MU-NLPC/Calc-aqua_rat huggingface dataset:
How many days will there be from 28th January,1996 to 15th May,1996(both days included)?	Pick.
A) 102
B) 103
C) 111
D) 109
E) 121

Solution: Explanation:   Number of days from 28-Jan-1996 to 15-May-1996 (both days included)   = 4(Jan) + 29(Feb) + 31 (Mar) + 30(Apr)+ 15(May) = 109   Answer: Option 109
Answer: D
A car ferry can hold up to 70 tons of cargo. What is the greatest number of vehicles that the ferry can carry if half the vehicles are cars with an average (arithmetic mean) weight of 0.75 tons and half of the vehicles are trucks with an average (arithmetic mean) weight of 6 tons?	Choose the correct option.
A) 20  B) 24  C) 28  D) 32  E) 36

Solution: The weight of one car and one truck is 6.75 tons.   70/6.75 = 10 plus a remainder   The ferry could carry 10 cars and 10 trucks for a total of 20 vehicles.   The answer is 20.
Answer: A
Which of the following correctly lists the data sets in order of least to greatest standard deviation?
I. 2, 2, 2, 2, 1 2
II. 42, 22, 32, 42, 32, 42
III. 30, 30, 32, 30, 31, 32  Choose the correct choice from the following answers.
A) I, II, III B) I, III, II C) II, I, III D) II, III, I E) III, II, I

Solution: (D) To answer a question such as this, you DO NOT need to know how to calculate standard deviation. You simply need to understand how to compare standard deviations of different sets. The more spread out the numbers are, the greater the standard deviation will be. Even one or two numbers that are much larger or smaller than the others will cause the standard deviation to rise drastically.   sequence = I,III,II   I, III, II
Answer: B
A man's speed with the current is 15 km/hr and the speed of the current is 2.5 km/hr. The man's speed against the current is:	Select the correct option:	A) 8.5 km/hr	B) 9 km/hr	C) 10 km/hr	D) 12.5 km/hr	E) 25km/hr

Solution: Explanation:   Man's rate in still water = (15 - 2.5) km/hr = 12.5 km/hr.   Man's rate against the current = (12.5 - 2.5) km/hr = 10 km/hr.   Answer: 10 km/hr
Answer: C
In Country T, the unemployment rate among construction workers dropped from 16 percent on September 1, 1992, to 9 percent on September 1, 1996. If the number of construction workers was 20 percent greater on September 1, 1996, than on September 1, 1992, what was the approximate percent change in the number of unemployed construction workers over this period?
Choose the correct choice from the following answers
A) 50% decrease B) 30% decrease C) 15% decrease D) 30% increase E) 55% increase

Solution: Country T 1992 1996   No of construction workers 100 120   Unemployment Rate 16% 9%   Unemployed workers 16 11   % change in unemployed workers=(16-11)= 
(16-11) = 5
5/16=~33% decrease   Closest ans=30% decrease   Ans=30% decrease
Answer: B
In a meeting of 4 representatives from each of 5 different companies, each person shook hands with every person not from his or her own company. If the representatives did not shake hands with people from their own company, how many handshakes took place? Choose the correct choice from the following options:
A) 170 B) 160 C) 180 D) 190 E) 200

Solution: In fact, all 20 people will shake hands with 16 others.   So, it SEEMS like the TOTAL number of handshakes = (20)(16)   HOWEVER, we need to keep in mind that we have counted each handshake TWICE.   To account for this DUPLICATION, we must divide (20)(16) by 2.   So, the TOTAL # of handshakes = (20)(16)/2 = 160   Answer : 160
Answer: B
It is being given that (2^32 + 1) is completely divisible by a whole number. Which of the following numbers is completely divisible by this number?	Choose the correct choice from the following choices
A) (2^16 + 1) B) (2^16 - 1) C) (7 x 2^23) D) (2^96 + 1) E) (2^98 + 1)

