MU-NLPC/Calc-aqua_rat huggingface dataset:
A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?	Choose the correct choice.
A) 276 m
B) 279 m
C) 240 m
D) 207 m
E) 202 m

Solution: Speed = [54 * 5/18] m/sec   = 15 m/sec.   Length of the train = (15 * 20)= 
(15 * 20) = 300
300 m.   Let the length of the platform be x meters.   Then, x + 300 / 36= 15   x + 300 = 540   x =240 m.   Answer: 240 m
Answer: C
A sells a bicycle to B at a profit of 80% and B sells it to C at a loss of 40%. Find the resultant profit or loss.  Choose the correct option: A) -4% B) 5% C) -5% D) 8% E) -7%

Solution: The resultant profit or loss = 80 - 40 - (80*40)/100= 
80 - 40 - (80*40)/100 = 8
8%   Profit= 8%   Answer is 8%
Answer: D
Which number need to add to 8679921 to get a number exactly divisible by 330?  Choose one:
A) 69 B) 62 C) 61 D) 63 E) 64

Solution: 8679921 / 330 = 26302 and reminder = 261.   330-261= 
330-261 = 69
69   So, the next number divisible by 339 is 69 places in front of 8679921   Which means 69 + 8679921= 
69 + 8679921 = 8_679_990
8679990   69 should be added to 8679921   69
Answer: A
How many integers between 324,700 and 478,600 have tens digit 1 and units digit 3?
Select:
A) 10,300
B) 10,030
C) 1,353
D) 1,352
E) 1,539

Solution: There is one number in hundred with 1 in the tens digit and 3 in the units digit:13, 113, 213, 313, ...   The difference between 324,700 and 478,600 is 478,600-324,700=153,900 - one number per each hundred gives 153,900/100=1,539 numbers.   Answer: 1,539.
Answer: E
If Rs. 762 be divided into three parts, proportional to 1/2:2/3:3/4, then the first part is?  Choose the correct choice from the following answers:
A) A)426
B) B)526
C) C)207
D) D)199
E) E)297

Solution: Given ratio   = 1/2:2/3:3/4 = 6:8:9   1st part = 762 * 6/23   = Rs. 199.   Answer:199
Answer: D
The total car population in a Mumbai is 90,000 out of which 50,000 are made by Honda. Out of every 100 Honda cars, 90 are red in color, but only 60% of the total car population is red. Find the % of non-Honda cars that are red
Choose the correct choice from the following options:
A) 12.5%
B) 19.5%
C) 22.5%
D) 21.5%
E) 20.5%

Solution: Total Honda brand red cars = 90/100 *50000= 
90/100 *50000 = 45_000
45000   Total red cars= 60/100*90000= 
60/100*90000 = 54_000
54000   No. of Non-Honda cars= 90000-50000= 
90000-50000 = 40_000
40000   No. of Non-Honda red cars= 54000 - 45000= 
54000 - 45000 = 9_000
9000   % of Non-Honda red cars= 9000/40000*100= 
9000/40000*100 = 45/2 = around 22.5
22.5%   Answer : 22.5%
Answer: C
If a committee of 3 people is to be selected from among 5 married couples so that the committee does not include two people who are married to each other, how many such committees are possible?	Select:
A) 20 B) 40 C) 50 D) 80 E) 120

Solution: total people=10.. ways to select 3 out of them=10c3=120...   it includes comb including couple..   ways in which couple are included =8c1*5=40..   so ans reqd 120-40=80...   ANS:80
Answer: D
97 students take part in a test and the median score is 85. Which of the following descriptions must be correct?
I. . At most 49 students’ score are equal to or more than 85..
II. At least 49 students’ score are equal to or more than 85.
III. At least 49 students’ score are less than 85. Answers
A) I  B) II  C) III  D) III  E) IIII

