MU-NLPC/Calc-aqua_rat huggingface dataset:
For integers a and b, 16a = 32^b. Which of the following correctly expresses a in terms of b?	Choose the correct choice from the following options
A) a = 2^b
B) a = 4^b
C) a = 2^(5b − 4)
D) a = 4^(5b − 4)
E) a = 2^(5b)

Solution: I tried this one with an example, although I am not quite sure if this is correct. I would appreciate if there would be a common rule for this.   I tried it out with b = 2 and only c correctly expresses the following:   16a = 32^b b = 2   16a = 1024   a = 64   choice c --> a = 2^6 = 64   However, this is a quite time consuming process. Is there something faster?   Answer a = 2^(5b − 4)
Answer: C
A, B and C invested Rs.6300, Rs.4200 and Rs.10500 respectively, in a partnership business. Find the share of A in profit of Rs.12100 after a year?  Choose the correct choice from the following answers: A) 3630 B) 2979 C) 2789 D) 2662 E) 2123

Solution: 6300:4200:10500   3:2:5   3/10 * 12100= 
3/10 * 12100 = 3_630
3630   3630nswer:3630
Answer: A
A man has Rs. 412 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ? Select the correct option:
A) 45	B) 60	C) 77.25	D) 90	E) 105

Solution: Let number of notes of each denomination be x.   Then x + 5x + 10x = 412   16x = 412   x = 25.75.   Hence, total number of notes = 3x = 77.25.   Answer = 77.25
Answer: C
The average (arithmetic mean) of 8 numbers is Z, and one of the numbers is 14. If 14 is replaced with 28, then what is the new average (arithmetic mean) in terms of Z?
Choose the correct choice from the following
A) Z + 1/2  B) Z + 7/4  C) Z + 2  D) Z + 4  E) 2Z + 1

Solution: (8z−14+28)/8   Or, (8z+14)/8   Or, (4z+7)/4   Or, z+7/4   So, correct answer will be (Z + 7/4) z+7/4
Answer: B
Find the odd man out. 1050, 510, 242, 107, 46, 16, 3
Choose the correct choice from the following choices.
A) 107  B) 106  C) 510  D) 1050  E) None of these

Solution: Explanation :   1050   (1050 - 30)/2= 
(1050 - 30)/2 = 510
510   (510 - 26)/2= 
(510 - 26)/2 = 242
242   (242 - 22)/2= 
(242 - 22)/2 = 110
110   (110 - 18)/2= 
(110 - 18)/2 = 46
46   (46- 14)/2= 
(46- 14)/2 = 16
16   (16- 10)/2= 
(16- 10)/2 = 3
3   Hence, 110 should have come in place of 107. 107nswer : Option 107
Answer: A
A plane flying north at 500 kmph passes over a city at 12 noon. A plane flying east at the same attitude passes over the same city at 12.30 pm. The plane is flying east at 400 kmph. To the nearest hundred km, how far apart are the two planes at 2 pm?	Choose the correct option:
A) 600 km B) 1000 km C) 1100 km D) 1200 km E) 1300 km

Solution: The plane flying north would have traveled for 2 hours at 2 PM.   It travels at 500 kmph.   Hence, the plane flying north would have covered 1000 kms from the city at 2 PM.   The plane flying east would have traveled for 1.5 hours at 2 PM.   It travels at 400 kmph.   Hence, the plane flying east would have covered 1.5*400= 
1.5*400 = 600
600 kms from the city at 2 PM.   The two planes are flying at right angles to each other.   The shortest distance between the two planes is the length of the hypotenuse of the right triangle whose legs are the distances covered by the two planes.   Hence, distance= 1000square + 200 square = 1166 km   The nearest 100 km distance between the two planes = 1200 kms.   Answer 1200 km
Answer: D
John started driving on a highway at a constant speed of R miles per hour at 13:00. Then, 2 hours later, Tom started driving on the same highway at a constant speed of 2R miles per hour at 15:00. If both drivers maintained their speed, how many miles had John driven on the highway when Tom caught up with John?	Choose the correct choice from the following choices:
A) 2R
B) 3R
C) 4R
D) 5R
E) 6R