Solution: Let 2^32 = x. Then, (2^32 + 1) = (x + 1).   Let (x + 1) be completely divisible by the natural number N. Then,   (2^96 + 1) = [(2^32)^3 + 1] = (x^3 + 1) = (x + 1)(x^2 - x + 1), which is completely divisible by N, since (x + 1) is divisible by N.   Answer:(2^96 + 1)
Answer: D
A student has to obtain 33% of the total marks to pass. He got 175 marks and failed by 56 marks. The maximum marks are?	Choose the correct choice
A) 450 B) 300 C) 500 D) 610 E) 700

Solution: Let the maximum marks be x   Then, 33% of x = 175+56   33x/100 = 231   x = 700   Answer is 700
Answer: E
Rosy has 8 shirts and 9 pants. How many clothing combinations does Barbara have, if she doesn’t wear 6 specific shirts with 5 specific pants?  Choose one: A) 41 B) 66 C) 42 D) 70 E) 56

Solution: Total no of combinations available is= 8 shirts X 9 pants = 72   Eliminate the 6 shirts X 5 pants combo = 30 which gives.......>> 72-30= 
72-30 = 42
42   ANSWER: 42
Answer: C
A certain set of numbers has an average (arithmetic mean) of 50 and a standard deviation of 50.5. If c and n, two numbers in the set, are both within 2 standard deviations from the average, then which of the following could be the sum of c and n?	Options:
A) -200	B) -130	C) -104	D) 51	E) 305

Solution: 2 standard deviations from the average is frommean - 2*SDtomean + 2*SD, thus from 50-2*50.5=51 to  50+2*50.5= 
 50+2*50.5 = 151
151:   -51 < c < 151   -51 < n < 151   -102 < c+n < 302.   Only option D is in this range.   Answer: 51.
Answer: D
Seven machines at a certain factory operate at the same constant rate. If six of these machines, operating simultaneously, take 42 hours to fill a certain production order, how many fewer hours does it take all seven machines, operating simultaneously, to fill the same production order?  Choose the correct option:
A) 3  B) 4  C) 5  D) 6  E) 7

Solution: The total work is 6*42= 
6*42 = 252
252 machine hours   The time required for seven machines is 252/7= 
252/7 = 36
36 hours, thus 6 fewer hours.   The answer is 6.
Answer: D
How many cubes of 5 cm edge can be put in a cubical box of 1 m edge.	Options:
A) 1770cm  B) 8000 cm  C) 7860 cm  D) 6170 cm  E) 1870 cm

Solution: Number of cubes =100âˆ—100âˆ—100/5*5*5=8000   Note: 1 m = 100 cm   Answer:8000 cm
Answer: B
A, B and C enter into partnership. A invests some money at the beginning, B invests double the amount after 6 months, and C invests thrice the amount after 8 months. If the annual gain be Rs.18000. A's share is?	Pick: A) 9887 B) 2792 C) 6000 D) 2876 E) 2791

Solution: x* 12 : 2x* 6: 3x* 4   1:1:1   1/3 * 18000= 
1/3 * 18000 = 6_000
6000   Answer: 6000
Answer: C
X starts a business with Rs.45000. Y joins in the business after 7 months with Rs.30000. What will be the ratio in which they should share the profit at the end of the year?  Choose the most appropriate option
A) 1:2 B) 18:5 C) 1:5 D) 3:1 E) 1:1

Solution: Explanation:   Ratio in which they should share the profit   = Ratio of the investments multiplied by the time period   =45000Ã—12:30000Ã—5   =45Ã—12:30Ã—5   =3Ã—12:2Ã—5   =18:5   Answer: Option 18:5
Answer: B
Brenda caught three less than twice as many fish as Olga. Together they caught 33 fish. How many fish did Olga catch?	Choose the correct choice from the following choices.
A) 21	B) 20	C) 13	D) 12	E) 15

