, {H} can be arranged in 6! ways. Each couple within their unit can be arranged in 2! ways.
Therefore the final answer is 6!*2!*2!=2,880.
Answer: E.
Answer: E
Question: What is the perimeter of a rectangular field whose diagonal is 5m and length is 4m ?
Options:
A)20 m
B)15 m
C)14 m
D)10 m
E)25 m
Rationale: Sol:
Breadth of the rectangular plot is=5^2-4^2=3m
Therefore,
Perimeter of the rectangular plot= 2(4+3)=14m
C) 14m
Answer: C
Question: The average (arithmetic mean) of four different positive integers is 16. If the first of these integers in 3 times the second integer and the second integer is 2 less than the third integer, what is the least possible value of the fourth integer?
Options:
A)5
B)4
C)3
D)2
E)1
Rationale: Let the second integer be x and the fourth be a.
Then [3x + x + (x+2) + a]/4 = 16
=> 5x + 2 + a = 64
=> 5x + a = 62
=> a = 62 - 5x
From the above equation we can see that a is minimum when x is maximum, provided both are positive
The maximum value that x can take in the above equation while still keeping a positive is x=12
This gives us a= 62 - 60 = 2
Therefore the minimum value that the fourth integer can have is 2. Option D.
Answer: D
Question: John and Amanda stand at opposite ends of a straight road and start running towards each other at the same moment. Their rates are randomly selected in advance so that John runs at a constant rate of 3, 4, or 5 miles per hour and Amanda runs at a constant rate of 4, 5, 6, or 7 miles per hour. What is the probability that John has traveled farther than Amanda by the time they meet?
Options:
A)1/16
B)1/12
C)1/8
D)1/6
E)1/3
Rationale: John will run farther if he runs at 5 mph and Amanda runs at 4 mph.
P(John runs farther) = 1/3 * 1/4 = 1/12
The answer is B.
Answer: B
Question: Amber works 20 days a month at d dollars per day for m months out of the year. Which of the following represents her monthly pay?
Options:
A)m/(20d)
B)20d
C)10md/6
D)20d/m
E)20md
Rationale: Total income of Amber in a year = d*20*m dollars.
Now Monthly income = Total/12 = d*20*m / 12 = 10md/6
Answer is C
Answer: C
Question: Find the set of all points (x, y) such that the area of the triangle with vertices (0, 0), (6, 4) and (x, y) is 4.
Options:
A)3
B)9
C)7
D)8
E)2
Rationale: Explanation:
Area of a triangle if one of the point is (0, 0) = 12|(x1y2−x2y1)|12|(x1y2−x2y1)|
⇒ 12|(6×y−4×x)|12|(6×y−4×x)| = 4
⇒ 6y – 4x = 8
Answer: D
Answer: D
Question: In a lottery, there are 10 prizes and 25 blanks. A lottery is drawn at random. What is the probability of getting a prize?
Options:
A)2/7
B)3/7
C)4/8
D)9/2
E)3/8
Rationale: P (getting a prize) =	10/(10 + 25)= 10/35 =2/7	.
A
Answer: A
Question: The average of six numbers is S and the average of three of these is T.If the average of the remaining three is U, then
Options:
A)S= T + U
B)2S= T + U
C)S= 2T + 2U
D)None of these
E)Cannot ne determined
Rationale: Explanation :
Clearly, we have S =(3T+3U/6)
or 2S= T + U
Answer : B
Answer: B
Question: 3889 + 15.952 - ? = 3854.002
Options:
A)47.95
B)50.95
C)45.97
D)47.59
E)45.79
Rationale: Let 3889 + 15.952 - x = 3854.002.
Then x = (3889 + 15.952) - 3854.002
= 3904.952 - 3854.002
= 50.95.
Answer is B
Answer: B
Question: October 9, 2012, fell on a Tuesday. On which day of the week did June 25, 2013, fall? (Note: 2012 was a leap year.)