Solution: In 2 hours, John drove 2R miles.   Tom can catch John at a rate of 2R - R = R miles per hour.   The time it takes Tom to catch John is 2R / R = 2 hours.   In 2 hours, John can drive another 2R miles for a total of 4R miles.   The answer is 4R.
Answer: C
If n=5p where p is a prime number greater than 1, how many different positive even divisors does n have, including n?
Choose the correct choice from the following:  A) 1  B) 2  C) 32  D) 4  E) 3

Solution: N = 5P and that P is a prime number greater than 1. Let's TEST P = 2; so N = 10   The question now asks how many DIFFERENT positive EVEN divisors does 10 have, including 10?   10:   1,10   5,2   How many of these divisors are EVEN? 2, 10…..2 even divisors.   ANSWER:2
Answer: B
Before January, the price of a dress was D and the price of a matching pair of shoes was H. In January, the price of the dress increased by 40% and the price of the shoes increased by 50%. In March, Roberta bought both items with a 30% discount. If D = 5H, which of the following represents the amount that Roberta paid?  Choices
A) D + 40
B) D + H – 1
C) D + 2H
D) 5.95H
E) 1.21D

Solution: Before 5.95Hiscount price was: 1.45.95H+1.5H   After 5.95Hiscount: 1.45.95H +1.5H-.425.95H-.45H   substitute 5.95H=5H   final value: 5.95H   Ans Is 5.95H : 5.95H
Answer: D
In march Mrs Bil's earnings were 80 percent of the Bil family's total income. In april Mrs Bil earned 10 percent more than in May. If the rest of the family's income was the same both months, then, in June, Mrs Bil's earnings were approximately what percent of the Bil family's total income ? Choose the correct answer:
A) 83
B) 56
C) 34
D) 12
E) 26

Solution: Lets say the Family Income is 100   In May, lee earned 80Family income is 20   In june, Lee earned 20% more than May, so it is (80+20*80/100 = 96)   Family Income is same 20   In June Lee's Income percent is 96*100/116 ~ 83   83ns is 83
Answer: A
A started a business with Rs. 18000. After 4 months B joins with Rs. 24000. After 2 more months C joins with Rs. 30000. At the end of 10 months C received Rs. 1850 as his share. Find the total profit. Select:
A) Rs. 7955
B) Rs. 7030
C) Rs. 8510
D) Rs. 6845
E) None of these

Solution: Explanation:   Ratio of capitals of A, B and C   = (18000 × 10) : (24000 × 6) : (30000 × 4)   = 15 : 12 : 10   Let the total profit be Rs. x.   C's share = Rs. 10x/37   => 10x/37 = 1850   => x (1850 × 37)/10 = 6845   Hence, the total profit = Rs. 6845   Answer: Option Rs. 6845
Answer: D
A beggar on the street can make one cigarette out of every 6 cigarette butts he finds. After one whole day of searching and checking public ashtrays the beggar finds a total of 72 cigarette butts. How many cigarettes can he make and smoke from the butts he found?	Choose the correct choice from the following answers:  A) 4  B) 10  C) 14  D) 16  E) 8

Solution: If the begger can make a whole cigarette from 6 butts then he can make 12 cigarettes from the 72 he found. Once he smokes those, he then will have another 12 butts, which gives him enough to make another 2 cigarettes 12+2= 
12+2 = 14
14. A total of 14.
Answer: C
Which of the following numbers is between 2⁄3 and 1⁄2?
Choose the correct option.
A) .45  B) .35  C) .29  D) .22  E) .55

Solution: Isn't it .55?   2/3 = .66   1/2= 
1/2 = 1/2 = around 0.5
.50   The only answer between that is .55, .55.
Answer: E
What is the dividend. divisor 17, the quotient is 9 and the remainder is 5?  Choose the most appropriate option.
A) 130  B) 134  C) 148  D) 158  E) 160

