MU-NLPC/Calc-aqua_rat huggingface dataset:
Beth received 2/10 of the votes cast in a certian election. What franction of the other votes cast would she have needed in order to have received 1/2 of the votes cast?  Choose one:
A) 1/5
B) 3/7
C) 3/10
D) 7/20
E) 1/2

Solution: Let the total votes be 10. Beth received 2 votes, other votes  10-2= 
 10-2 = 8
8. In order to have received 1/2 of the votes she needed 5 votes so 3 more, which is 3/7 of the other votes.   Answer: 3/7.
Answer: B
A box contains 100 balls, numbered from 1 to 100. If 3 balls are selected at random and with replacement from the box. If the 3 numbers on the balls selected contain two odd and one even. What is the probability L that the first ball picked up is odd numbered?
Choose the correct option: A) 0 B) 1/3 C) 1/2 D) 2/3 E) 1

Solution: Answer-D   Selecting the balls either Even or Odd is having probability 50/100=1/2   We have already selected 3 balls with 2 odd numbers and 1 even number.   So we have 3 combinations OOE, OEO, EOO. We have 3 outcomes and 2 are favourable as in 2 cases 1st number is odd. So probability L is 2/3.2/3
Answer: D
If x and y are different integers and x^2 = xy, which of the following must be true ?
I. x = 2
II. x = 0
III. x = -y
Pick: A) I only B) II only C) III only D) I and III only E) I, II, and III

Solution: Answer choice A is correct.   The question gives you x^2=xy   you can simplify that as x^2-xy=0   x(x-y)=0 the solution will be either x=0 or x=y, since x and y are different integers x cannot equal y, that leaves you x=0 to be the only answer.   Answer II only
Answer: B
In how many different number of ways a combination of 3 men and 2 women can be selected from 6 men and 5 women.  Pick one
A) 10	B) 20	C) 30	D) 35	E) 40

Solution: 6C3   = 6!/(3! . 3!)   = (6 × 5 × 4)/(3 × 2)   = 5 × 4 = 20.   20)
Answer: B
If anangletis defined as 1 percent of 1 degree, then how many anglets are there in a sixth of a circle?  Pick one
A) 0.36	B) 3.6	C) 360	D) 6000	E) 36,000

Solution: 1 degree * 1/100 = 1 anglet   So 1 degree = 100 anglets   => 60 degrees = 6000 anglets   Answer - 6000
Answer: D
Mrs. Napier has 86 stickers to give to 10 students for a reward. How many
stickers will each student get? Will there be any stickers left over? Choose the correct choice from the following.
A) 8-6	B) 2-4	C) 2-6	D) 2-3	E) 2-8

Solution: 86/10 = 8 R 6 Mrs. Napier will give each student 8 stickers and there   will be 6 left over.   correct answer 8-6
Answer: A
Two persons A and B can complete a piece of work in 18 days and 24 days respectively. If they work together, what part of the work will be completed in 2 days?  Choose the correct choice from the following.
A) 7/36	B) 9/35	C) 4/37	D) 8/35	E) 5/3

Solution: A's one day's work = 1/18   B's one day's work = 1/24   (A + B)'s one day's work = 1/18 + 1/24 = 7/72   The part of the work completed in 3 days = 2 (7/72) = 7/36.   7/36nswer:7/36
Answer: A
The length of the longest tape in cm which can be used to measure exactly, the length 2m; 400cm; and 5m is:	Options
A) 130
B) 500
C) 100
D) 400
E) 200

Solution: The three lengths in cm are 200, 400& 500.   HCF of 200, 400& 500 is 100   Hence, the answer is 100 cm.   ANSWER:100
Answer: C
The radius of a wheel is 22.4 cm. What is the distance covered by the wheel in making 1500 resolutions? Pick one:
A) 2112 m
B) 2704 m
C) 2278 m
D) 2288 m
E) 2378 m

