MU-NLPC/Calc-aqua_rat huggingface dataset:
One morning is starts to snow at a constant rate. Later, at 6:00am, a snow plow sets out to clear a straight street. The plow can remove a fixed volume of snow per unit time, in other words its speed it inversely proportional to the depth of the snow. If the plow covered twice as much distance in the first hour as the second hour, what time did it start snowing?	Choose the correct choice from the following answers
A) 4.15 am	B) 3.20 am	C) 5.22 am	D) 6.10 am	E) 2.40 am

Solution: Let the depth of snow at time t to be t units. The speed of the plow at time t will be 1/t. Define t=0 as the time it started snowing and t=x the time the plow started.   The distance covered in the first hour is the integral from x to x+1 of 1/t dt. The antiderivative of 1/t is ln(t) so the total distance covered in the first hour is ln((x+1)/x).   By the same reasoning the distance covered in the second hour in ln((x+2)/(x+1)).   Using the fact that it the plow traveled twice as far in the first hour as the second: ln((x+1)/x) = ln((x+2)/(x+1))2   Exp both sides and you have (x+1)/x = ((x+2)/(x+1))2.   Solving for x you get x=(51/2-1)/2, which is the number of hours that elapsed between the time it started snowing and the snow plow left.It started snowing at (51/2-1)/2 hours before 6:00am, or 5:22:55am.
Answer: C
If x+y=17z, then which of the following represents the average (arithmetic mean) of x, y, and z, in terms of z?
Choose the correct option.
A) 2z+1 B) 3z C) 6z D) z/3 E) 3z/2

Solution: Pick any number like X=12, Y=22 and Z= 2 so that X+Y=17Z, now then the arithmetic mean will be   (12+22+2)/3= 
  (12+22+2)/3 = 12
12. Now, just look at the answers and put the value of Z there.   (A) 2.2+1=5, no   (B) 3.2=6, no   (6z) 6.2=12, it can be the answer, lets check us the other options   (D) 2/3, no   (E) (3.2)/2=3, no   so the answer will be 6z..
Answer: C
If a code word is defined to be a sequence of different letters chosen from the 10 letters A, B, C, D, E, F, G, H, I, and J, what is the ratio of the number of 5-letter code words to the number of 3-letter code words? Pick one
A) 36
B) 38
C) 40
D) 42
E) 44

Solution: Method #1: Using the permutation formula   # of 5 letter code words:   nPr = n! / (n – r)! = 10! / (10 – 5)! = 10*9*8*7*6   # of 3 letter code words:   nPr = 10! / (10 – 3)! = 10*9*8   # of 5 words / # of 4 words = (10*9*8*7*6)/(10*9*8)= 
(10*9*8*7*6)/(10*9*8) = 42
42   42
Answer: D
The age of father 10 years ago was thrice the age of his son. Ten years hence, father's age was five times the age of the son. After 6 years, son's age will be? Choose the correct choice from the following:
A) 7:6
B) 7:3
C) 7:4
D) 7:2
E) 7:1

Solution: Let the age of father and son 10 years ago be 3x and x years respectively.   Then, (3x + 10) + 10 = 2[(x + 10) + 10]   3x + 20 = 2x + 40 => x = 20.   Required ratio = (3x + 10):(x + 10)   = 70:30   = 7:3   Answer: 7:3
Answer: B
10 different biology books and 8 different chemistry books lie on a shelf. In how many ways can a student pick 2 books of each type? Choose the correct choice from the following choices:
A) 80	B) 160	C) 720	D) 1100	E) 1260

Solution: No. of ways of picking 2 biology books(from 10 books) = 10c2 = (10*9)/2= 
(10*9)/2 = 45
45   No. of ways of picking 2 chemistry books(from 8 books)= 8c2 = (8*7)/2= 
(8*7)/2 = 28
28   Total ways of picking 2 books of each type= 45*28= 
45*28 = 1_260
1260   (Option 1260)
Answer: E
A bank offers 5% C.I. calculated on half-yearly basis . A customer deposits Rs. 1600 each on 1st January and 1st July of a year. At the end of the year, the amount he would have gained by way of interest is?  Choose one:
A) Rs. 122 B) Rs. 121 C) Rs. 129 D) Rs. 111 E) Rs. 191

