MU-NLPC/Calc-aqua_rat huggingface dataset:
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:  Select:	A) 1900	B) 3500	C) 4000	D) 2000	E) 2500

Solution: 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 :3500
Answer: B
If 4 is the remainder when m is divided by 10, what is the remainder when 4m is divided by 10? Choose one:  A) 2  B) 4  C) 6  D) 8  E) 0

Solution: 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, (6).
Answer: C
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?
Pick:
A) π  B) 3π/2  C) 2π  D) 5π/2  E) 8π

Solution: 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 - πnswer choice π.
Answer: A
A number when divided by 296 leaves 75 as remainder. When the same number is divided by 37, the remainder will be:
Choose one: A) 1 B) 5 C) 3 D) 4 E) 11

Solution: 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.   1NSWER 1
Answer: A
Find the fourth proportional to 2.4, 4.6 and 7.6?	Choose the correct choice from the following options
A) 14  B) 14.56  C) 15.14  D) 15.17  E) 15.26

Solution: Formula = Fourth proportional = (b × c)/a   A = 2.4 , 14.56 = 4.6 and C = 7.6   (4.6 × 7.6)/2.4 = 14.56   14.56
Answer: B
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?	Choose the correct choice from the following choices
A) 24	B) 45	C) 48	D) 51	E) 44

Solution: Relative speed = 45 + 30= 
45 + 30 = 75
75 km/hr.   75 * 5/18= 125/6 m/sec.   Distance covered = 250 + 250= 
250 + 250 = 500
500 m.   Required time= 500 * 6/125= 
500 * 6/125 = 24
24 sec.   24nswer: Option 24
Answer: A
Find the sum of all 2 digit numbers divisible by 3.
Choose the correct choice from the following answers.
A) 1565  B) 1665  C) 1300  D) 1448  E) 1465

Solution: 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= 
( 99-12) /3 + 1 = 30
30   Required sum= 30/2*( 12 + 99 ) = 15*111= 
15*111 = 1_665
1665   ANSWER:1665
Answer: B
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?  Select:
A) 12  B) 18  C) 22  D) 35  E) 26

Solution: SP per bowl = 12000/600 = Rs. 20 Loss per bowl = Rs. 2 CP per bowl = 20 + 2= Rs. 22Answer: 22
Answer: C
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?
Pick one:
A) 1328
B) 1000
C) 2378
D) 8287
E) 1872

Solution: Total entries are 3000 So fee collected through entry fee = 3000 x 1 = Rs.3000   Income generated through rides = 7200 - 3000= 
7200 - 3000 = 4_200
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 )= 
3000 - (600 + 600 + 800 ) = 1_000
1000   Answer:1000
Answer: B
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? Choose the most appropriate option:
A) 30 days	B) 20 days	C) 25 days	D) 35 days	E) 45 days

Solution: 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.   30 daysNSWER:30 days
Answer: A
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?
Choose the correct choice from the following:
A) 36.6
B) 36.1
C) 36.5
D) 36.2
E) 36.9

Solution: Correct sum   = (36 * 50 + 48 - 23)= 
(36 * 50 + 48 - 23) = 1_825
1825.   36.5orrect mean= 1825/50= 
1825/50 = 73/2 = around 36.5
36.5   Answer:36.5
Answer: C
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?  Choose the correct choice from the following: A) $50 B) $64 C) $75 D) $96 E) Cannot be determined

Solution: Solution: 3x+4y+2z=40 7x+2y+2z=60   adding both the equations= 10x+6y+4z=100   5x+3y+2z=50   ans $50
Answer: A
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

Solution: 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 : 4C3+9
Answer: B
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?	Choose the correct choice.
A) 360
B) 1720
C) 2880
D) 5040
E) 10080

Solution: 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.   360nswer: 360.
Answer: A
The area of a triangle is with base 8.4m and height 5.8m?	Choose the correct choice from the following choices:
A) 11.36 m2
B) 10.36m2
C) 18.36 m2
D) 19.36 m2
E) 24.36 m2

Solution: 1/2 * 8.4 * 5.8= 
1/2 * 8.4 * 5.8 = 24.36
24.36 m2   Answer: 24.36 m2
Answer: E
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?	Choose the correct option
A) A.1296	B) B.1850	C) C.4200	D) D.3546	E) E.2880

Solution: 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.2880.
Answer: E
What is the perimeter of a rectangular field whose diagonal is 5m and length is 4m ? Choose the correct choice from the following
A) 20 m B) 15 m C) 14 m D) 10 m E) 25 m

Solution: Sol:   Breadth of the rectangular plot is=5^2-4^2=3m   Therefore,   Perimeter of the rectangular plot= 2(4+3)=14m   14 m) 14m
Answer: C
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? Choose the correct answer.
A) 5  B) 4  C) 3  D) 2  E) 1