Solution: 158 = d * Q + R   158 = 17 * 9 + 5   158 = 153 + 5   158 = 158
Answer: D
Bruce and Anne can clean their house in 4 hours working together at their respective constant rates. If Anne’s speed were doubled, they could clean their house in 3 hours working at their respective rates. How many W hours does it currently take Anne to clean the house on her own?  Choose the correct choice from the following choices.
A) 6 B) 7 C) 8 D) 12 E) 14

Solution: Lets suppose Anne and Bruce take A and B hrs working separately   So in 1 hour they can together finish 1/A + 1/B portion of the work which equals 1/4 (As the work is completed in 4 hours)   After anne doubles her rate of work the portion completed by the both is 1/A +2/B which is W equal to 1/3 (As the work is completed in W=3 hours)   Solving these 2 equations we can find B as 12   So, 12
Answer: D
Find (7x + 4y ) / (x-2y) if x/2y = 5/2 ? Pick
A) 13 B) 25 C) 26 D) 27 E) 29

Solution: x/2y=3/2   =>x=10y/2=5y   10 /2= 
10 /2 = 5
5y=>(7x+4y)/(x-2y)=((7*(5y))+4y)/(5y-2y)   =>39y/3y=13   13NSWER:1339 /3= 
39 /3 = 13
13   13NSWER:13
Answer: A
If a committee of 3 people is to be selected from among 5 married couples so that the committee does not include two people who are married to each other, how many B such committees are possible?  Choose the correct choice:
A) B=20	B) 40	C) 50	D) B=80	E) 120

Solution: Each couple can send only onerepresentativeto the committee. Let's see in how many ways we can choose 3 couples (as there should be 3 members) each to send onerepresentativeto the committee: 5C3=10.   But these 3 chosen couples can send two persons (either husband or wife): 2*2*2=2^3=8.   Total # of ways: 5C3*2^3=80.   Answer: B=80.
Answer: D
There are two concentric circles such that the area of the outer circle is four times the area of the inner circle. Let A, B and C be three distinct points on the perimeter of the outer circle such that AB and AC are tangents to the inner circle. If the area of the outer circle is 12 square centimetres then the area (in square centimetres) of the triangle ABC would be  Choose the correct choice from the following answers
A) π√​12
B) 9/π
C) 9√3/π square centimetres
D) 6√3/π
E) None of these

Solution: Explanation :   Outer circle:   Since πR² = 12, R = √(12/π) = 2√(3/π).   Inner circle:   Since the area is 1/4 the area of the outer circle, πr² = 3 and r = √(3/π).   AO is the Radius of the outer circle and OD is the radius of the inner circle.   A line tangent to a circle and a radius drawn to the point of tangency form a right angle.   Thus, ∆AOD is a right triangle.   Hypotenuse AO is twice the length of leg OD.   A right triangle whose hypotenuse is twice the length of a leg is a 30-60-90 triangle.   Thus, ∆AOD is a 30-60-90 triangle.   In a 30-60-90 triangle, the sides are proportioned x : x√3 : 2x.   Thus, AD = √3 * √(3/π) * = 3/√π.   Using the same reasoning for ∆OCD, we can deduce that CD = 3/√π.   Thus, AC = 2 * 3/√π = 6/√π.   The formula for the area of an equilateral triangle = (s²√3)/4.   Since AC = 6/√π, the area of ∆ABC = (6/√π)² * √3/4 = 36/π * √3/4 = (9√3)/π.   Answer : 9√3/π square centimetres
Answer: C
A policeman noticed a criminal from a distance of 180 km. The criminal starts running and the policeman chases him. The criminal and the policeman run at the rate of 8 km and 9 km per hour respectively. What is the distance between them after 5 minutes ? Pick one
A) 96.7 m	B) 120 m	C) 130 m	D) 150 m	E) None of these

