MU-NLPC/Calc-aqua_rat huggingface dataset:
The weights of one liter vegetable ghee packet of two brands ‘A’ and ‘B’ are 900 gm and 800 gm respectively. If they are mixed in the ratio of 3 : 2 by volumes to form a mixture of 4 liters, what is the weight (in kg) of the mixture?	Choose one
A) 3.84  B) 1.75  C) 3.44  D) 2.72  E) None of these

Solution: Here's how I did it. My notes from reading the problem were:   1L A = 900 gm   1L B = 800 gm   We are mixing five parts (3 parts A plus 2 parts B, 5 parts total) to get 4L, so 5x = 4 ---> x = 4/5. Each part is 4/5 of a liter.   So if we have 3 parts A, we have 900*3*(4/5)= 
900*3*(4/5) = 2_160
2160   If we have 2 parts B, we have 800*2*(4/5)= 
800*2*(4/5) = 1_280
1280   2160 + 1280= 
2160 + 1280 = 3_440
3440   Solving for units gives us 3.44   So the answer is 3.44
Answer: C
A 300 meter long train crosses a platform in 39 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform?  Choose the correct answer.
A) 388 B) 656 C) 350 D) 771 E) 211

Solution: Speed = [300 / 18] m/sec = 50/3 m/sec.   Let the length of the platform be x meters.   Then, x + 300 / 39 = 50/3   3(x + 300) = 1950 è x = 350m.Answer: 350
Answer: C
A invested some money in 10% stock at 96. If B wants to invest in an equally good 12% stock, he must purchase a stock worth of :	Choices:
A) Rs.80  B) Rs.115.20  C) Rs.120  D) Rs.125.40  E) None of these

Solution: Explanation:   For an income of Rs. 10, investment = Rs. 96.   For an income of Rs. 12, investment = (96/10x12) =115.20   Answer: Rs.115.20
Answer: B
an isosceles triangle with sides 13 13 10 and there is a circle inscribed it .find the radius of circle?	Choose the correct option
A) 1.32	B) 3.33	C) 3.58	D) 4.34	E) 5.18

Solution: height of triangle = √(13^2 - (10/2)^2) = 12   area of triangle = r * s   where, r = radius of inscribed circle & s=(a+b+c)/2   area of triangle = 1/2 *b*h = 1/2 *10 *12= 
1/2 *10 *12 = 60
60   s= (13+13+10)/2= 
(13+13+10)/2 = 18
18   r= area of triangle / s = 60/18 = 10/3 = 3.33   ANSWER:3.33
Answer: B
The price of 2 sarees and 4 shirts is Rs. 1600. With the same money one can buy 1 saree and 6 shirts. If one wants to buy 12 shirts, how much shall he have to pay ?	Choose one: A) 1800 B) 2000 C) 2200 D) 2400 E) 2600

Solution: Let the price of a saree and a shirt be Rs. x and Rs. y respectively.   Then, 2x + 4y = 1600 .... (i)   and x + 6y = 1600 .... (ii)   Divide equation (i) by 2, we get the below equation.   = x + 2y = 800. --- (iii)   Now subtract (iii) from (ii)   x + 6y = 1600 (-)   x + 2y = 800   ----------------   4y = 800   ----------------   Therefore, y = 200.   Now apply value of y in (iii)   = x + 2 x 200 = 800   = x + 400 = 800   Therefore x = 400   Solving (i) and (ii) we get x = 400, y = 200.   Cost of 12 shirts = Rs. (12 x 200) = Rs. 2400.   answer : 2400
Answer: D
Dany bought a total of 18 game cards some of which cost $0.25 each and some of which cost $0.15 each. If Dany spent $4.2 to buy these cards, how many cards of each type did he buy?	Choose the correct choice from the following answers:
A) 4	B) 10	C) 7	D) 3	E) 12