Solution: In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 1500 resolutions.   = 1500 * 2 * 22/7 * 22.4= 
1500 * 2 * 22/7 * 22.4 = 211_200
211200 cm= 2112 m   2112 mnswer: 2112 m
Answer: A
Tom and Marry each have a bag of marbles, each of which contains 4 Red marbles, 10 blue marbles, and 6 yellow marbles. If Tom and Marry each select one marble from their respective bags, what is the probability that either Tom or Marry select a blue marble? Select
A) 1/7 B) 2/4 C) 3/4 D) 1/8 E) 1/16

Solution: Probability that either selects a red marble,P(Either) = 1- probability that neither selects a blue marble, P(Neither)   Probability that Tom selects non blue = 10c1 / 20c1 = 1/2   Probability that Marry selects non blue = 10c1 / 20c1 = 1/2   => P(Either)=1- (1/2*1/2) = 1-1/4= 3/4.   3/4)
Answer: C
In a class of 50 students, 12 enrolled for both English and German. 22 enrolled for German. If the students of the class enrolled for at least one of the two subjects, then how many students enrolled for only English and not German?
Choose the correct choice from the following choices:
A) 30 B) 10 C) 18 D) 28 E) 32

Solution: Total=English+German-Both+Neither --> 50=English+22-12+0 --> English=40 --> Only English=English-Both=40-12= 
40-12 = 28
28.   Answer: 28.
Answer: D
A, B and C can do a piece of work in 14, 30 and 40 days respectively. They start the work together but C leaves 4 days before the completion of the work. In how many days is the work done? Choose the correct choice from the following options:
A) 7.6 days	B) 7.7 days	C) 6.7 days	D) 5.7 days	E) 8.7 days

Solution: x/14 + x/30 + x/40 = 1   x = 7.7 days   ANSWER:7.7 days
Answer: B
Of all the homes on Gotham Street, 1/3 are termite-ridden, and 4/5 of these are collapsing. What fraction of the homes are termite-ridden, but NOT collapsing? Choose one
A) a) 1/15 B) b) 3/15 C) c) 4/5 D) d) 2/5 E) e)1/5

Solution: let total homes be 15   termite ridden= 1/3(15)= 5   termite ridden and collapsing = 4/5(5)=4   thus homes that are termite ridden, but not collapsing = 5-4= 
5-4 = 1
1   thus required ratio= 1/15   a) 1/15nswer a) 1/15
Answer: A
If x, y, and z are consecutive positive integers greater than 1, not necessarily in that order, then which of the following is (are) true?
I. x > z
II. 3(x+ y) > 3z
III. yz > xz
IV. xy > y + z Options:
A) I only
B) II only
C) II and III only
D) II and IV only
E) III and IV only

Solution: we do not know the values or the relative values but that the three are consecutive..   so the max difference in any two number is 2 and min 1..   lets see the choices..   I. x > z...   we do not know the values or the relative values... need not be true..   II. 3(x+ y) > 3z or x+ y > z   we take the worst case that z is teh largest and x and y are lowest possible..... so 2+3>4.. 5>4.. always true   III. yz > xz   we do not know the values or the relative values between x and y..need not be true   IV. xy > y + z   xy-y>z or y(x-1)>z...   again lets take the worst scenario..   we take the worst case that z is the largest and x and y are lowest possible..... so (2-1)3>4.. 3>4.. not true   only ii is true   ans II only
Answer: B
if in one hour, a canoe rows at 16 km/hr downstream and 9 km/hr upstream, Calculate the speed of a boat in still water (in km/hr).  Choose the correct answer:
A) 18 kmph  B) 15.5 kmph  C) 12.5 kmph  D) 13.5 kmph  E) 22.5 kmph

Solution: Speed in still water = (16 + 9)1/2 kmph = 12.5 kmph.   answer :12.5 kmph
Answer: C
8+88+888+.....+8888........8888. There are 21 “8” digits in the last term of the series.
Find the last three digits of the sum.
Choose the correct choice from the following choices
A) 958  B) 968  C) 978  D) 988  E) 999