Solution: Explanation :   Solution: Relative speed = (9 - 8)= 
(9 - 8) = 1
1 km/hr.   Distance covered in 3 minutes= (1 * 5/60) km = 1/12 km = 83.3 m.   .'. Distance between the criminal and policeman = (180 - 83.3)= 
(180 - 83.3) = 96.7
96.7 m.   96.7 mnswer : 96.7 m
Answer: A
Raffle tickets numbered consecutively from 101 through 450 are placed in a box. What is the probability that a ticket selected at random will have a number with a hundreds digit of 2 ?
Choose the correct choice from the following answers.
A) 2/5  B) 2/7  C) 10/35  D) 99/250  E) 100/249

Solution: SOLUTION   The number of integers from 101 to 450, inclusive is 250, out of which 100 (from 200 to 299) will have a hundreds digit of 2. Thus the probability is 100/350   Answer: 10/35
Answer: C
Mr. Wayne bungee jumps from the top of a building straight to the ground at a constant speed. 3 seconds after he starts plummeting he passes the 20th floor. 15 seconds after he starts plummeting he passes the 5th floor. Each floor is 3.6 meters high. What is Mr. Wayne's speed in meters per second? Choose the most appropriate option:
A) 3 B) 3.75 C) 4.5 D) 4.25 E) 5

Solution: IMO: 4.5   15 Floors * 3.6 Meter/Floor = 54 Meters   Time= 12 sec   Rate * 12 = 54   Rate= 54/12= 
54/12 = 9/2 = around 4.5
4.5   Answer 4.5
Answer: C
The speed of a boat in still water is 50kmph and the speed of the current is 20kmph. Find the speed downstream and upstream? Answers:
A) 40, 68 kmph  B) 40, 30 kmph  C) 70, 30 kmph  D) 40, 60 kmph  E) 20, 60 kmph

Solution: Speed downstream = 50 + 20= 
50 + 20 = 70
70 kmph   Speed upstream= 50 - 20= 
50 - 20 = 30
30 kmph   Answer: 70, 30 kmph
Answer: C
A man rows his boat 85 km downstream and 45 km upstream, taking 2 1/2 hours each time. Find the speed of the stream?
Choose the correct choice from the following choices:
A) 76 kmph	B) 6 kmph	C) 14 kmph	D) 8 kmph	E) 4 kmph

Solution: Speed downstream = d/t = 85/(2 1/2)   = 34 kmph   Speed upstream = d/t = 45/(2 1/2)   = 18 kmph   The speed of the stream = (34 - 18)/2= 
(34 - 18)/2 = 8
8 kmph   Answer:8 kmph
Answer: D
A 300 m long train crosses a platform in 39 sec while it crosses a signal pole in 18 sec. What is the length of the platform? Choose the correct choice from the following choices:
A) 389 m B) 350 m C) 289 m D) 299 m E) 219 m

Solution: Speed = 300/18 = 50/3 m/sec.   Let the length of the platform be x meters.   Then, (x + 300)/39 = 50/3   3x + 900 = 1950 => x = 350 m.   Answer:350 m
Answer: B
A, B and C enter into a partnership. They invest Rs. 40,000, Rs. 80,000 and Rs. 1,20,000 respectively. At the end of the first year, B withdraws Rs. 40,000, while at the end of the second year, C withdraws Rs. 80,000. In what ratio will the profit be shared at the end of 3 years ? Choose the correct choice from the following options:
A) 8:7:4  B) 1:3:5  C) 3:4:7  D) 4:5:9  E) 5:7:10

Solution: Explanation:   A:B:C =(40000Ã—36) :(80000Ã—12+40000Ã—24) :(120000Ã—24+40000Ã—12)   =144:192:336=144:192:336 =3:4:7.   ANSWER IS 3:4:7
Answer: C
If a committee of 3 people is to be selected from among 5 married couples so that the committee does not include two people who are married to each other, how many such committees are possible?
A.
B.
C.
D.
E. Choices:  A) 20  B) 40  C) 50  D) 80  E) 120