Solution: 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= 
62 - 60 = 2
2   Therefore the minimum value that the fourth integer can have is 2. Option 2.
Answer: D
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?
Choices.
A) 1/16	B) 1/12	C) 1/8	D) 1/6	E) 1/3

Solution: 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 1/12.
Answer: B
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

Solution: Total income of Amber in a year = d*20*m dollars.   Now Monthly income = Total/12 = d*20*m / 12 = 10md/6   Answer is 10md/6
Answer: C
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

Solution: 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: 8
Answer: D
In a lottery, there are 10 prizes and 25 blanks. A lottery is drawn at random. What is the probability of getting a prize?  Choose the correct choice.
A) 2/7 B) 3/7 C) 4/8 D) 9/2 E) 3/8

Solution: P (getting a prize) =	10/(10 + 25)= 10/35 =2/7	.   2/7
Answer: A
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
Choose the correct choice from the following options
A) S= T + U	B) 2S= T + U	C) S= 2T + 2U	D) None of these	E) Cannot ne determined

Solution: Explanation :   Clearly, we have S =(3T+3U/6)   or 2S= T + U   Answer : 2S= T + U
Answer: B
3889 + 15.952 - ? = 3854.002
Choose the most appropriate option
A) 47.95  B) 50.95  C) 45.97  D) 47.59  E) 45.79

Solution: Let 3889 + 15.952 - x = 3854.002.   Then x = (3889 + 15.952) - 3854.002   = 3904.952 - 3854.002   = 50.95.   Answer is 50.95
Answer: B
October 9, 2012, fell on a Tuesday. On which day of the week did June 25, 2013, fall? (Note: 2012 was a leap year.)  Pick one:
A) Sunday B) Monday C) Tuesday D) Wednesday E) Thursday

Solution: 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= 
22 + 28 + (2 * 30) + (4 * 31) + 25 = 259
259 total days in the date range.   Divide by 7 to determine how much the day of the week advances:   259 / 7= 
  259 / 7 = 37
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 Tuesday.
Answer: C
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 ?
Choose the correct choice from the following options.
A) -2  B) -1  C) 0  D) 1  E) 2

Solution: (1) x = 11y + 4   (2) 2x = 15y + 4   Let's subtract equation (1) from equation (2).   4y = x   4y - x = 0   The answer is 0.
Answer: C
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 ?
Select the correct option:
A) a) 2 : 3
B) b) 3 : 4
C) c) 4 : 3
D) d) 3 : 2
E) e) 2 : 1

Solution: Ahhhh....my bad. Thank you, you're correct. 8q = 6y --> q/y = 3/4.   Actually b) 3 : 4 is the right answer.
Answer: B
If a particular player is always chosen, in how many ways can a cricket-be chosen out of 15 players? Answers:
A) 1243 B) 1345 C) 1788 D) 1346 E) 1365

Solution: 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   1365
Answer: E
Which of the following ratios is greatest ?  Options:  A) 7 :15  B) 15 :23  C) 17 :25  D) 21 :29  E) 1 : 2

Solution: 7/15 = 0.466,   15/23 = 0.652,   17/25= 
17/25 = 17/25 = around 0.68
0.68   21/29= 0.724   Clearly, 0.724 is greatest   therefore, 21 : 29 is greatest   ANSWER:21 :29
Answer: D
If f(a)=a^2, what is the value of (f(a-b)−f(a))/b ?  Choose the correct choice from the following options:
A) a
B) b
C) 2a
D) -2a + b
E) 2b - a

Solution: 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 : -2a + b
Answer: D
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?
Choose one:
A) 48
B) 60
C) 56
D) 64
E) 68

Solution: By the formula, speed= 64istance/ Time   = (240 + 240)/27 x (18/5)   = 480/27 x 18/5 = 64 km/h   Answer :64
Answer: D
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?
Choose the most appropriate option:
A) 31%.  B) 71%.  C) 49%.  D) 29%.  E) 28%.

Solution: 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%   ANSW28%.R:28%.
Answer: E
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?
Pick one:
A) 98 B) 104 C) 100 D) 61 E) 51

Solution: cube use to make perfect 5 * 5 * 5= 
5 * 5 * 5 = 125
125   No need of cube to make hollow=(5-2)*(5-2)*(5-2)= 
(5-2)*(5-2)*(5-2) = 27
27   so total cube need to make hollow cube is=125-27= 
125-27 = 98
98   98NSWER:98
Answer: A
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?
Pick:  A) 5/2  B) 8/3  C) 9/4  D) 10/3  E) 12/5

Solution: 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 9/4.
Answer: C
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? Select the correct option:  A) 24  B) 44  C) 58  D) 60  E) 62