Options:
A)Sunday
B)Monday
C)Tuesday
D)Wednesday
E)Thursday
Rationale: The date range contains a partial year. The number of days in the partial year is:
October - 22, February - 28, November and April - 30, December, January, March, and May - 31, and June - 25.
22 + 28 + (2 * 30) + (4 * 31) + 25 = 259 total days in the date range.
Divide by 7 to determine how much the day of the week advances: 259 / 7 = 37 remainder 0.
Since the remainder is 0 the second date has the same day of the week as the first date.
Even though 2012 is a leap year, with 366 days, the extra day does not come into play unless the date range contains February 29. Since this did not occur, the extra day had no effect on the day of the week.
The answer is C.
Answer: C
Question: When positive integer x is divided by 11, the quotient is y and the remainder is 4. When 2x is divided by 5, the quotient is 3y and the remainder is 4. What is the value of 4y – x ?
Options:
A)-2
B)-1
C)0
D)1
E)2
Rationale: (1) x = 11y + 4
(2) 2x = 15y + 4
Let's subtract equation (1) from equation (2).
4y = x
4y - x = 0
The answer is C.
Answer: C
Question: Two sides of a triangle have lengths q and y and meet at a right angle. If the perimeter of the triangle is 4q, what is the ratio of q to y ?
Options:
A)a) 2 : 3
B)b) 3 : 4
C)c) 4 : 3
D)d) 3 : 2
E)e) 2 : 1
Rationale: Ahhhh....my bad. Thank you, you're correct. 8q = 6y --> q/y = 3/4.
Actually B is the right answer.
Answer: B
Question: If a particular player is always chosen, in how many ways can a cricket-be chosen out of 15 players?
Options:
A)1243
B)1345
C)1788
D)1346
E)1365
Rationale: A particular player is always chosen, it means that 10 players are selected out of the remaining 14 players.
=. Required number of ways = 14C10 = 14C4
= 14!/4!x19! = 1365
E
Answer: E
Question: What is the minimum value of |x-4| + |x+2| + |x-5| ?
Options:
A)-3
B)3
C)5
D)7
E)8
Rationale: A cannot be the answer as all the three terms are in modulus and hence the answer will be non negative.
|x-4| >= 0 --> Minimum occurs at x = 4
|x+2| >= 0 --> Minimum occurs at x = -2
|x-5| >= 0 --> Minimum occurs at x = 5
x = -2 --> Result = 6 + 0 + 7 = 13. Also any negative value will push the combined value of |x-4| + |x-5| to a value > 9.
x = 4 --> Result = 0 + 6 + 1 = 7
x = 5 --> Result = 1 + 7 + 0 = 8
x = 2 --> Result = 2 + 4 + 3 = 9
So minimum value of the expression occurs at x = 4 and the resultant value = 7
Answer: D
Answer: D
Question: Which of the following ratios is greatest ?
Options:
A)7 :15
B)15 :23
C)17 :25
D)21 :29
E)1 : 2
Rationale: 7/15 = 0.466,
15/23 = 0.652,
17/25 = 0.68
21/29 = 0.724
Clearly, 0.724 is greatest
therefore, 21 : 29 is greatest
ANSWER:D
Answer: D
Question: If f(a)=a^2, what is the value of (f(a-b)−f(a))/b ?
Options:
A)a
B)b
C)2a
D)-2a + b
E)2b - a
Rationale: start with f(a+b) before start calculations: f(a-b)=(a-b)^2= a^2-2ab+b^2
a^2-2ab+b^2 - a^2/b = (simplify a^2)
-2ab+b^2/b = (cancel b's)
= -2a+b
Ans : D
Answer: D
Question: 36.	A 240 m long train crosses a platform of equal length in 27 s. What is the speed of the train in km/h?