Solution: Let X be the number of cards that cost $0.25 each and Y the number of cards that cost $0.15 each. The total number of cards is 18. Hence   X + Y = 18   If X is the number of cards at $0.25, then the X cards cost   0.25 X   If Y is the number of cards at $0.15, then the Y cards cost   0.15 Y   The total cost of the X cards and the the Y cards is known to be $4.2 and also given by   0.25 X + 0.15 Y = 4.2   We now need to solve the system of equations   X + Y = 18   0.25 X + 0.15 Y = 4.2   The first equation gives Y = 18 - X. Substitute y by 18 - x in the second equation and solve   0.25 X + 0.15 (18 - X) = 4.2   X(0.25 - 0.15) + 2.7 = 4.2   0.1 X = 1.5   X = 15 and Y = 18 - 15= 
18 - 15 = 3
3   correct answer 3
Answer: D
If you divide a number into 3 equal groups and then divide each group in half, you end up with 13. What number did you start with?  Select the correct option:
A) 76
B) 77
C) 78
D) 79
E) None of these

Solution: Solution:   Suppose the start number is x Division into 3 equal groups is: x/3, and then in half is (x/3)/2 = 13   x/6 = 13   x = 13 * 6= 
13 * 6 = 78
78   Answer 78
Answer: C
A man can row a boat at 12 kmph in still water. If the speed of the stream is 4 kmph, what is the time taken to row a distance of 50 km downstream?	Choose the correct choice
A) 25/8 B) 29/8 C) 23/8 D) 27/8 E) 21/8

Solution: Speed downstream = 12 + 4= 
12 + 4 = 16
16 kmph.   Time required to cover 50 km downstream= d/s = 50/16   = 25/8 hours.   25/8nswer: 25/8
Answer: A
Find the greatest number which on dividing 1428 and 2206, leaves a reminder of 9 and 13 respectively  Choose the correct choice from the following answers
A) 125	B) 127	C) 129	D) 131	E) 141

Solution: Explanation:   In this type of question, its obvious we need to calculate the H129F, trick is   H129F of (1428 - 9) and (2206 -13)   = H129F (1419, 2193) = 129   Option 129
Answer: C
Which one of the given numbers is divisible by 11? Choose the correct choice.
A) 4823718	B) 8423718	C) 8432718	D) 4832817	E) 4852718

Solution: Explanation:   4832817 = (4+3+8+7) – (8+2+1)= 
(8+2+1) = 11
11   So, the given number is divisible by 11   Answer:4832817
Answer: D
(500 + 200) × 4 × (3 + 2) = ?	Choose the most appropriate option:  A) 2902  B) 14000  C) 8402  D) 16800  E) None of these

Solution: (500 + 200) × 4 × (3 + 2) = ?   or, ? = 700 × 4 × 5 = 14000   Answer 14000
Answer: B
Two trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 121 hours and 100 hours respectively. The ratio of their speeds is:
Choices.
A) 2 : 3	B) 4 : 3	C) 6 : 7	D) 9 : 16	E) None of these

Solution: Let us name the trains as A and B. Then,   (A's speed) : (B's speed) = âˆšb : âˆša = âˆš100 : âˆš121 = 10 : 11.   Answer None of these
Answer: E
What is the measure of the radius of the circle that circumscribes a triangle whose sides measure 11, 60 and 61?  Choose the correct option:  A) 6.5  B) 12.5  C) 28  D) 30.5  E) 40

Solution: Some of pyhtagron triplets we need to keep it in mind.   Like {( 2,3,5) , ( 5,12,13) ,( 7, 24,25), ( 11, 60,61).   So now we know the triangle is an right angle triangle. The circle circumscribes the triangle.   The circumraduis of the circle that circumscribes the right angle triangle = hypotanse / 2 = 61 / 2= 
61 / 2 = 61/2 = around 30.5
30.5   Ans. 30.5
Answer: D
January 1, 2008 is Monday. What day of the week lies on Jan 1, 2009?	Pick one
A) Saturday B) Wednesday C) Thursday D) Tuesday E) Monday

