MU-NLPC/Calc-aqua_rat huggingface dataset:
A pipe can filled a tank in 40 minutes and another pipe can empty it in 1hour. If the tank is already half full and both the taps are opened together, then the tank is filled in how many minutes?
Choose one
A) 25min  B) 20min  C) 15min  D) 10min  E) 30min

Solution: T = 1/2 (25*50 / 50-25) = 25 minutes   Tank is filled in 25 minutes   25minnswer is 25min
Answer: A
Two people P Q start a race in a circular track in opposite way different but constant speed. First they meet 900m cw from the starting pt. Then they meet 800m ccw from the starting pt. What's the circumference of the circle.  Pick one:  A) 2600  B) 2700  C) 2800  D) 2900  E) 2500

Solution: when they first met 900m cw from the starting pt.   second time, they will meet at 1800 m cw from starting point which is 800 m CCW from starting point.   so circumference of circle = 1800+800= 
1800+800 = 2_600
2600 m   2600NSWER:2600
Answer: A
In a triangle, the ratio of two angles is 7:2, and the third angle is the difference between the first two angles. What is the smallest angle, in degrees? Pick:
A) 90/11
B) 120/7
C) 150/11
D) 180/7
E) 25

Solution: the three angles are 7x, 2x, and (7x-2x)=5x for some value x (to create the ratio)   the three angles of a triangle add up to 180, so 7x+2x+5x   (7 -2 )= 
  (7 -2 ) = 5
5x for some value x (to create the ratio)   the three angles of a triangle add up to 180, so 7x+2x+5x= 180   14x = 180   x=180/14   x = 90/7   the smallest angle is 2x = 2*(90/7) = 180/7   180/7
Answer: D
Ravi and sunil are partners in a business. Ravi invests Rs.12,000 for 4 months and Sunil invested Rs.10000 for 5 months then after one year ratio of their profits will be	Select:
A) 1:3  B) 2:3  C) 24:25  D) 20:22  E) 3:4

Solution: =(12000*4):(10000*5)   =48000:50000   =24:25   ANSWER:24:25
Answer: C
A train covers a distance in 50 min, if it runs at a speed of 48kmph on an average. The speed at which the train must run to reduce the time of journey to 50min will be. Choose the correct choice from the following choices:
A) 60 km/h B) 55 km/h C) 48 km/h D) 70 km/h E) 65 km/h

Solution: Time=50/60 hr=5/6hr   Speed=48mph   distance=S*T=48*5/6= 
48*5/6 = 40
40km   time=50/60hr=5/6hr   New speed = 40* 6/5= 
40* 6/5 = 48
48kmph   Answer : 48 km/h
Answer: C
135 kg of an alloy A is mixed with 145 kg of alloy B. If alloy A has lead and tin in the ratio 3:5 and alloy B has tin and copper in the ratio 2:3, then the amount of tin in the new alloy is?
Choose the correct choice from the following
A) 100.6kg
B) 142kg
C) 135kg
D) 110.8kg
E) 114kg

Solution: Quantity of tin in 135kg of A = 135*5/8 = 84kg   Quantity of tin in 145kg of 142kg = 145*2/5= 
145*2/5 = 58
58kg   Quantity of tin in the new alloy= 84+58= 
84+58 = 142
142kg   Answer is 142kg
Answer: B
Carrie likes to buy t-shirts at the local clothing store. They cost $9.65 each. One day, she bought 12 t-shirts. How much money did she spend?	Choose the most appropriate option:
A) $115.8  B) $248.75  C) $200  D) $171.6  E) $190

Solution: $9.65*12=$115.8. $115.8nswer is $115.8.
Answer: A
On Thursday Mabel handled 90 transactions. Anthony handled 10% more transactions than Mabel, Cal handled 2/3rds of the transactions that Anthony handled, and Jade handled 14 more transactions than Cal. How much transactions did Jade handled? Choose the correct answer
A) 80
B) 81
C) 82
D) 83
E) 84

