MU-NLPC/Calc-aqua_rat huggingface dataset:
If rupee one produces rupees nine over a period of 40 years, find the rate of simple interest?	Choose the correct option.
A) 22 1/8 %  B) 22 9/2 %  C) 22 1/7 %  D) 22 1/2 %  E) 21 1/2 %

Solution: 9 = (1*40*R)/100   R = 22 1/2 %   Answer:22 1/2 %
Answer: D
The height of the wall is 6 times its width and lenght of the wall is 7 times its height .if the volume of the wall be 16128 cu.m.its width is  Select
A) 4m B) 5m C) 6m D) 7m E) 8m

Solution: Explanation:   Let width = x   Then, height=6x and length=42x   42x × 6x × x = 16128   x = 4   4mnswer: 4m
Answer: A
The value of a machine is Rs 6,250. It decreases by 20% during the first , 40% during the second year and 30% during the third year. What will be the value of the machine after 3 years?
Options: A) Rs 2,100 B) Rs 2,200 C) Rs 2,152 D) Rs 2,252 E) none of these

Solution: Here Rs 2,100 = 6250, x = - 20, y = - 40 and z = - 30   Therefore value of the machine after 3 years   = Rs 2,100 ( 1 + x/100) ( 1 + y/100) ( 1 + z/100)   = 6250 ( 1 - 20/100) ( 1 - 40/100) ( 1 - 30/100)   = (6250 x 80 x 60 x 70) / (100 x 100 x 100)   = Rs 2,100   Rs 2,100NSWER:Rs 2,100
Answer: A
Solve the equation for x : 6x - 27 + 3x = 4 + 9 - x
Pick
A) 4  B) 5  C) 7  D) 9  E) 3

Solution: 4   4   9 x + x = 13 + 27   10 x = 40 => x = 4
Answer: A
In a fraction, if 1 is added to both the numerator at the denominator, the fraction becomes 1/2. If numerator is subtracted from the denominator, the fraction becomes 3/4. Find the fraction. Pick one:
A) 3/7  B) 4/7  C) 5/7  D) 6/7  E) 8/7

Solution: Let fraction be a/b, where a and b are integers.   "If 1 is added to both the numerator and denominator, the fraction becomes 1/2"   (a+1)/(b+1) = 1/2   2(a+1)  ( +1)/( +1)= 
 ( +1)/( +1) = 1
1/2   2(a+1)= b+1   2a + 2 = b + 1   2a - b = -1   "If numerator is subtracted from the denominator, the fraction becomes 3/4"   a/(b-a) = 3/4   4a = 3(b-a)   4a = 3b - 3a   4a + 3a - 3b = 0   7a - 3b = 0   Now we just need to solve system of linear equations:   2a - b = -1 . . . [1]   7a - 3b = 0 . . . [2]   From [1], we get:   b = 2a + 1   Substituting in this value of b into [2], we get   7a - 3(2a+1) = 0   7a - 6a - 3 = 0   a - 3 = 0   a = 3   b = 2(3)+1   b = 7   So original fraction is a/b = 3/7   3/7NSWER:3/7
Answer: A
Given f(x) = 3x – 5, for what value of x does 2*[f(x)] – 10 = f(x – 2) ?  Choose the correct choice from the following choices.
A) 1  B) 2  C) 3  D) 4  E) 5

Solution: 2(3x-5)-10 = 3(x-2) - 5   3x = 9   x = 3   The answer is 3.
Answer: C
Can you get total of 720 by using six zeros 0,0,0,0,0,0 and any maths operators.
Options:
A) 650  B) 550  C) 700  D) 720  E) 500

Solution: 720   720   (0!+0!+0!+0!+0!+0!)!   =(1+1+1+1+1+1)!   =(5)!   =6! is   6*5*4*3*2*1= 
  6*5*4*3*2*1 = 720
720
Answer: D
A four-digit code can consist of the digits 0 ~ 9 except that it does not contain the digits 1, 2, and 4 at all. If repeated digits are allowed, what is the probability that it has at least one even digit?  Choose the correct choice from the following choices:	A) 145/401	B) 845/901	C) 1145/1401	D) 2145/2401	E) 3145/3401