Solution: If Olga = f, Brenda= 2(f)-3   Brenda+Olga =33   (2f-3)+(f) =33   2f+f-3+3=33+3   3f=36   f=12   Olga has 12 fish, the answer is 12)
Answer: D
The toll for crossing a certain bridge is $0.75 each crossing. Drivers who frequently use the bridge may instead purchase a sticker each month for $11.00 and then pay only $0.30 each crossing during that month. If a particular driver will cross the bridge twice on each of x days next month and will not cross the bridge on any other day, what is the least value of x for which this driver can save money by using the sticker?	Choose the correct answer
A) 14  B) 15  C) 16  D) 28  E) 29

Solution: Option #1: $0.75/crossing....Cross twice a day = $1.5/day   Option #2: $0.30/crossing....Cross twice a day = $0.6/day + $13 one time charge.   If we go down the list of possible answers, you can quickly see that 14 days will not be worth purchasing the sticker. 1.5x14 (21) is cheaper than 0.6x14 +13 (21.4)...it's pretty close so let's see if one more day will make it worth it... If we raise the number of days to 15, the sticker option looks like a better deal...1.5x15 (22.5) vs 0.6x15 + 13 (22). Answer: 29
Answer: E
A train 150 m long running at 72 kmph crosses a platform in 25 sec. What is the length of the platform?
Choose the most appropriate option:
A) 287	B) 298	C) 350	D) 726	E) 267

Solution: D = 72 * 5/18 = 25   = 500 – 150   = 350   Answer: 350
Answer: C
A train speeds past a pole in 11 seconds and a platform 120 m long in 22 seconds. Its length is?  Choose the most appropriate option: A) 128 B) 177 C) 199 D) 120 E) 150

Solution: Let the length of the train be x meters and its speed be y m/sec.   They, x / y = 11 => y = x/11   x + 120 / 22 = x / 11   x = 120 m.   Answer:120
Answer: D
Pavan travelled for 15 hours. He covered the first half of the distance at 30 kmph and remaining half of the distance at 25 kmph. Find the distance travelled by Pavan.  Choose the correct choice from the following options:
A) 408 km
B) 409 km
C) 410 km
D) 412 km
E) 419 km

Solution: Let the distance travelled be x km.   Total time = (x/2)/30 + (x/2)/25 = 15   => x/60 + x/50 = 15   => (5x + 6x)/300 = 15   => x = 409 km   ANSWER:409 km
Answer: B
The ratio of radius of a circle and the side of a square is 2 : 13. Find the ratio of their areas:  Choose the correct choice from the following choices.
A) 2 : 1 B) 4 : 7 C) 8 : 77 D) 4 : 169 E) None

Solution: radius/side = 2/13   â‡’ area of circle/area of square= 4/169   Answer: 4 : 169
Answer: D
Sonika deposited Rs.8000 which amounted to Rs.9200 after 3 years at simple interest. Had the interest been 2% more. She would get how much?
Pick.
A) 9680	B) 2277	C) 2999	D) 2774	E) 1212

Solution: (8000*3*2)/100= 
(8000*3*2)/100 = 480
480   9200   --------   9680   9680nswer:9680
Answer: A
A contractor hires 100 men to finish a job in 50 days. After 24 days, n men leave. After some more days, the contractor hires 2n more men to complete the job on time. For how many days did these 2n men work?	Choose the correct choice:
A) 20
B) 18
C) 16
D) 13
E) 8

Solution: Step1: Find Each day what % of work is finished ; it requires 50 days to complete which means each day 1/50= 2% work will be completed.   Step 2 : After 24 Days = 24* 2= 
24* 2 = 48
48% of work is finished. remaining is 52% ( which means if same 100 men were about to complete the job they would have required 26 more days)   Step3: Let us assume all people have left job. therefore contractor hires 2n people. initially it was taking 26 days to compete for n people. at present 2n people are present to finish job. hence 13 more days.   13
Answer: D
A $500 investment and a $1,500 investment have a combined yearly return of 13 percent of the total of the two investments. If the $500 investment has a yearly return of 7 percent, what percent yearly return does the $1,500 investment have? Choose the correct option.
A) 9%
B) 15%
C) 105/8%
D) 11%
E) 12%