Solution: If we order the scores increasingly, then on the 49th place we have the score of 85. There must be 48 scores (those on the right of the 85 score) greater or equal to 85. So, I is necessarily correct.   The scores on the left of the 49th place, all have to be equal or less than 85. Since we can have the extreme case of all the scores 85, neither II, nor III is correct. The question asks for descriptions thatmustbe correct.   Answer II.
Answer: B
What is the probability of drawing a queen from a deck of 52 cards?  Pick one
A) 4/13
B) 1/13
C) 4
D) 1
E) 2/13

Solution: Total number of cards,n(s)=52   Total number of queen cards,n(e)=4   p(e)=n(e)/n(s)=4/52=1/13   Option 1/13 is answer
Answer: B
Find the 2nd least number of four digits which is exactly divisible by 12, 15 and 18?	Pick: A) A)1080 B) B)6480 C) C)3240 D) D)9720 E) E)1240

Solution: The largest five digit numbers are   1080,1240,3240,6480,9720   1080 is divisible by 12,15, and 18 -----(1st least no)   1240 is not divisible by 18, 12 and 15   3240 is divisible by 12,15, and 18 -----(2nd least no)   ANSWER:3240
Answer: C
Sam invested Rs. 6000 @ 10% per annum for one year. If the interest is compounded half-yearly, then the amount received by Sam at the end of the year will be?  Options:	A) 5300.0	B) 24580.0	C) 16537.5	D) 7120.0	E) 6615.0

Solution: P = Rs. 6000 ; R = 10% p.a. = 5% per half-year; T = 1 year   = 2 half-year   Amount = [6000 * (1 + 5/100)2]   = (6000 * 21/20 * 21/20)   = Rs.6615.00   Answer:6615.0
Answer: E
If the numerator of a fraction W is tripled, and the denominator of a fraction is doubled, the resulting fraction will reflect an increase of what percent?  Select: A) 16 1⁄6% B) 25% C) 33 1⁄3% D) 50% E) 66 2⁄3%

Solution: This question can be dealt with conceptually or by TESTing VALUES.   We're told that the numerator of a fraction W is tripled and the denominator of that same fraction is doubled. We're asked for the resulting increase, in percentage terms, of that fraction.   Let's TEST 2/1   If we triple the numerator and double the denominator, we end up with....   (2x3)/(1x2) = 6/2= 
6/2 = 3
3   Since we're increasing 2 to 3, we're increasing that fraction by (3-2)/2= 1/2 of itself = 50%   50%
Answer: D
The first half of a 400-mile trip was travelled in x hours and the second half in y hours. Which of the following is equal to the average speed, in miles per hour, for the entire trip? Choose the correct choice from the following answers.
A) 200/(x + y) B) 400/(x + y) C) 50/x + 50/y D) 200/x + 200/y E) 100/x + 100/y

Solution: Time taken to cover first half i.e 200 miles of a 400 mile trip = x   time taken to cover the second half i.e 200 miles of a 400 mile trip = y   Total time taken = x+y   Average speed for the entire trip =total distance /total time   =400/(x+y)   Answer 400/(x + y)
Answer: B
Which of the following will come in place of the question mark (?) in the following letter series?
BXF, DVI, FTL, HRO,?
Choices
A) JPL
B) KPL
C) JOL
D) JOK
E) None of these

Solution: firstword B then D so theres a diff of 1 word ,so after F then H then J...then second word of BXF is X then -1 word so V ,then with J it will be P ...so ans is JPL...   JPLNSWER:JPL
Answer: A
Pakistan, India and Srilanka are engaged in a missile war, such that they fire one after the other, in a sequence, the sequence selected by draw of lots. The rules of war are such that the 3 countries keep on shooting at each other until they hit with the missile. This goes on until there is one last country left unhit, and then the war ends. The chances that Pakistan hits its target is 100%, Srilanka hits the target is 80% and India hits the target is 50%.
Who has the highest chance of winning the war? Pick one:	A) India	B) Pakistan	C) Srilanka	D) None of these	E) Cannot be determined