Solution: Each couple can send only one "representative" to the committee. Let's see in how many ways we can choose 3 couples (as there should be 3 members) each to send one "representative" to the committee: 5C3=10.   But these 3 chosen couples can send two persons (either husband or wife): 2*2*2=2^3=8.   Total # of ways: 5C3*2^3=80.   Answer: 80.
Answer: D
Ratio between Rahul and Deepak is 4:3, After 6 Years Rahul age will be 26 years. What is Deepak present age.  Choose the correct choice from the following:
A) 14
B) 15
C) 20
D) 22
E) 23

Solution: Explanation:   Present age is 4x and 3x,   => 4x + 6 = 26 => x = 5   So Deepak age is = 3(5) = 15   Answer: Option 15
Answer: B
The average weight of four boys A, B, C, and D is 75 kg. The fifth boy E is included and the average weight decreases by 4 kg. A is replaced by F. The weight of F is 6 kg more than E. Average weight decreases because of the replacement of A and now the average weight is 72 kg. Find the weight of A.  Choose the correct choice from the following answers
A) 57 kg  B) 54 kg  C) 56 kg  D) 60 kg  E) 58 kg

Solution: Sum of the weight of A, B, C and D = 75 × 4 = 300 kg   and average weight of A, B, C, D and E = 71 kg   sum of the weight of A, B, C, D and E   = 71 × 5 = 355 kg   weight of E = 355 – 300 = 55 kg   weight of F = 55 + 6= 
55 + 6 = 61
61 kg   Now, average weight of F, B, C, D and E= 72 kg   Sum of the weight of F, B, C, D and E = 72 × 5 = 360 kg   B + C + D = 360 – 55 – 61 = 244 kg.   Weight of A = 300 – 244 = 56 kg.   ANSWER:56 kg
Answer: C
A train leaves Mumabai at 9 am at a speed of 40 kmph. After one hour, another train leaves Mumbai in the same direction as that of the first train at a speed of 60 kmph. When and at what distance from Mumbai do the two trains meet?
Choose the correct choice from the following answers:  A) 187  B) 279  C) 120  D) 278  E) 379

Solution: When the second train leaves Mumbai the first train covers 40 * 1= 
40 * 1 = 40
40 km   So, the distance between first train and second train is 40 km at 10.00am   Time taken by the trains to meet= Distance / relative speed = 40 / (60 -40)= 
40 / (60 -40) = 2
2 hours   So, the two trains meet at 12 a.m. The two trains meet 2 * 60= 
2 * 60 = 120
120 km away from Mumbai.   Answer:120
Answer: C
On a man's tombstone, it is said that one sixth of his life was spent in childhood and one twelfth as a teenager. One seventh of his life passed between the time he became an adult and the time he married; five years later, his son was born. Alas, the son died four years before he did. He lived to be twice as old as his son did. How old did the man live to be?  Choose one.
A) 82	B) 83	C) 84	D) 85	E) 86

Solution: Let the age of man is x so that of son = x/2 (given)   now according to the given condition   (x/6) + (x/12) + (x/7) + 5 + (x/2) + 4 = x   or x = 84   ANSWER:84
Answer: C
If the annual interest on a principal is 16%, how many years before the amount is double?	Choose one:  A) 6.25  B) 20  C) 17.2  D) 15.2  E) 15.2

Solution: P = (P*16*R)/100   R = 6.25   6.25nswer: 6.25
Answer: A
Josh spends a total of $7.50 buying N items in the convenience store. If each of the items is either a 5 cents single bubblegum, or a 50 cents bubblegum pack, then N may be which of the following?	Choices:
A) 99	B) 100	C) 101	D) 109	E) 141

Solution: Let x be 0.05$ single bubblegum and y be the total 0.5$ packs ---> 0.05x+0.5y=7.5 ---> x+10y=150 ...(1)   Also, x+y=N ...(2)   Solving 1 and 2 , we get, N = 150-9y ---> only value satisfied is when y = 1---> N = 150-9= 
150-9 = 141
141. E is the correct answer. Other options are not equal to multiples of 9 removed from 150.
Answer: E
The area of Circle O is added to its diameter. If twice the circumference of Circle O is then subtracted from this total, the result is 8. What is the diameter of Circle O?
Answers
A) 4/π  B) 4  C) 8  D) 10  E) 6