Solution: P(no even digits) = 4/7*4/7*4/7*4/7 = 256/2401   P(at least one even digit) = 1 - 256/2401 = 2145/2401   The answer is 2145/2401.
Answer: D
A certain car traveled twice as many miles from Town A to Town B as it did from Town B to Town C. From Town A to Town B, the car averaged 10 miles per gallon, and from Town B to Town C, the car averaged 12 miles per gallon. What is the average miles per gallon that the car achieved on its trip from Town A through Town B to Town C?	Pick one.
A) 11.5 B) 9.5 C) 13.5 D) 10.6 E) 14.5

Solution: step 1) took LCM of 10 and 12.. came as 30. just multiplied by 10...(to make easy calculation)   step 2) 300 distance between B to C... do 300/12 hence 25 gallons used   step 3) twice distance.. hence 300*2= 600... do as above.. 600/10= 60 gallons used   step 4) total gallons.. 25+60=85 gallons   step ) total miles= 300+600= 
300+600 = 900
900 miles   hence.. average of whole journey= 900/85 which comes to 10.6   Answer : 10.6
Answer: D
An average age of A, B and C is 45. If the averageage of A and B be 40 and that of B and C be 43, then the weight of B is	Options:  A) 25  B) 29  C) 31  D) 35  E) 36

Solution: Let A, B, C represent their respective age's. Then, we have:   A + B + C = (45 x 3) = 135 .... (i)   A + B = (40 x 2) = 80 .... (ii)   B + C = (43 x 2) = 86 ....(iii)   Adding (ii) and (iii), we get: A + 2B + C = 166 .... (iv)   Subtracting (i) from (iv), we get : B = 31.   B's age= 31   31
Answer: C
Find the principle on a certain sum of money at 5% per annum for 2 2/5 years if the amount being Rs.1456? Select: A) 1000 B) 2217 C) 2889 D) 2777 E) 1300

Solution: 1456 = P [1 + (5*12/5)/100]   P= 1300   Answer: 1300
Answer: E
Annie has 100 cards numbered 1 through 100. If she deals seven cards to Alex, without replacing any of them, what is the probability that Alex will get five consecutive numbers? Choices:
A) 95!/100! B) (94! X 7!)/100! C) (95! X 5!)/100! D) (96! X 5!)/100! E) (97! X 4!)/100!

Solution: Alex to get 7 consecutive cards in ascending order, to have 7 consecutive at the end is good enough.   There are 94 consecutive numbers in 100: {1, 2, 3, 4, 5, 6, 7}, {2, 3, 4, 5, 6, 7, 8}, ..., {94, 95, 96, 97, 98, 99, 100};   Total ways to pick 7 cards out of 100 is {7!*94!}{100!}.   Answer: (94! X 7!)/100!.
Answer: B
A bar over a sequence of digits in a decimal indicates that the sequence repeats indefinitely. What is the value of (10^4 -10^2)(0.0018)?	Options.
A) 16.82	B) 19.82	C) 17.82	D) 20	E) 22

Solution: You get 10^2 (100-1) (.0018)   we know   18/10000= 
  18/10000 = 9/5_000 = around 0.0018
.0018   10^2 (99) * (18/10000)   10^2= 100 and 100^2 = 10000   Cancel out the 100 with the 10^2   Left with 99(18/100).   0.99*18= 
0.99*18 = 17.82
17.82   Answer : 17.82
Answer: C
Find the option to replace the question mark in the series below
5 ? 15 75 525 4725
Choose the correct choice from the following choices
A) 2 B) 6 C) 7 D) 5 E) 8

Solution: ol: 5 x 1 = 5   5 x 3 = 15   15 x 5 = 75   75 x 7 = 525   525 x 9 = 4725   So ? = 5   Answer:5
Answer: D
If one and a half women, drink one and a half tea in one and a half minutes.
How many tea can 9 women drink in 3 minutes ?  Choose the correct option.
A) 11	B) 8	C) 37	D) 15	E) 18