Solution: Solution:   India has the highest chances of winning the war (47/90)   Missile Firing order:   Chances of Remaining Unhit - Pakistan:   Chances of Remaining Unhit - Srilanka:   Chances of Remaining Unhit - India   Pakistan - Srilanka - India   1/2 0 1/2   Pakistan - India - Srilanka   1/2 0 1/2   India - Pakistan - Srilanka   1/10 16/45 49/90   Srilanka- Pakistan - India   1/2 0 1/2   Srilanka - India - Pakistan   1/10 16/45 49/90   India - Srilanka - Pakistan   1/10 16/45 49/90   Total chances of being unhit (sum of the probabilities divided by 6):   27/90 16/90 47/90   Answer None of these
Answer: D
A certain list consists of 21 different numbers. If n is in the list and n is 4 times the average(arithmetic mean) of the other 20 numbers in the list, then n is what fraction W of the sum of the 21 numbers in the list?	Choose the correct answer: A) 1/20 B) 1/6 C) 1/5 D) 4/21 E) 5/21

Solution: This is how I used to calculate which I think works pretty well:   if you let the average of the 20 other numbers equal a, can you write this equation for sum of the list (S)   n + 20a = S   the question tells us that   n = 4a   plug this back into the first equation and you get that the sum is 24a   4a + 20a = 24a   therefore fraction W of n to the total would be   4a/24a or 1/6   answer 1/6 4  + 20= 
 4  + 20 = 24
24a   therefore fraction W of n to the total would be   4a/24a or 1/6   answer 1/6
Answer: B
A gold mine has 5% depletion rate. i.e. after each year of mining, the miners extract 5/100 of the mine's ore. If the current quantity of the gold reserves of the mine is currently estimated at 2 tons, how much gold would the miners be able extract over the next 4 years?	Choices:
A) 0.400 tons B) 0.200 tons C) 0.175 tons D) 0.160 tons E) 0.185 tons

Solution: X is the quantity of gold reserves of the mine   After a year of mining the quantity of gold left would be X1=X-5/100X i.e. X1=95/100X   Same thing for X2, X3, X4, respectively representing the quantity of gold left after 2, 3, 4 years of mining.   So we have:   X1=95/100 X   X2=95/100 X1   X3=95/100 X2   X4=95/100 X3   By multiplying both ends of the equations we get:   X1*X2*X3*X4 = (95/100)^4 X*X1*X2*X3   Simplification leaves us with:   X4 = (95/100)^4 X   X4 is the quantity of gold left after four years of mining. So the cumulative quantity of gold (Q4) which has been extracted after 4 years is: Q4= X-X4=X-(95/100)^4X i.e. Q4 = X (1-(95/100)^4)   In this case, given X was: X=2 tons   So Q4 = 2 * (1-(95/100)^4) = 2 * (1-81450625/10^8) =2 * 18549375/10^8 = 0.1854 tons round to Q4=0.185 ton   Answer 0.185 tons.
Answer: E
In how many ways can seven friends be seated in a row having 35 seats, such that no two friends occupy adjacent seats?  Choose the correct choice from the following answers:
A) 29P7
B) 29C7
C) 28P7
D) 28C7
E) None

Solution: Solution:   First let us consider the 28 unoccupied seats.   They create 29 slots- one on the left of each seat and one on the right of the last one.   We can place the 7 friends in any of these 29 slots i.e. 29P7 ways.   29P7nswer 29P7
Answer: A
A fraction becomes 2/3 when 1 is added to both, its numerator and denominator.
And ,it becomes 1/2 when 1 is subtracted from both the numerator and denominator. Find the fraction.
Select
A) 1/2  B) 3/4  C) 2/3  D) 3/5  E) 2/5