Solution: As their is 21 no of 8 will add in first summation then 20 and then 19.   so 21*8= 
21*8 = 168
168 from that 8 will come 16 as a carry   and 20*8= 
20*8 = 160
160 , 160 + 16 (carry from first term)= 176 and from that 6 will come 17 as a carry   at last  19*8= 
 19*8 = 152
152 , 152+17=169 , so from that 9 will come   and answer become 968   ANSWER:968
Answer: B
A gardener wants to plant trees in his garden in such a way that the number of trees in each row should be the same. If there are 2 rows or 4 rows or 4 rows, then no tree will be left. Find the least number of trees required Choose the correct answer:
A) 22  B) 60  C) 4  D) 8  E) 10

Solution: Explanation:   The least number of trees that are required = LCM(2,4,4) = 4.   Answer: 4
Answer: C
After getting two successive discounts, a shirt with a list price of Rs. 300 is available at Rs. 210. if the second discount is 12.5%, find the first discount.  Choose the correct choice from the following options.
A) 15%
B) 20%
C) 25%
D) 12.5%
E) None of these

Solution: Explanation :   Solution: let the first discount be x%.   Then, 87.5% of(100-x)% of 300 =210.   87.5/100 * (100-x)/100 of 300 =210 ==> 100-x = 210*100*100/(300*87.5)= 
210*100*100/(300*87.5) = 80
80==> x = (100-80)= 
(100-80) = 20
20.   .'. First discount= 20%.   Answer : 20%
Answer: B
In how many ways can 5 boysand 2 girls be arranged at a table if 2 girls are never together? Answers
A) 346 B) 356 C) 378 D) 390 E) 480

Solution: Total ways of arranging 7 person in a circle = 6! = 720 ways   If we consider two women as one, then we have   5+1= 
  5+1 = 6
6 persons. Arranging these six persons in circle will take= 5! = 120 ways   And two women can arrange themselves in 2! ways   Total ways in which two women sit together in circle = 5!*2! = 240 ways   Total ways in which two women doesn’t sit together in circle = 6! - 5!*2! = 720 - 240= 
720 - 240 = 480
480 ways   480
Answer: E
An outlet pipe can empty 2/3 rd of a cistern in 12 minutes. In 8 minutes, what part of the cistern will be emptied?  Pick one.
A) 4/9
B) 2/3
C) 4/7
D) 1/6
E) 2/5

Solution: Explanation:   2/3 ---- 12   ? ----- 8 ==> 4/9   4/9NSWER IS 4/9
Answer: A
Of the following values of n, the value of (-1/6 )^(-n) will be greatest for n =
Choose the correct choice from the following choices.
A) 2	B) 3	C) 0	D) -2	E) -3

Solution: imo -2   (-1/6)^-2=   1/(1/36)= 
1/(1/36) = 36
36   oops i meant 2   2
Answer: A
A line has a slope of 3/4 and intersects the point Q (-12, -39). At which point does this line intersect the x-axis? Select the correct option.
A) (40,0)
B) (30,0)
C) (0,40)
D) (40,30)
E) (0,30)

Solution: Assume that the equation of the line is y=mx+c, where m and c are the slope and y-intercept.   You are also given that the line crosses the point (-12,-39), this means that this point will also lie on the line above.   Thus you get -39=m*(-12)+c , with m=3/4 as the slope is given to be 3/4.   After substituting the above values, you get c = -30.   Thus the equation of the line is y=0.75*x-30 and the point where it will intersect the x-axis will be with y coordinate = 0.   Put y=0 in the above equation of the line and you will get, x=40.   Thus, the point Q of intersection is (40,0).   (40,0) is the correct answer.
Answer: A
If 4b^4 − 41b^2 + 100 = 0, then what is the sum of the two greatest possible values of b ?  Choose the correct choice from the following:
A) 4	B) 9/2	C) 7	D) 41/4	E) 25

