MU-NLPC/Calc-aqua_rat huggingface dataset:
The sides of a triangle are in the ratio of
1/2:1/3:1/4. If the perimeter is 52 cm, then find the length of the smallest side.
Choose the correct choice from the following answers.
A) 12 cm  B) 14 cm  C) 16 cm  D) 18 cm  E) None of these

Solution: Explanation:   Ratio of sides =1/2:1/3:1/4=6:4:3   Perimeter=52cm   So sides are =(52∗6/13)cm,   (52∗4/13)cm,   (52∗3/13)cm   a = 24 cm, b = 16 cm and c = 12 cm   Length of the smallest side = 12 cm   Option 12 cm
Answer: A
What is the total number of positive integers that are less than 1000 and that have no positive factor in common with 1000 other than 1? Choose the correct answer
A) 100	B) 200	C) 300	D) 400	E) 500

Solution: Since 1000=2^3*5^3 then a number can not have 2 and/or 5 as a factor.   The odd numbers do not have 2 as a factor and there are 500 odd numbers from 1 to 1000.   We then need to eliminate the 100 numbers that end with 5, that is 5, 15, 25,...,995.   There are a total of 500 - 100= 
500 - 100 = 400
400 such numbers between 1 and 1000.   The answer is 400.
Answer: D
A reduction of 10% in the price of rice enables a lady to obtain 20kgs more for Rs.1000, find the original price per kg?  Select the correct option:
A) 6.0
B) 5.0
C) 5.2
D) 5.6
E) 5.4

Solution: Answer:	1000*(10/100)= 
1000*(10/100) = 100
100 --- 20   ? --- 1=> Rs.5   1000 --- 900   ? --- 5 => Rs.5.6.Answer: 5.6
Answer: D
Set A = {1, 2, 3, 4, 5, 6, q}
Which of the following possible values for q would cause Set A to have the smallest standard deviation?	Choose the correct choice from the following answers:
A) 1  B) 2.5  C) 3  D) 3.5  E) 7

Solution: I agree. The mean of the set q =1,2,3,4,5,6 is 3.5 . Now if we add one extra number to the set, in order for the standard deviation to be minimum, that number must be as close as possible to the original set (1,2,3,4,5,6). Therefore we have to choose the number closest to 3,5 from the options we have, leaving D as the best choice.   Answer 3.5.
Answer: D
If X = the product of five distinct prime numbers, how many factors does X have besides 1 and itself?  Pick
A) 24  B) 30  C) 36  D) 42  E) 48

Solution: Since X has 5 distinct prime factors, X has a total of 2^5 = 32 factors.   Besides 1 and itself, X has 30 factors.   The answer is 30.
Answer: B
Pipe P can drain the liquid from a tank in 3/4 the time that it takes pipe Q to drain it and in 3/3 the time that it takes pipe R to do it. If all 3 pipes operating simultaneously but independently are used to drain liquid from the tank, then pipe Q drains what portion of the liquid from the tank? Choose one.
A) 9/29  B) 8/23  C) 3/8  D) 3/11  E) 3/4

Solution: Suppose Q can drain in 1 hr. So, rQ = 1/1= 
1/1 = 1
1   So, rP= 1/[(3/4)rQ] = 4/3   Also, rP = rR/(3/3) => 4/3 = rR/(3/3) => rR = 4/3   Let H is the time it takes to drain by running all 3 pipes simultaneously   So combined rate = rC = 1/H = 1 + 4/3 + 4/3 = 11/3= 1/(3/11)   Thus running simultaneously, Pipe Q will drain 3/11 of the liquid.   Thus answer = 3/11.
Answer: D
In Sam's hanger there are 23 boxes, 19 out of the boxes are filled with toys and the rest are filled with electrical appliances. 8 boxes are for sale, 5 of them are filled with toys. How many boxes with electrical appliances are in Sam's hanger that is not for sale?  Choices.
A) 1.
B) 2.
C) 3.
D) 4.
E) 5.