Solution: Explanation:   Amount = [1600 * (1 + 5/(2 * 100)2 + 1600 * (1 + 5/(2 * 100)]   = [1600 * 41/40(41/40 + 1)   = [(1600 * 41 * 81)/(40 * 40)] = Rs. 3321.   C.I. = 3321 - 3200 = Rs. 121.   Answer:Rs. 121
Answer: B
It takes ten minutes to fry a steak (five minutes for each side). You are frying the steaks in a pan that can accommodate only two steaks at one time. What is the least amount of time by which you can fry all the three steaks you have?  Choices.
A) 15 B) 19 C) 12 D) 17 E) 10

Solution: A   Fifteen Minutes.   After frying for five minutes, you can take out one steak and put the third one inside while turning the other one inside. After five more minutes, one steak is fried from both sides and you can take it out. Now put in the steak that we removed and turn the other one inside. 15fter five more minutes, they both will also be fried from both sides.
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. 13000, then the share of B is?
Pick one
A) 6000  B) 12000  C) 18000  D) 24009  E) 24002

Solution: Ratio of investments of A and B is (70000 * 12) : (120000 * 6) = 7 : 6   Total profit = Rs. 13000   Share of B = 6/13 (13000) = Rs. 6000   6000nswer: 6000
Answer: A
A man swims downstream 30 km and upstream 18 km taking 3 hours each time, what is the speed of the man in still water? Pick:	A) 9	B) 8	C) 5	D) 2	E) 1

Solution: 30 --- 3 DS = 10   ? ---- 1   18 ---- 3 US = 6   ? ---- 1 M = ?   M = (10 + 6)/2= 
(10 + 6)/2 = 8
8   Answer:8
Answer: B
A, E, F, and G ran a race. A said "I did not finish 1st /4th E said "I did not finish 4th" F said "I finished 1st" G said "I finished 4th" If there were no ties and exactly 3 children told the truth, when who finishes 4th? Pick one.
A) J B) H C) K D) G E) H

Solution: Answer : G
Answer: D
A batsman makes a score of 95 runs in the 11th inning and thus increases his average by 5. Find his average after 11th inning. Choose the correct option.
A) 40 B) 50 C) 62 D) 45 E) 56

Solution: Let the average after 11th inning = x   Then, average after 10th inning = x-5   10(x-5)+95 = 11x   x = 95-50= 
95-50 = 45
45   Answer is 45
Answer: D
The avg weight of A,B & C is 84 kg. If D joins the group, the avg weight of the group becomes 80 kg.If another man E who weights is 3 kg more than D Replaces A, Then the avgof B,C,D&E becomes 79 kg. What is the weight of A?	Choose the most appropriate option
A) 25	B) 35	C) 75	D) 80	E) 90

Solution: A + B + C = 3 *84= 
3 *84 = 252
252   A + B + C + D= 4 * 80= 
4 * 80 = 320
320 ---- (i)   So, D= 68& E = 68 + 3= 
68 + 3 = 71
71   B + C + D +E= 79 * 4= 
79 * 4 = 316
316 --- (ii)   From Eq. (i) & (ii)   A-E= 320 – 316 = 4   A = E +4 = 71 + 4= 
71 + 4 = 75
75   75
Answer: C
A and B start a business jointly. A invests Rs.20000 for 8 months and B remains in the business for 4 months. Out of the total profit B claims 2/7th share. How much money is contributed by B? Choose the correct option:  A) A)Rs.12829  B) B)Rs.16000  C) C)Rs.12293  D) D)Rs.12804  E) E)Rs.12830

