MU-NLPC/Calc-aqua_rat huggingface dataset:
What is the diffference between the place value and face value of 2 in the numeral 6328? Select.
A) 10	B) 12	C) 14	D) 16	E) 18

Solution: place value of 2 = 2 * 10= 
2 * 10 = 20
20   face value of 2= 2   20 - 2= 
20 - 2 = 18
18   18
Answer: E
A cistern has three pipes, A, B and C. The pipes A and B can fill it in 4 and 5 hours respectively and C can empty it in 2 hours. If the pipes are opened in order at 1, 2 and 3 A.M. When will the cistern be empty?	Choose the correct option.
A) 8 PM  B) 4 PM  C) 7 PM  D) 5 PM  E) 2 PM

Solution: 1 to 2 = 1/4   2 to 3 = 1/4 + 1/5 = 9/20   After 3 AM = 1/4 + 1/5 - 1/2 = -1/20   1/4 + 9/20 = 14/20   1 h ---- 1/20   ? ----- 14/20   14 hours ==> 5 PM   Answer: 5 PM
Answer: D
20. A certain church bell rings the bell twice at half past the hour and four
times at the hour plus an additional number of rings equal to what ever
time it is. How many rings will the clock make from 6:20 in the morning
to 9:10 in the morning?
Choose the most appropriate option
A) 32.	B) 36.	C) 42.	D) 46.	E) 50.

Solution: @ 6:30 - 2   @ 7 - 4+7 =11   @ 7:30 - 2   @ 8 - 12   @ 8:30 - 2   @ 9 - 13   totals to 42=42.
Answer: C
The cost C, in dollars, to remove p percent of a certain pollutant from a pond is estimated by using the formula C = 100,000p/(100 - p). According to this estimate, how much more would it cost to remove 90 percent of the pollutant from the pond than it would cost to remove 80 percent of the pollutant?
Pick one.
A) $500,000	B) $100,000	C) $50,000	D) $10,000	E) $5,000

Solution: Cost to remove 90% - Cost to remove 80% = 100,000*90/(100 - 90) - 100,000*80/(100 - 80) = 9*100,000 - 4*100,000 = 5*100,000 =500,000   $500,000nswer: $500,000
Answer: A
If y ≠ 3 and 3x/y is a prime integer greater than 2, which of the following must be true?
I. x = y
II. y = 1
III. x and y are prime integers. Choose the most appropriate option
A) None
B) I only
C) II only
D) III only
E) I and III

Solution: There are other possibilities here: 3 might be a factor of y, and might therefore cancel in the fraction, leaving us with a prime that comes from the factors of x. For example, if x = 10, and y = 6, then 3x/y = 5. So we can see that none of I, II, or III need to be true   NoneNSWER:None
Answer: A
A and B together can complete work in 10 days. A alone starts working and leaves it after working for 6 days completing only half of the work. In how many days it can be completed if the remaining job is undertaken by B?
Pick one:
A) 4
B) 8
C) 5
D) 6
E) 30

Solution: 30xplanation:   (A+B) one day work =1/10   now A does half of the work in 6 days so A can complete the whole work in 12 days   A’s one day work =1/12   B’s one day work=1/10 - 1/12= 2/120= 1/60   B alone can complete the work in 60 days so half of the work in 30 days   Answer: Option 30
Answer: E
Find the odd man out
2, 5, 10, 17, 26, 37, 50, 64	Choose the correct option:
A) 50  B) 26  C) 64  D) 27  E) 17

Solution: Difference is series of ODD numbers   2+3= 
2+3 = 5
5   5+5= 
5+5 = 10
10   10+7= 
10+7 = 17
17   17+9= 
17+9 = 26
26   26+11= 
26+11 = 37
37   37+13= 
37+13 = 50
50   50+15= 
50+15 = 65
65   ANSWER:64
Answer: C
The speeds of three motor bikes are in the ratio 12 : 4 : 2. The ratio between the time taken by them to travel the same distance is : Choose the correct answer.
A) 1 : 3 : 4 B) 1 : 3 : 6 C) 1 : 2 : 6 D) 1 : 3 : 5 E) 1 : 4 : 6