Solution: Total boxes = 23   Filled with toys = 19   Filled with appliance = 4   Total boxes for sale = 8   Toy boxes for sale = 5   1.ppliance boxes for sale = 3   1.ppliance boxes not for sale = 4 - 3= 
4 - 3 = 1
1   Correct Option: 1.
Answer: A
The length of the bridge, which a train 130 meters long and travelling at 45 km/hr can cross in 30 seconds, is: Choose the correct choice from the following options:
A) 2399  B) 277  C) 245  D) 88  E) 232

Solution: Speed = (45 * 5/18) m/sec = (25/2) m/sec. Time = 30 sec. Let the length of bridge be x meters. Then, (130 + X)/30   = 25/2 ==> 2(130 + X) = 750 ==> X = 245 m.   Answer: 245
Answer: C
In a factory, an average of 60 TV's are produced per day for the fist 25days of the months. A few workers fell ill for the next 5days reducing the daily avg for the month to 58 sets/day . The average production per day for day last 5days is ?	Choose the correct choice from the following choices:  A) 20  B) 36  C) 48  D) 50  E) 59

Solution: Production during these 5 days = Total production in a month - production in first 25 days.   = 30 x 58 - 25 x 60   = 240   ∴ Average for last 5 days = 240 / 5= 
240 / 5 = 48
48   48
Answer: C
What will be the day of the week 15th August, 2010?
Choose the correct choice from the following answers:
A) Sunday  B) Saturday  C) Monday  D) Thursday  E) Wednesday

Solution: 15th Aug 2010 = (2009 years + period from 1-Jan-2010 to 15-Aug-2010)   We know that number of odd days in 400 years = 0   Hence the number of odd days in 2000 years = 0 (Since 2000 is a perfect multiple of 400)   Number of odd days in the period 2001-2009   = 7 normal years + 2 leap year   = 7 x 1 + 2 x 2 = 11 = (11 - 7x1) odd day = 4 odd day   Days from 1-Jan-2010 to 15-Aug-2010   = 31 (Jan) + 28 (Feb) + 31 (Mar) + 30 (Apr) + 31(may) + 30(Jun) + 31(Jul) + 15(Aug)   = 227   227 days = 32 weeks  + 3= 
 + 3 = 3
3 odd day   Total number of odd days= (0 + 4 + 3)= 
(0 + 4 + 3) = 7
7 odd days= 0 odd day   0 odd day = Sunday   Hence 15th August, 2010 is Sunday.   Sundaynswer is Sunday
Answer: A
Paul's income is 40% less than Rex's income, Quentin's income is 20% less than Paul's income, and Sam's income is 40% less than Paul's income. If Rex gave 60% of his income to Paul and 40% of his income to Quentin, Paul's new income would be what fraction of Quentin's new income?	Choose one
A) 11/12	B) 13/17	C) 13/19	D) 15/11	E) 11/19

Solution: MAKE R = 10   P = 0.6R = 6   Q = 0.8P = 4.8   S= 0.6P = 3.6   FOR THAT WE GET P = 12   AN15/11 Q 8.8   SO 12/8.8 = 3/ 2.2   Ans:15/11
Answer: D
If n is even, which of the following cannot be odd?
I	n + 3
II	3n
III	n^2 - 1 Choose one:
A) I only
B) II only
C) III only
D) I and II only
E) I, II and III

Solution: Let take a look at I   n + 3   we have this formula : even + odd = odd   => n + 3 is odd   III: n^2 - 1   n^2 always be even   so n^2 - 1 is odd   => only II is always even   => answer is II only
Answer: B
In how many ways can 5 boys and 3 girls be seated on 7 chairs so that no two girls are together? Pick one
A) 5760  B) 14400  C) 480  D) 56  E) 1440