Solution: 20*8: x*4 = 5:2   x = 16 =>   Rs.16000   Answer: Rs.16000
Answer: B
If a is a positive integer, and if the units digit of a^2 is 9 and the units digit of (a+1)^2 is 4, what is the units X digit of (a+2)^2?  Options.
A) 1
B) 3
C) 5
D) 6
E) C. 14

Solution: I also got A. By punching in numers:   X...7^2=...9   ...8^2=...4   ...9^2=...1.1
Answer: A
Aish started a business investing Rs. 25,000 in 2010, In 2011, he invested an additional amount of Rs. 10,000 and Roshan joined him with an amount of Rs. 35,000. In 2012, Aish invested another additional amount of Rs. 10,000 and Atul joined them with an amount of Rs. 35,000. What will be Roshan’s share in the profit of Rs. 1,80,000 earned at the end of 3 years from the start of the business in 2010?
Choices:
A) Rs.45000  B) Rs.50000  C) Rs.60000  D) Rs.70000  E) None of these

Solution: Explanation :   Aish : Roshan : Atul   = (25000 x 12 + 35000 x 12 + 45000 x 12) : (35000 x 24) : (35000 x 12)   = 1260000 : 840000 : 420000 = 3 : 2 : 1   Roshan's share = Rs. 180000 x 2/6   = Rs. 60000.   Answer : Rs.60000
Answer: C
The average of 5 numbers is calculated as 15. It is discovered later on that while calculating the average, one number namely 36 was wrongly read as 26. The correct average is? Choices
A) 12.5	B) 26.2	C) 6.5	D) 7.5	E) 12

Solution: 5 * 15 + 36 – 26   = 75/10= 
75/10 = 15/2 = around 7.5
7.5   Answer: 7.5
Answer: D
In an election between two candidates, one got 55% of the total valid votes, 20% of the votes were invalid. If the total number of votes was 5000, the number of valid votes that the other candidate got, was:	Choose one:	A) 1800	B) 2700	C) 2900	D) 2200	E) 2300

Solution: A   Number of valid votes = 80% of 5000 = 4000.   Valid votes polled by other candidate = 45% of 4000   = (45/100 x 4000) = 1800.
Answer: A
Find the product of the local value and absolute value of 2 in 564823	Choose the correct choice from the following.
A) 40	B) 60	C) 80	D) 100	E) 18000

Solution: Explanation:   Place value = Local value   Face value = Absolute value   The place value of 2 in 564823 is 2 x 10 = 20   The face value of 2 in 564823 is nothing but 2.   => 20 x 2 = 40   40nswer: Option 40
Answer: A
If each of 4 subsidiaries of Corporation R has been granted a line of credit of $710,500 and each of the other 3 subsidiaries of Corporation R has been granted a line of credit of $112,000, what is the average (arithmetic mean) line of credit granted to a subsidiary of Corporation R?  Answers:
A) $1,568,000
B) $454,000
C) $406,000
D) $313,600
E) $116,000

Solution: My take is B.   (710500*4 + 112000*3)/7= 
(710500*4 + 112000*3)/7 = 454_000
454000
Answer: B
What is the remainder when 43^92 is divided by 5?
Pick: A) 0 B) 1 C) 2 D) 3 E) 4

Solution: The units digit of the exponents of 3 cycle in a group of 4: {3, 9, 7, 1}   92 has the form 4k so the units digit of 43^92 is 1.   The remainder when dividing by 5 is 1.   The answer is 1.
Answer: B
A and B start a business, with A investing the total capital of Rs.500000, on the condition that B pays A interest @ 10% per annum on his half of the capital. A is a working partner and receives Rs.15000 per month from the total profit and any profit remaining is equally shared by both of them. At the end of the year, it was found that the income of A is twice that of B. Find the total profit for the year?
Choose the correct choice from the following choices:
A) A)590280	B) B)590100	C) C)591900	D) D)590000	E) E)927000