Solution: The equation we can form the question :   Return on Total Investment = Sum of individual Investments   (500+1500)(13)=(500âˆ—7)+(1500x), where x is the return on investment of 1500.   Solving the equation, we get x = 15% ( Option 15%)	ANSWER:15%
Answer: B
Three people with different speeds of 4.5kmph,0.5kmph and 8kmph move around a circular track of 11km.at what time they meet each other?
Answers: A) 21 hours B) 22 hours C) 20 hours D) 23 hours E) 24 hours

Solution: Time taken by 1st person to cover the circular track = 11/4.5 = 22/9   Time taken by 2nd person to cover the circular track = 11/0.5= 
11/0.5 = 22
22   Time taken by 3rd person to cover the circular track= 11/8   They meet for the 1st time after   time t = LCM (22/9,22,11/8)   = 22 hours   ANSWER:22 hours
Answer: B
January 1, 2007 was Monday. What day of the week lies on Jan. 2, 2008?	Select:	A) Monday	B) Tuesday	C) Wednesday	D) Friday	E) Sunday

Solution: The year 2007 is an ordinary year. So, it has 1 odd day.   day of the year 2007 was Monday   day of the year 2008 will be 2 days beyond Monday   Hence, It will be Wednesday. answer : Wednesday
Answer: C
What is the smallest number which when diminished by 16, is divisible 4, 6, 8 and 10?  Choose the correct choice from the following answers:
A) 136 B) 192 C) 198 D) 122 E) 142

Solution: Required Number   = (LCM of 4,6,8, and 10) + 16   = 120 + 16= 
120 + 16 = 136
136   Option 136
Answer: A
The probability that event M will not occur is 0.6 and the probability that event R will not occur is 0.6. If events M and R cannot both occur, which of the following is the probability that either event M or event R will occur?  Choose the correct choice from the following answers: A) 1/5 B) 2/5 C) 3/5 D) 4/5 E) 12/25

Solution: p(m) =0.4   p(r) =0.4   p(m intersection r) = 0 (If events M and R cannot both occur)   p(m or r) = 0.4+0.4= 
0.4+0.4 = 0.8
0.8   Corrected !!   Answer 4/5
Answer: D
To save money, Arkadelphia Cream Cheese will reduce each dimension of its rectangular box container (which is entirely full of cream cheese) by 60%, and reduce the price it charges its consumers by 60% as well. By what percentage does this increase the price-per-cubic-inch that each consumer will pay for cream cheese?	Choose one
A) 1. No change B) 2. 50% C) 3. 525% D) 4. 300% E) 5. 400%

Solution: Take smart numbers   Let,   L = 20: B = 10: H= 10 of initial box and Price = 100$   Therefore Price / cubic inch = 100 / (20*10*10)= 
100 / (20*10*10) = 1/20 = around 0.05
0.05   Now, when dimensions are reduced by 60% and price also reduced by 60%   L= 8; B=4; H=4 and Price = 40$   Therefore price / cubic inch = 40 / (8*4*4)= 
40 / (8*4*4) = 5/16 = around 0.3125
0.3125   Percentage change= (0.3125- 0.05) *100/ 0.05= 
(0.3125- 0.05) *100/ 0.05 = 525
525%   Answer is 3. 525%
Answer: C
A rower can row upstream at 7 km/hr and downstream at 12 km/hr. What is the rower's rate in still water?	Choose the correct choice from the following answers.
A) 8.0 km/hr B) 8.5 km/hr C) 9.0 km/hr D) 9.5 km/hr E) 10 km/hr

