MU-NLPC/Calc-aqua_rat huggingface dataset:
The average weight of 25 boys sitting in a boat had some value. A new person added to them whose weight was 60 kg only. Due to his arrival, the average weight of all the boys decreased by 10 kg. Find the average weight of first 25 boys? Pick:
A) 302  B) 203  C) 320  D) 260  E) 192

Solution: 25x + 60 = 26(x - 10)   x = 320   320
Answer: C
On one particular day, Beth's garden bloomed 1235 flowers. If Beth separates her flowers evenly across 9 different vases, how many flowers would remain with her. Options
A) 1 Flowers B) 2 Flowers C) 3 Flowers D) 4 Flowers E) 5 Flowers

Solution: This is equivalent to finding the first number that is divisible by 9 that occurs before 1235.   In order to divide the sum in 9 parts, the amount must be divisible by 9   Divisibility rule of 9: The sum of the digits must be divisible by 9   Sum of digits of 1235 = 11 and 9 is divisible by 9.   Therefor, we need to remove 2 to this number for it to be divisible by 9   Correct Option: 2 Flowers
Answer: B
A girl sold a book at a profit of 7%. Did she sold it for Rs.7.50 more, 22% would have been gained. Find the CP?
Choose the correct answer.
A) 40% B) 45% C) 50% D) 60% E) 69%

Solution: 50%   50%
Answer: C
Which of the following number should be added to 11158 to make it exactly divisible by 77?  Choose the correct choice from the following choices:
A) 6  B) 5  C) 8  D) 7  E) 9

Solution: Ondividing 11158 by 77, the remainder is 70   Thus, Number to be added = (77 - 70)= 
(77 - 70) = 7
7   ANSWER:7
Answer: D
If p is a positive integer and p^2 is divisible by 12, then the largest positive integer that must divide p ^3 is	Select:
A) 2^3
B) 2^6
C) 3^3
D) 6^3
E) 12^2

Solution: Since p is an integer so p cannot have a 2 and sqrt 3 (because squaring this will give us a 2^2 and 3 (making the product as 12, and making p^2 as a multiple of 12))   p^2 is divisible by 12 (12 = 2*2*3), So, p should have at least one 2 and one 3 so that p^2 has a 2^2 and two 3   So, p will have a 2 and a 3. Or p will be a multiple of 6   So, largest possible integer than should divide p^3 is 6^3   So, Answer will be 6^3
Answer: D
40, 45, 50, 55, 65, 75, 75, 100, 100, 100.
The list above shows the scores of 10 schoolchildren on a certain test. If the standard deviation of the 10 scores is 22.2, rounded to the nearest tenth, how many of the scores are more than 1 standard deviation below the mean of the 10 scores?
Select:
A) 1	B) 2	C) 3	D) 4	E) 5

Solution: The average of {40, 45, 50, 55, 65, 75, 75, 100, 100, 100} is 70.5   1 standard deviation below the mean is 70.5 - 22.2 = 48.3. Hence there are two scores (40 and 45) more than 1 standard deviation below the mean.   Answer 2.
Answer: B
Each of the products produced yesterday was checked by worker x or worker y. 0.5% of the products checked by worker x are defective and 0.8% of the products checked by worker y are defective. If the total defective rate of all the products checked by worker x and worker y is 0.74%, what fraction of the products was checked by worker y?  Pick.
A) 1/2 B) 2/3 C) 3/5 D) 3/4 E) 4/5

Solution: x: 0.5% is 0.24%-points from 0.74%.   y: 0.8% is 0.06%-points from 0.74%.   Therefore the ratio of products checked by y:x is 4:1.   Thus, worker y checked 4/5 of the products.   The answer is 4/5.
Answer: E
seven family members: 5 grandchildren (3 brothers and 2 sisters) and their 2 grandparents are to be seated around a circular table. How many different seating arrangements are possible so that 2 sisters are seated between any two of the three brothers? Options
A) 72	B) 480	C) 1440	D) 2880	E) 8640