Options:
A)48
B)60
C)56
D)64
E)68
Rationale: By the formula, speed= Distance/ Time
= (240 + 240)/27 x (18/5)
= 480/27 x 18/5 = 64 km/h
Answer :D
Answer: D
Question: A vessel of capacity 2 litre has 20% of alcohol and another vessel of capacity 6 litre had 40% alcohol. The total liquid of 8 litre was poured out in a vessel of capacity 10 litre and thus the rest part of the vessel was filled with the water. What is the new concentration of Mixture?
Options:
A)31%.
B)71%.
C)49%.
D)29%.
E)28%.
Rationale: 20% of 2 litres = 0.4 litres
40% of 6 litres = 2.4 litres
Therefore, total quantity of alcohol is 2.8 litres.
This mixture is in a 10 litre vessel. Hence, the concentration of alcohol in this 10 litre vessel is 28%
ANSWER:E
Answer: E
Question: Smita Was Making A Cube With Dimensions 5*5*5 Using 1*1*1 Cubes. What Is The Number Of Cubes Needed To Make A Hollow Cube Looking Of The Same Shape?
Options:
A)98
B)104
C)100
D)61
E)51
Rationale: cube use to make perfect 5 * 5 * 5 = 125
No need of cube to make hollow=(5-2)*(5-2)*(5-2)=27
so total cube need to make hollow cube is=125-27 =98
ANSWER:A
Answer: A
Question: Working alone, printers X, Y, and Z can do a certain printing job, consisting of a large number of pages, in 15, 10, and 20 hours, respectively. What is the ratio of the time it takes printer X to do the job, working alone at its rate, to the time it takes printers Y and Z to do the job, working together at their individual rates?
Options:
A)5/2
B)8/3
C)9/4
D)10/3
E)12/5
Rationale: The time it takes printer X is 15 hours.
The combined rate of Y and Z is 1/10 + 1/20 = 3/20
The time it takes Y and Z is 20/3
The ratio of times is 15 / (20/3) = 3*15/20 = 9/4
The answer is C.
Answer: C
Question: Alice walked for 3 days. She walked 18 miles on the first day, walking 3 miles per hour. On the second day she walked for one less hour but she walked one mile per hour, faster than on the first day. On the third day she walked the same number of hours as on the first day, but at the same speed as on the second day. How many miles in total did she walk?
Options:
A)24
B)44
C)58
D)60
E)62
Rationale: Alice walked 18 miles on the first day, walking 3 miles per hour i.e. total time of walk on Day-1 = 18/3 = 6 Hours
Second day time of walk = 6-1 = 5 hours and Speed = 3+1=4 miles per hour i.e. Distance walked on second day = 5*4 = 20 miles
Third day time of walk = 6 hours and Speed = 4 miles per hour i.e. Distance walked on second day = 6*4 = 24 miles
Total Distance travelled on three days = 18+20+24 = 62
Answer: Option E
Answer: E
Question: A, B and C are partners. A receives 2/3 of profits, B and C dividing the remainder equally. A's income is increased by Rs.200 when the rate to profit rises from 5 to 7 percent. Find the Capital of B?
Options:
A)2500
B)3000
C)3500
D)4000
E)4500
Rationale: A:B:C = 2/3:1/6:1/6 = 4:1:1
x * 2/100 * 2/3 = 200
B capital = 15000*1/6 = 2500
ANSWER A
Answer: A
Question: In each series, look for the degree and direction of change between the numbers. In other words, do the numbers increase or decrease, and by how much
Look at this series: 1.5, 3.5, 5.5, 7.5, ... What number should come next?
Options:
A)4.7
B)3.6
C)9.5
D)5.0
E)4.4
Rationale: 9.5
In this simple addition series, each number increases by 2.0
Answer : C
Answer: C
Question: Amar takes as much time in running 18 meters as a car takes in covering 48 meters. What will be the distance covered by Amar during the time the car covers 1.8 km?