Solution: The rate in still water is 1/2 * (12 + 7)= 
1/2 * (12 + 7) = 19/2 = around 9.5
9.5 km/hr   The answer is 9.5 km/hr.
Answer: D
How many trailing Zeroes does 53! + 54! have?  Options:
A) 12 B) 13 C) 14 D) 15 E) 16

Solution: 53! + 54! = 53! + 54 * 53!   = 53! (1 + 54)   = 53! * 55   Number of trailing 0s in 53! = number of 5s in the expansion of 53!   = 10 + 2= 
10 + 2 = 12
12   There is 1 more 5 in 55.   Hence, total number of trailing 0s= 12 + 1= 
12 + 1 = 13
13   Answer (B).   In most cases, when we are adding multiple terms, all of which have trailing 0s, the sum will have as many trailing 0s as that in the lowest term. Example:  20 + 2300 + 34210000= 
 20 + 2300 + 34210000 = 34_212_320
34212320 -> one 0 because lowest term 20 has one 0.   This case has an exception because of an additional 5 in 55. answer is 13
Answer: B
A computer factory produces 5376 computers per month at a constant rate, how many computers are built every 30 minutes assuming that there are 28 days in one month? Select
A) 2.25.  B) 3.125.  C) 4.5.  D) 4.00.  E) 6.25.

Solution: Number of hours in 28 days = 28*24   Number of 30 mins in 28 days = 28*24*2   Number of computers built every 30 mins = 5376/( 28*24*2)= 
5376/( 28*24*2) = 4
4.00   Answer 4.00.
Answer: D
A mixture of 150 liters of wine and water contains 20% water. How much more water should be added so that water becomes 25% of the new mixture? Choose the correct choice from the following options
A) 65 liters
B) 44
C) 10 liters water
D) 45 liters
E) 8 liters

Solution: Number of liters of water in150 liters of the mixture = 20% of 150 = 20/100 * 150= 
20/100 * 150 = 30
30 liters.   P liters of water added to the mixture to make water 25% of the new mixture.   Total amount of water becomes (30 + P) and total volume of mixture is (150 + P).   (30 + P)= 25/100 * (150 + P)   120 + 4P = 150 + P => P = 10 liters. Answer: 10 liters water
Answer: C
If x > 7, which of the following is equal to (x^2 + 10x + 25)/(x^2 - 25) ?	Choose the correct answer:
A) (x + 5)/(x - 5) B) (x - 4)/(x + 4) C) (x - 2)/(x + 4) D) (x + 4)/(x - 4) E) (x - 8)/(x - 4)

Solution: (x^2 + 10x + 25)/(x^2 - 25)   = (x + 5)(x + 5) / (x + 5)(x - 5)   =(x + 5)/(x - 5)   A. (x + 5)/(x - 5)
Answer: A
For any positive integer n, n>1, thelengthof n is the number of positive primes (not necessary distinct) whose product is n. For ex, the length of 40 is 3, since 50=2x5x5. What is the greatest possible length of a positive integer less than 1000. Choose the correct choice from the following answers:
A) 10 B) 9 C) 8 D) 7 E) 6

Solution: you are missing something in your post:   For any positive integer n , n > 1, thelengthof n is the number of positive primes (not distinct) whose product is n. For example, the length of 50 is 3 since 50 = (2)(5)(5)   the lenght of 1000 = (2)(5)(2)(5)(2)(5) = 6   but we need n < 1000   using 2 as the base = (2)(2)(2)(2)(2)(2)(2)(2)(2) = 6 the length of 512.   the answer is (6)
Answer: E
A certain sum of money at simple interest amounted Rs.900 in 9 years at 5% per annum, find the sum? Options.
A) 337 B) 268 C) 198 D) 620 E) 168

