MU-NLPC/Calc-aqua_rat huggingface dataset:
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 10 percent of revenues. The profits in 2009 were what percent of the profits in 2008?
Choose the correct choice from the following options: A) 105% B) 80% C) 120% D) 124.2% E) 138%

Solution: the profit 0f 2009 in terms of 2008 = (0.8*10/10)*100= 
(0.8*10/10)*100 = 80
80%   80%
Answer: B
What is the perimeter of a square with area 25p^2/16 ?  Choose the correct choice from the following.
A) 3p/4  B) 3p^2/4  C) 5p  D) 3p^2  E) 4p/3

Solution: Area of square, (side)^2 = (5p/4)^2   Therefore side of the square = 5p/4   Perimeter of square = 4*side = 4* (5p/4) = 5p   Answer is 5p.4* (5 /4)= 
4* (5 /4) = 5
5p   Answer is 5p.
Answer: C
A man is 24 years older than his son. In two years, his age will be twice the age of his son. The present age of the son is:	Options:	A) 14 years	B) 18 years	C) 20 years	D) 22 years	E) 23 years

Solution: Let the son's present age be x years.   Then, man's present age = (x + 24) years.   (x + 24) + 2 = 2(x + 2) x + 26 = 2x + 4 => x = 22.   ANSWER:22 years
Answer: D
Excluding stoppages,the speed of the bus is 54kmph and
including stoppages,it is 36kmph. For how many minutes does the bus stop per hr	Choose the correct option
A) 12 min B) 11 min C) 13 min D) 19 min E) 20 min

Solution: Due to stoppages,it covers 18km less.   time taken to cover 18 km is [  18/54 *60= 
  18/54 *60 = 20
20min   Answer is 20 min.
Answer: E
In one hour, a boat goes 14 km/hr along the stream and 8 km/hr against the stream. The speed of the boat in still water (in km/hr) is:
Select the correct option:	A) 12 km/hr	B) 11 km/hr	C) 18 km/hr	D) 10 km/hr	E) 13 km/hr

Solution: Speed in still water =1/2(14+8) kmph = 11 kmph.   Answer : Option 11 km/hr
Answer: B
12 men complete a work in 9 days. After they have worked for 6 days, 6 more
men joined them. How many days will they take to complete the remaining work? Choose the correct choice from the following:
A) 3days	B) 4days	C) 2days	D) 8days	E) 5days

Solution: 1 man's 1 day work = 1/108   12 men's 6 days work = 6/9 = 2/3   remaining work = 1 – 2/3 = 1/3   18 men's 1 days work = 18/108 = 1/6   1/6 work is done by them in 1 day   therefore, 1/3 work is done by them in  6/3= 
 6/3 = 2
2 days.   ANSWER 2days 2days
Answer: C
A can do a piece of work in 8 days. B can do it in 6 days. With the assistance of C they completed the work in 2 days. Find in how many days can C alone do it?
Options
A) 8.7 days  B) 2.0 days  C) 6.6 days  D) 7.7 days  E) 4.8 days

Solution: C = 1/2 - 1/8 - 1/8 = 5/24   => 4.8 days   Answer: 4.8 days
Answer: E
Annie and Sam set out together on bicycles traveling at 15 and 12 km per hour respectively. After 40 minutes, Annie stops to fix a flat tire. If it takes Annie 20 minutes to fix the flat tire and Sam continues to ride during this time, how many minutes will it take Annie to catch up with Sam assuming that Annie resumes riding at 15 km per hour?	Choose the most appropriate option:
A) 20
B) 40
C) 60
D) 80
E) 100

Solution: Annie gains 3 km per hour (or 1 km every 20 minutes) on Sam.   After 40 minutes Annie is 2 km ahead.   Sam rides 1 km every 5 minutes.   In the next 20 minutes, Sam rides 4 km so Sam will be 2 km ahead.   It will take Annie 40 minutes to catch Sam.   The answer is 40.
Answer: B
Find the area of trapezium whose parallel sides are 20 cm and 18 cm long, and the distance between them is 15 cm.  Select:
A) 235 cm2  B) 265 cm2  C) 285 cm2  D) 295 cm2  E) 284 cm2