Solution: Solution:   Mabel handled 90 transactions   Anthony handled 10% more transactions than Mabel   Anthony = 90 + 90 × 10%   = 90 + 90 × 0.10   = 90 + 9= 
90 + 9 = 99
99   Cal handled 2/3rds of the transactions than Anthony handled   Cal= 2/3 × 99   = 66   Jade handled 14 more transactions than Cal.   Jade = 66 + 14= 
66 + 14 = 80
80   Jade handled= 80 transactions.   80nswer: 80
Answer: A
The length of a rectangle is twice its breadth. If its length is decreased by 5 cm and breadth is increased by 5 cm, the area of the rectangle is increased by 70 sq. cm. Find the length of the rectangle.	Choose the correct choice from the following answers:
A) 12cm
B) 14cm
C) 16cm
D) 18cm
E) 20cm

Solution: Explanation:   Let breadth = x. Then, length = 2x. Then,   (2x - 5) (x + 5) - 2x * x = 70 => 5x - 25 = 70 => x = 18.   Length of the rectangle = 18 cm.   Answer: Option 18cm
Answer: D
A batsman in his 11th inning makes a score of 69 and their by increasing his average by 1. What is his average after the 11th inning?
Answers:
A) 58	B) 59	C) 68	D) 69	E) 78

Solution: 10x + 69 = 11(x + 1)   x = 58 + 1= 
58 + 1 = 59
59   Answer:59
Answer: B
A man sells a horse for Rs.800 and loses something, if he had sold it for Rs.980, his gain would have been double the former loss. Find the cost price of the horse? Choose the correct choice from the following options:
A) 27
B) 98
C) 27
D) 60
E) 71

Solution: CP = SP + 1CP = SP - g   800 + x = 980 - 2x   3x = 180 => x = 60   Answer:60
Answer: D
In how many different number of ways 7 boys and 4 girls can sit on a shopa which can accommodate 3 persons?  Options
A) 800
B) 900
C) 200
D) 990
E) None

Solution: Option '990'   11p3 = 11x10x9 = 990
Answer: D
Sun Life Insurance company issues standard, preferred and ultra-preferred policies. Among the company's policy holders of a certain age, 50 are standard with the probability of 0.01 dying in the next year, 30 are preferred with a probability of 0.008 of dying in the next year and 20 are ultra-preferred with a probability of 0.007 of dying in the next year. If a policy holder of that age dies in the next year, what is the probability of the decreased being a preferred policy holder?
Select:  A) 0.1591  B) 0.2727  C) 0.375  D) 0.2767  E) None of these

Solution: Explanation :   The percentage of three different types of policy holders and the corresponding probability of dying in the next 1 year are as follow :   Type, Standard, Preferred, Ultra-Preferred   Percentage	, 50	, 30, 20   Probability, 0.01 , 0.008, 0.007   The expected number of deaths among all the policy holders of the given age [say P] during the next year.   =>T×(50×0.01/100)+(30×0.008/100)+(20×0.007/100).   =>T×(0.88/100).   Where T= Total number of policy holder of age P   If any of these policy holders (who die during the next year) is picked at random, the probability that he is a preferred policy holder is :-   =>((30x0.88xT)/100)/ (Tx(0.88/100)).   =>24/88.   =>3/11.   =>0.2727.   Answer : 0.2727
Answer: B
A train 100 meters long completely crosses a 300 meters long bridge in 45 seconds. What is the speed of the train is? Choose the correct answer
A) 25 kmph  B) 32 kmph  C) 40 kmph  D) 38 kmph  E) 92 kmph

Solution: S = (100 + 300)/45 = 400/45 * 18/5= 
400/45 * 18/5 = 32
32 kmph   answer :32 kmph
Answer: B
Nine friends are planning to attend a concert. If another friend also goes with them, they will get a group discount on their tickets. If the new total price of the tickets with the group discount is the same as the original total price of the tickets without the group discount, how much is the discount?	Choose the correct choice
A) 5%
B) 10%
C) 20%
D) 25%
E) 33%