Options:
A)660 m
B)650 m
C)570 m
D)670 m
E)680 m
Rationale: Distance covered by Amar = (18/48)*1800 = 670 m
ANSWER:D
Answer: D
Question: The ratio of the number of boys and girls in a college is 7 : 8. If the percentage increase in the number of boys and girls be 20% and 10% respectively, what will be the new ratio?
Options:
A)21:22
B)7:8
C)2:1
D)21:24
E)14:16
Rationale: Originally, let the number of boys and girls in the college be 7x and 8x respectively.
Their increased number is (120% of 7x) and (110% of 8x).
= (120/100) 7x and (110/100) 8x
= 42x/5 and 44x/5
Therefore, The required ratio = (42x/5):(44x/5)
= 21 : 22. Answer is A.
Answer: A
Question: Akhil's club with a total membership of 30 has formed 3 committees, M, S and R which have 8,12, and 5 members respectively. If no member of committee M is on either of the other 2 committees, what is the greatest possible number of members in the club who are on none of the committees.
Options:
A)5
B)7
C)8
D)10
E)12
Rationale: Akhil's club with a total membership of 30 has formed 3 committees Given no member of committee M is on either of the other 2 committees -- hence (M n R) and (M n S) and (M n R n S) is zero.
Hence only M is 8. Now we need to consider only S, (S n R) and R.
(M U R U S) = M + R + S - (M n R) - (M n S) - (R n S) + (M n R n S) + Neither.
30 = 8 + (12 - x) + (5 - x) + 0 + 0 + x + 0 + Neither.
22 = (12-x) + (5-x) + x + Neither.
Now the max value of x could be 5 and the min value of x could be 0.
When x is 5 (max), Neither is 10.
When x is 0 (min), Neither is 5. We need maximum no of people who do not belong to any group. Hence max value of neither is 10.
Answer 10 (D).
Answer: D
Question: Maxwell leaves his home and walks toward Brad's house. One hour later, Brad leaves his home and runs toward Maxwell's house. If the distance between their homes is 24 kilometers, Maxwell's walking speed is 4 km/h, and Brad's running speed is 6 km/h. What is the total time it takes Maxwell before he meets up with Brad?
Options:
A)3
B)4
C)5
D)6
E)8
Rationale: Total Distance = 24 kms
Maxwell Speed = 4 kms/hr
Maxwell travelled for 1hour before Brad started , therefore Maxwell traveled for 4 kms in 1 hour.
Time taken = Total Distance / Relative Speed
Total Distance after Brad started = 20 kms
Relative Speed (Opposite side) (As they are moving towards each other speed would be added ) = 6+ 4 = 10 kms/hr
Time taken to meet Brad after Brad Started = 20 / 10 = 2 hrs
Distance traveled by Maxwell = Maxwell's speed * time taken = 4 * 2 = 8+4 = 12 kms...
Therefore Total Time taken by Maxwell to meet Brad = Distance travelled by Maxwell / Maxwell's Speed = 12 /4 = 3 hrs ... Answer A
Answer: A
Question: Find the compound interest on $15,624 for 9 months at 16% per annum compounded quarterly.
Options:
A)$4152
B)$1951
C)$2258
D)$8978
E)$8875
Rationale: P=$15625, n=9 months=3 quarters, R=16% p.a=4% per quarter.
amount=$[15625*(1+(4/100)^3)] = $(15625*(26/25)*(26/25)*(26/25)) = $17576.
C.I = $(17576-15625)= $1951.
answer(B)
Answer: B
Question: Boy sells a book for Rs. 450 he gets a loss of 10 %, To gain 10 %, what should be the SP?
Options:
A)Rs.320
B)Rs.450
C)Rs.550
D)Rs.640
E)Rs.680
Rationale: Find Selling Price to gain 10 %.
Now, we are asked to find selling price to gain 10% profit.
Hint:
Selling Price = (100 + Gain%) × C.P.
100
Selling Price = (100 + 10) × 500
100
Selling Price = (110) × 500
100
Therefore, selling Price = Rs.550
C
Answer: C
Question: In what time will a railway train 65 m long moving at the rate of 36 kmph pass a telegraph post on its way?