Solution: Explanation:   Area of a trapezium = 1/2 (sum of parallel sides) * (perpendicular distance between them) = 1/2 (20 + 18) * (15) = 285 cm2   Answer: Option 285 cm2
Answer: C
Myra drove at an average speed of 30 miles per hour for the first 30 miles of a trip & then at an average speed of 60 miles/hr for the remaining 30 miles of the trip. If she made no stops during the trip what was her average speed in miles/hr for the entire trip?	Pick:
A) The average speed is 35 miles per hour.
B) The average speed is 40 miles per hour.
C) The average speed is 55 miles per hour.
D) The average speed is 66 miles per hour.
E) The average speed is 45 miles per hour.

Solution: Here, distance for which Myra traveled at the two speeds is same.   Average Speed = 2ab/(a+b) = 2*30*60/(30 + 60)= 
2*30*60/(30 + 60) = 40
40 mph   Answer (The average speed is 40 miles per hour.)
Answer: B
In a particular 100 meter race, 5 athletes are participating that are numbered 1-5. In how many ways can athlete #5 finish ahead of #2 provided there's no tie among the athletes?
Pick one
A) 60  B) 100  C) 120  D) 180  E) 240

Solution: The total number of ways for the athletes to finish is 5! = 120.   #5 will be ahead of #2 in exactly half of these possibilities.   120/2= 
120/2 = 60
60   The answer is 60.
Answer: A
A and B started a business in partnership investing Rs.20,000 and Rs.15,000 respectively. After 6months, C joined them with Rs.20,000. Whatwill be B's share in total profit of Rs.22,000 earned at the end of 2years from the startingof the business? Options:
A) s. 5,000 B) s. 5,500 C) s. 5,700 D) s. 6,600 E) s. 7,500

Solution: A : B : C = (20,000 x 24) : (15,000 x 24) : (20,000 x 18) = 4 : 3 : 3.   B's share = Rs. 22000 x	3/10	= Rs. 6,600.   s. 6,600
Answer: D
Walking 9/8 of his usual rate, a boy reaches his school 4 min early. Find his usual time to reach the school? Choose the correct answer:	A) 22	B) 99	C) 27	D) 36	E) 20

Solution: Speed Ratio = 1:9/8 = 8:9   Time Ratio = 9:8   1 -------- 9   4 --------- ? 36 m.Answer:36
Answer: D
In a group of 80 people, 45 have visited Iceland and 33 have visited Norway. If 41 people have visited both Iceland and Norway, how many people have visited neither country? Choose the correct choice from the following answers:
A) 30  B) 31  C) 32  D) 33  E) 34

Solution: This is an example of a standard Overlapping Sets question. It has no 'twists' to it, so you'll likely find using the Overlapping Sets Formula to be a fairly easy approach. If you're not familiar with it, then here is the Formula:   80= 45 + 33 - 41 + (# in Neither Group)   =33   The prompt gives you all of the numbers you need to get to the correct answer. Just plug in and solve.   33
Answer: D
A boy wanted to calculate his speed on his bike. His starting point was 350 meters from the turning point. He made the round trip 5 times in 30 minutes. What was the boy's speed in kilometers per hour? Choose one
A) 1.75  B) 1  C) 2.25  D) 2.4  E) 3.2

Solution: The distance between the the starting point and the turning point was 350 meters.   The boy made the round trip 5 times so that was 10 times he traveled 350 meters.   10 * 350= 
10 * 350 = 3_500
3500 meters or 3.5 km.   30 minutes is half of an hour.   Divide the 3500 meters in half to put in the right time interval    3500/2= 
 3500/2 = 1_750
1750 meters or 1.75 km   Correct answer is 1.75
Answer: A
A palindrome is a number that reads the same front-to-back as it does back-to-front (e.g. 202, 575, 1991, etc.) p is the smallest integer greater than 300 that is both a prime and a palindrome. What is the sum of the digits of p? Choose the correct choice from the following:
A) 3
B) 4
C) 5
D) 6
E) 7