Solution: Explanation:   Number of odd days in 2008 = 2 (since it is a leap year)   (we have taken the complete year 2008 because we need to find out the odd days from 01-Jan-2008 to 31-Dec-2008, that is the whole year 2008)   Given that January 1, 2008 is Monday.   Hence January 1, 2009 = (Monday+ 2 odd days) = Wednesday   Answer: Option Wednesday
Answer: B
Which of the following points is closest to line y=x	Choose the correct choice from the following choices.
A) (2, -1)	B) (-2, -4)	C) (-1, 1)	D) (-2, 1)	E) (-2, 0)

Solution: Attachment:   m12-20.pngAs you can see point (-2, -4) is the closest to line y=x.   Answer: (-2, -4).
Answer: B
Train X crosses a stationary train Y in 60 seconds and a pole in 25 seconds with the same speed. The length of the train X is 300 m. What is the length of the stationary train Y ?	Choose the correct choice from the following options: A) 360 m B) 420 m C) 460 m D) 320 m E) 340 m

Solution: Explanation:   Let the length of the stationary train Y be LY   Given that length of train X, LX = 300 m   Let the speed of Train X be V.   Since the train X crosses train Y and a pole in 60 seconds and 25 seconds respectively.   => 300/V = 25 ---> ( 1 )   (300 + LY) / V = 60 ---> ( 2 )   From (1) V = 300/25= 
300/25 = 12
12 m/sec.   From (2) (300 + LY)/12= 60   => 300 + LY = 60 (12) = 720   => LY = 720 - 300= 
720 - 300 = 420
420 m   Length of the stationary train= 420 m   ANSWER IS 420 m
Answer: B
Two containers of equal capacity are full of a mixture of oil and water . In the first, the ratio of oil to water is 4:7 and in the second it is 7:11. Now both the mixtures are mixed in a bigger container. What is the resulting ratio of oil to water.	Choose the correct answer:	A) 149 : 247	B) 247 : 149	C) 143 : 241	D) 241 : 143	E) 341 : 243

Solution: Two Container C1, C2 of equal capacity x.   For C1:   Oil= 4/11 x   Water= 7/11 x   For C2   Oil= 7/18 x   Water = 7/11 x   Mix C1 and C2.   Total Oil= 4/11 x + 7/18 x = 149/198 x   Total Water= 7/11 x + 7/11 x = 247/198 x   resulting ratio of oil to water = (149/198 x) / (247/198 x)   = 149:247.   149 : 247NSWER:149 : 247
Answer: A
The C.P of 15 books is equal to the S.P of 18 books. Find his gain% or loss%?
Pick one.
A) 16 2/3% loss B) 22 2/3% loss C) 88 2/3% loss D) 66 2/3% loss E) 22 2/5% loss

Solution: 15 CP = 18 SP   18 --- 3 CP loss   100 --- ? => 16 2/3% loss   16 2/3% lossnswer: 16 2/3% loss
Answer: A
If log 27 = 1.431, then the value of log 9 is:	Options.
A) 0.934  B) 0.945  C) 0.954  D) 0.958  E) 0.965

Solution: log 27 = 1.431   log (33 ) = 1.431   3 log 3 = 1.431   log 3 = 0.477   log 9 = log(32 ) = 2 log 3 = (2 x 0.477) = 0.954.   Answer: Option 0.954
Answer: C
The population of a town is 10000. It increases annually at the rate of 20% p.a. What will be its population after 1 year?
Answers.
A) 14300 B) 12000 C) 14500 D) 14600 E) 15400

Solution: Formula :   ( After =100 denominator   Ago = 100 numerator)   10000 × 120/100 = 12000   12000)
Answer: B
A pool can be filled in 4 hours and drained in 5 hours. The valve that fills the pool was opened at 9:00 am and some time later the drain that empties the pool was also opened. If the pool was filled by 9:00 pm and not earlier, when was the drain opened? Select the correct option.
A) at 10:00 am  B) at 11:00 am  C) at 12:00 pm  D) at 1:00 pm  E) at 2:00 pm

Solution: The filling rate is 1/4 and the draining rate is 1/5.   The combined rate of filling and draining is 1/4 - 1/5 = 1/20.   Let x be the number of hours before the drain was opened.   x/4 + (12-x)/20 = 1   5x + 12 - x = 20   4x = 8   x = 2   The answer is 11:00 am.   The answer is at 11:00 am.
Answer: B
Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 25 seconds. The ratio of their speeds is?  Choose the most appropriate option:
A) 3/7 B) 3/2 C) 3/5 D) 8/1 E) 3/3