Solution: Let us take opposite of the constraint.   2 girls sitting together:	:   1 case is GGBGBBBB.   Total number of ways=3!*5!*5 with just shifting the rightmost girl.   Then the 2 leftmost girls can shift one position , and using the above reasoning, the total number of ways = 3!*5!*4 and so on till the rightmost girl has 1 position.   So total number of ways = 3!*5!(5+4+3+2+1)=120*90= 
120*90 = 10_800
10800   Similarly another case is:   GBGGBBBB.   Using the above reasoning, the total number of cases is: 3!*5!*(15)=10800   Let us take 3 girls sitting together   GGGBBBBB   There are 3! *5! Ways. The 3 leftmost girls can shift 6 positions. So there are a total of 3!*5!*6=4320 ways   So total is   2*10800 + 4320= 
  2*10800 + 4320 = 25_920
25920   The total number of possibilities= 8! Ways =40,320   Answer is 40320-25920=1440   Hence 1440.
Answer: E
Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 3 or 5?
Choices.
A) 1/2  B) 1/2  C) 8/15  D) 9 by 20  E) 9/24

Solution: Explanation :   Here, S = {1, 2, 3, 4, ...., 19, 20}.   Let E = event of getting a multiple of 3 or 5 = {3, 6 , 9, 12, 15, 18, 5, 10, 20}.   P(E) = n(E)/n(S) = 9/20   Answer : 9 by 20
Answer: D
A bag contains 12 red marbles. If someone were to remove 2 marbles from the bag, one at a time, and replace the first marble after it was removed, the probability that neither marble would be red is 49/64. How many marbles are in the bag?
Choose the correct option
A) 24
B) 48
C) 60
D) 96
E) 84

Solution: ok let me see if i can explain what went on in the previous post   lets say i have x marbles in the bag in total --> out of them 12 are red   so the probability of pulling a non-red marble is (x -12) / x   now the marble is placed back in the bag and we have x marbles again, of which again 12 are red. so the probability of pulling a non-red marble out is (x-12) / x   probability theorm states that if the probability of event A occuring is m and the probability of event B occuring is n then the probability of both A and B occuring is m*n   so therefore the probability of 2 non-red marbles getting pulled out is [(x-12)/x ] * [(x-12)/x]   this is given as 49/64   -->(x-12)^2= 49/64   x^2   square rooting u have x-12/x = 7/8 or x = 96   96
Answer: D
What least number must be added to 9599, so that the sum is completely divisible by 100 ?  Choose one:
A) 1 B) 2 C) 4 D) 6 E) 8

Solution: If we divide 9599 by 100 remainder is 99   100-99= 
100-99 = 1
1   1nswer : 1
Answer: A
A can do a piece of work in 8 days. B can do it in 12 days. With the assistance of C they completed the work in 4 days. Find in how many days can C alone do it?
Answers
A) 87 days B) 20 days C) 16 days D) 24 days E) 36 days

Solution: C = 1/4 - 1/8 - 1/12 = 1/24   => 24 days   Answer:24 days
Answer: D
The speed at which a boy can row a boat in still water is 60 kmph. If he rows downstream, where the speed of current is 12 kmph, what time will he take to cover 220 metres?	Pick one:
A) 7 B) 8 C) 9 D) 10 E) 11

Solution: Speed of the boat downstream = 60 + 12= 
60 + 12 = 72
72 kmph= 72 * 5/18= 
72 * 5/18 = 20
20 m/s   Hence time taken to cover 220 m= 220/20= 
220/20 = 11
11 seconds. Answer: 11
Answer: E
A shop owner professes to sell his articles at certain cost price but he uses false weights with which he cheats by 50% while buying and by 10% while selling. What is his percentage profit?
Choices
A) 10.22%
B) 20.22%
C) 21.22%
D) 50%
E) Can't be calculated

Solution: The owner buys 100kg but actually gets 150kg;   The owner sells 100kg but actually gives 90kg;   Profit: (150-90)/90*100=50%   Answer: 50%.
Answer: D
A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?
Pick.
A) 40 sec  B) 65 sec  C) 18 sec  D) 16 sec  E) 17 sec

Solution: Speed = 45 * 5/18   = 25/2 m/sec   Total distance covered   = 360 + 140= 
360 + 140 = 500
500 m   Required time= 500 * 2/25= 
500 * 2/25 = 40
40 sec   40 secnswer:40 sec
Answer: A
Find the fourth proportional to 4, 9, 12
Pick.
A) 17  B) 37  C) 47  D) 67  E) 27