Solution: just forget about the value of b^4 for the moment and let b^2= X. (its better to work with power of 2 than 4)   now we have equation as 4x^2 -41x +100 =0, factoring them gives us 4X^2 -16x -25x +100 =0. which can be solved as (4x-25)(x-4) , so x= 4 and 25/4.   so b^2 = 4 and 25/4   so b= +2 and minus 2 and +5/2 and minus 5/2   The two greatest values are +2 and +5/2. so their sum 2+5/2 =9/2 = 9/2
Answer: B
Brenda and Sally run in opposite direction on a circular track, starting at diametrically opposite points. They first meet after Brenda has run 100 meters. They next meet after Sally has run 100 meters past their first meeting point. Each girl runs at a constant speed. What is the length of the track in meters? Choose the correct choice from the following choices:  A) 250  B) 300  C) 350  D) 400  E) 500

Solution: Nice problem. +1.   First timetogetherthey run half of the circumference.   Second timetogetherthey run full circumference.   First time Brenda runs 100 meters, thus second time she runs 2*100= 
2*100 = 200
200 meters.   Since second time (when they run full circumference) Brenda runs 200 meters and Sally runs 100 meters, thus the circumference is 200 + 100= 
200 + 100 = 300
300 meters.   Answer: 300.
Answer: B
Of the four numbers, whose average is 60, the first is one-fourth of the sum of the last three. The first number is ?	Choose the correct choice from the following answers:
A) 28
B) 29
C) 11
D) 48
E) 10

Solution: Explanation:   Let the first number be x,   Then, sum of the four numbers = x + 4x = 5x.   so, 5x/4 = 60 or x = (60 * 4) / 5= 
(60 * 4) / 5 = 48
48.   Answer: 48
Answer: D
How many paying stones, each measuring 2 1/2 m * 2 m are required to pave a rectangular court yard 30 m long and 16 1/2 m board? Choose the correct choice from the following:
A) 99	B) 87	C) 57	D) 54	E) 23

Solution: 30 * 33/2 = 5/2 * 2 * x => x   = 99   99nswer:99
Answer: A
Which of the following functions does not intersect with w = 3x^2 + 2x + 1 Select the correct option
A) W = 3x^2 + 3x + 1	B) W = 2x^2 + 3x + 1	C) W = 3x^2 + 2x + 3	D) W = 4x^2 + 2x - 3	E) W = x^2 + 2x + 3

Solution: Let’s find the actual intersecting point of given function and each choice w   A. 3x^2 + 2x + 1 = 3x^2 + 3x + 1 --> x=0   B. 3x^2 + 2x + 1 = 2x^2 + 3x + 1 --> x^2 – x =0 --> x=0 or 1   C. 3x^2 + 2x + 1 = 3x^2 + 2x + 3 --> 1=3(X) --> they don’t have any intersect.   D. 3x^2 + 2x + 1 = 4x^2 + 2x - 3 --> x^2 –4=0 --> x= 2 or -2   E. 3x^2 + 2x + 1 = x^2 + 2x + 3 --> 2x^2 –2 =0 --> x= 1 or –1.   So only choice (C) has no intersecting point. The answer is (W = 3x^2 + 2x + 3).
Answer: C
In a certain city, 60% of the registered voters are democrats and the rest are republicans.In a mayoral race, if 75% of the registered voters who are democrats and 20% of the registered voters who are republicans are expected to vote for candidate A,What % of the registered voters are expected to vote for candidate A?
Select the correct option.
A) 50% B) 53% C) 54% D) 55% E) 57%

Solution: Let total voters = 100   so D= 60, vote for the mayor 60*75%=45 (60*3/4)   R= 40, vote for the mayor 40*20%= (40*1/5)   45+8= 
45+8 = 53
53   53/100*100= 
53/100*100 = 53
53%   ANSWER:53%
Answer: B
At the end of three years what will be the compound interest at the rate of 10% p.a. on an amount of Rs.20000?
Choose the correct choice from the following options.
A) Rs.6620	B) Rs.6500	C) Rs.6800	D) Rs.6400	E) None of these