Solution: Let the required fraction be x/y. Then,   x+1 / y+1 = 2 / 3 => 3x – 2y = - 1 …(i) and x – 1 / y – 1 = 1 / 2   	2x – y = 1 …(ii)   Solving (i) and (ii), we get : x = 3 , y = 5   therefore, Required fraction= 3 / 5.   Answer is 3/5.
Answer: D
Given that there are 5 basketball players per team, how many ways can you select 3 basketball players from 3 teams if no more than one player can be selected from each team? Choose the correct answer:
A) 25
B) 30
C) 60
D) 75
E) 90

Solution: 3 teams can be selected from 3 teams in 3C3 ways = 1 ways   as the condition is that the 2 players should be from different teams   one player can be chosen from 1st team in 5 ways   similarly another player can be chosen from 2nd team in 5 ways   Total number of ways to choose the player = 5 * 5 * 1= 
5 * 5 * 1 = 25
25 ways   Correct 25nswer - 25
Answer: A
At what time will the train reach city X from city Y?
I.The train crosses another train of equal length of 200 metres and running in opposite directions in 15 seconds.
II.The train leaves city Y and 7.15 a.m. for city X situated at a distance of 558 km.
III.The 200 metres long train crosses a signal pole in 10 seconds.
Choose the correct option:
A) I only  B) II only  C) III only  D) II and III only  E) All I, II and III are required.

Solution: Explanation:   From the statement I, we get length of the train is 200 metres (Redundant info while comparing with Statement III).   The rest of the info given in this statement cannot be used for calculating the speed of the train,   because the two trains might run at different speed.   III gives, speed =200/1o m/sec = 20 m/sec = {20 x 18/5} km/hr = 72 km/hr.   II gives, time taken =(558/72) hrs = 31/4 hrs = 7 3/4 hrs = 7 hrs 45 min.   So, the train will reach city X at 3 p.m.   .’. Hence II and III only gives the answer.   Answer II and III only
Answer: D
How to additions fast. For example we have to do a simple addition like 234 + 563+ 985 + 349.	Choose the correct choice from the following answers:
A) 2131	B) 7399	C) 2997	D) 2769	E) 2771

Solution: Instead of doing like this we first add all the digits in the hundred's place. 2 + 5 + 9 + 3 = 19. Put 2 zero's to the right hand side so we get 1900.   Now add the digits in the tenth's place. 3 + 6 + 8 + 4 = 21. Put 1 zero to the right hand side so we get 210.   Now add the digits in the units place   4 + 3 + 5 + 9= 
  4 + 3 + 5 + 9 = 21
21.   Now  1900 + 210 + 21= 
 1900 + 210 + 21 = 2_131
2131   2131nswer:2131
Answer: A
Of the 11 members of a football team in school, 9 are trained to play the offensive position, 6 can play defensive position, and 4 can play both position. If one member is chosen at random, what is the probability that the member chosen will be someone who play either position ?
Choose one
A) a) 3/11	B) b) 4/11	C) c) 0	D) d) 6/11	E) e) 7/11

Solution: You know how to solve for Total number of people who can play at one position:   Total = n(A) + n(B) - n(A and B)   Total people who can play at least one position = 9+6-4= 
9+6-4 = 11
11   So all 11 people know how to play at least one position. Hence, if you pick anyone, the probability is 0 that he wouldn't know how to play any position   Answer (c) 0)
Answer: C
Josh spends a total of $6.00 buying N items in the convenience store. If each of the items is either a 5 cents single bubblegum, or a 50 cents bubblegum pack, then N may be which of the following?	Choose one
A) 99 B) 111 C) 101 D) 109 E) 140

Solution: Let x be 0.05$ single bubblegum and y be the total 0.5$ packs ---> 0.05x+0.5y=6.00 ---> x+10y=120 ...(1)   Also, x+y=N ...(2)   Solving 1 and 2 , we get, N = 120-9y ---> only value satisfied is when y = 1---> N = 120-9= 
120-9 = 111
111. B is the correct answer. Other options are not equal to multiples of 9 removed from 120.
Answer: B
Define a* by the equation a* = π-x. Then ((−π)*)* =
Choose the correct choice from the following choices:
A) −2π B) -1 C) −π D) 2π E) 4π