Solution: Ratio of time taken :   1/12 :1/4 : 1/2 = 1 : 3 : 6   ANSWER:1 : 3 : 6
Answer: B
Joe’s average (arithmetic mean) test score across 4 equally weighted tests was 40. He was allowed to drop his lowest score. After doing so, his average test score improved to 45. What is the lowest test score that was dropped? Choose the correct choice from the following answers.
A) 20 B) 25 C) 55 D) 65 E) 80

Solution: The arithmetic mean of 4 equally weighted tests was 40. So what we can assume is that we have 4 test scores, each 40.   He dropped his lowest score and the avg went to 45. This means that the lowest score was not 40 and other three scores had given the lowest score 5 each to make it up to 40 too. When the lowest score was removed, the other 3 scores got their 5 back. So the lowest score was  3 *5= 
 3 *5 = 15
15 less than 40.   So the lowest score= 40 - 15= 
40 - 15 = 25
25   Answer (25)
Answer: B
If x+|x|+y=4 and x+|y|-y=6 what is x+y=?  Select the correct option:
A) 11  B) -1  C) 3  D) 5  E) 13

Solution: If x<0 and y<0, then we'll have x-x+y=7 and x-y-y=6. From the first equation y=7, so we can discard this case since y is not less than 0.   If x>=0 and y<0, then we'll have x+x+y=7 and x-y-y=6. Solving gives x=4>0 and y=-1<0 --> x+y=3. Since in PS questions only one answer choice can be correct, then the answer is C (so, we can stop here and not even consider other two cases).   Answer: C.   11dding both eqn we get 2x +IxI+IyI = 13   Now considering X <0 and y>0   2x-x +y = 13   we get x+y =11   Hence answer should be 11
Answer: A
Bob is about to hang his 8 shirts in the wardrobe. He has four different styles of shirt, two identical ones of each particular style. How many different arrangements are possible if no two identical shirts are next to one another? Choose the most appropriate option:	A) 764	B) 864	C) 964	D) 1064	E) None of these

Solution: Explanation :   Total number of 8-perms of 8 shirts, recognising identical pairs, is:=8!2!4=2520In order to find the number of perms with no adjacency we subtract from this the number of perms with 4 pairs adjacent, 3 pairs adjacent, 2 pairs adjacent and 1 pair adjacent.The following four intermediate results aid explanation of the final calculation :Let the shirts be called A, A, B, B, C, C, D, D and let {A,.....} be the set of 8-perms that have only the styles named in the argument list adjacent to each other. So, for instance, {B,D} is the set of perms that contain BB and DD but not AA and CC. Let s{A,....} be the number of perms in {A,...}(i) s{A,B,C,D} = 24. This is because we can imagine each pair as one object and simply permute the four twin objects amongst themselves in 4! ways to give {A,B,C,D}.(ii) s{A,B,C} = 36. To see this we first permute the 5 objects AA, BB, CC, D, D. This can be done in5!2!=60 ways but includes {A,B,C,D}. Hence s{A,B,C} =5!2!−24(iii) s{A,B}=84. As before, we first permute the 6 objects AA, BB, C, C, D, D. This can be done in 6!/(2!)^2 ways but includes {A,B,C}, {A,B,D} and {A,B,C,D}.Hence s{A,B} =6!2!2–2×36−24(iv) s{A}=246. This time we start by permuting the 7 objects AA, B, B, C, C, D, D in7!2!3ways and then removing from it the subsets {A,B}, {A,C}, {A,D}, {A,B,C}, {A,B,D}, {A,C,D} and {A,B,C,D}. Hence s{A}=7!2!3−3×36−3×84–24Assembling the total number of perms with some adjacency:There are 4C4 subsets of type (i) ie {A,864,C,D}Total number of 8-perms of this type is 24.There are 4C3 subsets of type (ii) ie {A,864,C} {A,864,D} {A,C,D} {864,C,D}Total number of 8-perms of this type is 4×36=144There are 4C2 subsets of type (iii) ie {A,864} {A,C} {A,D} {864,C} {864,D} {C,D}Total number of 8-perms of this type is 6×84=504Finally there are 4C1 subsets of type (iv) ie {A} {864} {C} {D}Total number of 8-perms of this type=4×246=984Therefore, number of perms with some adjacency is  24+144+504+984= 
 24+144+504+984 = 1_656
1656Number of perms with no adjacency is 2520−1656= 864   Answer : 864
Answer: B
In a race of 1000 m, A can beat by 100 m, in a race of 800m, B can beat C by 100m. By how many meters will A beat C in a race of 600 m? Choices:
A) 128.9 m
B) 127.5 m
C) 812.9 m
D) 127.7 m
E) 712.7 m