Solution: Let x be the original price of one ticket.   The total original cost is 9x.   The new cost is 10y, where y is the discounted price of one ticket.   9x = 10y   y = 9x/10 = 0.9x which is a discount of 10%.   The answer is 10%.9 /10= 
9 /10 = 9/10 = around 0.9
0.9x which is a discount of 10%.   The answer is 10%.
Answer: B
A certain sum of money is divided among A, B and C so that for each Rs. A has, B has 65 paisa and C 40 paisa. If C's share is Rs.40, find the sum of money?	Choose the correct option
A) 228
B) 267
C) 911
D) 205
E) 212

Solution: A:B:C = 100:65:40   = 20:13:8   8 ---- 40   41 ---- ? => Rs.205   Answer: 205
Answer: D
A rectangular park 60 m long and 40 m wide has two concrete crossroads running in the middle of the park and rest of the park has been used as a lawn. If the area of the lawn is 2109 sq. m, then what is the width of the road?  Choose the correct option
A) 2.91 m
B) 3 m
C) 5.82 m
D) None of these
E) Cannot be determined

Solution: Explanation:   Area of the park = (60 x 40) m2 = 2400 m2   Area of the lawn = 2109 m2   Area of the crossroads = (2400 - 2109)= 
(2400 - 2109) = 291
291   Let the width of the road be x metres. Then,   60x + 40x - x2= 291   => x2 - 100x + 291 = 0   => (x - 97)(x - 3) = 0   => x = 3   Answer: 3 m
Answer: B
15.06 * 0.000001 = ? Select the correct option:
A) 15060000 B) 0.001506 C) 0.01506 D) 1.506e-05 E) None of these

Solution: Explanation:   Clearly after decimal 8 digits should be there.   Option 1.506e-05
Answer: D
How many 3-letter words with or without meaning, can be formed out of the letters of the word, 'LOGARITHMS', if repetition of letters is not allowed? Choose the correct choice.
A) 720	B) 420	C) 450	D) 350	E) 5040

Solution: Explanation:   The word 'LOGARITHMS' has 10 different letters.   Hence, the number of 3-letter words(with or without meaning) formed by using these letters =10X9X8   =720   720NSWER IS 720
Answer: A
A fish tank is half full of water. If 10 gallons of water were added, the tank would be 7/8 full. What is the capacity of the tank (in gallons)?	Choose the correct choice:
A) 11 3/7 B) 22 3/7 C) 26 2/3 D) 30 3/8 E) 32 1/8

Solution: Solution -   Let capacity of tank be X gallons.   Water level increased to 7/8 from 1/2 when 10 gallons of water added ---> (7/8 - 1/2)*X = 10   X = 80/3 = 26 2/3.   ANS 26 2/3.
Answer: C
For what value of k will the two equations 2x + 4 = 4(x - 2) and -x + k = 2x - 1 have the same solution?
Choose the correct choice from the following
A) 15
B) 16
C) 18
D) 19
E) 17

Solution: Solve the first equation 2x + 4 = 4(x - 2) to obtain .   x = 6   Substitute x by 6 (same solution) in the second equation and solve for k.   - 6 + k = 2(6) - 1   solve for k.   k = 17   correct answer 17
Answer: E
The banker's discount on a bill due 4 months hence at 15% is Rs. 420. The true discount is: Choose the correct choice from the following answers.
A) 400 B) 360 C) 480 D) 320 E) 380

Solution: T.D.	=	B.D. x 100 / 100 + (R x T)   = Rs.(420 x 100	/ 100 + (15 x 1/3))   = Rs. (420 x 100 / 105)   = Rs. 400.   Correct 400nswer is 400.
Answer: A
A worker is paid a regular rate of Rs.20 for completing a survey. The worker completes 50 surveys per week. For any survey involving the use of her cellphone, she is paid at a rate of that is 10% higher than her regular rate. If she completed 35 surveys involving the use of her cellphone, how much did she get that week?  Select.
A) 570  B) 670  C) 1070  D) 470  E) 2070