Solution: E   18   Explanation:   More minutes implies more tea.   More women implies more tea.   The time become twice (3 minutes / 1.5 minutes).   women become six times (9 / 1.5).   Number of tea = 2 * 6 * Original(1.5)
Answer: E
A shop sells bicycles and tricycles. In total there are 10 cycles (cycles include both bicycles and tricycles) and 21 wheels. Determine how many of each there are, if a bicycle has two wheels and a tricycle has three wheels.	Choose the correct choice from the following answers
A) b=9,t=1  B) b=7,t=3  C) b=6,t=2  D) b=2,t=5  E) b=6,t=4

Solution: Let b be the number of bicycles and let t be the number of tricycles.   Set up the equations   b+t=10............(1)   2b+3t=21............(2)   Rearrange equation (1) and substitute into equation (2)   2b+30-3b=21   -b=-9   b=9   Calculate the number of tricycles t   t=10−b   =10−9   =1   There are 1 tricycles and 9 bicycles.   b=9,t=1nswer is b=9,t=1.
Answer: A
Which of the following are roots of an equation (x^-2)+(3x^-1)-10=0 Pick one.
A) 1/5 and -1/2
B) -1/5 and 1/2
C) 1/5 and 1/2
D) -1/5 and -1/2
E) -5/2 and -1/2

Solution: Given: (x^-2) + (3x^-1) - 10 = 0   Rewrite as: 1/(x²) + 3/x - 10 = 0   Remove fractions by multiplying both sides by x² to get: 1 + 3x - 10x² = 0   Rearrange to get: 10x² - 3x - 1 = 0   Factor to get: (5x + 1)(2x - 1) = 0   So, EITHER 5x + 1 OR 2x - 1 = 0   If 5x + 1 = 0, then x = -1/5   If 2x - 1 = 0, then x = 1/2   So, the roots (solutions) are -1/5 and 1/2   The answer is -1/5 and 1/2.
Answer: B
S and T are two-digit positive integers that have the same digits but in reverse order. If the positive difference between S and T is less than 50, what is the greatest possible value of S minus T?  Choose the correct answer.
A) 40
B) 42
C) 44
D) 45
E) 48

Solution: A two-digit integer "ab" can be expressed algebraically as 10a+b.   S-T=(10a+b)-(10b+a)=9(a-b)<50.   The greatest multiple of 9 which is less than 50 is 45.   The answer is 45.
Answer: D
Rose is two years older than Bruce who is twice as old as Chris. If the total of the ages of Rose, B and Chris be 27, the how old is Bruce ?  Select the correct option:	A) 8 years	B) 10 years	C) 12 years	D) 13 years	E) 14 years

Solution: Let Chris's age be x years. Then, Bruce's age = 2x years.Rose's age = (2x + 2) years.   (2x + 2) + 2x + x = 27   5x = 25   x = 5.   Hence, Bruce's age = 2x = 10 years.   10 years
Answer: B
The true discount on a bill due 9 months hence at 16% per annum is Rs. 180.The amount of the bill is  Choose the correct answer:	A) Rs. 1386	B) Rs. 1764	C) Rs. 1500	D) Rs. 2268	E) None of these

Solution: Solution   32.5   Let P.W. be Rs. x.Then,S.I. on Rs.x at 16% for 9 months =Rs.180.   ∴ x 16 x9/ 12x 1/100}= 180 or x = 1500.   ∴ P.W. = Rs. 1500.   Answer Rs. 1500
Answer: C
A store raised the price of an item by exactly 25 percent. Which of the following could NOT be the resulting price of the item?
Choose one
A) 130  B) 250  C) 375  D) 500  E) 62.5

Solution: If it raised the value by 25% then the resulting price is 1.25 times the original price. So the final answer has to be a multiple of 1.25. Check the answers.   130 - No   250 - Yes   375 - Yes   500 - Yes   62.50 - Yes   130nswer : 130
Answer: A
How many shots of 1cm radius can be prepared from a sphere of 7cm radius? Choose the correct choice
A) 343	B) 388	C) 327	D) 88	E) 99