Solution: Let the fourth proportional to 4, 9, 12 be x.   Then, 4 : 9 : : 12 : x   =4 x x=9x12   =X=(9 x 12)/14=27;   Fourth proportional to 4, 9, 12 is 27.   Answer is 27
Answer: E
After taking N tests, each containing 100 questions, John had an average of 70% of correct answers. How much does John need to score on the next test to make his average equal 75%?
M13-03. Choose the correct choice from the following answers.
A) N−35
B) N+72
C) 2N+78
D) 2N+72
E) 2N−35

Solution: Say N=1.   So, after 1 test John has 70 correct answers.   In 2 tests, so in 200 questions he needs to have  0.75*200= 
 0.75*200 = 150
150 correct answers, so in the second test he must get   150-70= 
  150-70 = 80
80 questions correctly.   Now, plug N=1 into the answer choices to see which one yields 80. Only option D fits.   Answer: 2N+78.
Answer: C
If X,Y is 15%,30% smaller than Z then how much percentage is Y greater than X?	Choose one.
A) 12 1/2 %	B) 13%	C) 13 1/2%	D) 14%	E) 17 11/17%

Solution: X = 85 %   Y = 70 %   Z = 100 %   X-Y/X × 100 = 5/85× 100 = 17 11/17 % greater than X   17 11/17%
Answer: E
What is the greatest power that 3 can be raised to so that the resulting number is a factor of 9!?
Select the correct option.
A) 2 B) 3 C) 4 D) 5 E) 6

Solution: the number of 3s in 9!= 9/3=3..   ans 3
Answer: B
In the faculty of Reverse-Engineering, 350 second year students study numeric methods, 250 second year students study automatic control of airborne vehicles and 100 second year students study them both. How many students are there in the faculty if the second year students are approximately 25% of the total?	Choices:
A) 1800
B) 1900
C) 2100
D) 2000
E) 2200

Solution: Total number of students studying both are 350 + 250 - 100= 
350 + 250 - 100 = 500
500 (Subtracting the 100 since they were included in the both the other numbers already).   So 25% of total is 500, so 100% is 2000   Answer is 2000
Answer: D
66% of respondents to a survey consisted of those who used both M and N and those who used neither M nor N. 53% of respondents did not use M. 47% used N. What percent of respondents used only N? Options.
A) 19.5%  B) 21.5%  C) 20%  D) 18.5%  E) 17%

Solution: From the question, we can summarize the information as follows:   N Not N   M X   Not M Ans y 53   47 100   Then we can set a system of 3 equations 3 unknowns described below:   X + Y = 66   X + Ans = 47   Y + Ans = 53   Sum up all three equations to get 2X + 2Y + 2Ans = 166   Divide both sides by 2 to get X + Y + Ans = 83   Replace X + Y with 66 to get 66 + Ans = 83   Substract 66 from both sides to get Ans = 83 - 66= 
83 - 66 = 17
17   The answer must be 17%.
Answer: E
A sum was put at simple interest at a certain rate for 10 years . Had it been put at 5% higher rate , it would have fetched Rs.600 more. What was the Sum? Choose the correct choice from the following
A) 1200 B) 2877 C) 2779 D) 1770 E) 1887

Solution: Explanation:   At 5% more rate, the increase in S.I for 10 years = Rs.600 (given)   So, at 5% more rate, the increase in SI for 1 year = 600/10 = Rs.60/-   i.e. Rs.60 is 5% of the invested sum   So, 1% of the invested sum = 60/5   Therefore, the invested sum = 60 × 100/5 = Rs.1200   1200nswer: 1200) Rs.1200
Answer: A
A can do a piece of work in 21 days and B in 28 days. Together they started the work and B left after 4 days. In how many days can A alone do the remaining work?	Choose the correct choice from the following:	A) 14	B) 8	C) 20	D) 10	E) 7