Solution: for a* f(f(−π)) = f(π − (−π)) = f(π + π) = f(2π) = π − 2π = −π=−π
Answer: C
If two sides of a triangle are 12 and 2, which of the following could be the area of triangle?
1. 35
2. 48
3. 56	Choose the correct choice from the following answers: A) a) 1 only B) b) 1 and 2 only C) c) 1 and 3 only D) d) 2 and 3 only E) e) 1, 2 and 3 only

Solution: when two sides of a triangle are known , the maximum area occurs when the angle between those two sides is 90.   lets say base = 12 , height =8 (angle = 90)   maximum area = (1/2)*12*8= 
(1/2)*12*8 = 48
48 ( this is the same maximum area even when base is 8 and height is 12).   if we fix the base and keep lowering the angle, it will result in a lower height . hence the resulting area will always be < 48.   C,D and E are ruled out.   1, 2 and 3 are possible areas as their areas are less than 48.   Hence the answer is e) 1, 2 and 3 only.
Answer: E
A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If three marbles are picked at random, what is the probability that they are all blue?	Choose the correct choice from the following
A) 1/45	B) 1/29	C) 1/455	D) 2/275	E) 1/495

Solution: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles.   Probability that all the three marbles picked at random are blue = Â³1/455â‚ƒ/Â¹âµ1/455â‚ƒ = (1 * 3 * 2 * 1)/(15 * 14 * 13) = 1/455   Answer: 1/455
Answer: C
At 3:40, the hour hand and the minute hand of a clock form an angle of: Choose the correct choice:
A) 130 B) 125 C) 140 D) 154 E) 145

Solution: Angle traced by hour hand in 12 hrs. = 360Â°.   abgle traced it in 11/3 hrs = (360/12 * 11/3)= 
(360/12 * 11/3) = 110
110   angle traced by min hand in 60 min= 360   angle traced by it in 40 min = (360/60*40)= 
(360/60*40) = 240
240   req  (240-110)= 
 (240-110) = 130
130d
Answer: A
If there are 30 red and blue marbles in a jar, and the ratio of red to blue marbles is 2:3, what is the probability that, drawing twice, you will select two red marbles if you return the marbles after each draw?	Select
A) 1/25  B) 2/25  C) 3/25  D) 4/25  E) 21/25

Solution: 0 red and blue marbles in a jar, and the ratio of red to blue marbles is 2:3   So, 5x=30 ---> x=6   Red marbles = 2*x = 2*6= 
2*6 = 12
12   Blue marbles= 3*x = 3*6= 
3*6 = 18
18   Prob to select a red marble= 12/30 = 2/5   Prob to select 2 red marbles with replacement = 2/5*2*5= 
2/5*2*5 = 4
4/25   Hence, answer will be 4/25.
Answer: D
A certain car dealership sells economy cars, luxury cars, and sport utility vehicles. The ratio of economy to luxury cars is 3:5. The ratio of economy cars to sport utility vehicles is 4:3. What is the ratio of luxury cars to sport utility vehicles? Choose the most appropriate option
A) 9:8
B) 8:9
C) 3:2
D) 20:9
E) 1:2

Solution: The ratio of economy to luxury cars is 3:5 --> E:L = 3:5 = 12:20.   The ratio of economy cars to sport utility vehicles is 4:3 --> E:S = 4:3 = 12:9.   Thus, L:S = 20:9.   Answer: 20:9.
Answer: D
The ratio of kamla and nisha is 6:5 and the sum of their ages is 44.what will be the ratio of their ages after 8 years.  Choose the most appropriate option:  A) 5:6  B) 7:8  C) 8:7  D) 12:11  E) 14:13