Solution: 4/3 Ï€ * 7 * 7 * 7 = 4/3 Ï€ * 1 * 1 * 1 * x   x =343   343nswer: 343
Answer: A
Seed mixture X is 40 percent ryegrass and 60 percent bluegrass by weight; seed mixture Y is 25 percent ryegrass and 75 % fescue. If a mixture of X and Y contains 30% ryegrass, what percent of the weight of the mixture is X?  Select the correct option:  A) 10%  B) 33 1/3%  C) 40%  D) 50%  E) 66 2/3%

Solution: Assuming the weight of the mixture to be 100g**, then the weight of ryegrass in the mixture would be 30g.   Also, assume the weight mixture X used in the mixture is Xg, then the weight of mixture Y used in the mixture would be (100-X)g.   So we can now equate the parts of the ryegrass in the mixture as:   0.4X + 0.25(100-X) = 30   0.4X + 25 - 0.25X = 30   0.15X = 5   X = 5/0.15 = 500/15 = 100/3   So the weight of mixture X as a percentage of the weight of the mixture   = (weight of X/weight of mixture) * 100%   = (100/3)/100 * 100%   = 33%   ANSWER:33 1/3%
Answer: B
In 1970 there were 8,902 women stockbrokers in the United States. By 1978 the number had increased to 19,947. Approximately what was the percent increase?
Choose the correct choice from the following answers.
A) 45%
B) 125%
C) 145%
D) 150%
E) 225%

Solution: We can use approximation to get the answer quickly.   Like,   19,947 is approx 20000   8902 is approx 8900   So, Total increase = 20000 - 8900= 
20000 - 8900 = 11_100
11100   Hence, % increase= 11100 / 8900 = approx. 11/9 = 1.22 = approx. 1.25   So, Choice is 125%.
Answer: B
The area of a square is equal to five times the area of a rectangle of dimensions 125 cm * 64 cm. What is the perimeter of the square?
Choose the correct option: A) 700 B) 800 C) 900 D) 600 E) 500

Solution: Area of the square = s * s = 5(125 * 64)=> s = 25 * 8= 
25 * 8 = 200
200 cm   Perimeter of the square= 4 * 200= 
4 * 200 = 800
800 cm.   Answer: Option 800
Answer: B
The expression (11.98 x 11.98 + 11.98 x x + 0.02 x 0.02) will be a perfect square for x equal to:
Choose the correct choice from the following answers:	A) 0.02	B) 0.2	C) 0.04	D) 0.4	E) None

Solution: EXPLANATION   Given expression = (11.98)2 + (0.02)2 + 11.98 x x.   For the given expression to be a perfect square, we must have   11.98 x x = 2 x 11.98 x 0.02 or x = 0.04   Answer 0.04
Answer: C
In digging a grave 200 m * 100 m * 3 m the volumes of the dirt to be extracted will be? Options
A) 600 cu.m B) 12000 cu.m C) 6000 cu.m D) 60000 cu.m E) 4000 cu.m

Solution: 200 * 100 * 3= 
200 * 100 * 3 = 60_000
60000   ANSWER:60000 cu.m
Answer: D
Sreenivas sells a table to Shiva at 10% profit and Shiva sells it to Mahesh at 10% loss. At what price did Sreenivas purchase the table if Mahesh paid Rs. 2178?	Choose the correct choice from the following options
A) 2887  B) 2665  C) 2200  D) 2665  E) 2771

Solution: Let the cost price of table for Sreenivas be Rs. x and given that, cost price of table for Mahesh = Rs. 2178.   => (90%) of (110%) of x = Rs. 2178.   => (90/100)(110/100)x = 2178   => x = (2178 * 100)/(9 * 11)   => x = Rs. 2200   Answer:2200
Answer: C
A company has two types of machines, type R and type S. Operating at a constant rate, a machine of type R does a certain job in 20 hrs and a machine of type S does the same job in 60 hours. If the company used the same number of each type of machine to do the job in 3 hours, how many machines of type R were used?	Options:	A) 3	B) 4	C) 5	D) 6	E) 8

Solution: Type R completes 1/20 of the job each hour.   Type S completes 1/60 of the job each hour.   Together R and S complete 1/20 +1/60 = 1/15 of the job each hour.   Let n be the number of each type of machine.   3*n*(1/15) = 1 job completed   n = 5   The answer is 5.
Answer: C
The ages of X and Y are in the proportion of 6:5 and total of their ages is 44 years. The proportion of their ages after 8 years will be  Select:
A) 3:6	B) 6:3	C) 8:7	D) 9:5	E) None of these