Solution: When A runs 1000 m, B runs 900 m and when B runs 800 m, C runs 700 m.   When B runs 900 m, distance that C runs   = (900 * 700)/800   = 6300/8= 
6300/8 = 1_575/2 = around 787.5
787.5 m.   In a race of 1000 m, A beats C by   (1000 - 787.5)= 
  (1000 - 787.5) = 212.5
212.5 m to C.   In a race of 600 m, the number of meters by which A beats C= (600 * 212.5)/1000= 
(600 * 212.5)/1000 = 127.5
127.5 m.   Answer: 127.5 m
Answer: B
If the area of a circle decreases by 25%, then the radius of a circle decreases by  Choose the correct choice from the following options
A) 13%	B) 18%	C) 36%	D) 64%	E) None of these

Solution: If area of a circle decreased by x % then the radius of a circle decreases by   (100−10√100−x)%=(100−10√100−25)%   = (100−10√75)%   = 100 - 87= 
100 - 87 = 13
13%   13%nswer 13%
Answer: A
A and B complete a work in 50 days. A alone can do it in 40 days. If both together can do the work in how many days? Choose the most appropriate option.
A) 1.075 days	B) 0.185 days	C) 0.065 days	D) 0.045 days	E) 0.0775 days

Solution: 1/50 + 1/40= 
1/50 + 1/40 = 9/200 = around 0.045
0.045 days   ANSWER:0.045 days
Answer: D
Three dice are thrown together, Find the probability of getting a total of atmost 6?
Pick.
A) 1/3
B) 1/8
C) 3/13
D) 2/25
E) 5/54

Solution: Three different dice are thrown at the same time.   Therefore, total number of possible outcomes will be 63 = (6 × 6 × 6) = 216.   Number of events of getting a total of atmost 6 = 20   i.e. (1, 1, 1), (1, 1, 2), (1, 2, 1), (2, 1, 1), (1, 1, 3), (1, 3, 1), (3, 1, 1), (2, 2, 1), (1, 2, 2), (1, 1, 4), (1, 4, 1), (4, 1, 1), (1, 2, 3), (1, 3, 2), (2, 1, 3), (2, 3, 1), (3, 1, 2), (3, 2, 1) and (2, 2, 2).   Therefore, probability of getting a total of atmost 6   P(5/54) = Number of favorable outcomes/Total number of possible outcome   = 20/216   = 5/54
Answer: E
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?
Options
A) 287	B) 350	C) 828	D) 277	E) 122

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
Answer: B
Two vessels A and B contain spirit and water in the ratio 5 : 2 and 7 : 6 respectively. Find the ratio in which these mixtures be mixed to obtain a new mixture in vessel C containing spirit and water in the ratio 8 : 5 ? Choose one
A) 3: 4
B) 4 : 3
C) 9 : 7
D) 7 : 9
E) 8 : 1