Solution: 72nswer: 72.
Answer: A
A father said to his son, "I was as old as you are at present at the time of your birth." If the father's age is 42 years now, the son's age five years back was:  Choices:
A) 19 years
B) 14 years
C) 33 years
D) 16 years
E) 39 years

Solution: Let the son's present age be x years.   Then, (42 - x) = x   2x = 42=> x = 21   Son's age 5 years back = (21 - 5)= 
(21 - 5) = 16
16 years.   ANSWER:16 years
Answer: D
In the circular region shown above, sections A and B represent 3/8 and 5/11, respectively, of the area of the circular region. Section C represents what fractional part of the area of the circular region?  Options: A) 15/88 B) 2/11 C) 5/22 D) 45/88 E) 73/88

Solution: A , B and C represent complete area of circle and c fraction be x.   3/8+5/11+x = 1.   => x = 1- ( 3/8+5/11)   x = 15/88.   15/88nswer:option 15/88 is correct answer..
Answer: A
Which of the following is(are) false for a@b=b@a?
I. a@b=ab+ba
II. a@b=(a+b)(a-b)
III. a@b=(a/b)+(b/a) Choose the most appropriate option
A) only Ⅰ	B) only Ⅱ	C) only Ⅲ	D) only ⅠⅢ	E) only ⅡⅢ

Solution: -> If I. a@b=ab+ba, a@b=ab+ba=ba+ab=b@a (X).   If II. a@b=(a+b)(a-b), a@b=(a+b)(a-b)≠(b+a)/(b-a)=b@a (O).   If III.a@b=(a/b)+(b/a), a@b=(a/b)+(b/a)=(b/a)+(a/b)=b@a (O).   Thus, ⅠⅢ are the answers. Therefore, only Ⅰ is the answer.
Answer: A
You have 5 sticks of lengths 10, 30, 40, 50, and 60 centimeters. The number of non-congruent triangles that can be formed by choosing three of the sticks to make the sides is
Select the correct option.
A) 3 B) 4 C) 7 D) 10 E) 12

Solution: The length of any side of a triangle must be larger than the positive difference of the other two sides, but smaller than the sum of the other two sides.   Based on this there can be only 4 triangles formed:(30, 40, 50), (30, 40, 60), (30, 50, 60), (40, 50, 60).   Answer; 4
Answer: B
10 men working 6 hrs per day manufacture 200 shoes in 18 days. How many hours a day must 15 men work to manufacture the same 200 shoes in 12 days?	Choose one.
A) 6 B) 10 C) 12 D) 15 E) 18

Solution: Let the required number of hours be x.   More men, less hours per day (Indirect proportion)   Less days, more working hours per day (Indirect proportion)   men 15 : 10   } : : 6 : x   days 12 : 18   .'. 15*12*x = 10*18*6   = x = 10*18*6/(15*12)   = x = 6 6NSWER : 6
Answer: A
Which of the following inequalities is equivalent to −1 < x < 5? Select the correct option
A) |x - 1| < 7  B) |x + 2| < 3  C) |x + 3| < 5  D) |x - 2| < 3  E) None of the above

Solution: We know that |x| < a means -a < x < a, where Sum of lower limit of x (i.e -a) and the upper limit of x (i.e a), is 0   Given is, -1 < x < 5, let's say by adding y to this inequality we will get into the above format   -1+y < x+y < 5+y   Now, to move this into the mod format, we need to have (-1+y) + (5+y) = 0 => y = -2   Thus, -3< x-2 < 3 => |x-2| < 3.   Hence, answer is |x - 2| < 3
Answer: D
P and Q started a business investing Rs. 85,000 and Rs. 15,000 respectively. In what ratio the profit earned after 2 years be divided between P and Q respectively?
Choose the correct option
A) 17:6 B) 17:4 C) 17:8 D) 17:1 E) 17:3