Solution: area+diameter-2*circumference=8   pi*r^2+2r=8+2*2pi*r   isolate r and get r(pi*r+2)=8+4pi*r   r=(8+4pi*r)/(pi*r+2) =>4(pi*r+2)/(pi*r+2)   r=4   Diameter = 2r = 8   8
Answer: C
What is the dividend. divisor 18, the quotient is 9 and the remainder is 4  Choose the correct option:
A) A)166	B) B)148	C) C)150	D) D)153	E) E)158

Solution: D = d * Q + R   D = 18 * 9 + 4= 
18 * 9 + 4 = 166
166   166nswer : 166
Answer: A
A reduction of 20% in the price of oil enables a house wife to obtain 5kgs more for Rs.800, what is the reduced price for kg?	Choose the correct choice from the following answers:
A) 30	B) 31	C) 32	D) 33	E) 34

Solution: 800*(20/100)= 
800*(20/100) = 160
160 ---- 5   ? ---- 1=> Rs.32   Answer: 32
Answer: C
A can contains a mixture of two liquids A and B is the ratio 7 : 5. When 9 litres of mixture are drawn off and the can is filled with B, the ratio of A and B becomes 7 : 9. How many litres of liquid A was contained by the can initially? Choose the correct option: A) 18 B) 19 C) 21 D) 26 E) 28

Solution: Suppose the can initially contains 7x and 5x of mixtures A and B respectively.   Quantity of A in mixture left = 7x -	7	x 9 litres = 7x -	21 litres.   12	4   Quantity of B in mixture left = 5x -	5	x 9 litres = 5x -	15 litres.   12	4   7x -	21   4   =	7   5x -	15 + 9   4   9   28x - 21	=	7   20x + 21	9   252x - 189 28  - 21= 
28  - 21 = 7
7   20x + 21	9   252x - 189= 140x + 147   112x = 336   x = 3.   So, the can contained 21 litres of A.   Option 21
Answer: C
The angle between the minute hand and the hour hand of a clock when the time is 4.20, is:	Choose the correct option
A) 0
B) 5
C) 12
D) 8
E) 10

Solution: angle 13/3 hrs = 360/12 * 13/3= 
360/12 * 13/3 = 130
130deg   angle hand in 20 min   360/60*20= 
  360/60*20 = 120
120 deg   req= 130-120= 
130-120 = 10
10deg   ANSW10R 10
Answer: E
In a mixture of 45 litres the ratio of milk to water is 4:1. Additional 18 litres of water is added to the mixture. Find the ratio of milk to water in the resulting mixture.	Answers.
A) 2/1  B) 4/3  C) 2/3  D) 3/4  E) 3/2

Solution: Given that Milk/Water=4x/x and 4x+x=45 --> x=9.   Thus Milk=4x=36 liters and Water=x=9 liters.   New ratio = 36/(9+18) = 36/27 = 4/3.   Answer: 4/3.
Answer: B
Without any stoppages a person travels a certain distance at an average speed of 40 km/hr and with stoppages he covers the same distance at an average of 20 km/hr. How many minutes per hour does he stop?
Choose the correct choice from the following answers.
A) 15 minute
B) 20 minutes
C) 30 minutes
D) 45 minutes
E) None of these

Solution: Explanation :   In one hour the distance covered at actual speed = 40km and with stoppages it covers only 20 km   so to travel 20 km at original speed i.e. 20 = 40*t, so t = 1/2 hour = 30   minutes   Answer – 30 minutes
Answer: C
Divide Rs. 720 among A, B and C so that A receives 1/3 as much as B and C together and B receives 2/3 as A and C together. A's share is?  Choose the correct choice from the following
A) s.800	B) s.400	C) s.600	D) s.180	E) s.900