Solution: Let the speeds of the two trains be x m/sec and y m/sec respectively. Then, length of the first train = 27 x meters, and length of the second train = 17 y meters. (27 x + 17 y) / (x + y) = 25   ==> 27 x + 17 y = 25 x + 25 y ==> 2x = 8 y ==> x/y   = 8/1.   Answer: 8/1
Answer: D
Rice weighing 29/4 pounds was divided equally and placed in 4 containers. How many ounces of rice were in each container? (Note that 1 pound = 16 ounces) Options:
A) 21 B) 25 C) 29 D) 33 E) 37

Solution: 29/4 ÷ 4 = 29/16 pounds in each container   29/16 pounds * 16 ounces / pound = 29 ounces in each container   The answer is 29.
Answer: C
A man rows downstream 32 km and 14 km upstream. If he takes 6 hours to cover each distance, then the velocity (in kmph) of the current is:	Choose the correct choice:  A) 1.5 kmph  B) 1.75 kmph  C) 2 kmph  D) 3 kmph  E) None

Solution: Sol.   Rate downstream = [32/6] kmph; Rate upstream = [14/6] kmph.   ∴ Velocity of current = 1/2[32/6 - 14/6] kmph = 3/2= 
3/2 = 3/2 = around 1.5
1.5 kmph.   1.5 kmphnswer 1.5 kmph
Answer: A
What day of the week was 11th January 1801	Choose one
A) Monday B) Sunday C) Friday D) Thursday E) Tuesday

Solution: Explanation:   11th Jan 1801 = (1800 years + 11th Jan 1801)   We know that number of odd days in 400 years = 0   Hence the number of odd days in 1600 years = 0 (Since 1600 is a perfect multiple of 400)   Number of odd days in the period 1601-1800   = Number of odd days in 200 years   = 5 x 2 = 10 = 3   (As we can reduce perfect multiples of 7 from odd days without affecting anything)   11th Jan 1801 = 4 odd day   Total number of odd days = (0 + 3 + 4)= 
(0 + 3 + 4) = 7
7=0   0 odd days = Sunday   Hence 11th January 1801 is Sunday.   Answer: Option Sunday
Answer: B
The food in a camp lasts for 30 men for 40 days. If ten more men join, how many days will the food last? Choose the correct option:
A) 40 days  B) 20 days  C) 30 days  D) 50 days  E) 45 days

Solution: one man can consume the same food in 30*40= 
30*40 = 1_200
1200 days.   10 more men join, the total number of men= 40   The number of days the food will last = 1200/40= 
1200/40 = 30
30 days.   ANSWER:30 days
Answer: C
Find the value of (875 233/899) × 899 Select
A) 786858 B) 786900 C) 786920 D) 786913 E) 786960

Solution: (875 233/899) × 899   (786625 + 233)/899 × 899   786858/899 × 899   786858   786858
Answer: A
A money lender finds that due to a fall in the annual rate of interest from 8% to 7 1/5 % his yearly income diminishes by Rs.61.50. his capital is	Choose the correct answer.
A) 22.378 B) 37.78 C) 76.88 D) 27.888 E) 12.771

Solution: Explanation:   76.88apital = Rs.x , then   4/5 x =61.5   x = 76.88   Answer: 76.88) Rs.76.88
Answer: C
Leona bought a 1-year, $10,000 certificate of deposit that paid interest at an annual rate of 8 percent compounded semiannually. What was the total amount of interest paid on this certificate at maturity?	Choose the correct option:  A) $10,464  B) $ 864  C) $ 816  D) $ 800  E) $ 480