Solution: P:Q = 85000 : 15000 = 17:3.   Answer:17:3
Answer: E
A part-time employee’s hourly wage was increased by 10%. She decided to decrease the number of hours worked per week so that her total income did not change. By approximately what percent should the number of hours worked be decreased?
Choose the correct option
A) 9%  B) 15%  C) 25%  D) 50%  E) 100%

Solution: Let's say the employee used to make $1/hour and worked 100 hours/week   So, the TOTAL weekly income was $100/week   After the 10% wage increase, the employee makes $1.10/hour   We want the employee's income to remain at $100/week.   So, we want ($1.10/hour)(new # of hours) = $100   Divide both sides by 1.10 to get:   new # of hours = 100/1.10   ≈ 90 hours   So, the number of hours decreases from 100 hours to (approximately) 90 hours.   This represents a 10% decrease (approximately) .   9%nswer choice 9% is the closest answer.
Answer: A
The C.I. on a certain sum for 2 years Rs.41 and the simple interest is Rs.40. What is the rate percent?
Pick one
A) 8%	B) 5%	C) 6%	D) 4%	E) 2%

Solution: SI = 20 + 20   CI = 20 + 21   20 ---- 1   100 ---- ? => 5%   Answer: 5%
Answer: B
In how many ways can four different rings be worn on four fingers of one hand?	Choose the correct option.
A) 10  B) 1  C) 15  D) 16  E) 18

Solution: Required number of ways = ways of selecting 4 objects out of 4 given objects   = 4C4 = 4*3*2*1/24= 
4*3*2*1/24 = 1
1   Answer 1
Answer: B
If six persons sit in a row, then the probability that three particular persons are always together is ?
Choose the correct choice from the following options
A) 1/5
B) 1/7
C) 1/2
D) 1/1
E) 1/9

Solution: Six persons can be arranged in a row in 6! ways. Treat the three persons to sit together as one unit then there four persons and they can be arranged in 4! ways. Again three persons can be arranged among them selves in 3! ways. Favourable outcomes = 3!4! Required probability   = 3!4!/6! = 1/5   Answer:1/2
Answer: C
Seven family members are seated around their circular dinner table. If only arrangements that are considered distinct are those where family members are seated in different locations relative to each other, and Michael and Bobby insist on sitting next to one another, then how many distinct arrangements around the table are possible?  Choose the correct choice from the following choices
A) 120 B) 240 C) 360 D) 480 E) 720

Solution: As I see it : 7 members, and Michael & Bobby sit together. So treat those two like a single person. Now you have to arrange 6 people around a table. This may be done in 5! or 120 ways   The number of ways to arrange Michael & Bobby is 2 (MB or BM).   So net there are 240 ways or 240
Answer: B
What is the sum of two consecutive even numbers, the difference of whose squares is 84?	Choose the correct choice from the following answers:
A) 34 B) 38 C) 42 D) 46 E) 48

Solution: Solution   Let the numbers be x and x + 2.   Then, (x + 2)2–x2 = 84   ‹=›4x + 4 = 84   ‹=›4x = 80   ‹=›x = 20.   Required sum = x+(x+2)= 2x+2 +( +2)= 
+( +2) = 2
2x+2= 42.   Answer 42
Answer: C
In what time will a train 140 meters long cross an electric pole, if its speed is 210 km/hr  Choose the correct choice from the following answers.
A) 5 seconds	B) 4.5 seconds	C) 3 seconds	D) 2.4 seconds	E) None of these

Solution: Explanation:   First convert speed into m/sec   Speed = 210*(5/18) = 58 m/sec   Time = 2.4 secondsistance/speed   = 140/58 = 2.4 seconds   Option 2.4 seconds
Answer: D
Bell and Carol are partners in a business, they invested Rs. 25,800 and Rs. 32,000 respectively.If the business yielded a total profit of Rs. 21,500, what is Carol's share?	Answers:
A) 11903.11	B) 12703.11	C) 15103.11	D) 11979.11	E) 11990.11