Solution: Interest received by A from B = 10% of half of Rs.500000 = 10% * 250000 = 25000.   Amount received by A per annum for being a working partner = 15000 * 12 = Rs.180000.   Let 'P' be the part of the remaining profit that A receives as his share. Total income of A = (25000 + 180000 + P)   Total income of B = only his share from the remaining profit = 'P', as A and B share the remaining profit equally.   Income of A = Twice the income of B   (25000 + 180000 + P) = 2(P)   P = 205000   Total profit = 2P + 180000   = 2*205000 + 180000= 
2*205000 + 180000 = 590_000
590000   Answer:590000
Answer: D
What is the maximum number R of 27 cubic centimetre cubes that can fit in a rectangular box measuring 8 centimetre x 9 centimetre x 12 centimetre ?  Choose the correct choice from the following:
A) 36
B) 32
C) 24
D) 21
E) 15

Solution: 27 cubic centimetre cubes gives side = 3cm   so if:   L*W*H is 9*12*8, then max. cube we can have are  3*4*2= 
 3*4*2 = 24
24   L*W*H is 9*8*12, then max. cube we can have are  3*2*4= 
 3*2*4 = 24
24   L*W*H is 12*8*9, then max. cube we can have are  4*2*3= 
 4*2*3 = 24
24   L*W*H is 12*9*8, then max. cube we can have are  4*3*2= 
 4*3*2 = 24
24   L*W*H is 8*12*9, then max. cube we can have are  2*4*3= 
 2*4*3 = 24
24   L*W*H is 8*9*12, then max. cube we can have are  2*3*4= 
 2*3*4 = 24
24   In all cases we get R=24 cubes.   Ans. 24
Answer: C
If x and y are integers such that (x+1)^2 is less than or equal to 49 and (y-1)^2 is less than 64, what is the sum of the maximum possible value of xy and the minimum possible value of xy? Choose one:
A) -16  B) -14  C) 0  D) 14  E) 16

Solution: (x+1)^2 <= 49   x <= 6   x >= -8   (y-1)^2 < 64   y < 9   y > -7   Max possible value of xy is -8 × -6 = 48   minimum possible value of xy is -8 × 8 = -64   -64 + 48 = -16   -16nswer : -16
Answer: A
A cistern normally takes 6 hours to be filled by a tap but because of a leak, 2 hours more. In how many hours will the leak empty a full cistern ?	Choose the most appropriate option:
A) 20 hours
B) 24 hours
C) 26 hours
D) 18 hours
E) None of these

Solution: ∵ cistern fill in 6 hours.   ∴ in 1 hour, filled part = 1⁄6th   Now, due to leakage, filled part in 1 hour = 1⁄8th   Part of the cistern emptied, due to leakage in 1 hour   = 1⁄6 - 1⁄8 = 1⁄24th   ∴ The leakage will empty the full cistern in 24 hrs.   Answer 24 hours
Answer: B
If the two hands in a clock are 24 minutes divisions apart,then the angle between them is	Choose the correct choice from the following options
A) 3Â° B) 18Â° C) 24Â° D) 60Â° E) None of these

Solution: In a clock, each minute makes 6Â°   âˆ´ 24 minutes will make 6 Ã— 24 = 144Â°   Answer None of these
Answer: E
A train passes a station platform in 24 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) 123 B) 60 C) 240 D) 157 E) 198

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) / 24= 15   x + 300 = 360   x = 60 m.   Answer: 60
Answer: B
Michael, Steve and Tyler shared a box of cookies. Michael ate 1/8 of the cookies, Steve ate one half and Tyler ate 150 more cookies than Michael. If no cookies remain in the box, how many cookies were in the box?  Choose the most appropriate option:
A) 1200. B) 800. C) 600 D) 550 E) 400

Solution: Let no of cookies that Michael, Steve and Tyler ate are M, S, T   M+S+T = Total no of cookies (Let it be C)----------------(1)   Then : M=C/8, S=C\2, T= C/8 +150   Putting the Values in (1)   We get C as 600.. hence the answer : 600
Answer: C
Two trains are moving in the same direction at 72 kmph and 36 kmph. The faster train crosses a man in the slower train in 27 seconds. Find the length of the faster train?  Select.
A) 270	B) 2877	C) 187	D) 1776	E) 191