Solution: amount earned by using her cell phone = 35 * 22= 
35 * 22 = 770
770   amount earned as usual= 15 * 20= 
15 * 20 = 300
300   Total= 770+300= 
770+300 = 1_070
1070   Answer : 1070
Answer: C
Six students are equally divided into 3 groups, then, the three groups were assigned to three different topics. How many different arrangements Q are possible?	Select: A) 30 B) 60 C) 90 D) 180 E) 540

Solution: 90 is the number of ways you can assign 3 teams formed out of 12 people to 3 different tasks.   But now you can order the 3 tasks in 3! ways. T1 T2 T3 or T2 T1 T3.... etc etc.   I was confused between 90 and 540 but since question used the wordarrangementsdecided to go with complete arrangements Q including the order of tasks.   could you explain the highlighted step... i'm getting 90 = 15 * 3!   suppose the students are numbered 1,2,3,4,5,6 and tasks are X,Y and Z   one of the 15 possible ways of forming teams is 12, 34, 56. these teams can be assigned to 3 tasks in 3! = 6 ways   X--	Y--	Z   12--	34--	56   12--	56--	34   34--	12--	56   34--	56--	12   56--	12--	34   56--	34--	12   so the answer should be 15*6= 
15*6 = 90
90   But now you can fruther decide which task you want to perform first X Y or Z..=90
Answer: C
A batsman in his 19th inning makes a score of 100 and their by increasing his average by 2. What is his average after the 19th inning? Options:
A) 58
B) 60
C) 62
D) 64
E) 66

Solution: 18x + 100 = 19(x + 2)   x = 62 + 2= 
62 + 2 = 64
64   Answer:64
Answer: D
A certain lab experiments with white and brown mice only. In one experiment, 2/3 of the mice are white. If there are 13 brown mice in the experiment, how many mice in total are in the experiment?  Choices:
A) 39
B) 33
C) 26
D) 21
E) 10

Solution: Let total number of mice = M   Number of white mice = 2/3 M   Number of brown mice = 1/3 M = 13   => M = 39   39nswer 39
Answer: A
A team of eight entered for a shooting competition. The best marks man scored 85 points. If he had scored 92 points, the average scores for. The team would have been 84. How many points altogether did the team score? Choose the correct answer:
A) 288
B) 665
C) 168
D) 127
E) 664

Solution: Explanation:   8 * 84= 
8 * 84 = 672
672 â€“ 7= 665   Answer:665
Answer: B
How many integers are there between 55 and 108, inclusive?
Options
A) 51	B) 54	C) 56	D) 57	E) 58

Solution: I guess the easiest way to answer this is -   Say you have two positive integers, x and y where y > x   Then the number of integers between x and y is given by - (y - x) + 1   In this case, it's (108 - 55) + 1= 
(108 - 55) + 1 = 54
54. Option 54
Answer: B
3 of the 4 expressions (1), (2), (3) & (4) given below are exactly equal . Which of the expression is not equal to the other four expressions?	Choose the correct option
A) (A + B)2 - 4AB  B) (A – B)2 + 4AB  C) A2 + B2 - 4AB + 2AB  D) A2 – B2 + 2B(B – A)  E) None of these

Solution: 1) (A + A)(A + 2 - 4AB)2 – 4AA)(A + 2 - 4AB = A2 + 2AA)(A + 2 - 4AB + A)(A + 2 - 4AB2 - 4AA)(A + 2 - 4AB = A2 + A)(A + 2 - 4AB2 - 2AA)(A + 2 - 4AB   2) (A – A)(A + 2 - 4AB)2 + 4AA)(A + 2 - 4AB = A2 – 2AA)(A + 2 - 4AB + A)(A + 2 - 4AB2 + 4AA)(A + 2 - 4AB = A2+ A)(A + 2 - 4AB2 + 2AA)(A + 2 - 4AB   3) A2 +A)(A + 2 - 4AB2 – 4AA)(A + 2 - 4AB + 2AA)(A + 2 - 4AB = A2 + A)(A + 2 - 4AB2 - 2AA)(A + 2 - 4AB   4) A2 – A)(A + 2 - 4AB2 + 2A)(A + 2 - 4AB(A)(A + 2 - 4AB – A) = A2 – A)(A + 2 - 4AB2 + 2A)(A + 2 - 4AB2 – 2AA)(A + 2 - 4AB = A2 + A)(A + 2 - 4AB2 – 2AA)(A + 2 - 4AB   Therefore, (1) = (3) = (4) ≠ (2)   Therefore, expression (2) is wrong   ANSWER IS A)(A + 2 - 4AB
Answer: B
P is three times as fast as Q and working together, they can complete a work in 36 days. In how many days can Q alone complete the work? Choose the correct choice.
A) 16 B) 48 C) 88 D) 55 E) 778