Solution: Explanation:   Ratio of their shares = 25,800 : 32,000 = 129 : 160.   Carol's share = Rs. (21,500 * 160/289) = Rs. 11903.11.   11903.11nswer: 11903.11) 11903.11
Answer: A
Two different primes may be said torhymearound an integer if they are the same distance from the integer on the number line. For instance, 3 and 7 rhyme around 5. What integer R between 1 and 20, inclusive, has the greatest number of distinct rhyming primes around it?
Pick one:
A) 12  B) 15  C) 17  D) R=18  E) 20

Solution: Since we are concerned with integers between 1 and 20, write down the primes till 40.   2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37   (you should be very comfortable with the first few primes... )   2, 3, 5, 7, 11,12, 13, 17, 19, 23, 29, 31, 37 - Three pairs (11,13), (7,17), (5, 19)   2, 3, 5, 7, 11, 13,15,17, 19, 23, 29, 31, 37 - Three pairs (13, 17), (11, 19), (7, 23)   2, 3, 5, 7, 11, 13,17, 19, 23, 29, 31, 37 - Three pairs (11, 23), (5, 29), (3, 31)   2, 3, 5, 7, 11, 13, 17,18,19, 23, 29, 31, 37 - Four pairs (17, 19), (13, 23), (7, 29), (5, 31)   2, 3, 5, 7, 11, 13, 17, 19,20,23, 29, 31, 37 - definitely cannot be more than 4 since there are only 4 primes more than 20. So must be less than 4 pairs. Ignore.   Answer (R=18).
Answer: D
There is a 100 pound watermelon laying out in the sun. 99 percent of the watermelon's weight is water. After laying out for a few hours 98 percent of the watermelon's weight is water.
How much water evaporated? Choose one:  A) A)20  B) B)30  C) C)40  D) D)50  E) E)10

Solution: In the beginning it is 99 pounds water and 1 pound other stuff. At the end the 1 pound other stuff is 2 percent so the total weight is 50 pounds. 50 pounds - 1 pound other stuff = 49 pounds water. So 99 pounds - 49 pounds = 50 pounds water lost.answer is 50
Answer: D
What is the dividend. divisor 19, the quotient is 9 and the remainder is 5?  Choose the correct choice from the following answers.
A) A)130  B) B)134  C) C)148  D) D)176  E) E)160

Solution: 176 = d * Q + R   176 = 19 * 9 + 5   176 = 171 + 5   176 = 176   Answer 176
Answer: D
A person spends 1/3rd of the money with him on clothes, 1/5th of the remaining on food and 1/4th of the remaining on travel. Now, he is left with Rs 600. How much did he have with him in the beginning?	Choose the correct choice from the following: A) s 200 B) s 1500 C) s 300 D) s 450 E) s 550

Solution: Suppose the amount in the beginning was Rs ’x’   Money spent on clothes = Rs 1x/3 s 1500alance = Rs 2x/3   Money spent on food = 1/5 of 2x/3 = Rs 2x/15   s 1500alance = 2x/3 - 2x/15 = Rs 8x/15   Money spent on travel = 1/4 of 8x/15 = Rs 2x/15 = 8x/15 - 2x/15 = 6x/15 = Rs2x/5   Therefore 2x/5 = 100 = 1500   ANSWER:s 1500
Answer: B
Steve traveled the first 2 hours of his journey at 40 mph and the last 3 hours of his journey at 80 mph. What is his average speed of travel for the entire journey?
Choose the correct choice from the following answers
A) 61mph
B) 62mph
C) 63mph
D) 64mph
E) 65mph