Solution: Explanation:   Let Cost Price(CP) of 1 litre spirit be Rs.1   Quantity of spirit in 1 litre mixture from vessel A =5/7   Cost Price(CP) of 1 litre mixture from vessel A = Rs. =5/7   Quantity of spirit in 1 litre mixture from vessel B =7/13   Cost Price(CP) of 1 litre mixture from vessel B =Rs. =7/13   Quantity of spirit to be obtained in 1 litre mixture from vessel C =8/13   Cost Price(CP) of 1 litre mixture from vessel C(Mean Price) = Rs. =8/13   => Mixture from Vessel A : Mixture from Vessel B   =1/13:9/91 =7:9   Answer IS 7 : 9
Answer: D
Three investors, A, B, and C, divide the profits from a business enterprise in the ratio of 5 : 7 : 8, respectively. If investor A earned $ 4,500, how much money did investors B and C earn in total?
Pick.
A) $4,000	B) $4,900	C) $5,600	D) $9,500	E) $13,500

Solution: Let profit for A = 5x   profit for B = 7x   profit for C = 8x   Investor A earned = 34500   5x = 4500=>x=900   Total profit for B and C = 7x+ 8x = 15x   Therefore , 15x 7 + 8= 
7 + 8 = 15
15x   Therefore , 15x= 15*900 = 13,500   Answer $13,500
Answer: E
The salary of A, B, C, D, E is Rs. 8000, Rs. 5000, Rs. 15000, Rs. 7000, Rs. 9000 per month respectively, then the average salary of A, B, C, D, and E per month is Choose the correct choice from the following options:	A) Rs. 7000	B) Rs. 8000	C) Rs. 8800	D) Rs. 9000	E) None

Solution: Answer   Average salary   = 8000 + 5000 + 15000 + 7000 + 9000 / 5   = Rs. 8800   Rs. 8800orrect Option: Rs. 8800
Answer: C
x varies inversely as square of y. Given that y=3 for x=1. The value of x for y = 9 will be equal to:  Choose the correct choice from the following answers.
A) 3  B) 6  C) 1/9  D) 1/3  E) 9

Solution: Explanation :   Solution: Given x = k/y^2, where k is constant. Now, y=3 and x =1 gives k = 9.   .'. x = 9/y^2   => x =9 /9^2 = 1/9   Answer : 1/9
Answer: C
What amount does Kiran get if he invests Rs. 16000 at 15% p.a. simple interest for four years?  Answers
A) Rs. 25800
B) Rs. 15600
C) Rs. 21600
D) Rs. 24800
E) Rs. 25600

Solution: Simple interest = (16000 * 4 * 15)/100 = Rs. 9600   Amount = P + I = 16000 + 9600 = Rs. 25600   ANSWRs. 25600R:Rs. 25600
Answer: E
Sam purchased 20 dozens of toys at the rate of Rs. 375 per dozen. He sold each one of them at the rate of Rs. 33. What was his percentage profit?
Select:
A) 3.5  B) 4.5  C) 5.6  D) 6.5  E) None of these

Solution: Explanation :   C.P. of 1 dozen of toys = Rs. 375   So, C.P. of 1 toy = Rs. 375/12 = Rs. 125/4   S.P. of 1 toy = Rs. 33   Profit = Rs. 33 - (125/4) = Rs. 7/4   % Profit = 7/4∗4/125∗100%= 5.6%   Answer : 5.6
Answer: C
At 30 minutes past 8 o'clock, what is the angle between the two hands?  Pick:
A) 15 B) 30 C) 45 D) 60 E) 75

Solution: The hour hand moves 360 degrees in 12 hours.   The hour hand moves 30 degrees in 1 hour and 15 degrees in 30 minutes.   The minute hand moves 360 degrees in 60 minutes and 180 degrees in 30 minutes.   At 30 minutes past 8, the hour hand has moved 255 degrees.   At 30 minutes past 8, the hour hand has moved 180 degrees.   The angle between the two hands is 75 degrees.   The answer is 75.
Answer: E
I. m-14, m, m, m, m+14
II. b, b+1, b+2, b+3, b+4
III. c, c, c, c, c
The data sets I, II, and III above are ordered from greatest standard deviation to least standard deviation in which of the following? Choose the correct choice from the following options:
A) I, II, III  B) I, III, II  C) II, III, I  D) III, I, II  E) III, II, I