Solution: Approach #1:   8 percent compounded semiannually --> 4% in 6 moths.   For the first 6 moths interest was 4% of $10,000, so $400;   For the next 6 moths interest was 4% of $10,000, plus 4% earned on previous interest of $400, so $400+$16=$416;   Total interest for 1 year was $400+$416  400+ 16= 
  400+ 16 = 416
$416;   Total interest for 1 year was $400+$416=$816.   Answer: $ 816.  400+ 416= 
  400+ 416 = 816
$816.   Answer: $ 816.
Answer: C
A certain population of bacteria doubles every 10 minutes. If the number of bacteria in the population initially was 10^5, then what was the number in the population 50 minutes later?	Pick one:
A) 2(10^5)
B) 5(10^5)
C) (2^5)(10^5)
D) (10^5)(10^5)
E) (10^5)^5

Solution: Every 10 minutes, the population is double the previous population.   In 50 minutes, the population doubles 5 times.   The population then is 2^5*10^5.   The answer is (2^5)(10^5).
Answer: C
Calculate the circumference of a circular field whose radius is 7 centimeters.
Choose the correct choice:
A) 11 π cm B) 15 π cm C) 1 π cm D) 4 π cm E) 14 π cm

Solution: Circumference C is given by   C = 2πr = 2π*7 = 14 π cm   Answer: 14 π cm2 *7= 
2 *7 = 14
14 π cm   Answer: 14 π cm
Answer: E
A student chose a number, multiplied it by 2, then subtracted 140 from the result and got 102. What was the number he chose?	Pick one.
A) 90	B) 100	C) 120	D) 160	E) 121

Solution: Solution:   Let x be the number he chose, then   2*x*140=102   2x=242   x=121   correct answer 121
Answer: E
Of the 70 electronics components that a factory must manufacture, 90 percent would be most e¢ ciently manufactured by Machine A and the remaining 10 percent would be most efficiently manufactured by Machine B, though either machine could manufacture any of the 70 components. If 50 percent of the components were manufactured by Machine A and the remainder were manufactured by Machine B, what is thehighest possible number of components that were manufactured by the machine that would manufacture them the most efficiently?	Options
A) 30
B) 32
C) 42
D) 35
E) 36

Solution: A can manufacture 90 % of 70 efficiently, which is 63.   B can manufacure 10 % of 70 efficiently, which is 7.   Now 50 % of 70 are produced by A. This means 35 parts. Since A can produce 63 efficiently, all 35 are produced efficiently. Rest (35) is produced by B, which can produce max. 7 parts efficiently.   Hence parts that were produced efficiently = 7+35= 
7+35 = 42
42. (42).
Answer: C
A box measuring 25 inches long by 30 inches wide by 15 inches deep is to be filled entirely with identical cubes. No space is to be left unfilled. What is the smallest number of cubes that can accomplish this objective?  Choose the correct option:  A) 80  B) 82  C) 84  D) 88  E) 90

Solution: least number of cubes will be required when the cubes that could fit in are biggest.   5 is the biggest number that could divide all three, 25, 30 and 15.   Thus side of cube must be 5, and total number of cubes = 25/5 * 30/5*15/5= 
25/5 * 30/5*15/5 = 90
90   Ans 90.
Answer: E
Little John had $16.10. He spent $3.25 on sweets and gave to his two friends $2.20 each. How much money was left?	Choose one:	A) $6.45	B) $8.35	C) $8.75	D) $8.85	E) $8.45

Solution: John spent and gave to his two friends a total of   3.25 + 2.20 + 2.20= 
3.25 + 2.20 + 2.20 = 7.65
$7.65   Money left    16.10 - 7.65= 
 16.10 - 7.65 = 8.45
$8.45   Answer :$8.45
Answer: E
If Jake loses 8 pounds, he will weigh twice as much as his sister. Together they now weigh 278 pounds. What is Jake’s present weight, in pounds?
Pick
A) 131  B) 135  C) 139  D) 147  E) 188

Solution: Consider Sister weight Now as x   Jakes weight (2times +8) = 2x+8   (2x+8)+(x) =278   x=90   Jake's weight is ....188   Correct answer is 188
Answer: E
Of 70 players on a football team, 40 are throwers. The rest of the team is divided so one third are left- handed and the rest are right handed. Assuming that all throwers are right handed, how many right- handed players are there total?
Choose the correct option
A) 54  B) 59  C) 60  D) 71  E) 92