Solution: (2*40+3*80)/5= 
(2*40+3*80)/5 = 64
64mph   ANSWER:64mph
Answer: D
x, y, a, and b are positive integers of H. When x is divided by y, the remainder is 6. When a is divided by b, the remainder is 9. Which of the following is NOT a possible value for y + b?  Choose the correct answer.
A) 24
B) 21
C) 20
D) 17
E) 15

Solution: x, y, a, and b are positive integers of H. When x is divided by y, the remainder is 6. When a is divided by b, the remainder is 9.Answer: 15.
Answer: E
John, a painter, has 9 jars of paint: 4 are white, 2 are yellow, and the rest are brown. John will combine 3 jars of paint into a new container to make a new colour, which he will name according to the following conditions: 1) C1, if the paint contains 2 jars of brown paint and no white paint 2) C2, if the paint contains 3 jars of brown paint. 3) J1, if the paint contains at least 2 jars of white paint 4) J2, if the paint contains exactly 1 jar of white paint What is the probability that the new colour will be a shade of J (J1 or J2)? Choose the correct choice from the following options:
A) 42/37  B) 84/37  C) 21/37  D) 74/42  E) 37/42

Solution: the probability that it would be J1 or J2 is same as 1-()probability that it is C1 or C2   For C1-3C2(Brown)*2C1(Yellow)=3*2= 
3*2 = 6
6   For C2-3C3(all brown)=1   Total=9C3=84   1-7/84=77/84= 37/42   Answer : 37/42
Answer: E
A sum of money amounts to Rs.6690 after 3 years and to Rs.10,035 after 6 years on compound interest.find the sum.	Choose the correct choice from the following answers:
A) 333  B) 4460  C) 37687  D) 26698  E) 2911

Solution: Explanation:   Let the sum be Rs.P.then   P(1+R/100)^3=6690…(i) and P(1+R/100)^6=10035…(ii)   On dividing,we get (1+R/100)^3=10025/6690=3/2.   Substituting this value in (i),we get:   P*(3/2)=6690 or P=(6690*2/3)= 
(6690*2/3) = 4_460
4460   Hence,the sum is rs.4460.   Answer: 4460) 4460
Answer: B
Arun Kumar, Chennakesavan , Raghu and Krishnan always have discussions on various issues such as politics, international affairs, current affairs, studies etc. Once Raghu posed the following query to other group members:Find the range of real values of x satisfying the inequalities 4x - 5 > 7 and 5x - 14 > 16"	Choose the correct answer
A) x > 3 B) x > 6 C) x < 3 D) x < 6 E) none

Solution: 4x - 5 > 7 => 4x > 12 => x > 3 ...(1)   and 5x - 14 > 16 => 5x >30 => x > 6 ...(2)   Since 6 is greater than 3, for both inequalities namely (1) and (2) to be satisfied, x should be greater than 6 or x > 6.   ANSWER:x > 6
Answer: B
A searchlight on top of the watchtower makes 4 revolutions per minute. What is the probability that a man appearing near the tower will stay in the dark for at least 12 seconds?	Pick one.
A) 1/2	B) 2/3	C) 1/3	D) 1/4	E) 1/5

Solution: The searchlight completes one revolution every 15 seconds.   The probability that the man's area will be lit up is 12/15=4/5.   The probability that he will stay in the dark is 1-4/5=1/5   The answer is 1/5.
Answer: E
John and Steve are speed walkers in a race. John is 16 meters behind Steve when he begins his final push. John blazes to the finish at a pace of 4.2 m/s, while Steve maintains a blistering 3.7 m/s speed. If John finishes the race 2 meters ahead of Steve, how long was John’s final push? Select the correct option: A) 13 seconds B) 17 seconds C) 36 seconds D) 34 seconds E) 51 seconds

Solution: Let t be the time that John spent for his final push.   Thus, per the question,   4.2t = 3.7t+16+2 ---> 0.5t = 18 ---> t = 36 seconds.   36 seconds is the correct answer.
Answer: C
The compound ratio of 2/3, 6/7, 1/3 and 1/8 is given by?  Select
A) 1/45 B) 1/42 C) 1/46 D) 1/48 E) 1/43