Solution: Option D   Explanation:   Let A worked for x days.   x/21 + 4/28 = 1 => x/21 = 6/7 => x = 18   A worked for 18 days. So, 14 can complete the remaining work in 18 - 4= 
18 - 4 = 14
14 days.
Answer: A
If a and b are the two values of t that satisfy
the equation t^2 â€“ 7t + 10 = 0, with a > b, what is the value of a â€“ b?  Choose the correct choice from the following options.
A) 2	B) 3	C) 4	D) 5	E) 6

Solution: Factor the left side of the equation:   t^2 â€“ 7t + 10 = 0   (t â€“ 2)(t â€“ 5) = 0   t = 2, t = 5   Thus, a = 5 and b = 2. So a â€“ b = 5 â€“ 2 = 3.   The answer is 3.
Answer: B
If 6 Men or 7 Women take 6 days to complete some work, how many days will 10 Men and 6 Women working together take to complete the work?
Can anyone explain please?
Pick one:
A) 1. 3/2 days  B) 2. 2 Days  C) 3. 9/4 days  D) 4.5/2 days  E) 5.126/53 days

Solution: 6 men or 7 women takes 6 days to complete the work   So 6M = 7W   W = 6/7M   1 man in 1 day does 1 unit of work   so 6 M in 6 M = 36 units of work   now 10 M and 6 W = 10 M + 6(6/7)M   = 10M + 36M/7   = 106M/7   Since both set do the same work   106M/7 in n Days = 36 units of work   n = 36 *7/106 = 126/53 days.   5.126/53 days
Answer: E
A train passes a station platform in 38 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 answer.
A) 328  B) 279  C) 270  D) 288  E) 231

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 / 38= 15   x + 300 = 570   x = 270 m. Answer:270
Answer: C
Raman mixed 24 kg of butter at Rs. 150 per kg with 36 kg butter at the rate of Rs. 125 per kg. At what price per kg should he sell the mixture to make a profit of 40% in the transaction? Answers.
A) 228  B) 2767  C) 189  D) 266  E) 211

Solution: CP per kg of mixture = [24(150) + 36(125)]/(24 + 36) = Rs. 135   SP = CP[(100 + profit%)/100]   = 135 * [(100 + 40)/100] = Rs. 189.   Answer: 189
Answer: C
In how many Q ways can 5 people from a group of 6 people be seated around a circular table Choose the correct choice from the following options.
A) 56  B) 80  C) 100  D) 120  E) 144

Solution: Q=6C5 * (5-1)! (Select 5 out of 6 and arrange them in circular manner)   = 6 * 4!   = 6 * 24= 
6 * 24 = 144
144   Answer - 144
Answer: E
At the end of the month, a certain ocean desalination plant’s reservoir contained 40 million gallons of water. This amount is one fifth of the normal level. If this amount represents 80% of the reservoir’s total capacity, how many million gallons short of total capacity is the normal level? Choices.
A) 20  B) 30  C) 40  D) 50  E) 60

Solution: the Q talks of total capacity, normal level, present level, shortage etc..   so it is all about not going wrong in these terms   40 MG= 80% of Total..   total = 40/.8= 
40/.8 = 50
50MG..   Normal level= 1/5 of 50=10MG..   shortage of normal level=50-10= 
50-10 = 40
40MG..   40
Answer: C
A motor pool has 300 vehicles of which 30 percent are trucks. 20 percent of all the vehicles in the motor pool are diesel, including 30 trucks. What percent of the motor pool is composed of vehicles that are neither trucks nor diesel?
Choose the correct answer:
A) 165%
B) 90%
C) 65%
D) 55%
E) 60%

Solution: Trucks = 30% of 300 = 90   Other Vehicles (60%xcluding Trucks) = 300-90= 
300-90 = 210
210   Diesel Vehicle= 20% of 300 = 60 (Including 15 Trucks)   Other Diesel Vehicles (60%xcluding Trucks) = 60-30= 
60-30 = 30
30   Trucks that are NOT diesel= 90 - 30= 
90 - 30 = 60
60   Other Vehicles that are NOT diesel Vehicles= 210-30= 
210-30 = 180
180   Required %= (180/300)*100= 
(180/300)*100 = 60
60%   Answer: option 60%
Answer: E
A man is 29 years older than his son. In two years, his age will be twice the age of his son. The present age of his son is:	Select the correct option
A) 14 years B) 18 years C) 20 years D) 27 years E) 16 years