Solution: Total = 70   Thrower = 40   Rest = 70 - 40= 
70 - 40 = 30
30   Left Handed= 30/3= 
30/3 = 10
10   Right handed= 20   If all Throwe0r are right handed then total right handed is  40 + 20= 
 40 + 20 = 60
60   so C. 60 is the right answer
Answer: C
S is the set of all fractions defined by the formula n/(n + 1), where n is a positive integer less than 20. What is the product X of all the fractions that are in S?
Choose the correct option:	A) 1) 1/20	B) 2) 1/21	C) 3) 1/2	D) 4) 19/40	E) 5) 19/20

Solution: 1/2 * 2/3 * 3/4 * ... 19/20   = 1/20   1) 1/20nswer - 1) 1/20
Answer: A
Four staff members at a certain company worked on a project. The amounts of time that the four staff members worked on the project were in the ratio 2 to 3 to 5 to 6. If one of the four staff members worked on the project for 15 hours, which of the following CANNOT be the total number of hours that the four staff members worked on the project?  Answers:
A) 40
B) 48
C) 80
D) 192
E) 120

Solution: Four members worked in ration 2:3:5:6, hence as everyone mentioned, individual work could be taken as 2x, 3x,5x, and 6x. Also this gives us total work as 16x.   But we are told that one of these individual works is 30hrs. hence, possible scenarios, if   (1)2x =15 => 16x = 120 (2) 3x =15 => 16x = 80 (3) 5x =15 => 16x = 48 (4) 6x =15 => 16x = 40   Hence Answer is 192 192 which can not be any of these.
Answer: D
In a race of 800 mtr gives Mary a start of 200 mtr and then loses the race by 20 seconds. What is the speed of Mary & Rose respectively ? If the ratio of respective speeds be 3:2?
Select.
A) 10 m/s	B) 12 m/s	C) 16 m/s	D) 20 m/s	E) 30 m/s

Solution: Let the speed of Kaushik be and speed of Piyush be and let the time taken by Piyush be t second then,   t = 20 s   Speed of Priya = 30 m/s   and Speed of Kala = 20 m/s   20 m/s
Answer: D
A thief is spotted by a policeman from a distance of 200metres. When the policeman starts the chase, the thief also starts running. If the speed of the thief be 16km/hr and that of the policeman 20km/hr, how far the thief will have run before he is overtaken ? Options
A) 1km	B) 500m	C) 650m	D) 750m	E) 800m

Solution: Relative speed of the policeman = 20-16= 
20-16 = 4
4 km/hr   time taken by policeman to cover 200m= (200/1000)*(1/4) = 1/20 hr   In 1/20 hr the thief covers a distance of 16/20 km = 4/5 km = 800m   Answer is 800m
Answer: E
There are 720 students in a school. The ratio of boys and girls in this school is 3:5. Find the total of girls & boys are there in this school?
Answers:  A) 320  B) 345  C) 450  D) 380  E) 400

Solution: In order to obtain a ratio of boys to girls equal to 3:5, the number of boys has to be written as 3 x and the number of girls as 5 x where x is a common factor to the number of girls and the number of boys. The total number of boys and girls is 720. Hence   3x + 5x = 720   Solve for x   8x = 720   x = 90   Number of boys   3x = 3 × 90 = 270   Number of girls   5x = 5 × 90 = 450   450
Answer: C
Find the last non-zero digit of 30^2345  Choose the most appropriate option.
A) 1  B) 2  C) 3  D) 4  E) 5

Solution: 30^2345=(3*10)^2345=3^2345*10^2345   so 30^2345 has 2345 zeroes,the last non-zero digit of 30^2345 will be same as unit digit of 3^2345   3^2345=3^(4*586+1)=> 3^1=3   last non-zero digit of 30^2345= 3   ANSWER:3
Answer: C
The labelled price of a cupboard is Rs. 6500. The shopkeeper sold it by giving 5% discount on the labelled price and earned a profit of 15%. What approximately is the cost price of the cupboard?
Choose the correct option:
A) 5350	B) 5450	C) 5500	D) 5700	E) None