Solution: Relative speed = (72 - 36) * 5/18 = 2 * 5= 
2 * 5 = 10
10 mps.   Distance covered in 27 sec= 27 * 10= 
27 * 10 = 270
270 m.   The length of the faster train= 270 m.   270nswer:270
Answer: A
A 20% product produces 50%. The market value of the product is:
Choose the correct choice from the following answers:
A) Rs. 40 B) Rs. 60 C) Rs. 45 D) Rs. 80 E) Rs. 70

Solution: Let the face value of the product is Rs.100   It produces Rs.20   Market value of the stock=(20/50)*100=Rs.40   Rs. 40NSWER:Rs. 40
Answer: A
A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 58 years now, the son's age five years back was:
Choose the correct choice: A) 14 B) 17 C) 19 D) 22 E) 24

Solution: Let the son's present age be x years. Then, (58 - x) = x   2x = 58.   x = 29.   Son's age 5 years back (29 - 5)= 
(29 - 5) = 24
24 years.   answer :24
Answer: E
Machine R can produce x units in 3/4 of the time it takes machine N to produce x units. Machine N can produce x units in 2/3 the time it takes machine O to produce x units. If all three machines are working simultaneously, what fraction of the total output is produced by machine N?	Choose the correct option:
A) 1/2	B) 1/3	C) 4/13	D) 8/29	E) 6/33

Solution: Let the following be true:   R makes x in time t   Then the following follows:   N makes x in 4t/3   O makes x in 3/2(4t/3) = 2t   M:N:O = 1:4/3:2=3:4:6   So N=4/(3+4+6)=4/13=4/13
Answer: C
If abc < 0 and bc > 0, which of the following must be positive? Choose one:	A) xy	B) ac	C) (a^2)bc	D) a(b^2)c	E) xy(z^2)

Solution: Given that bc is positive and abc is negative, you can say that a MUST be negative. As for b and c either they are both positive or both negative.   Option (C) has a^2 which is positive and bc which is positive. So ((a^2)bc) must be positive.
Answer: C
What is the cost of leveling the field in the form of parallelogram at the rate of Rs.50/10 sq.metre, whose base & perpendicular distance from the other side being 54m & 24m respectively? Choose the correct option:
A) Rs. 6000
B) Rs. 6250
C) Rs. 6400
D) Rs. 6480
E) Rs. 7000

Solution: Area of the parallelogram = Length of the base * Perpendicular height   = 54 * 24= 
54 * 24 = 1_296
1296 m.   Total cost of levelling= Rs. 6480   Rs. 6480
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. 2970? Choose the correct choice from the following choices: A) 3000 B) 2669 C) 2200 D) 2766 E) 2998

Solution: Let the cost price of table for Sreenivas be Rs. x and given that, cost price of table for Mahesh = Rs. 2970.   => (90%) of (110%) of x = Rs. 2970.   => (90/100)(110/100)x = 2970   => x = (2970 * 100)/(9 * 11)   => x = Rs. 3000   3000nswer: 3000
Answer: A
The public library has exactly 2 floors. It has 1/4 as many shelves on its 2nd floor as it does on its 1st. If the second floor has 5/6 as many books per shelf as the first floor, what fraction of the library's books are on the first floor?	Choose the correct choice from the following answers
A) 1/4  B) 5/14  C) 5/9  D) 24/29  E) 5/6

Solution: Let x be the no of shelves and y be the no of books per shelf on first floor.   Now no of shelves on 2nd floor = (1/4)*x   no of books per shelf on 2nd floor = (5/6) * y   So total no books on first floor = xy and total no of books on 2nd floor = (1/4)*x*(5/6)*y = (5/24)*xy   fraction of library books on first floor = (xy)/(xy + (5/24)*xy)   =1 / (1+(5/24))   =24/29   So 24/29
Answer: D
The population of a town increased from 1,75,000 to 2,80,000 in a decade. The average percent increase of population per year is Options:	A) 4.37%	B) 5%	C) 6%	D) 8.75%	E) None