Solution: P = 3Q   P + Q = 3Q + Q = 4Q   These 4Q people can do the work in 36 days, which means Q can do the work in 144 days.   Hence, P can do the work in 48 days.   Answer:48
Answer: B
Difference between two numbers is 5, six times of the smaller lacks by 8 from the four times of the greater. Find the numbers? Pick one.
A) 5,1 B) 7,3 C) 9,8 D) 11,6 E) 13,7

Solution: Explanation:   x – y = 5   4x – 6y = 8   x = 11 y = 6   11,6)
Answer: D
A, B and C can do a piece of work in 20, 30 and 60 days respectively. In how many days can A do the work if he is assisted by B and C on every third day?
Choose the correct answer:
A) 12	B) 13	C) 15	D) 16	E) 18

Solution: 2 day work = 1/20*2=1/10   A+B+15 1 day work = 1/10   work done in 3 days = 1/5   1/5 work is done in 3 days   whole work will done in   (3*5)= 
  (3*5) = 15
15 days
Answer: C
Some of 10%-intensity red paint is replaced with 20% solution of red paint such that the new paint intensity is 15%. What fraction of the original paint was replaced?  Choose the correct option
A) 2/5 B) 2/3 C) 1/2 D) 1/3 E) 1/5

Solution: Let total paint = 1   Let amount replaced = x   10 (1-x) + 20x = 15   x = 1/2   ANSWER:1/2
Answer: C
Solve x2 â€“ 7x = 0
Choose one:
A) 0,7 B) 1.7 C) 2.7 D) 3,7 E) 4,7

Solution: This quadratic factors easily: Copyright Â© Elizabeth Stapel 2002-2011 0,7ll Rights Reserved   x2 â€“ 7x = 0   x(x â€“ 7) = 0   x = 0 or x â€“ 7 = 0   x = 0 or x = 7   The solution is x = 0, 7   0,7NSWER 0,7
Answer: A
The ratio of the present ages of P and Q is 3:4. 5 years ago, the ratio of their ages was 5:7. Find the their present ages?	Choose the correct choice from the following choices
A) 30, 40  B) 30, 46  C) 30, 29  D) 31, 40  E) 30, 90

Solution: Their present ages be 3X and 4X.   5 years age, the ratio of their ages was 5:7, then (3X - 5):(4X - 5) = 5:7   X = 35 - 25 => X = 10.   Their present ages are: 30, 40.   30, 40nswer: 30, 40
Answer: A
Can you analyze what is the probability of meeting someone in your lifetime who is having an above average no of arms?	Choose the most appropriate option:
A) impossible	B) unlikely	C) fifty fifty	D) fairly likely	E) Certain

Solution: Correct Answer : Certain   The average number of arms is less than 2
Answer: E
Three business people wish to invest in a new company. Each person is willing to pay one third of the total investment. After careful calculations, they realize that each of them would pay $2,200 less if they could find two more equal investors. How much is the total investment in the new business?
Options:  A) $11,000  B) $50,000  C) $16,500  D) $ 6,600  E) $ 3,600

Solution: Total Investment between 5: (x/5)   Total investment including 2200 less between 3 people(x-(2200*3))/3   Set both eq. equal to each other.   16,500   Answer $16,500)
Answer: C
In a game of billiards, A can give B 20 points in 60 and he can give C 30 points in 60. How many points can B give C in a game of 100? Select.
A) 15  B) 77  C) 25  D) 18  E) 12