Solution: 2/3 * 6/7 * 1/3 * 1/8 = 1/42   Answer:1/42
Answer: B
How many words, with or without meaning, can be formed using all letters of the word GOOD using each letter exactly once?	Choices
A) 18  B) 20  C) 22  D) 23  E) 24

Solution: The Word GOOD has exactly 4 letters which are all different.   Therefore the number of words that can be formed = Number of permutations of 4 letters taken all at a time.   = P (4, 4) = 4!   = 4 x 3 x 2 × 1   = 24   ANSW24R:24
Answer: E
At what time between 7 and 8 o'clock will the hands of a clock be in the same straight line but, not together?	Choose the correct choice from the following choices:	A) 5 min past 7	B) 5x6/11 min past 7	C) 5x5/22 min past 7	D) 5x5/11 min past 7	E) 5/22 min past 7

Solution: Explanation:   When the hands of the clock are in the same straight line but not together, they are 30 minute spaces apart.   At 7 o'clock, they are 25 min. spaces apart.   Minute hand will have to gain only 5 min. spaces.   55 min. spaces are gained in 60 min.   5 min. spaces are gained in60/55x 5	min	= 5X 5/11	min.   Required time = 5x 5/11	min. past 7.   Answer is 5x5/11 min past 7
Answer: D
Running at the same constant rate, 6 identical machines can produce a total of 270 bottles per minute. At this rate, how many bottles could 20 such machines produce in 4 minutes? Choose the correct choice from the following:
A) 648 B) 1,800 C) 2,700 D) 3,600 E) 64,800

Solution: 6 machines produce 270 bottles per minute;   1 machine produces 270/6= 
270/6 = 45
45 bottles per minute;   20 machines produce 45*20= 
45*20 = 900
900 bottles per minute;   In 4 minutes 10 machines produce 900*4=3,600 bottles.   Answer: 3,600.
Answer: D
X divided by 899 gives a remainder 63. What remainder will be obtained by dividing X by 29?
Choose the correct choice from the following options:
A) 100598
B) 10052
C) 100528
D) 10057
E) 100182

Solution: ANSWER: 10057
Answer: D
Twelve men can complete a piece of work in 32 days. The same work can be completed by 16 women in 36 days and by 48 boys in 16 days. Find the time taken by one man, one woman and one boy working together to complete the work?  Choose the correct choice:
A) (64 * 36)/13 days
B) (44 * 36)/23 days
C) (64 * 39)/13 days
D) (84 * 36)/13 days
E) (61* 36)/13 days

Solution: 12 men take 32 days to complete the work.   One man will take (12 * 32) days to complete it.   Similarly one woman will take (16 * 36) days to complete it and one boy will take (48 * 16) days to complete it.   One man, one woman and one boy working together will complete = 1/(12 * 32) + 1/(16 * 36) + 1/(48 * 16)   = 1/(4 * 3 * 16 * 2) + 1/(16 * 4 * 9) + 1/(16 * 3 * 4 * 4)   = 1/64(1/6 + 1/9 + 1/12) = 1/64 * 13/36 of the work in a day.   They will take (64 * 36)/13 days to complete the work working together.   (64 * 36)/13 daysnswer: (64 * 36)/13 days
Answer: A
A man rows 750 m in 675 seconds against the stream and returns in 7 and half minutes. His rowing
speed in sƟll water is  Choose the correct choice from the following choices:
A) 4 kmph
B) 5 kmph
C) 6 kmph
D) 7 kmph
E) None of these