Solution: Answer:	let age of kamla is 6x and age of nisha is 5x.   then,6x+5x=44,11x=44,x=4   after 8 year the ratio of their ages=6x+8/5x+8=8:7   answer 8:7
Answer: C
The ratio of two quantities is 7 to 12. If each of the quantities is divided by 3, what is the ratio of these 2 new quantities?  Choose the correct choice from the following answers
A) 3.5:6
B) 14:24
C) 7:12
D) 2.3:4
E) It cannot be determined from the information given

Solution: If both sides of a ratio are divided by the same number there is no change in the ratio.   5:6 means 7x:12x...   The ratio starts as 7/(1): 12/(1). So when you diveide by three it becomes 7/(3): 12/(3)..   So if the Xs are equal the ratio does not change..   ANSWER:7:12
Answer: C
There are six cards in which it has two king cards. all cards are turned down and two cards are opened what is the possibility to get two kings.
Choose one:
A) 1/15 B) 2/15 C) 3/15 D) 4/15 E) 6/15

Solution: P0SSIBLITY TO GET TWO KINGS IS 2C2/6C2=1/15   1/15NSWER:1/15
Answer: A
A fruit seller sells mangoes at the rate of Rs.8 per kg and thereby loses 20%. At what price per kg, he should have sold them to make a profit of 5%  Choose the most appropriate option
A) Rs 8.5 B) Rs 9.5 C) Rs 10.5 D) Rs 11.5 E) None of these

Solution: Explanation:   80 : 8 = 105 : x   x= (8×105/80)   = Rs 10.5   Option Rs 10.5
Answer: C
A, B and C enter into a partnership. A invests 3 times as much as B invests and 2/3 of what C invests. At the end of the year, the profit earned is Rs. 44000. What is the share of C? Choose the most appropriate option:
A) Rs. 12000 B) Rs. 13375 C) Rs. 11750 D) Rs. 11625 E) None of these

Solution: Explanation:   Let the investment of C be Rs. x.   The inverstment of B = Rs.(2x/3)   The inverstment of A = Rs. (3 × (2/3)x) = Rs. (2x)   Ratio of capitals of A, B and C = 2x : 2x/3 : x = 6 : 2 : 3   C's share = Rs. [(3/11) × 44000] = Rs. 12000   Rs. 12000nswer: Option Rs. 12000
Answer: A
7 points are marked on a straight line and another 6 points are marked on a second straight line with no points in common. How many triangles can be constructed with vertices from among the above points? Select.
A) 91 B) 105 C) 196 D) 21 E) 231

Solution: getting the answer 231 which is not in the choices, what is the source of the problem?   7C2* 6C1 + 6C2* 7C1 =231   231
Answer: E
At exactly what time past 8:00 will the minute and hour hands of an accurate working clock be precisely perpendicular to each other for the first time?  Choose the most appropriate option
A) 20 13/21 minutes past 7:00	B) 21 9/11 minutes past 8:00	C) 21 3/23 minutes past 7:00	D) 21 9/11 minutes past 7:00	E) 22 4/9 minutes past 7:00

Solution: 5.5 is the angle between minute n hour, this is what I was taught...so shouldn't it be solve by dividing 90 with 5.5?   That would have been the case if your initial difference between the hour and the minute hand was = 0 degrees or in other words, both minute and hour hands were at the same location. But as per the question, you are asked for time AFTER 8:00. At 8:00, the angle between the hour and the minute hand is 210 degrees. you need to take this into account as well.   So in order for the difference to decrease to 90 degrees, the minute hand must eat away this difference of   210-90= 
  210-90 = 120
120 degree at the rate of 5.5 degrees per minute ---> 120/5.5= 21 9/11 minutes.   Thus, 21 9/11 minutes past 8:00 is the correct answer.
Answer: B
Nancy works 2 days per week at a rate of x dollars per day. If Nancy works more than 3 days per week, any extra days are paid at double her normal rate. Nancy worked 4 weeks with no overtime, and then worked 3 more weeks, each with y days of overtime. Which of the following represents Nancy’s total earnings over this period? Choose the correct choice from the following options.
A) a) 3y(7x+2xy)	B) b) 3x+12y	C) c) 3xy(7x+2)	D) d) 3x(2y+7)	E) e) 17x+6xy