Solution: Given that p is smallest integer greater than 300 - assume there is a 3-digit that satisfies the above conditions. Let the number be xyx ; question asks us the values of 2x+y   We can straight away cross out options A) and 6) - sum of digits 3 or 6 implies it is divisible by 3 ---> we know that p is a prime number   Coming to option B) 2x + y = 4 --> only x = 2 and y = 0 satisfy this equation ( x> 2 will never give sum of digits = 4) ; but 202 is divisible by 2 ; we know that p is a prime number   Similarly option C) 2x+y = 5 --> only x = 2 and y = 1 satisfy this equation ( x> 2 will never give sum of digits = 5) ; but 212 is divisible by 2 ; we know that p is a prime number   Therefore answer option should be E ---> can be verified by taking 2x+y = 7 ---> x = 3 and y = 1 ; gives 313   6
Answer: D
If six persons sit in a row, then the probability that three particular persons are always together is ?	Choose the correct answer:
A) 1/9 B) 1/4 C) 1/5 D) 1/3 E) 1/7

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:1/5
Answer: C
A sum fetched a total simple interest of $4016.25 at the rate of 9 p.c.p.a. in 5 years. What is the sum? Choices
A) $8829  B) $2840  C) $6578  D) $7782  E) $8925

Solution: $8925   8925   Principal   = $100 x 4016.25/9 x 5   = $401625/45= 
401625/45 = 8_925
$8925.
Answer: E
A clock shows the time as 3:30 P.m. If the minute hand gains 2 minutes every hour, how many minutes will the clock gain by 2 a.m.?
Choices:
A) 23 Minutes
B) 21 Minutes
C) 25 Minutes
D) 26 Minutes
E) None of these

Solution: if the minute hand gains 2 minutes in 1 hour the from 3:30 p.m-4:00 p.m it gains 1 min   then from 4:00p.m-2:00 a.m =10*2= 
10*2 = 20
20 total=21   ANSWER:21 Minutes
Answer: B
If 30% of (x-y) = 20% of (x+y), then what percent of x is y? Choose the correct choice.
A) 50.5% B) 44.4% C) 22.2% D) 33.3% E) 20%

Solution: 30% of (x-y) = 20% of (x+y)   30/100 (x-y) = 20/100 (x+y)   x = 5y   Required percentage = y/x *100 = y/5y * 100 = 20%   Answer is 20%
Answer: E
Find the fraction which has the same ratio to 2/5 that 3/7 has to 6/5
Choose the correct choice:
A) 2/4 B) 6/78 C) 4/7 D) 3/5 E) 1/7

Solution: P : 2/5= 3/7 : 6/5   As the product of the means is equal to the product of the extremes.   P*6/5 = 2/5 * 3/7   P*6/5 = 6/35   P = 1/7 => P = 1/7   ANSW1/7R:1/7
Answer: E
Find the middle one when The sum of three consecutive even numbers is 36? Choose the correct answer:	A) 10	B) 12	C) 14	D) 16	E) 18

Solution: 3 consecutive numbers can be a - 1, a, a + 1   So sum of numbers = 3a = 36.   Hence a = 12.   12
Answer: B
A six digit number which is consisting of only one digitseither 1, 2, 3, 4, 5, 6, 7, 8 or 9, e.g., 111111, 222222... etc.This number is always divisible by :
Choose the correct choice from the following
A) 7 B) 11 C) 13 D) All of these E) None of these