Solution: Sol.   S.P. = 95% of Rs. 6500 = Rs. [95 / 100 * 6500] = Rs. 6175.   Profit = 15%.   ∴ C.P. = Rs. [110 / 115 * 6175] = Rs. 5369.56 = Rs. 5350.   5350nswer 5350
Answer: A
If the true discount on s sum due 2 years hence at 14% per annum be Rs. 196, the sum due is:  Pick.
A) s. 768	B) s. 968	C) s. 896	D) s. 2400	E) s. 2800

Solution: td=pw*r*t/100 so 196=pw*14*2/100 so pw=700   sum=pw+td..   sum=700+196= 
700+196 = 896
896   ANSWER:s. 896
Answer: C
The roof of an apartment building is rectangular and its length is 4 times longer than its width. If the area of the roof is 576 feet squared, what is the difference between the length and the width of the roof?
Pick:
A) 38.	B) 40.	C) 36.	D) 44.	E) 46.

Solution: Let the width= x   x*4x=576   x^2= 144   x= 12   Length= 4*12= 
4*12 = 48
48   difference= 48-12= 
48-12 = 36
36   36. is the answer
Answer: C
A group of n students can be divided into equal groups of 4 with 1 student left over or equal groups of 7 with 3 students left over. What is the sum of the two smallest possible values of n?
Choices:
A) 54 B) 58 C) 62 D) 66 E) 70

Solution: n = 4k+1 = 7j+3   Let's start at 1 = 4(0)+1 and keep adding 4 until we find a number in the form 7j+3.   1, 5, 9, 13, 17 = 7(2)+ 3   The next such number is 17 + 4*7= 
17 + 4*7 = 45
45.   17+45= 
17+45 = 62
62   The answer is 62.
Answer: C
Two pumps are connected to an empty tank. Pump X fills the tank with water at a constant rate, while pump Y drains water out of the tank at a constant rate. The two pumps finish filling the tank in five times the duration it would take pump X alone to fill the tank. If pump Y alone can empty a whole tank in 45 minutes, then how many minutes does it take pump X alone to fill the tank? Choose the correct choice from the following choices:
A) 27
B) 30
C) 33
D) 36
E) 39

Solution: Let V be the volume of the tank.   Let R be the rate per minute that pump X fills the tank.   Let T be the time it takes pump X to fill the tank.   The rate at which pump Y empties the tank is V/45 per minute.   (R - V/45)*5T=V=RT.   (R-V/45)*5=R   4R=V/9.   R=V/36.   It takes pump X 36 minutes to fill the tank.   The answer is 36.
Answer: D
In what time will a railway train 30 m long moving at the rate of 36 kmph pass a telegraph post on its way? Choose one.
A) 6 sec  B) 7 sec  C) 3 sec  D) 9 sec  E) 2 sec

Solution: T = 30/36 * 18/5= 
30/36 * 18/5 = 3
3 sec   Answer:3 sec
Answer: C
A and B started a business in partnership investing Rs.20,000 and Rs.15,000 respectively. After 6months, C joined them with Rs.20,000. Whatwill be B's share in total profit of Rs.25,000 earned at the end of 2years from the startingof the business? Choose the correct choice from the following answers:	A) Rs. 5,000	B) Rs. 5,500	C) Rs. 5,700	D) Rs. 6,500	E) Rs. 7,500

Solution: A : B : C = (20,000 x 24) : (15,000 x 24) : (20,000 x 18) = 4 : 3 : 3.   B's share = Rs. 25000 x	3/10	= Rs. 7,500.   Rs. 7,500
Answer: E
Share Rs.5400 among John, Jose & Binoy in the ration 2 : 4 : 6.Find the amount received by John? Select.
A) 1800  B) 980  C) 1200  D) 1240  E) 1400

Solution: Amount received by sanjay.   4 / 12 X 5400 = 1800= ( related ratio / sum of ratio ) x Total amount   So, the Amount received by sanjay is 1800.   1800
Answer: A