Solution: Explanation:   Rate upstream = (750/675) = 10/9 m/sec   Rate downstream (750/450) m/sec = 5/3 m/sec   Rate in still water = (1/2)*[(10/9) + (5/3)] m/sec.   = 25/18 m/sec   = (25/18)*(18/5)= 
(25/18)*(18/5) = 5
5 kmph   Answer: 5 kmph
Answer: B
There are 5 men and 11 women. In how many ways one can select a group of 6 with at-least 3 men?	Choose the correct choice from the following answers:
A) 1935
B) 1936
C) 1937
D) 1938
E) 1939

Solution: 5c3*11c3+5c4*11c2+5c5*11c1=1936   ANSWER:1936
Answer: B
Four staff members at a certain company worked on a project. The amounts of time that the four staff members worked on the project were in the ratio 2 to 3 to 5 to 6. If one of the four staff members worked on the project for 60 hours, which of the following CANNOT be the total number of hours that the four staff members worked on the project?  Select the correct option
A) 480 B) 160 C) 320 D) 192 E) 240

Solution: Four members worked in ration 2:3:5:6, hence as everyone mentioned, individual work could be taken as 2x, 3x,5x, and 6x. Also this gives us total work as 16x.   But we are told that one of these individual works is 60hrs. hence, possible scenarios, if   (1)2x =60 => 16x = 480 (2) 3x =60 => 16x = 320 (3) 5x =60 => 16x = 192 (4) 6x =60 => 16x = 160   Hence Answer is 240
Answer: E
A, B and C rents a pasture for Rs.870. A put in 12 horses for 8 months, B 16 horses for 9 months and 18 horses for 6 months. How much should C pay?	Choose the correct answer:  A) 270  B) 278  C) 268  D) 266  E) 121

Solution: 12*8 :16*9 = 18*6   8: 12: 9   9/29 * 870= 
9/29 * 870 = 270
270   270nswer: 270
Answer: A
Laura has a deck of standard playing cards with 12 of the 72 cards designated as aheart.If Laura shuffles the deck thoroughly and then deals 10 cards off the top of the deck, what is the probability that the 10th card dealt is a heart? Choose the correct choice from the following answers.
A) 1/4
B) 1/5
C) 5/26
D) 12/42
E) 1/6

Solution: No replacement there, 10 cards are dealt and we are asked to find the probability that 10th card is a heart.   If there is no replacement then how is the (P) that the 10th card is 12/72 ??   there are many cases here to be considered here if there is no replacement such as:   H- Denotes heart X-may be any diamond, spade or club.   1. HXXXXXXXXH   2. HHXXXXXXXH   3. HHHXXXXXXH   .   .   .   .   .   9. HHHHHHHHHH   10. XXXXXXXXXH   All cases from 1 to 10 will have different probabilities for heart to be at the 10th place and it will take hell lot of time to calculate all of them.   For according to me the above solution by Ian is only valid if cards are replaced (Every card has a 12/72 = 1/6 chance of being a heart; it doesn't matter if it's the top card in the deck or the tenth card in the deck.)If that's the case that brings back me to my original question ----how do we determine that the cards are replaced or not?? based on the question given ....   1/6
Answer: E
What is the least number which should be added to 2597 so that the sum is exactly divisible by 5, 6, 4, and 3?  Pick.
A) 17	B) 23	C) 26	D) 35	E) 43

Solution: L.C.M. of 5, 6, 4 and 3 = 60.   When dividing 2597 by 60, the remainder is 17.   The number to be added = 60 - 17= 
60 - 17 = 43
43.   The answer is 43.
Answer: E
The age of a person is thrice the total ages of his 2 daughters. 0.5 decades hence, his age will be twice of the total ages of his daughters. Then what is the father’s current age?
[0.5 Decades = 5 Years] Choose the correct answer.
A) 45 years	B) 55 years	C) 42 years	D) 46 years	E) 52 years

Solution: A   45 years   Let, Total of current ages of the 2 daughters is A years.   Then, father’s current age = 3A years.   (345 years + 5) = 2 (45 years +10)   345 years + 5 = 245 years + 20   45 years = 15   Therefore, father’s current age = 45 years.
Answer: A