Solution: Solution   Since the 7, 11 and 13 all are the factors of such a number.   Answer All of these
Answer: D
Circles X and Y are concentric. If the radius of circle X is five times that of circle Y, what is the probability that a point selected inside circle X at random will be outside circle Y?
Choose the correct choice:
A) 13
B) Pi/3
C) Pi/2
D) 5/6
E) 24/25

Solution: Small circle radius = a, so area = PI a ^ 2   Large circle radius = 5a, so area = 9. PI a ^ 2   Area of shaded region = 25PI a^2 - PI a^2 = 24 PI a^2   So, probability = ( 24 PI a^2 ) / (25 PI a^2 )   = 24/25 = Answer = 24/25
Answer: E
$8,000 is deposited in a savings account that pays 12% annual interest compounded semiannually. To the nearest dollar, how much is in the account at the end of the year?	Select
A) $8288.55 B) $8985.10 C) $8988.80 D) $8977.14 E) $8964.95

Solution: this is the case of semi-annual compoundingso, multiply time period by 2 and divide rate by 2   So,   new time=2periods and new rate=12/2= 
12/2 = 6
6%   Now,   $8988.80A=8000(1+6/100)^2=$8988.80   Hence answer is $8988.80
Answer: C
In a bag, there are seven 6-sided dice (numbered 1 to 6), three 12-sided dice (numbered 1 to 12), and two 20-sided dice (numbered 1 to 20). If four of these dice are selected at random from the bag, and then the four are rolled and we find the sum of numbers showing on the four dice, how many different possible totals are there for this sum?	Choose the correct answer
A) 46	B) 60	C) 42	D) 61	E) 96

Solution: As 'complex-looking' as this question might appear, it's actually rather simple. Pay careful attention to what the specific questions asks for - the number of DIFFERENT possible SUMS from 4 dice. Since we're dealing with some 'special' dice (some 12-sided and 20-sided dice), we have to adjust out math accordingly, but the possibilities are rather limited:   1) The minimum number on any given die is 1   2) The maximum possible sum would only occur if we took the 4 biggest possible dice and rolled the highest possible number on each.   With 4 dice, we could end up with any SUM between:   4 (if we rolled 1s on all 4 dice)   to   64 (if we rolled two 20s on the 20-sided dice and two 12s on the 12-sided dice).   Thus, there are only 61 possible sums.   61
Answer: D
An article is bought for Rs.600 and sold for Rs.500, find the loss percent?  Pick one:	A) 16 2/5%	B) 16 8/3%	C) 16 2/7%	D) 16 2/3%	E) 12 2/3%

Solution: 600 ---- 100   100 ---- ? => 16 2/3%   Answer: 16 2/3%
Answer: D
The Salary of a Labourer increase consistently by 40% per year. If his present salary is Rs. 3000 then what will his salary be after 3 years ?
Select the correct option.
A) 8232	B) 3282	C) 4282	D) 8242	E) 2382

Solution: Explanation :   Salary = 3000 x 1.4 x 1.4 x 1.4 = 8232   8232nswer : Option 8232
Answer: A
The speeds of three asteroids were compared. Asteroids X-13 and Y-14 were observed for identical durations, while asteroid Z-15 was observed for 2 seconds longer. During its period of observation, asteroid Y-14 traveled three times the distance X-13 traveled, and therefore Y-14 was found to be faster than X-13 by 2500 kilometers per second. Asteroid Z-15 had an identical speed as that of X-13, but because Z-15 was observed for a longer period, it traveled five times the distance X-13 traveled during X-13's inspection. Asteroid X-13 traveled how many kilometers during its observation?	Choose the most appropriate option
A) 500  B) 625  C) 1,000  D) 1,500  E) 2,500