Options:
A)8 sec
B)7 sec
C)2 sec
D)6.5 sec
E)9 sec
Rationale: T = 65/36 * 18/5
= 6.5 sec
Answer:D
Answer: D
Question: In a group of 22 boys, 13 play basketball and 15 play football. 3 of the boys play neither. how many play both ?
Options:
A)18
B)20
C)21
D)22
E)25
Rationale: 18 boys play something. If b play both, then
13+15-b = 18
Answer is A
Answer: A
Question: If n is an integer and 5^n > 40,000,000, what is the least possible value of n?
Options:
A)7
B)8
C)9
D)10
E)11
Rationale: When you seperate the 40000000 into factors of 5 and 2 you get - > 10^7 x 2^2 = 5^7 x 2^9
2 to the ^ 9 = 512 so its 512 x 5^7
that means 5^7 x 5^x must be greater
5^x > 512
5^1=5
5^2=25
5^3= 125
5^4= 625 - > so x must be at least 4
5^(7+4)= 5^11
E
Answer: E
Question: Suppose we have six marbles: 3 yellow marbles, 2 red marbles, and one green marble. Suppose we are going to put them into three cups: a black cup, a white cup, and a purple cup. We could put all six in any cup and leave two cups empty; or we could put marbles in two cups and leave one cup empty; or we could put some marbles in each of the three cups. How many combinations are possible?
Options:
A)180
B)160
C)149
D)150
E)175
Rationale: # ways to distribute yellow marbels(3) is :
1 in each cup= 1
2 in one cup and 1 in other=6
all 3 in one cup = 3
total 1+6+3=10 possibilities
# ways to distribute Red marbels(2) is :
1 in each cup = 3 ways
all in one cup = 3ways
total 6ways.
# ways to distribute Green marbels(1) is :
3 ways
total number of ways = 10*6 *3 = 180
A
Answer: A
Question: P and Q started a business with respective investments of Rs. 4 lakhs and Rs. 10 lakhs. As P runs the business, his salary is Rs. 5000 per month. If they earned a profit of Rs. 2 lakhs at the end of the year, then find the ratio of their earnings?
Options:
A)2 : 5
B)5 : 2
C)3 : 5
D)1 : 1
E)None of these
Rationale: Ratio of investments of P and Q is 2 : 5
Total salary claimed by P = 12 * 5000 = Rs. 60000
Total profit = Rs. 2 lakhs.
Profit is to be shared = Rs. 140000
Share of P = (2/7) * 140000 = Rs. 400000
Share of Q = Rs. 100000
Total earnings of P = (60000 + 40000) = Rs. 100000
Ratio of their earnings = 1 : 1
ANSWER:D
Answer: D
Question: There are 36 students in a certain geometry class. If two thirds of the students are boys and one half of the boys are under six feet tall, how many boys in the class are under six feet tall?
Options:
A)6
B)12
C)18
D)24
E)27
Rationale: Total Students = 36
Two thirds of the students are boys = 2/3*36 = 24
One half of the boys are under six feet tall = 1/2*24 = 12 ...
Therefore Number of boys in the class under six feet tall = 12 ... Answer B....
Alternatively... Number of boys in the class under six feet tall = 1/2 of 2/3 of Total Students = 1/2*2/3*36 = 12...
Answer B
Answer: B
Question: If 2^z is a factor of 22!, which of the following could be the value of z?
I. 22
II. 23
III. 24
Options:
A)I ​ only
B)II only
C)I​ and II
D)I, II, and III
E)None
Rationale: 22! contains all numbers from 1 to 22. To find the factor with the highest power of 2, we count the number of multiples of 2, 4, 8 and 16.
Multiples of 2 = 11
Multiples of 4 = 5
Multiples of 8 = 2
Multiples of 16 = 1
Total count = 19
The answer is E.
Answer: E