Solution: A scores 60 while B score 40 and C scores 30.   The number of points that C scores when B scores 100 = (100 * 30)/40 = 25 * 3= 
25 * 3 = 75
75.   In a game of 100 points, B gives (100 - 75)= 
(100 - 75) = 25
25 points to C.   Answer:25
Answer: C
A car dealer has only blue and white cars in his show room. He has 24 blue cars and 30 white cars. He wants to have 60% more blue cars then white. How many whites cars does he have to sell to achieve his sales goal? Select the correct option:
A) 12  B) 13  C) 14  D) 15  E) 16

Solution: We can use simple arithmetic to solve this problem by testing our answers.   Lets test B:   If he sold 13 white cars:   24 blue cars and 17 white cars for a total of 41 cars   24/41=58.5% not quite our answer   Lets test 14   If he sold 14 white cars   24 blue cars and 16 white cars for a total of 40 cars   24/40=60%   Our answer is 14
Answer: C
if x:y = 1:5, then find the value of
(7x+3y):(2x+y)	Choose one.
A) 14:5  B) 15:5  C) 16:5  D) 22:7  E) None of these

Solution: Explanation:   let x = 1k and y = 5k, so   =7(k)+3(5k)/ 2(k)+1(5k)   =22k/7k   =22:7   Option 22:7
Answer: D
If the arithmetic mean of seventy five numbers is calculated, it is 35. If each number is increased by 5, then mean of new number is?
Select:
A) 43  B) 40  C) 87  D) 77  E) 22

Solution: A.M. of 75 numbers = 35   Sum of 75 numbers = 75 * 35= 
75 * 35 = 2_625
2625   Total increase= 75 * 5= 
75 * 5 = 375
375   Increased sum= 2625 + 375= 
2625 + 375 = 3_000
3000   Increased average= 3000/75= 
3000/75 = 40
40.   Answer:40
Answer: B
The denominator of a fraction is 6 greater than the numerator. If the numerator and the denominator are increased by 1, the resulting fraction is equal to 4â„5. What is the value of the original fraction? Pick one
A) 17/23  B) 23/29  C) 29/35  D) 31/37  E) 33/39

Solution: Let the numerator be x.   Then the denominator is x+6.   x+1 / x+7 = 4/5.   5x+5=4x+28.   x=23.   The original fraction is 23/29.   The answer is 23/29.
Answer: B
An article is bought for Rs.600 and sold for Rs.1000, find the gain percent?	Pick
A) 73 1/3% B) 63 1/3% C) 33 1/3% D) 66.66% E) 33 1/3%

Solution: Explanation:   600 ---- 400   100 ---- ? => 66.66%   Answer:66.66%
Answer: D
The function f is defined by subtracting 25 from the square of a number and the function c is defined as the square root of one-half of a number. If c(f(x))=10, then which of the following is a possible value of x? Choose the correct choice from the following:
A) -15  B) -5  C) 0  D) 5  E) 25

Solution: f(x) = x^2-25   c(x) = sqrt(x/2) not sqrt(x)/2, because the question clearly says its square root of (half of the number).   c(f(x)) = 10   c(x^2-25) =10   sqrt((x^2-25)/2) = 10   => (x^2-25)/2 = 100   =>x^2 = 225   => x = 15 or -15   -15nswer is -15.
Answer: A
Seven years ago the average age of a family of 2 members was 25 years. A child has been born. due to Which the average age of the family is 23 years today. What is the present age of the child?	Choices
A) 7 years  B) 5 years  C) 3 years  D) 8 years  E) 10 years

Solution: Explanation:   Average of the family of two numbers   7 years ago = 25   = (25+ 7) * 2= 
(25+ 7) * 2 = 64
64 years   Average age of the family of three members at present= 23 years   = 23 * 3= 
23 * 3 = 69
69 YEARS   Age of child= 69 - 64= 
69 - 64 = 5
5 years   Answer: Option 5 years
Answer: B
A machine puts c caps on bottles in m minutes. How many hours will it take to put caps on b bottles  Select the correct option: A) 60bm/c B) bm/60c C) bc/60m D) 60b/cm E) None of these