Solution: X13: (t, d, s)   Y14: (t, 3d, s+2500mi/hour)   Z15: (t+2 seconds, s, 5d)   d=?   Distance = Speed*Time   x13: d = s*t   x14: 3d = (s+2500)*t ===> 3d = ts+2500t   z15: 5d = s*(t+2t) ===> 5d = st+2st ===> 5d - 2st = st   3d 5  - 2= 
5  - 2 = 3
st   3d= 5d - 2st + 2500t   -2d = -2st + 2500t   2d = 2st - 2500t   d = st - 1250t   x13: d = s*t   st - 1250t = s*t   s - 1250 = s   -625 = s   I got to this point and couldn't go any further. This seems like a problem where I can set up individual d=r*t formulas and solve but it appears that's not the case. For future reference how would I know not to waste my time setting up this problem in the aforementioned way? Thanks!!!   The distance of Z15 is equal to five times the distance of X13 (we established that x13 is the baseline and thus, it's measurements are d, s, t)   S(T+2) = 5(S*T)What clues would I have to know to set up the equation in this fashion? Is it because I am better off setting two identical distances together?   ST+2S = 5ST   T+2 = 5T   2=4T   t= 1/2   We are looking for distance (d=s*t) so we need to solve for speed now that we have time.   Speed y14 - speed x13   Speed = d/t   3d/t - d/t = 2500 (remember, t is the same because both asteroids were observed for the same amount of time)   2d = 2500   2 = 1250   d=s*t   d=1250*(1/2)= 
1250*(1/2) = 625
625   ANSWER: 625
Answer: B
How many ways are there to select a subcommittee of 7 members from among a committee of 17?
Select
A) 22888 B) 19448 C) 28791 D) 27711 E) 12111

Solution: Explanation:   Since it does not matter what order the committee members are chosen in, the combination formula is used.   Committees are always a combination unless the problem states that someone like a president has higher hierarchy over another person. If the committee is ordered, then it is a permutation.   C(17,7)= 19,448   Answer: 19448) 19448
Answer: B
A man is walking at a speed of 10 km per hour. After every kilometre, he takes rest for 5 minutes. How much time will be take to cover a distance of 5 kilometres?  Choices
A) 48 min.  B) 50 min.  C) 45 min.  D) 55 min.  E) None of these

Solution: Rest time = Number of rest × Time for each rest   = 4 × 5 = 20 minutes   Total time to cover 5km   = (5⁄10 × 60)minutes + 20 minutes = 50 minutes   Answer 50 min.
Answer: B
In what ratio should a variety of wheat costing Rs. 3 per kg be mixed with another variety of wheat costing Rs. 6.25 per kg to obtain a mixture costing Rs. 4.50 per kg?	Choose one
A) 8 : 6 B) 7 : 6 C) 5 : 6 D) 7 : 5 E) 6 : 7

Solution: Let us say the ratio of the quantities of cheaper and dearer varieties = x : y   7 : 6y the rule of allegation, x/y = (6.25 - 4.50) / (4.50 - 3) = 7/6   ANSWER:7 : 6
Answer: B
Two circular signs are to be painted. If the radius of the larger sign is five times that of the smaller sign, how many times more paint is needed to paint the larger sign? (We can assume that a given amount of paint covers the same area on both signs.)
Choose the correct choice:
A) 5 B) 15 C) 25 D) 35 E) 45

Solution: Let R be the radius of the smaller sign.   The area A of the smaller sign is A = piR^2.   The area of the larger sign is pi(5R)^2=25piR^2=25A.   Since the area is 25 times larger, we need 25 times more paint for the larger sign.   The answer is 25.
Answer: C
Philip is going with 6 friends on a trip to London for spring break. Airfare and hotel costs a total of $2800.00 for the group of 7 friends. How much does each person have to pay for their hotel and airfare?
Choose the correct choice from the following options:
A) $100 B) $200 C) $300 D) $400 E) $500

Solution: Answer= $400   The total cost of the trip ($2800.00) divided by 7 equals $400.00.
Answer: D
A small island country of 5000 people has an emigration and immigration statistic per 500 persons of 50.4 and 15.4 respectively. How long will it take for the population to be half of its current number.  Choose the correct choice from the following options.
A) 6.8
B) 8.5
C) 6.1
D) 9.1
E) 7.14