Solution: S.D is a non-negative entity. Also, for a given set with all the elements same, the S.D is Zero(It is zero even if there is only one element in the set too). From the given sets, we can see that the last set has a standard deviation of zero. Also, because the other sets can not have all the terms equal for any values of m or b, thus the S.D for the third set(III) has to be the minimum. Select the option which has III in the end.   I, II, III.
Answer: A
A certain office supply store stocks 2 sizes of self-stick notepads, each in 5 colors. The store packs the notepads in packages that contain either 3 notepads of the same size and the same color or 3 notepads of the same size and of 3 different colors. If the order in which the colors are packed is not considered, how many different packages of the types described above are possible?  Choose the correct choice:
A) 6
B) 8
C) 16
D) 20
E) 30

Solution: Notepads of the same color = 5 (we have 5 colors). As we have two sizes then total for the same color=5*2= 
5*2 = 10
10   Notepads of the different colors= 5C3=10 (we should choose 3 different colors out of 5). As we have two sizes then total for the different color=10*2= 
10*2 = 20
20   Total=10+20= 
10+20 = 30
30   Answer: 30.
Answer: E
City X has a population 8 times as great as the population of City Y, which has a population twice as great as the population of City Z. What is the ratio of the population of City X to the population of City Z?	Choose the correct option
A) 1:8
B) 1:4
C) 2:1
D) 4:1
E) 16:1

Solution: x= 8y, y= 2*z   X : Y , Y : Z   8 : 1 , 2 : 1   16 : 2 , 2 : 1   So, X : Z = 16 : 1   (16:1)
Answer: E
Diana is painting statues. She has 7/8 of a gallon of paint remaining. Each statue requires 1/16 gallon of paint. How many statues can she paint?  Choices.
A) 10	B) 20	C) 28	D) 14	E) 19

Solution: number of statues=all the paint÷amount used per statue   =7/8 ÷ 1/16   =7/8*16/1   =112/8= 
112/8 = 14
14.   Answer is 14.
Answer: D
If the area of a circle is 49pi square feet, find its circumference.
Choose the correct choice:  A) 14 pi feet  B) 43 pi feet  C) 42 pi feet  D) 18 pi feet  E) 64 pi feet

Solution: The area is given by pi * r * r. Hence   pi * r *r = 491 pi   r *r = 49 ; hence r = 7 feet   The circumference is given by   2 *pi *r = 2 * pi * 7 = 14 pi feet   correct answer 14 pi feet
Answer: A
If m = ||n – 3| – 2|, for how many values of n is m = 5?  Choose the correct choice from the following options.
A) 5
B) 4
C) 2
D) 3
E) 1

Solution: m = ||n – 3| – 2| can be 4 only and only when n-3= +/-7. so there are 2 values of n   Answer : 2
Answer: C
The product of all the prime numbers less than 14 is closest to which of the following powers of 10 ?
Options.
A) 10^4
B) 10^8
C) 10^7
D) 10^6
E) 10^5

Solution: P = 2*3*5*7*11*13   = 21 * 11 * 13*10   ~ 10^ 4   10^4nswer : 10^4
Answer: A
In the faculty of Reverse-Engineering, 226 second year students study numeric methods, 423 second year students study automatic control of airborne vehicles and 134 second year students study them both. How many students are there in the faculty if the second year students are approximately 85% of the total?
Pick:
A) 515. B) 545. C) 606. D) 644. E) 666.