Solution: Explanation:   Substitute sensible numbers and work out the problem. Then change the numbers back to letters. For example if the machine puts 6 caps on bottles in 2 minutes, it will put 6 /2 caps on per minute, or (6 /2) x 60 caps per hour. Putting letters back this is 60c/m.If you divide the required number of caps (b) by the caps per hour you will get time taken in hours. This gives bm/60c   Answer: bm/60c
Answer: B
How many positive integers less than 100 are there such that they are multiples of 13 or multiples of 12 but not both?
Choose the correct choice from the following answers: A) 15 B) 16 C) 17 D) 18 E) 19

Solution: for 13: 13...91=13*7 = 7   for 12: 12...96=12*8 =8   but there is no integer 13*12. so   N=(7)+(8)= 
(7)+(8) = 15
15   15
Answer: A
On the xy-coordinate plane, point A lies on the y-axis and point B lies on the x-axis. Points A, B, and C form a right triangle with a 90-degree angle at point C and the triangle has an area of 30. If AC is parallel to the x-axis, and BC is parallel to the y-axis, which of the following could be the coordinates of point C? Options.
A) (−2, 30)	B) (−4, 12)	C) (6, −9)	D) (9, −8)	E) (10, −3)

Solution: The area of the triangle formed will be:   1/2 * base * height =   1/2 * |(X-coordinate of point C)| * |(Y-coordinate of point C)| = 30   Thus |product of coordinates of point C| = 60   The answer is (−2, 30).
Answer: A
Two pipes A and B together can fill a cistern in 4 hours. Had they been opened separately, then B would have taken 6 hours more than A to fill cistern. How much time will be taken by A to fill the cistern separately?	Choose the correct option:
A) 1 hr	B) 2 hrs	C) 6 hrs	D) 8 hrs	E) 10 hrs

Solution: Let the cistern be filled by pipe A alone in x hours.   Then, pipe B will fill it in (x + 6) hours.   1/x + 1/(x + 6) = 1/4   x2 - 2x - 24 = 0   (x - 6)(x + 4) = 0 => x = 6.   ANSWER:6 hrs
Answer: C
what will be the highest no. of students in which 1001 pen and 910 pencil should be distributed so that everyone get equal no. of pen and pencils? Choose the correct choice from the following answers.
A) 91
B) 910
C) 1011
D) 1911
E) 825

Solution: h.c.f of 910 and 1001=91   answer 91
Answer: A
A began business with Rs.45000 and was joined afterwards by B with Rs.5400. When did B join if the profits at the end of the year were divided in the ratio of 2:1?	Choices: A) 8 months B) 4 months C) 7 months D) 9 months E) 2 months

Solution: 45*12 : 54*x = 2: 1   x = 5   12 -5= 
12 -5 = 7
7   Answer:7 months
Answer: C
Two cans A & B contain 25% & 30 % of milk. If 6 parts of can A and 4 parts of can B acre mixed in a can C. What is the proportion of milk in can C. Options:
A) 25%	B) 26%	C) 27%	D) 28%	E) 29%

Solution: suppose we take 10 lits of solution in tank A and B then   25% of in A is 2.5 lits and 30% in B is 3 lits milk   6 parts of A can have 1.5 lits of milk and 4 parts of B have 1.2 lts of milk so   totally 2.7 lits of milk in c i.e 27%.   ANSWER:27%
Answer: C
If n and k are integers whose product is 900, which of the following statements must be true? Choose one
A) n+k>0 B) n does not equal k C) Either n or k is a multiple of 10 D) If n is even, then k is odd E) If n is odd, then k is even

Solution: If n is odd and k is odd, then the product is odd.   The answer is If n is odd, then k is even.
Answer: E
A group of 1200 persons consisting of captains and soldiers is travelling in a train. For every 15 soldiers there is one captain. The number of captains in the group is	Choose the correct choice:	A) 85	B) 80	C) 75	D) 70	E) 65

Solution: Explanation:   Clearly, out of every 16 persons, there is one captain. So, number of captains   (1200/16)= 
  (1200/16) = 75
75.   Answer: 75
Answer: C