Solution: A+B+C = 720   A = 1/3(B+C); B = 2/3(A+C)   A/(B+C) = 1/3   A = 1/4 * 720= 
1/4 * 720 = 180
> 180   ANSWER:s.180
Answer: D
The average mark of a class of thirty two students is 75. If three students whose marks are 28 and 34 are removed , then find the approximate average mark of the remaining students of the class.  Choose the correct choice from the following options.
A) 71
B) 74
C) 78
D) 70
E) 80

Solution: Exp. Total mark of 32 students = 75*32= 
75*32 = 2_400
2400,   Total mark after the removal of 2 students= 2400 –(28+34)   = 2400 – 62 = 2338   Approximate average mark = 2338/(32-2) = 2338/30 = 78   Answer: 78
Answer: C
The function f(x) = x + 4 is given. Solve the equation:
[3.f(x - 2)]/f(0) + 4 = f(2x + 1)  Choose the most appropriate option
A) 0.2 B) 0.3 C) 0.4 D) 0.5 E) None of these

Solution: Solution:   We calculate f(0), f(x -2), f(2x +1), namely f(0) = 0 + 4= 
0 + 4 = 4
4;   f(x - 2)= x - 2 + 4 = x + 2;   f(2x + 1) = 2x + 1 + 4 = 2x + 5 The equation gets this look   [3(x + 2)]/4 + 4 = 2x + 5 <=>   3(x + 2) +16 = 4(2x + 5) <=>   3x + 6 +16 = 8x + 20 <=>   22 - 20 = 8x - 3x <=>   2 = 5x <=> x = 0.4   Answer 0.4
Answer: C
If a quality control check is made inspecting a sample of 2 light bulbs from a box of 13 lighbulbs, how many different samples can be chosen?
Choose the correct answer:
A) 6	B) 24	C) 36	D) 66	E) 78

Solution: Try using the formula for combinations:   n!/r!(n-r)!   13!/2!(13-2)!   13!/2!*11!    13*12/2*1= 
 13*12/2*1 = 78
78   78
Answer: E
In a game of billiards, A can give B 20 points in 60 and he can give C 40 points in 60. How many points can B give C in a game of 100?	Choose the correct choice from the following
A) 18	B) 27	C) 50	D) 21	E) 17

Solution: A scores 80 while B score 40 and C scores 20.   The number of points that C scores when B scores 100 = (100 * 20)/40= 
(100 * 20)/40 = 50
50.   In a game of 100 points, B gives (100 - 50)= 
(100 - 50) = 50
50 points to C.   Answer: 50
Answer: C
The perimeter of a triangle is 40 cm and the inradius of the triangle is 2.5 cm. What is the area of the triangle Choose the most appropriate option:
A) A)72	B) B)828	C) C)50	D) D)34	E) E)35

Solution: Explanation:   Area of a triangle = r * s   Where r is the inradius and s is the semi perimeter of the triangle.   Area of triangle = 2.5 * 40/2= 
2.5 * 40/2 = 50
50 cm2   Answer: Option 50
Answer: C
The length Q of a rectangle is decreased by 15% and its width is increased by 40%. Does the area of the rectangle decrease or increase and by what percent?
Answers.
A) Decreases by 19%
B) Decreases by 25%
C) Increases by 6%
D) Increases by 19%
E) Increases by 25%

Solution: Let the length Q of the rectangle be 100x, and width be 100y. Area = 100x * 100y = 10000xy   Now after the change Length 100  * 100= 
100  * 100 = 10_000
10000xy   Now after the change Length= 85x, and width = 140 y. Area = 11900xy   % Change = (11900xy - 10000xy)/(10000xy) = 19 % Increase. Hence Increases by 19%.
Answer: D
The largest natural number which exactly divides the product of any four consecutive natural numbers is	Choose the correct choice from the following answers:  A) 6  B) 12  C) 24  D) 36  E) 48

Solution: Required numbers; 1×2×3×4 = 24, which is divisible by 24.   also checking 5 x 6 x 7 x 8 = 1680, which is also divisible by 24.   ANSWER:24
Answer: C