Solution: Answer is C :606   Solution : Total number of students studying both are 423 + 226 - 134= 
423 + 226 - 134 = 515
515 (Subtracting the 134 since they were included in the both the other numbers already).   So 85% of total is 515, so 100% is approx. 606.
Answer: C
A sells his goods 50% cheaper than B but 50% dearer than C. The cheapest is?
Choose the correct choice from the following answers:
A) A B) B C) C D) D E) ALL

Solution: Answer: Option C   Let b = 100   a = 50   c * (150/100) = 50   3c = 100   c = 33.3 then 'c' cheapest
Answer: C
How many integers from 0 to 50 inclusive have a remainder of 3 when divided by 8?
Select:
A) 5
B) 6
C) 7
D) 8
E) 9

Solution: The numbers should be of the form 8c+3.   The minimum is 3 when c=0.   The maximum is 43 when c=5.   There are six such numbers.   The answer is 6.
Answer: B
In a bag containing 3balls, a white ball was placed and then 1ball was taken out at random. What is the probability that the extracted ball would turnon to be white, if all possible hypothesis concerning thecolor of theballs that initiallyin the bag were equally possible ?
Pick:
A) 2/3	B) 5/8	C) 3/5	D) 3/8	E) 4/9

Solution: Since, all possible hypothesis regarding the colour of the balls are equally likely, therefore these could be 3 white balls, initially in the bag.   ∴ Required probability = 1/4 [1 + 3/4 + 1/2 + 1/4]   = 1/4 [(4 + 3 + 2 + 1)/4] = 5/8   5/8
Answer: B
The sale price Mobiles listed for Rs.8000 after successive discount is 20% and 10% is?	Pick one:
A) 5670 B) 5560 C) 5770 D) 5660 E) 5760

Solution: 8000*(80/100)*(90/100)= 
8000*(80/100)*(90/100) = 5_760
5760   Answer: 5760
Answer: E
The ratio of three numbers is 5:3:4 and their sum is 108. The second number of the three numbers is?  Choose the correct option:
A) 18 B) 19 C) 21 D) 22 E) 27

Solution: 5:3:4   Total parts = 12   12 parts --> 108   1 part ---->9   The second number of the three numbers is = 3   3 parts ----> 27   27
Answer: E
For a group of n people, k of whom are of the same sex, the (n-k)/n expression yields an index for a certain phenomenon in group dynamics for members of that sex. For a group that consists of 20 people, 6 of whom are females, by how much does the index for the females exceed the index for the males in the group?	Choose the correct choice from the following:
A) 0.4
B) 0.0625
C) 0.2
D) 0.25
E) 0.6

Solution: Index for females = (20-6)/20 = 7/10= 
7/10 = 7/10 = around 0.7
0.7   Index for males= (20-14/20 = 3/10= 
3/10 = 3/10 = around 0.3
0.3   Index for females exceeds males by   0.7 - 0.3= 
  0.7 - 0.3 = 0.4
0.4   0.4nswer: 0.4
Answer: A
In 2008, the profits of Company N were 10 percent of revenues. In 2009, the revenues of Company N fell by 20 percent, but profits were 12 percent of revenues. The profits in 2009 were what percent of the profits in 2008?
Choose the correct option
A) 80%  B) 105%  C) 120%  D) 96%  E) 138%

Solution: x = profits   r= revenue   x/r = 0,1   x= 10   r=100   2009:   r=80   x/80 = 0,12 = 12/100   x= 80*12/100= 
80*12/100 = 48/5 = around 9.6
9.6   9.6/10= 
9.6/10 = 0.96
0.96= 96%, Answer 96%
Answer: D
What must be added to each term of the ratio 4 : 15, so that it may become equal to 3 : 4?
Choose the correct choice
A) 18
B) 29
C) 39
D) 49
E) 59

Solution: Let x be added to each term of the ratio 4:15.   New ratio becomes (4+x)/(15+x), which is given to be equal to 3:4.   This means,   (4+x)/(15+x)=3/4   Solving we get, x = 29.   Ans 29
Answer: B
The cost C, in dollars, to remove p percent of a certain pollutant from a pond is estimated by using the formula C = 100,000p/(100 - p). According to this estimate, how much more would it cost to remove 80 percent of the pollutant from the pond than it would cost to remove 80 percent of the pollutant?	Options:	A) 0	B) $100,000	C) $50,000	D) $10,000	E) $5,000