Solution: Annual decrease is (500 +15.4 - 50.4)*10= 
(500 +15.4 - 50.4)*10 = 4_650
4650   Hence every year there is a decrease of 350   for the population to become half 2500 must emigrate   therefore 2500/350=133.3   correct option is 7.14)7.14
Answer: E
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 5R/4 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? Answers.
A) 6R  B) 8R  C) 10R  D) 12R  E) 14R

Solution: In 2 hours, John drove 2R miles.   Tom can catch John at a rate of 5R/4 - R = R/4 miles per hour.   The time it takes Tom to catch John is 2R / (R/4) = 8 hours.   In 8 hours, John can drive another 8R miles for a total of 10R miles.   The answer is 10R.
Answer: C
How many three letter words are formed using the letters of the word TWITCH?  Choose one.
A) 65
B) 60
C) 55
D) 50
E) 40

Solution: The number of letters in the given word is four.   The number of three letter words that can be formed using these four letters is 5P3   = 5 * 4 * 3= 
5 * 4 * 3 = 60
60.   Answer: 60
Answer: B
If x≠y and x·y≠0, which of the following may be true?  Answers:
A) x/y=−y/x	B) x^2=−y^2	C) (x−y)^2<0	D) x−y=y−x	E) (x+y)(x−y)=0

Solution: Answer:	A and B are effectively the same i.e x^2+y^2=0   C square can't be less than 0   D give x = y refuted is question stem   (x+y)(x−y)=0
Answer: E
P, Q and R have $5000 among themselves. R has two-thirds of the total amount with P and Q. Find the amount with R? Choices
A) 2400  B) 2403  C) 3998  D) 2539  E) 2000

Solution: 2000   2000   Let the amount with R be $ r   r = 2/3 (total amount with P and Q)   r = 2/3(5000 - r) => 3r = 10000 - 2r   => 5r = 10000 => r = 2000.
Answer: E
What is the least number to be subtracted from 11, 15, 21 and 30 each so that resultant numbers become proportional? Choose one:
A) 1	B) 5	C) 3	D) 6	E) 4

Solution: Let the least number to be subtracted be x, then 11 - x, 15 - x, 21 - x and 30 - x are in proportion.   <=> (11 - x) : (15 - x) = (21 - x) : (30 - x)   => (11 - x)(30 - x) = (15 - x)(21 - x)   From the options, when x = 3   => 8 * 27 = 12 * 18   Answer:3
Answer: C
1/3 of certain journey is covered at the rate of 25kmph,one-fourth at the rate of 30kmph and the rest at 50 kmph.Find the avg speed for the whole journey.	Choose the correct choice
A) 28.5 kmph B) 31 kmph C) 33.333 kmph D) 45.98 kmph E) 98 kmph

Solution: Average speed = total distance / total time   L33.333 kmphM = 3, 4 = 12   Average speed = 12 / (1/3*12*1/25 + ¼ * 12*1/30 +5/50)   = 12/ (4/25 + 3/30+ 5/30   = 150*12/54 = 33.333 kmph   33.333 kmph
Answer: C
Out of 7 constants and 4 vowels how many words of 3 consonants and 2 vowels can be formed?
Choose the correct choice from the following answers:
A) 200 B) 20000 C) 25200 D) 2500 E) 2000

Solution: Number of ways of selecting (3 consonants out of 7) and (2 vowels out of 4)   = 7252003 * 4252002   = 210   Number of groups each having 3 consonants and 2 vowels = 210   Each group contains 5 letters   Number of ways of arranging 5 letters among themselves   = 5! = (5 * 4 * 3 * 2 * 1)   = 210   Required number of words = (210 * 210)   = 25200   ANSWER 25200
Answer: C
Matt is touring a nation in which coins are issued in two amounts, 2¢ and 5¢, which are made of iron and copper, respectively. If Matt has five iron coins and ten copper coins, how many different sums from 1¢ to 60¢ can he make with a combination of his coins?  Choose the correct choice from the following answers:
A) 30  B) 22  C) 56  D) 44  E) 48