Solution: Let the son's present age be x years. Then, man's present age = (x + 24) years.   (x + 29) + 2 = 2(x + 2)   x + 31 = 2x + 4   x = 27.   answer :27 years
Answer: D
A can fill tank in 9 minutes, B can empty the tank in 18 minutes.. In what time the tank be filled, if both pipes work simultaneously? Choose one:
A) 14 minutes  B) 15 minutes  C) 16 minutes  D) 17 minutes  E) 18 minutes

Solution: Bigger no=18, Ratio=9:18=1:2   Time taken to fill the tank = 18/(2 - 1)= 
18/(2 - 1) = 18
18 minutes   ANSW18 minutesR:18 minutes
Answer: E
If (a-3)(b-2) =0, which of the following must be true ?
I. a=3 and b=2
II. if a is not = 3, then b=2
III. if a=3, then b is not=2
Choose the correct choice from the following answers:	A) I only	B) II only	C) III only	D) I and II	E) II and III

Solution: (a-3)(b-2)=0   So either a=3 or b=2 or both. It is 'or' not 'and', so it could be any of the three possibilities. Thus I and III are not necessarily true.   The answer is II only.
Answer: B
A man's speed with the current is 20 kmph and speed of the current is 1 kmph. The Man's speed
against the current will be
Choose the correct option:
A) 11 kmph  B) 12 kmph  C) 18 kmph  D) 17 kmph  E) None of these

Solution: Explanation:   Speed with current is 20,   speed of the man + It is speed of the current   Speed in sƟll water = 20 - 1= 
20 - 1 = 19
19   Now speed against the current will be   speed of the man - speed of the current= 19 - 1= 
19 - 1 = 18
18 kmph   Answer: 18 kmph
Answer: C
A number is doubled and 9 is added. If resultant is trebled, it becomes 69. What is that number
Choose the correct choice from the following choices:
A) 7 B) 10 C) 12 D) 14 E) 15

Solution: Explanation:   => 3(2x+9) = 69   => 2x+9 = 23   => x = 7   7nswer: Option 7
Answer: A
In a kilometer race, A beats B by 50 meters or 10 seconds. What time does A take to complete the race?
Choices
A) 187 sec	B) 190 sec	C) 278 sec	D) 268 sec	E) 987 sec

Solution: Time taken by B run 1000 meters = (1000 * 10)/50= 
(1000 * 10)/50 = 200
200 sec.   Time taken by A= 200 - 10= 
200 - 10 = 190
190 sec.   Answer: 190 sec
Answer: B
If A and B are two events such that P (A) = 2/4, P (B) = 1/2 and P (A n B) = 3/8,
find P (not A and not B). Choose the most appropriate option:  A) A)2/8  B) B)3/8  C) C)4/8  D) D)5/13  E) E)6/8

Solution: P(not A and not B) = 1 - (P(A) + P(B) - P(AB))   which you might find somewhere in your text.   Substituting in our probabilities we get:   P(not A and not B) = 1 - (2/4 + 1/2 - 3/8)   P(not A and not B) = 1 - (5/8)   P(not A and not B) = 3/8.   3/8
Answer: B
What is the probability of getting a sum 9 from two throws of a dice?  Choose the correct choice from the following choices:
A) 1/6  B) 1/8  C) 1/9  D) 1/12  E) 1/5

Solution: In two throws of a dice, n(S) = (6 x 6) = 36.   Let E = event of getting a sum ={(3, 6), (4, 5), (5, 4), (6, 3)}.   P(E) =	n(E)/n(S)	=	4/36	=	1/9	.   Answer :1/9
Answer: C
M is 25% of N. M is also 75% of D. D is 95% of L. How are N and L related?
Pick one: A) 180% B) 200% C) 300% D) 285% E) 231%