Solution: 900 = P [1 + (9*5)/100]   P = 620'   Answer:620
Answer: D
In an election, candidate Douglas won 66 percent of the total vote in Counties X and Y. He won 74 percent of the vote in County X. If the ratio of people who voted in County X to County Y is 2: 1, what percent of the vote did candidate Douglas win in County Y?  Choose one: A) 25% B) 30% C) 50% D) 75% E) 80%

Solution: given voters in ratio 2:1   let X has 200 votersY has 100 voters   for X 66% voted means 74*200=148 votes   combined for XY has 300 voters and voted 66% so total votes =198   balance votes=198-148= 
198-148 = 50
50   As Y has 100 voters so 50 votes means 50% of votes required   Ans 50%
Answer: C
A & B started one company. They invest Rs. 1,00,000/- each. They deposit the money to Bank. Bank give 1% interest per month. After 2 years B left from company and asked A to return the money with interest. A says it will take time to release the FD and he assure B to give the money withinterest @0.5%. B Agreed this. What is the profit of A? Select:
A) A)48000 B) B)12000 C) C)36000 D) D)24000 E) E)30000

Solution: Total Investment : 100000/-*2=200000/-   Interest rate @ 1%= 200000*1%*12*2= 48000/-   Total : 248000/-   Interest to B : 100000/-*0.5%*12*2 = 12000/-   Paid to B : 100000/- + 12000/- = 112000/-   profit of A : 36000/-   Answer is 36000
Answer: C
How many seconds will a 620 metre long train take to cross a man running with a speed of 8 km/hr in the direction of the moving train if the speed of the train is 80 km/hr? Choose the most appropriate option.
A) 25 B) 30 C) 31 D) 45 E) 60

Solution: Explanation :   Speed of train relatively to man = ( 80- 8)km/hr   = 72 km /hr   = (72 x 5 / 18)m/sec   = 20 m/sec   Time taken to pass the man = (620/ 20)= 
(620/ 20) = 31
31 sec.   Answer : 31
Answer: C
In how many ways, a committee of 5 members can be selected from 6 men and 5 ladies, consisting of 3men and 2 ladies?  Answers.
A) 75
B) 152
C) 175
D) 200
E) 212

Solution: (3 men out 6) and (2 ladies out of 5) are to be chosen   Required number of ways = (6C3 * 5C2) = 200   Answer is 200
Answer: D
By selling a house for Rs.35000, it was found that 1/6 of the outlay was gained, what ought the selling to price to have been in order to have lost 5 p.c?  Choose one
A) 38020	B) 28500	C) 38028	D) 38019	E) 38192

Solution: CP + CP/6 = 35000   CP = 30000   SP = 30000*(95/100)= 
30000*(95/100) = 28_500
28500   Answer: 28500
Answer: B
There are 5 sweets – Milk peda, Ice cream, Rasagulla Paper sweet and Rasamalai that I wish to eat on 5 consecutive days – Monday through Friday, one sweet a day, based on the following self imposed constraints:
1) Paper sweet is not eaten on Monday
2) If Milk peda is eaten on Monday, then Paper sweet must be eaten on Friday
3) If Paper sweet is eaten on Tuesday, Ice cream should be eaten on Monday
4) Rasagulla should be eaten on the day preceding to the day of eating Milk peda.
Based on the above, Rasagulla can be eaten on any day except?
Select the correct option:
A) Tuesday  B) Monday  C) Wednesday  D) Friday  E) Sunday

Solution: as Milk peda is eaten on Monday, then Paper sweet must be eaten on Friday   and Rasagulla should be eaten on the day preceding to the day of eating Milk peda   so milk peda cannot be eaten on monday as day preceding it is friday and condition 2 denies rasagulla on friday   ANSWER:Friday
Answer: D
If a bicyclist in motion increases his speed by 30 percent and then increases this speed by 10 percent, what percent of the original speed is the total increase in speed? Choose the correct choice from the following:
A) 10%	B) 40%	C) 43%	D) 64%	E) 140%