Solution: To remove 80% of pollutant   C= 100,000(80)/(100-80) = 400,000   To remove 80% of pollutant   C' = 100,000(80)/(100-80) = 400,000   Difference = C - C'=0   0nswer - 0
Answer: A
A tyre has two punctures. The first puncture alone would have made the tyre flat in 10 minutes and the second alone would have done it in 6 minutes. If air leaks out at a constant rate, how long does it take both the punctures together to make it flat ?  Choose the correct option:
A) 3 1/5min
B) 3 2/5min
C) 3 3/5min
D) 3 3/4min
E) 3 min

Solution: Explanation:   Do not be confused, Take this question same as that of work done question's. Like work done by 1st puncture in 1 minute and by second in 1 minute.   Lets Solve it:   1 minute work done by both the punctures =   (1/10+1/6)=(8/30) = (4/15)   So both punctures will make the type flat in   (15/4)mins=3 3/4mins   Option 3 3/4min
Answer: D
There are 4 red shoes & 4 green shoes . If two of red shoes are drawn what is the probability of getting red shoes
Choose the correct choice:
A) 1/3	B) 1/14	C) 3/14	D) 1/15	E) 1/16

Solution: taking 2 red shoe the probability is 43/142   from 8 shoes probability of taking 2 red shoes is 43/142/83/142=3/14   ANSWER:3/14
Answer: C
The 8 spokes of a custom circular bicycle wheel radiate from the central axle of the wheel and are arranged such that the sectors formed by adjacent spokes all have different central angles, which constitute an arithmetic series of numbers (that is, the difference between any angle and the next largest angle is constant). If the largest sector so formed has a central angle of 80°, what fraction of the wheel’s area is represented by the second largest sector? Choose the correct answer:
A) 1/72
B) 1/36
C) 1/18
D) 1/12
E) 7/36

Solution: Its an AP question .... it is given clearly in the question .   Let the smallest angle be a   and the circle has 8 sectors and hence 8 angle with a common difference d   hence all the angles can be written in AP form with Cd as d ,   a, a+d, a+2d, a+3d ,a+4d, a+5d, a+6d ,a+7d,   given that a+7d = 80 --------1   also   a + a+d + a+2d + a+3d +   a+4d + a+5d + a+6d + a+7d = 360 ( as sum of all the angle is 360)   which is 8a + 28d = 360 --------2   solving 1 and 2   we get a=10   We are almost done ,   now the question ask what fraction of the wheel’s area is represented by the smallest sector ?   (70/360)( pie r*r)/ (pie r*r) = 70/360= 7/36   7/36 ans ....
Answer: E
10 chess players take part in a tournament. Every player plays twice with each of his opponents. How many games are to be played?	Choose the correct choice from the following
A) 90 B) 98 C) 35 D) 99 E) 80

Solution: Though 2*(10C2) is the correct approcah to do this, but for people like me who find Perm, Comb n Prob a nightmare, an easy approach can be used.   The first guy has to play 2 matches with the rest of 9, so he'll play 18 matches.   Similarly, second guy has to play with the rest of 8 as his 2 games with the first guy are already played. So he plays 16 matches.   This continues like this and the total matches are 18+16+14...+2   18+16+...+2 = 2(9+8+...+1) = 2((9*10)/2) = 9*10= 
9*10 = 90
90.   90NSWER:90
Answer: A
A tennis championship is played on a knock-out basis, i.e., a player is out of the tournament when he loses a match.
(a) How many players participate in the tournament if 15 matches are totally played?
(b) How many matches are played in the tournament if 50 players totally participate? Choose the correct choice from the following answers
A) 15,49  B) 16,49  C) 16,48  D) 16,47  E) None of these

Solution: (a) u don’t need to sum it up. since it’s a knock out only 1 person emerges winner finally. so15+1= 
15+1 = 16
16 is answer.because after15 matches finally we shud’ve 15 losers and 1winner.   (b) 49:its always one less than no of players as per the idea given above.so no need to check okay cos its always true.ans is 49   Answer 16,49
Answer: B