Solution: The total sum is 5*2 + 10*5= 
5*2 + 10*5 = 60
60¢. If you can make each sum from 1 to 70 (1¢, 2¢, 3¢, ..., 60¢), then the answer would be 60 (maximum possible).   Now, with 2¢ and 5¢ we cannot make 1¢ and 3¢. We also cannot make 59¢ and 57¢ (since total sum is 60¢ we cannot remove 1¢ or 3¢ to get 59¢ or 57¢).   So, out of 60 sums 4 are for sure not possible, so the answer must be   60 - 4= 
  60 - 4 = 56
56 sums or less. Only A fits.   Answer: 56.
Answer: C
Three numbers are in the ratio 1:3:6 and their H.C.F is 4. The numbers are?	Choose the correct choice from the following options
A) 4, 12, 24 B) 4, 12, 20 C) 4, 12, 22 D) 4, 12, 28 E) 4, 16, 24

Solution: Let the required numbers be x, 3x and 6x. Then, their H.C.F = x. So, x = 4.   The numbers are 4, 12, 24.   4, 12, 24nswer: 4, 12, 24
Answer: A
If 1/2 of the air in a tank is removed with each stroke of a vacuum pump, what fraction of the original amount of air has been removed after 6 strokes ? Choose the correct option.
A) 63/64 B) 7/8 C) 1/4 D) 1/8 E) 1/16

Solution: Left 63/64fter 1st stroke = 1/2   Left 63/64fter 2nd stroke = 1/2 * 1/2 = 1/4   Left 63/64fter 3rd stroke = 1/2 * 1/4 = 1/8   Left 63/64fter 4th stroke = 1/2 * 1/8 = 1/16   Left 63/64fter 5th stroke = 1/2 * 1/16 = 1/32   Left 63/64fter 6th stroke = 1/2 * 1/32 = 1/64   So removed = 1- 1/64 = 63/64
Answer: A
A sum of money deposited at C.I. amounts to Rs.500 in 3 years and to Rs.650 in 4 years. Find the rate percent?
Choose the correct choice:
A) 25%
B) 30%
C) 35%
D) 40%
E) 45%

Solution: 500 --- 150   100 --- ? => 30%   Answer: 30%
Answer: B
If a number is 40% more than the another, how much % is the smaller number less than the first ?
Choose one:	A) 12(1/3)%	B) 16(2/3)%	C) 28(4/7)%	D) 16(4/3)%	E) none of these

Solution: Take a number 100,   Then the other number is 140   % the smaller number is less than the first = [(40/(140)) x 100]% = 28(4/7)%.   ANSWER:28(4/7)%
Answer: C
Adam borrowed some money at the rate of 6% p.a. for the first two years, at the rate of 9% p.a. for the next three years, and at the rate of 14% p.a. for the period beyond four years. If he pays a total interest of 11,800 at the end of nine years, how much money did he borrow? Options:	A) 10,421	B) 12,421	C) 14,000	D) 16,000	E) 16,421

Solution: Let the sum borrowed be x. Then,   (x×6×21/00)+(x×9×3/100)+(x×14×4/100)= 11800   ⇒ (3⁄25x + 27⁄100x + 14⁄25x) = 11400 ⇒ 95⁄100x = 11800   ⇒ x = (11800×100/95)= 12421   Hence, sum borrowed = 12,421   Answer 12,421
Answer: B
A bag contains 10 black and 20 white balls. One ball is drawn at random. What is the probability that the ball drawn is white?  Options:
A) 1/2
B) 3/4
C) 2/3
D) 1/5
E) 3/7

Solution: Total number of balls = 10+20= 
10+20 = 30
30   Number of white balls= 20   probability of drawing a white ball = 20/30 = 2/3   Answer is 2/3
Answer: C