Solution: Alice walked 18 miles on the first day, walking 3 miles per hour i.e. total time of walk on Day-1 = 18/3= 
18/3 = 6
6 Hours   Second day time of walk= 6-1= 
6-1 = 5
5 hours and Speed= 3+1= 
3+1 = 4
4 miles per hour i.e. Distance walked on second day= 5*4= 
5*4 = 20
20 miles   Third day time of walk= 6 hours and Speed = 4 miles per hour i.e. Distance walked on second day = 6*4= 
6*4 = 24
24 miles   Total Distance travelled on three days= 18+20+24= 
18+20+24 = 62
62   Answer: Option 62
Answer: E
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?	Answers.
A) 2500 B) 3000 C) 3500 D) 4000 E) 4500

Solution: 2500:B:C = 2/3:1/6:1/6 = 4:1:1   x * 2/100 * 2/3 = 200   B capital = 15000*1/6= 
15000*1/6 = 2_500
2500   2500NSWER 2500
Answer: A
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?	Choose the most appropriate option
A) 4.7	B) 3.6	C) 9.5	D) 5.0	E) 4.4

Solution: 9.5   In this simple addition series, each number increases by 2.0   Answer : 9.5
Answer: C
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?
Choose the correct choice:
A) 660 m
B) 650 m
C) 570 m
D) 670 m
E) 680 m

Solution: 670 mistance covered by Amar = (18/48)*1800 = 670 m   ANSWER:670 m
Answer: D
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?  Choose one
A) 21:22 B) 7:8 C) 2:1 D) 21:24 E) 14:16

Solution: 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. 21:22nswer is 21:22.
Answer: A
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.	Choose one: A) 5 B) 7 C) 8 D) 10 E) 12

Solution: 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 (10).
Answer: D
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?
Choices
A) 3	B) 4	C) 5	D) 6	E) 8

Solution: 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= 
6+ 4 = 10
10 kms/hr   Time taken to meet Brad after Brad Started= 20 / 10= 
20 / 10 = 2
2 hrs   Distance traveled by Maxwell= Maxwell's speed * time taken = 4 * 2= 
4 * 2 = 8
8+4= 
8+4 = 12
12 kms...   Therefore Total Time taken by Maxwell to meet Brad= Distance travelled by Maxwell / Maxwell's Speed = 12 /4= 
12 /4 = 3
3 hrs ... 3nswer 3
Answer: A
Find the compound interest on $15,624 for 9 months at 16% per annum compounded quarterly.  Choose the correct choice from the following answers.
A) $4152	B) $1951	C) $2258	D) $8978	E) $8875

Solution: 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))= 
(15625*(26/25)*(26/25)*(26/25)) = 17_576
$17576.   C.I= $(17576-15625)= 
(17576-15625) = 1_951
$1951.   answer($1951)
Answer: B
Boy sells a book for Rs. 450 he gets a loss of 10 %, To gain 10 %, what should be the SP?  Choices: A) Rs.320 B) Rs.450 C) Rs.550 D) Rs.640 E) Rs.680

Solution: 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   Rs.550
Answer: C
In what time will a railway train 65 m long moving at the rate of 36 kmph pass a telegraph post on its way? Pick
A) 8 sec B) 7 sec C) 2 sec D) 6.5 sec E) 9 sec

Solution: T = 65/36 * 18/5= 
65/36 * 18/5 = 13/2 = around 6.5
6.5 sec   Answer:6.5 sec
Answer: D
In a group of 22 boys, 13 play basketball and 15 play football. 3 of the boys play neither. how many play both ?  Choose the correct choice: A) 18 B) 20 C) 21 D) 22 E) 25

Solution: 18 boys play something. If b play both, then   13+15-b = 18   18nswer is 18
Answer: A
If n is an integer and 5^n > 40,000,000, what is the least possible value of n? Choose the correct answer:
A) 7  B) 8  C) 9  D) 10  E) 11

Solution: 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   11
Answer: E
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?
Choose the correct option.
A) 180
B) 160
C) 149
D) 150
E) 175

Solution: # 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= 
1+6+3 = 10
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= 
10*6 *3 = 180
180   180
Answer: A
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?
Select the correct option:
A) 2 : 5 B) 5 : 2 C) 3 : 5 D) 1 : 1 E) None of these

Solution: 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:1 : 1
Answer: D
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?  Select:
A) 6  B) 12  C) 18  D) 24  E) 27

Solution: Total Students = 36   Two thirds of the students are boys = 2/3*36= 
2/3*36 = 24
24   One half of the boys are under six feet tall= 1/2*24= 
1/2*24 = 12
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 12
Answer: B
If 2^z is a factor of 22!, which of the following could be the value of z?
I. 22
II. 23
III. 24 Select.
A) I ​ only	B) II only	C) I​ and II	D) I, II, and III	E) None

Solution: 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 None.
Answer: E