Solution: Explanation:   Rs.6620 = 20000(11/10)3   = 26620   = 20000   ----------   6620   Rs.6620nswer IS Rs.6620
Answer: A
In a sample of 800 high school students in which all students are either freshmen, sophomores, juniors, or seniors, 22 percent are juniors and 74 percent are not sophomores. If there are 160 seniors, how many more freshmen than sophomores are there among the sample of students?	Pick.
A) 42 B) 48 C) 56 D) 208 E) 256

Solution: Sophomores= 26%   Juniors = 22%   Seniors = 160/800 =20%   Total: 68%   1-68%=32% (Freshmen)   0,32*800-0,26*800=256-208= 
256-208 = 48
48.   Answer choice 48
Answer: B
A company’s four cars running 12 hrs a day consume 1200 lts of fuel in 10 days. In the next 6 days, the company will need to run 9 cars for 12 hrs each so it rents 5 more cars which consume 20% less fuel than the company’s four cars. How many lts of fuel will be consumed in the next 6 days?	Choose the correct option:
A) 1200 lt	B) 1440 lt	C) 1664 lt	D) 1728 lt	E) 4800 lt

Solution: Given that   4 cars running 12 hrs a day consume 1200 lts. of fuel in 10 days.   1 car consumption per hour per day = 1200 /4 *12 *10 = 2.5 litre   Now question say new car consume 20% less fuel than the company’s four cars = 80/100 of 2.5 = 2 ( 20 percent less than 2.5)   Hence we calculate total consumption for next 6 days, the company will need to run 5 new cars for 12 hrs = 2 *12 *6*5= 
2 *12 *6*5 = 720
720   similarly= old 4 car consumption for next 6 days for 12 hrs =2.5*6*12*4= 
2.5*6*12*4 = 720
720   hence total is= 720+720= 
720+720 = 1_440
1440 lt   Ans is 1440 lt .
Answer: B
The product of all the prime numbers less than 18 is closest to which of the following powers of 10 ? Choose the correct choice from the following:  A) 10^9  B) 10^8  C) 10^7  D) 10^6  E) 10^5

Solution: Product of Prime numbers less than 18 is 2*3*5*7*11*13*17   2*5= 
2*5 = 10
10 .   10*11*3*7*13*17= 10*10*3*10*10*20 (approximately) ~ Product will be >10^5 <10^7 i.e. 10^6   10^6 is the answer
Answer: D
6 workers should finish a job in 8 days. After 3 days came 4 workers join them. How many days X do they need to finish the same job?  Choices.
A) 3	B) 4	C) 5	D) 6	E) 7

Solution: Let Rate of one worker be R   => (6*R)*8 = 1 (Rate * Time = work)   => R = 1/48   => Work remaining after 3 days   1 - (3*6)/48 = 30/48   3fter 4 ppl joined in   ((6+4)*Time)/48 = 30/48   Time X= 3 days to finish the task   IMO 3
Answer: A
The sum of four consecutive even numbers is 36. Find the sum of the squares of these numbers? Choose the correct choice from the following choices.
A) 296 B) 252 C) 344 D) 388 E) None of these

Solution: Let the four numbers be x, x + 2, x + 4 and x + 6.   => x + x + 2 + x + 4 + x + 6 = 36   => 4x + 12 = 36 => x = 6   The numbers are 6, 8, 10 and 12.   Sum of their squares = 62 + 82 + 102 + 122 = 36 + 64 + 100 + 144= 
36 + 64 + 100 + 144 = 344
344.   ANSWER:344
Answer: C
A train sets off at 2 p.m. at the speed of 70 kmph. Another train starts at 3:30 p.m. in the same direction at the rate of 85 kmph. At what time the trains will meet?  Choose the correct choice from the following answers:
A) 10.18 p.m
B) 10.29 p.m
C) 10.30 p.m
D) 10.38 p.m
E) 10.32 p.m