Solution: Explanation:   Let current ages of X and Y correspondingly, is 6A & 5A   Given: 6A + 5A = 44   => A = 4   Proportion of ages after 0.8 decades will be   6A + 8 : 5A + 8 32:28 (or) 8:7 . Answer: 8:7
Answer: C
The sum of the present ages of A, B, C is 33 years. Three years ago their ages were in the ratio 1:2:3. What is the present age of A?
Choose the correct choice:	A) 5	B) 7	C) 9	D) 11	E) 13

Solution: Three years ago:   a:b:c = 1:2:3   Let a = 1x, b = 2x, and c = 3x.   Today:   (x+3) + (2x+3) + (3x+3) = 33   x = 4   So the present age of A is x+3 = 7   The answer is 7.
Answer: B
A shop owner has a sale of Rs. 6435, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 years. How much sale must she have in the 6th year so that she gets an average sale of Rs. 6500? Pick
A) 5000 B) 5500 C) 4991 D) 5600 E) 5700

Solution: Total sale for 5 months = Rs. (6435 + 6927 + 6855 + 7230 + 6562) = Rs. 34009.   Required sale = Rs. [ (6500 x 6) - 34009 ]   = Rs. (39000 - 34009)   = Rs. 4991   4991
Answer: C
The average age of husband, wife and their child 3 years ago was 27 years and that of wife and the child 7 years ago was 20 years. The present age of the husband is:  Pick one.
A) 20 years B) 30 years C) 60 years D) 36 years E) 35 years

Solution: D   36 years   Sum of the present ages of husband, wife and child = (27 x 3 + 3 x 3) years = 90 years.   Sum of the present ages of wife and child = (20 x 2 + 7 x 2) years = 54 years.   Husband's present age = (90 - 54)= 
(90 - 54) = 36
36 years.
Answer: D
At the end of the month, a certain ocean desalination plant’s reservoir contained 30 million gallons of water. This amount is twice the normal level. If this amount represents 75% of the reservoir’s total capacity, how many million gallons short of total capacity is the normal level?
Select the correct option
A) 10  B) 15  C) 20  D) 25  E) 30

Solution: the Q talks of total capacity, normal level, present level, shortage etc..   so it is all about not going wrong in these terms   30 MG= 75% of Total..   total = 30/.75= 
30/.75 = 40
40MG..   Normal level= 1/2 of 40=20MG..   shortage of normal level=40-20= 
40-20 = 20
20MG..   20
Answer: C
An elementary school houses primarily kindergartners, first graders, second graders, and third graders. If an assembly included 30 kindergartners, 20 first graders, and 80 other children, and the ratio of first graders to third graders is tripled, what is the ratio of the first graders to the rest of the children?  Select:
A) 40: 20
B) 42: 21
C) 50: 100
D) 15: 25
E) It cannot be determined by the information given.

Solution: While you can figure out most of this question, there is not enough information to completely tell. the answer is It cannot be determined by the information given..
Answer: E
The number 42 can be written as the sum of the squares of 3 different positive integers. What is the sum of these 3 integers?	Choose the correct choice from the following choices:  A) 17  B) 10  C) 15  D) 14  E) 13

Solution: I think brute force with some common sense should be used to solve this problem.   Write down all perfect squares less than 42: 1, 4, 9, 16, 25, 36.   Now, 42 should be the sum of 3 of those 8 numbers. Also to simplify a little bit trial and error, we can notice that as 42 is an odd numbers then either all three numbers must be odd (odd+odd+odd=odd) OR two must be even and one odd (even+even+odd=odd).   We can find that 42 equals to 1+16+25=1^2+4^2+5^2=42 --> 1+5+4=10.   Answer: 10.
Answer: B
In one hour, a boat goes 15 km/hr along the stream and 9 km/hr against the stream. The speed of the boat in still water (in km/hr) is:  Choose the most appropriate option:  A) 12 kmph  B) 13 kmph  C) 14 kmph  D) 15 kmph  E) 16 kmph