Solution: Solution   Increase in 10 years	= (280000 - 175000)= 
(280000 - 175000) = 105_000
105000.   Increase%= (105000/175000Ã—100)%   = 60%.   Required average	= (60/10)= 
(60/10) = 6
6%.   Answer 6%
Answer: C
At a certain conference, 150 students spoke one or more of the following languages: Spanish, English, and French. If 41 students spoke Spanish, 90 spoke English, 65 spoke French, and 32 spoke only 2 languages, how many students spoke three different languages?	Select the correct option:
A) 7
B) 9
C) 12
D) 15
E) 18

Solution: 150=41+90+65-32-2x   x=7   A. 7
Answer: A
If a rectangular room measures 9 meters by 5 meters by 4 meters, what is the volume of the room in cubic centimeters? (1 meter=100 centimeters)	Choose the correct choice from the following:	A) 24,000	B) 240,000	C) 18,000,000	D) 24,000,000	E) 240,000,000

Solution: C. 180,000,000   9*100*5*100*4*100 = 180,000,000
Answer: C
On dividing 109 by a number, the quotient is 9 and the remainder is 1. Find the divisor. Options.
A) 8  B) 12  C) 16  D) 18  E) 22

Solution: d = (D-R)/Q   = (109 - 1)/9   = 108/9= 
108/9 = 12
12   12)
Answer: B
What is the product of all the prime factors of 26? Choose one:
A) 24
B) 25
C) 22
D) 26
E) 21

Solution: 26 , factors are 2,13,1. Now again prime Numbers are Only Two i.e 2 and 13 , this time we would have  2*13= 
 2*13 = 26
26   Answer : 26
Answer: D
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 150? Options.
A) 15	B) 75	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 (150 - 75)= 
(150 - 75) = 75
75 points to C.   Answer:75
Answer: B
In the coordinate plane, a circle centered on point (3, -4) passes through point (1, 1). What is the area of the circle?	Select the correct option:
A) 29π
B) 18π
C) 25π
D) 37π
E) 41π

Solution: r^2=(3-1)^2+(-4-1)^2=4+25= 
4+25 = 29
29   29πrea of circle=πr^2=29π   29πnswer : 29π
Answer: A
The average of 10 numbers is calculated as 20. It is discovered later on that while calculating the average, one number namely 36 was wrongly read as 26. The correct average is?
Choose the correct choice from the following answers.
A) 12 B) 26 C) 16 D) 97 E) 20

Solution: 10 * 20 + 36 – 26   = 200/10= 
200/10 = 20
20   Answer: 20
Answer: E
A batsman in his 12th innings makes a score of 80 and thereby increases his average by 2 runs. What is his average after the 12th innings if he had never been ‘not out’?	Select the correct option.
A) 42	B) 43	C) 44	D) 45	E) 58

Solution: Let ‘x’ be the average score after 12 th innings   ⇒ 12x = 11 × (x – 2) + 80   ∴ x = 58   Answer 58
Answer: E
Two varieties of wheat - A and B costing Rs. 9 per kg and Rs. 15 per kg were mixed in the ratio 3 : 7. If 5 kg of the mixture is sold at 25% profit, find the profit made? Choose the correct choice from the following answers
A) Rs. 13.50  B) Rs. 16.54  C) Rs. 16.80  D) Rs. 16.50  E) Rs. 16.00

Solution: Explanation:   Let the quantities of A and B mixed be 3x kg and 7x kg.   Cost of 3x kg of A = 9(3x) = Rs. 27x   Cost of 7x kg of B = 15(7x) = Rs. 105x   Cost of 10x kg of the mixture = 27x + 105x = Rs. 132x   Cost of 5 kg of the mixture = 132x/10x (5) = Rs. 66   Profit made in selling 5 kg of the mixture = 25/100 (cost of 5 kg of the mixture) = 25/100 * 66 = Rs. 16.50   Answer: Option Rs. 16.50
Answer: D
An error 2% in excess is made while measuring the side ofa square. The % of error in the calculated area of the square is?  Choose the most appropriate option:
A) 4.01%  B) 4.04%  C) 4.16%  D) 5.12%  E) 5.16%