Solution: D = 70 * 1 ½ = 105 km   RS = 85 – 70 = 15   T = 105/15= 
105/15 = 7
7 h     3.30 + 7= 
  3.30 + 7 = 10.3
10.30 p.m.   Answer:10.30 p.m
Answer: C
If 10 gallons of grape juice are added to 40 gallons of a mixture, which contains 30 percent grape juice then what percent of the resulting mixture is grape juice?	Choose the correct choice from the following choices:
A) 14%
B) 25%
C) 48%
D) 34%
E) 50%

Solution: OFFICIAL SOLUTION:   If we start with 40 gallons of a mixture that is 10% grape juice, then we have:   40 × 0.30 = 12 gallons of grape juice.   40 × 0.70 = 28 gallons of other components.   If we add 10 gallons of grape juice, we will end up with 24 gallons of grape juice and 36 gallons of other components, and we will have a total of 50 gallons of the mixture.   So 24/50 of the new mixture is grape juice. Now we convert this to a percent:Percent Grape Juice = 24/50 = 48/100= 48%.   The correct answer is choice (48%)
Answer: C
Nicole cycles at a constant rate of 10 kilometers per hour, and is passed by Jessica, who cycles at a constant rate of 40 kilometers per hour. If Jessica cycles at her constant rate for x minutes after passing Nicole, then stops to wait for her, how many minutes will Jessica have to wait for Nicole to catch up to her?  Choose the correct choice from the following options
A) a) x minutes	B) b) x/2 minutes	C) c) 2x/3 minutes	D) d) 3x/2 minutes	E) e) 2x minutes

Solution: Speed of nicole = 20km/h or 20/60 km/min = 1/3 km/min.   Once jessica passed the nicole, the distance between the nicole and jessica will increase at the rate of   (30-20)= 
  (30-20) = 10
10km/h or 1/6 km/min   now jessica is cycling for x minutes after passing the nicole, so in those x minutes distance between jessica and nicole would be (1/6)*x= x/6 km.   So, the time taken by nicole to travel x/6 km = (x/6)/(1/3) = 3x/2. hence answer should be d) 3x/2 minutes.
Answer: D
In a class of 38 students, 2 students did not borrow any books from the library, 12 students each borrowed 1 book, 10 students each borrowed 2 books, and the rest borrowed at least 3 books. If the average number of books per student was 2, what is the maximum number of books any single student could have borrowed?  Choose the correct choice
A) 3	B) 5	C) 8	D) 13	E) 15

Solution: Total # of students = 38   Avg # of books per student = 2   Total # of books = 38*2= 
38*2 = 76
76   # of student borrowed at least 3 books= 38-2-12-10= 
38-2-12-10 = 14
14   # of books borrowed by above 14 students= 76-(12*1)+(10*2) = 44   Considering that 13 out of above 14 students borrowed only 3 books, # of books borrowed = 13*3= 
13*3 = 39
39   So maximum # of books borrowed by any single student= 44- 39= 
44- 39 = 5
5   Option 5
Answer: B
A fruit seller sells mangoes at the rate of Rs.10 per kg and thereby loses 15%. At what price per kg, he should have sold them to make a profit of 5%  Choose the correct choice from the following answers:
A) Rs 8.81  B) Rs 9.35  C) Rs 10.35  D) Rs 12.35  E) None of these

Solution: Explanation:   85 : 10 = 105 : x   x= (10×105/85)   = Rs 12.35   Option Rs 12.35
Answer: D
If the cost price is 80% of the selling price, then what is the profit percent?	Pick one.
A) 5%	B) 11%	C) 13%	D) 25%	E) 19%

Solution: Let S.P. = $100   C.P. = $80   Profit = $20   Profit% = 20/80 * 100= 
20/80 * 100 = 25
25/6= 25%   Answer is 25%
Answer: D
Anil and Ravi invest Rs.60,000 and Rs.40,000 and they got loss of Rs.5,000 at the end of year. Then what was the loss for Ravi in Percentage?
Choose the correct choice from the following answers:
A) 2% B) 3% C) 5% D) 6% E) 8%