Solution: Explanation:   Let the speed downstream be a km/hr and the speed upstream be b km/hr, then   Speed in still water =1/2(a+b) km/hr   Rate of stream = 1/2(a−b) km/hr   Speed in still water = 1/2(15+9) kmph = 12 kmph.   12 kmphnswer: Option 12 kmph
Answer: A
Nitrous oxide (laughing gas) worth Rs 126 per kg and Rs 135 per kg are mixed with a third variety in the ratio 1 : 1 : 2. If the mixture is worth Rs 153 per kg, then the price of the third variety per kg will be  Choose the correct option:	A) Rs 169.50	B) Rs 170	C) Rs 175.50	D) Rs 180	E) Rs 190

Solution: Suppose the quantities of Nitrous oxide worth Rs 126 per kg, Rs 135 per kg and Rs.x per kg purchased are Y, Y and 2Y kg respectively:   (126 Y +135 Y + 2XY )/ 4Y = 153   => 261 + 2X = 612   => X= 351/2= 
351/2 = 351/2 = around 175.5
175.50   Nitrous oxide of the third varity is purchased at the rate of Rs 175.50 per Kg   ANSWER:Rs 175.50
Answer: C
Walking at 25% of his usual speed a man takes 24 minutes more to cover a distance. What is his usual time to cover this distance? Choose the correct option.
A) 8 B) 16 C) 42 D) 48 E) 54

Solution: speed is inversly proprtional to time   walking at 25% of speed meand 1/4s takes 4t.   It takes 24 minutes extra to cover the distance. then   4t=t+24   3t=24   t=8.   Option 8 is correct
Answer: A
Population of a city in 20004 was 1000000. If in 2005 there isan increment of 15% , in 2006 there is a decrements of 35 % and in 2007 there is an increment of 45%, then find the population of city atthe end of the year 2007
Choose the most appropriate option:  A) 346656  B) 466577  C) 854343  D) 354567  E) 1083875

Solution: Required population = P (1 + R1/100)(1 - R2/100)(1 + R3/100)   = P (1 + 15/100)(1 - 35/100)(1 + 45/100)   = 1083875   1083875
Answer: E
What is the least integer greater than –4+0.5?
Options
A) –3	B) –1	C) 0	D) 1	E) 2

Solution: This question is just about doing careful Arithmetic and remembering what makes a numberbiggerorsmallercompared to another number.   First, let's take care of the Arithmetic:   (-4) + (0.5) = -3.5   On a number line, since we're ADDING +.5 to a number, the total moves to the RIGHT (so we're moving from -4 to -3.5).   Next, the question asks for the LEAST integer that is GREATER than -3.5   Again, we can use a number line. Numbers become greater as you move to the RIGHT. The first INTEGER to the right of -3.5 is -3.   Final –3nswer:   –3
Answer: A
A train passes a station platform in 28 seconds and a man standing on the platform in 10 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?	Choose the correct answer
A) 270	B) 277	C) 240	D) 88	E) 112

Solution: Speed = [54 * 5/18] m/sec = 15 m/sec.   Length of the train = (15 * 10)= 
(15 * 10) = 150
150 m.   Let the length of the platform be x meters.   Then, x + 150 / 28= 15   x + 150 = 420   x = 270 m.   270nswer:270
Answer: A
If x and y are negative integers, which of the following statements must be true?
I. (-x)^y is positive.
II. (-x)^(-y) is positive.
III. x^(-y) is positive.	Options.
A) None  B) II only  C) I and II  D) I and III  E) I, II and III

Solution: Let's x = -2 and y = -3   I. (-x)^y = (2)^(-3) = 1/(2^3) --> Positive   II. (-x)^(-y) is positive. = 2^3 --> Positive   III. x^(-y) is positive. = -2^3 --> Negative   Answer: I and II
Answer: C
The average of first 10 odd numbers is? Choose the correct choice
A) 11
B) 10
C) 18
D) 12
E) 19

Solution: Explanation:   Sum of 10 odd no. = 100   Average = 100/10= 
100/10 = 10
10   Answer:10
Answer: B
If Re.1 amounts to Rs.9 over a period of 20 years. What is the rate of simple interest?
Answers: A) 27 B) 29 C) 26 D) 40 E) 12