Solution: If...   M=.25N   M=.75D   D=.95L   Then...   .25N=.75285%   285%ivide both sides by .75   .33N=285%   .33N=.95L   285%ivide both sides by .33   N=2.85L   N is 285% of L   The answer is 285%
Answer: D
If 4 women can colour 48 m long cloth in 2 days, then 6 men can colour 36 m long cloth in?	Answers
A) day B) day C) days D) days E) days

Solution: The length of cloth painted by one woman in one day = 48 / 4 × 2 = 6 m   No. of days required to paint 36 m cloth by 6 women = 36/ 6 × 6 = 1 day.   day)
Answer: B
In how many ways can the letters of the word REPORT be arranged?	Options.
A) 1206
B) 360
C) 2520
D) 3000
E) 3478

Solution: REPORT has 6 words, but R is repeated two times. Thus ways = 6! / 2! = 360 ways   360
Answer: B
A can do a piece of work in 12 days. He worked for 15 days and then B completed the remaining work in 10 days. Both of them together will finish it in.	Choose the most appropriate option:
A) 12 1/2 days B) 12 1/8 days C) 12 1/2 days D) 22 1/2 days E) 12 6/2 days

Solution: 15/25 + 10/x = 1 => x = 25   1/25 + 1/25 = 2/25   25/2 = 12 1/2 days   12 1/2 daysnswer:12 1/2 days
Answer: A
x = y - (5/y), where x and y are both > 0. If the value of y is doubled in the equation above, the value of x will
Choices
A) decrease	B) stay the same	C) increase four fold	D) doubles	E) triples

Solution: Alternate approach   Plug in some values of y > 0   Let y = 10   So, x = y - (5/y)   Or, x = 10 - (5/10)= 
10 - (5/10) = 19/2 = around 9.5
9.5   Let y= 20   So, x = y - (5/y)   Or, x = 20 - (5/20)= 
20 - (5/20) = 79/4 = around 19.75
19.75   So, x increases from 9.5 to 19.75   Hence the number increases 2 times, thus the correct answer will be (doubles)
Answer: D
Which expression is the greatest	Options
A) 3252/3257	B) 3456/3461	C) 3591/3596	D) 3846/3951	E) 3453/3458

Solution: Options can be re-written as (x-5)x => 1-(5/x)   A) 1- (5/3257)   B) 1- (5/3461)   C) 1- (5/3596)   D) 1- (5/3951)   E) 1- (5/3458)   To get the largest among these second half should be the least and so denominator to be largest. Hence '3846/3951'.
Answer: D
A student needs 60% of the marks on a test to pass the test. If the student gets 80 marks and fails the test by 100 marks, find the maximum marks set for the test.  Choices:	A) 250	B) 300	C) 350	D) 400	E) 450

Solution: 60% = 180 marks   1% = 3 marks   100% = 300 marks   The answer is 300.
Answer: B
In a flight of 600 km, an aircraft was slowed down due to bad weather. Its average speed for the trip was reduced by 200 km/hr and the time of flight increased by 30 minutes. The duration of the flight is:	Select.
A) 1 hour
B) 2 hours
C) 3 hours
D) 4 hours
E) 5 hours

Solution: Let the duration of the flight be x hours   600/x - 600 (x+1/2)= 200   600/x - 1200/(2x+1) = 200   x(2x + 1) = 3   2x2 + x - 3  (2  + 1)= 
 (2  + 1) = 3
3   2x2 + x - 3= 0   (2x + 3)(x - 1) = 0   x can't be negative hence x=1   x = 1 hr.   Duration =1 hr   1 hourNSWER:1 hour
Answer: A
A started a business with an investment of Rs. 70000 and after 6 months B joined him investing Rs. 120000. If the profit at the end of a year is Rs. 78000, then the share of B is?
Choices.
A) 33888
B) 24000
C) 27778
D) 27772
E) 36000

Solution: Ratio of investments of A and B is (70000 * 12) : (120000 * 6) = 7 : 6   Total profit = Rs. 78000   Share of B = 6/13 (78000) = Rs. 36000   Answer: 36000
Answer: E