Solution: ratio of their investment is 3:2   so the lost of ravi is 2000rs   40000*(x/100)=2000   then x=5%   ANSWER:5%
Answer: C
How many different pairs of positive integers (a, b) satisfy the equation 1/a+1/b=34/53 ? Options.
A) 6
B) 3
C) 2
D) 1
E) 0

Solution: There is no certain way to solve 2 unknown with 1 equation. The best way is to look at the question and retrospect the most efficient way. In this question, a and b are only positive integers. So that is a big relief. Now, we can start with putting a=1,2,.. and so on till the time we are confident about one of the options.   So, we start with   a=1, we get b as -ve. out   a=2, we get b as 6. Yes (Now (a,b) = (2,6). We can directly see that (a,b)=(6,2) will also satisfy. So we have 2 possible solutions)   a=3, we get b as 3. Yes (Now we have 3 possible solutions)   a=4, we get b as fraction. Out   a=5, we get b again as some fraction. Out   a=6 already taken.   We have A,B options left. C,D,E are out.   A is 6. To have 6 as the answer, we will need one more pair like2,6and one more solution where a=b.   When a=b, we have only 1 solution = 3. So, one more solution, where a=b is not possible.   So, answer will be 2.
Answer: C
Jhaveri invested in Upendra&Upendra,Celco and Winger shares at Rs. 300,Rs.200 and Rs.5 per share respectively. He bought 100 shares for Rs.1000.The number of Upendra&Upendra and Celco shares he bought are respectively Choose the correct option:
A) 23,17
B) 17,23
C) 17,60
D) 15,25
E) 15,20

Solution: 300a + 200 b + 5c = 10000   a + b + c = 100   295 a + 195 b = 9500   59 a + 39 b = 1900   using options a = 17 b = 23 we can solve it   ANSWER:15,25
Answer: D
Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 3 or 5?	Options:
A) 1/2
B) 2/5
C) 8/15
D) 9/20
E) 7/8

Solution: Explanation:   Here, S = {1, 2, 3, 4, ...., 19, 20}.   Let E = event of getting a multiple of 3 or 5 = {3, 6 , 9, 12, 15, 18, 5, 10, 20}.   P(E) =	n(E)	/ n(S) = 9/20.   ANSWER IS 9/20
Answer: D
Which is the odd number?
1, 8, 27, 64, 125, 196, 216, 343
Pick: A) 196 B) 237 C) 2087 D) 277 E) 011

Solution: Explanation:   The pattern in the given question is 13, 23,,33...   In the series, 196 is not a perfect cube and therefore the odd number.   196NSWER: 196
Answer: A
A speaks english in 75% of cases and B in 80% of cases. In what percentage of cases are they likely to speak english?  Choose the correct choice from the following:
A) 25%  B) 26%  C) 35%  D) 45%  E) 56%

Solution: Let A = Event that A speaks the truth   B = Event that B speaks the truth   Then P(A) = 75/100 = 3/4   P(B) = 80/100 = 4/5   P(A-lie) = 1-3/4 = 1/4   P(B-lie) = 1-4/5 = 1/5   Now   A and B contradict each other =   [A lies and B true] or [B true and B lies]   = P(A).P(B-lie) + P(A-lie).P(B)   [Please note that we are adding at the place of OR]   = (3/5*1/5) + (1/4*4/5) = 7/20   = (7/20 * 100)= 
(7/20 * 100) = 35
35%   35%
Answer: C
Ram-Leela has $100 in her piggy bank. How much will she have in her bank 52 weeks from now if she puts $1 in the bank next week, $2 two weeks from now, $3 three weeks from now, and continues to increase the amount that she puts in by $1 each week?	Select
A) 1478 B) 1578 C) 1678 D) 1778 E) 1798

Solution: The dollar deposits are in an A.P.   1,2,3,4...52 with common difference 1   Sum of the terms is n(n+1) / 2   i.e 52* (52+1) /2   = 52* 53/2= 
52* 53/2 = 1_378
1378   Total deposit therefore with Chiu-Lihas is 100 + 1378= 
100 + 1378 = 1_478
1478$
Answer: A