Solution: 8 = (1*20*R)/100   R = 40%.Answer: 40
Answer: D
David completes a piece of work in 5 days, John completes the same work in 9 days. If both of them work together, then the number of days required to complete the work is?
Options:  A) 3.2 days  B) 8 days  C) 10 days  D) 12 days  E) 14 days

Solution: IfA can complete a work in x days and B can complete the same work in y days, then, both   of them together can complete the work in x y/ x+ y days.   That is, the required No. of days = 5 × 9/14= 3.2 days   3.2 daysnswer : 3.2 days
Answer: A
A vessel contains 20 liters of a mixture of milk and water in the ratio 3:2. 10 liters of the mixture are removed and replaced with an equal quantity of pure milk. If the process is repeated once more, find the ratio of milk and water in the final mixture obtained?  Options.
A) 4:5	B) 9:1	C) 2:5	D) 3:4	E) 6:7

Solution: Milk = 3/5 * 20= 
3/5 * 20 = 12
12 liters, water= 8 liters   If 10 liters of mixture are removed, amount of milk removed = 6 liters and amount of water removed = 4 liters.   Remaining milk = 12 - 6= 
12 - 6 = 6
6 liters   Remaining water= 8 - 4= 
8 - 4 = 4
4 liters   10 liters of pure milk are added, therefore total milk= (6 + 10)= 
(6 + 10) = 16
16 liters.   The ratio of milk and water in the new mixture= 16:4 = 4:1   If the process is repeated one more time and 10 liters of the mixture are removed, then amount of milk removed = 4/5 * 10= 
4/5 * 10 = 8
8 liters.   Amount of water removed= 2 liters.   Remaining milk = (16 - 8)= 
(16 - 8) = 8
8 liters.   Remaining water= (4 -2)= 
(4 -2) = 2
2 liters.   final mixture obtained= (8 + 10):2 = 18:2 = 9:1.   ANSWER 9:1
Answer: B
Car X began traveling at an average speed of 35 miles per hour. After 72 minutes, car Y began traveling at an average speed of 49 miles per hour. When both cars had traveled the same distance, both cars stopped. How many miles did car X travel from the time car Y began traveling until both cars stopped?
Choose the correct choice from the following options
A) 105	B) 120	C) 140	D) 147	E) 168

Solution: Car Y began travelling after 72 minutes or 1.2 hours.   Let t be the time for which car Y travelled before it stopped.   Both cars stop when they have travelled the same distance.   So,   35(t+1.2) = 49t   or 5t+6=7t   or t=3   Distance travelled by car X from the time car Y began traveling until both cars stopped is   35 x 3   = 105 miles   105nswer:- 105
Answer: A
The cost of fencing a square field @ Rs. 20 per metre is Rs.10.080.How much will it cost to lay a three meter wide pavement along the fencing inside the field @ Rs. 50 per sq m Choose the correct choice from the following choices:	A) 73889	B) 27788	C) 73879	D) 73800	E) 2799

Solution: Explanation:   perimeter = total cost / cost per m = 10080 /20= 
10080 /20 = 504
504m   side of the square= 504/4= 
504/4 = 126
126m   breadth of the pavement= 3m   side of inner square = 126 - 6= 
126 - 6 = 120
120m   area of the pavement= (126 x126) - (120 x 120) = 246 x 6 sq m   cost of pavement = 246*6*50 = Rs. 73800   Answer: 73800)
Answer: D
If n is an odd integer, which of the following must also be an odd integer?
Choose the correct choice from the following answers:
A) 2n B) 2n^2 C) n^2 + 2n D) n^2 + 3n E) n^2 + 2n + 3

Solution: (A)	2n = even*odd = even.   (B)	2n^2 = even*odd = even.   (C)	n^2 + 2n = odd + even*odd = odd + even = odd.   (D)	n^2 + 3n = odd + odd*odd = odd + odd = even.   (E)	n^2 + 2n + 3 = odd +even + odd = even.   Answer: n^2 + 2n.
Answer: C