Solution: 100 cm is read as 102 cm.   A1 = (100 x 100) cm2 and A2 (102 x 102) cm2.   (A2 - A1) = [(102)2 - (100)2]   = (102 + 100) x (102 - 100)   = 404 cm2.   Percentage error = 404 x 100 % = 4.04%   100 x 100   4.04%
Answer: B
A team won 40 percent of its first 30 games in a particular season, and 80 percent of its remaining games. If the team won a total of 70 percent of its games that season, what was the total number of games that the team played?  Choose the correct option:
A) 60
B) 90
C) 120
D) 150
E) 180

Solution: 70% is 30%-points above 40% and 10%-points below 80%.   Thus the ratio of "the first 30 games" to "remaining games" is 1:3.   So the team played a total of 30+90= 
30+90 = 120
120 games.   The answer is 120.
Answer: C
A specialized type of sand consists of 40% mineral X by volume and 60% mineral Y by volume. If mineral X weighs 2.5 grams per cubic centimeter and mineral Y weighs 4 grams per cubic centimeter, how many grams does a cubic meter of specialized sand combination weigh? (1 meter = 100 centimeters)	Choose the correct option.
A) 3,400,000	B) 2,800,000	C) 55,000	D) 28,000	E) 280

Solution: Let the volume be 1 m^3 = 1m * 1m * 1m = 100cm * 100cm * 100cm = 1,000,000 cm^3   By volume   40% is X = 400,000 cm^3   60% is Y = 600,000 cm^3   By weight,   In 1 cm^3, X is 2.5 gms   In 400,000 cm^3 , X = 2.5 * 400,000 = 1,000,000 grams   In 1 cm^3, Y is 4 gms   In 600,000 cm^3, Y = 4 * 600,000 = 2,400,000 gms   Total gms in 1 m^3 = 1,000,000 + 2,400,000 = 3,400,000   3,400,000NSWER:3,400,000
Answer: A
A man purchased 3 blankets @ Rs.100 each, 5 blankets @ Rs.150 each and two blankets at a certain rate which is now slipped off from his memory. But he remembers that the average price of the blankets was Rs.150. Find the unknown rate of two blankets?  Options:	A) 450	B) 992	C) 276	D) 187	E) 161

Solution: 10 * 150= 
10 * 150 = 1_500
1500   3 * 100 + 5 * 150= 
3 * 100 + 5 * 150 = 1_050
1050   1500 – 1050= 450   450nswer: 450
Answer: A
For which of the following functions f(x), is it always true that f(a/b) = f(b/a)?
Choices.
A) f(x) = 1/x B) f(x) = x^2 C) f(x) =1/(x/2) D) f(x) = x+1 E) None of the above

Solution: Consider a/b = 2 and b/a = 0.5   A) f(2)=1/2   f(0.5)=2   NO   B) f(2) = 2^2 = 4   f(0.5)= 0.5^2 = 0.25   NO   C) f(2)= 1/(2/2)= 
1/(2/2) = 1
1   f(0.5)= 1/(0.5/2)= 
1/(0.5/2) = 4
4   NO   D) f(2)=2+1= 
2+1 = 3
3   f(0.5)= 0.5+1= 
0.5+1 = 1.5
1.5   NO   Answer is None of the above
Answer: E
If x is Negative integer ,y is positive integer, and 7x+3y=14 , which of the following could be the value of x ? Choose the correct choice from the following options
A) -1
B) -5
C) -2
D) -3
E) -4

Solution: Use answer options to solve this problem -   x is negative integer (-1,-2,-3......)   put x=-1   7x+3y=14   7(-1)+3y=14   -7+3y=14   3y=14+7   3y=21   y=7   -1nswer will be (-1)
Answer: A