Solution: Payment of a week for 2 days a week = $2x   Payment of 4 weeks for 2 days a week = $2x*4 = $8x   Payment of a week for y days overtime a week 2 *4= 
2 *4 = 8
$8x   Payment of a week for y days overtime a week= $3x+$2xy   Payment of 3 weeks for y days overtime a week = ($3x+$2xy)*3   Total e) 17x+6xyarnings = $8x + ($3x+$2xy)*3 = 17x+6xy   Answer: option e) 17x+6xy
Answer: E
Two pipes A and B can separately fill a cistern in 60 min and 75 min respectively. There is a third pipe in the bottom of the cistern to empty it. If all the three pipes are simultaneously opened, then the cistern is full in 50 min. In how much time, the third pipe alone can empty the cistern?
Choices.
A) 90 min
B) 100 min
C) 110 min
D) 120 min
E) 130 min

Solution: Work done by the third pipe in 1 min = 1/50 - (1/60 + 1/75) = - 1/100.   [-ve sign means emptying]   The third pipe alone can empty the cistern in 100 min.   ANSWER:100 min
Answer: B
Can you please walk me through how to best approach this problem? Thanks
If #p# = ap^3+ bp – 1 where a and b are constants, and #-3# = 2, what is the value of #3#?	Choose one.
A) -4 B) 0 C) -2 D) -3 E) -5

Solution: #p# = ap^3 + bp - 1   #-3# = 2   putting p = -3 in above equation   -27a -(3b +1) = 2 or   #-5# = (27a+3b+1) = -2   therefore 27a+3b = -3 .....(1   now putting p = 3   #3# = 27 a+3b - 1   using equation 1(27a+3b = -3)   #3# = -3-1 = -4   hence -4
Answer: A
A, B, C and D enter into partnership. A subscribes 1/3 of the capital B 1/4, C 1/5 and D the rest. How much share did A get in a profit of Rs.2400 ?	Choices
A) s. 832	B) s. 830	C) s. 822	D) s. 812	E) s. 800

Solution: Let the total amount in the partnership be 'x'.   Then A's share = x/3   B's share = x/4   C's share = x/5   D's share = x - (x/3 + x/4 +x/5) = 13x/60   A : B : C : D = x/3 : x/4 : x/5 : 13x/60 = 20 : 15 : 12 : 13   A's share in the profit of Rs. 2400 = 20 (2400/60) = Rs. 800.   Answer: s. 800
Answer: E
Jenny can divide her sweets equally to 5 people and also to 6 people equally but not to 12 people. What could be the number? Choose the correct choice from the following:
A) 120	B) 134	C) 127	D) 30	E) 650

Solution: Option (B) and (C) are ruled out as they are not divisilble by 5 and 6.   120 is both divisible by 5 and 6 but also by 12, so it wrong.   650 is divisible by 5 but not by 6.   hence,   (30) is the answer, as it is both divisible by 5 or 6 but not by 12
Answer: D
If n=t^3 , when n and t are positive integers and 8, 9, 10 are each factors of n, which of the following must be a factor of n?	Choose one:
A) 16
B) 175
C) 225
D) 275
E) 625

Solution: n = 8p,n = 9q and n = 10r.Thus,n^3=t^6=2^4∗3^2∗5∗[k is some positive integers]   Thus, for t to be a positive integer, k must atleast have the value = 2^2∗3^4∗5^5   Thus,n=t3=2^3∗3^2∗5^2∗y[y is a positive integer]   225 is definitely a factor of n.   ANSWER:225
Answer: C