Solution: let the sped be 100   an increase of 30%   the speed now is 130   a further increase of 10% on 130 =13   total increase =43 on 100 =43% 43%
Answer: C
Find the least number with which 16200 should be multiplied, to make it a perfect cube.
Pick one:  A) 36  B) 48  C) 45  D) 360  E) 55

Solution: 16200 = 23 * 34 * 52   A perfect cube has a property of having the indices of all its prime factors divisible by 3.   Required number = 32 * 5 = 45.   ANSWER:45
Answer: C
A train 280 m long passed a pole in 28 sec. How long will it take to pass a platform 650 m long?
Choose the correct choice from the following
A) 93 sec
B) 89 sec
C) 54 sec
D) 27 sec
E) 22 sec

Solution: Speed = 280/28= 
280/28 = 10
10 m/sec.   Required time= (280 + 650)/10= 
(280 + 650)/10 = 93
93 sec.   93 secnswer: 93 sec
Answer: A
A particular library has 75 books in a special collection, all of which were in the library at the beginning of the month. These book are occasionally loaned out through an inter-library program. If, by the end of the month, 60 percent of books that were loaned out are returned and there are 65 books in the special collection at that time, how many books of the special collection were loaned out during that month?	Choose the correct choice from the following choices.
A) 20  B) 25  C) 35  D) 40  E) 55

Solution: Total = 75 books.   60% of books that were loaned out are returned --> 100%-60%=40% of books that were loaned out are NOT returned.   Now, there are 68 books, thus 75-65--  100 -60= 
--  100 -60 = 40
40% of books that were loaned out are NOT returned.   Now, there are 68 books, thus 75-65= 
75-65 = 10
10 books are NOT returned.   {loaned out}*0.4=10 --> {loaned out}=25.   Answer: 25.
Answer: B
The ratio of the number of students appearing for examination in the year 1998 in the states A, Band C was 3 : 5 : 6. Next year if the number of students in these states increases by 20%, 10% and 20% respectively, the ratio in states A and C would be 1 : 2. What was the number of students who appeared for the examination in the state A in 1998?  Options:  A) 7200  B) 6000  C) 7500  D) Data inadequate  E) None of these

Solution: Let the number of students appearing for examination in the year 1998 in the states A, B and C be 3x, 5x and 6x respectively.   According to the question,   3x×120/100 /6x×120/100=12   Hence data inadequate.   Answer Data inadequate
Answer: D
How many positive integers less than 5,000 are evenly divisible by neither 15 nor 20?
Choose the correct choice from the following
A) 4,514 B) 4,477 C) 4,521 D) 4,428 E) 4,349

Solution: integers less than 5000 divisible by 15 5000/15 =333.something , so 333   integers less than 5000 divisible by 20 5000/20 = 238.## , so 238   we have double counted some, so take LCM of 15 and 20 =105 and divide by 5000, we get 47. so all numbers divisible by 15 and 20 = 333 +238 -47= 
333 +238 -47 = 524
524   now subtract that from 4999. 4999- 524= 4477 answer 4,477.
Answer: B
If the sum of the first n positive integers is S, what is the sum of the first n positive integers divisible by 4, in terms of S ?	Choose the correct choice from the following answers.
A) S/2  B) S  C) 2S  D) 2S + 2  E) 4S

Solution: Answer is 4S   Given sum of 1 2 3.....n = S   sum of 4 , 8 , 12 ....2n = 4[sum(1 2 3....n) ] = 4S
Answer: E
In what proportion water must be added to spirit to gain 20% by selling it at the cost price ?	Choose the correct choice from the following
A) 1 : 9 B) 1 : 1 C) 1 : 5 D) 1 : 3 E) 1 : 4

Solution: Let the C.P of spirit be = Rs.10 per litre   S.P of the mixture = Rs. 10 per litre   Profit = 20   C.P of the mixture = Rs. = Rs. per litre   Ratio of water and spirit = 1 : 5   Answer:1 : 5
Answer: C