MU-NLPC/Calc-aqua_rat huggingface dataset:
Find the value for x from below equation: x/3=-7?  Choose the correct choice from the following choices:
A) -6
B) -21
C) -2
D) -3
E) 4

Solution: 1. Multiply both sides by 3:   x*3/3= -7/3   Simplify both sides:   x = -21   -21
Answer: B
David covered a distance of 50 miles on his first trip. On a later trip he travelled 300 miles while going three times as fast. His new time compared with the old time was: Choose the correct option.
A) twice as much  B) three times as much  C) the same  D) half as much  E) a third as much

Solution: B   Let speed of the 1st trip x miles / hr. and speed of the 2nd trip 3x / hr.   We know that   Speed = Distance/Time.   Or, Time = Distance/Speed.   So, times taken to covered a distance of 50 miles on his first trip = 50/x hr.   And times taken to covered a distance of 300 miles on his later trip = 300/3x hr.   = 100/x hr.   So we can clearly see that his new time compared with the old time was: twice as much.
Answer: A
Two taps can separately fill a cistern 5 minutes and 15 minutes respectively and when the waste pipe is open, they can together fill it in 6 minutes. The waste pipe can empty the full cistern in?
Select the correct option
A) 6 B) 8 C) 10 D) 9 E) 2

Solution: 1/5 + 1/15 - 1/x = 1/6   x = 10   Answer:10
Answer: C
A furniture manufacturer has two machines, but only one can be used at a time. Machine V is utilized during the first shift and Machine B during the second shift, while both work half of the third shift. If Machine V can do the job in 12 days working two shifts and Machine B can do the job in 15 days working two shifts, how many days will it take to do the job with the current work schedule? Pick
A) 14  B) 13  C) 11  D) 9  E) 7

Solution: machine V finish the job in 2*12= 
2*12 = 24
24 shifts   machine B finish the job in   2*15= 
  2*15 = 30
30 shifts   Lets assume total work require 120 shifts   Therefore,   rate of V= 5 shifts/day   rate of B = 4 shifts/day   rate of (V+B) = 9 shifts/day   According to current schedule work complete in a day = 5+4+(9/2)= 
5+4+(9/2) = 27/2 = around 13.5
13.5 shifts/day   Therefore, Time required to finish 120 shifts= (120/13.5) = 8.88.. days ~ 9 days=9
Answer: D
How many words with or without meaning, can be formed by using all the letters of the word, â€˜POWERâ€™, using each letter exactly once? Choose the correct choice
A) 700  B) 720  C) 750  D) 800  E) 120

Solution: The word â€˜POWERâ€™ contains 5 different letters.   Therefore, Required number of words= Number of arrangement of 5 letters, taken all at a time   =5P5   = 5!   = 5*4*3*2*1= 
5*4*3*2*1 = 120
120   ANSW120R:120
Answer: E
Ramesh can finish a piece of work in 18 days. Rohan is twice as efficient as Ramesh.If they work together how many days will they need to finish the same amount of work? Choose the correct option:  A) 8/3 days  B) 9/3 days  C) 6 days  D) 3 days  E) 7 days

Solution: Ramesh can finish a piece of work in 18 days. Rohan is twice as efficient as Ramesh.   So Rohan can finish a piece of work in 9 days.   days needed to finish the same amount of work = 1/(1/9+1/18)= 
1/(1/9+1/18) = 6
6 days   ANSWER:6 days
Answer: C
If n is an integer and 5^n > 400,000,000, what is the least possible value of n?  Pick.
A) 7 B) 13 C) 9 D) 10 E) 11

Solution: When you seperate the 400000000 into factors of 5 and 2 you get - > 10^8 x 2^2 = 5^8 x 2^10   2 to the ^ 8 = 1024 so its 1024 x 5^8   that means 5^8 x 5^x must be greater   5^x > 1024   5^1=5   5^2=25   5^3= 125   5^5= 3125 - > so x must be at least 5   5^(8+5)= 5^13   13
Answer: B
The ratio of the volumes of two cubes is 125 : 1728. What is the ratio of their total surface areas? Choose the correct choice from the following answers
A) 81 : 121 B) 9 : 11 C) 25 : 144 D) 27 : 121 E) None of these

Solution: Ratio of the sides = Â³âˆš125 : Â³âˆš1728 = 5 : 12   Ratio of surface areas = 5^2 : 12^2 = 25 : 144   ANSWER:25 : 144
Answer: C
Zachary is helping his younger brother, Sterling, learn his multiplication tables. For every question that Sterling answers correctly, Zachary gives him 3 pieces of candy. For every question that Sterling answers incorrectly, Zachary takes away two pieces of candy. After 14 questions, if Sterling had answered 2 more questions correctly, he would have earned 31 pieces of candy. How many of the 14 questions did Zachary answer correctly?  Choose the correct choice from the following answers
A) 6 B) 7 C) 8 D) 9 E) 10

Solution: i got two equations:   3x-2y=25   x+y=14   3x-2(14-x)=25   3x-28+2x=25   5x=53   x=10.6 or between 10 and 11. (ANS 10)
Answer: E
Find the value of 72515 x 9999 = m?  Select the correct option:
A) 345434667 B) 246465757 C) 465767867 D) 725077485 E) 645354643

Solution: 72515 x 9999 = 72515 x (10000 - 1)   = 72515 x 10000 - 72515 x 1   = 725150000 - 72515= 
725150000 - 72515 = 725_077_485
725077485   725077485
Answer: D
Point X is located on line segment AB and point Y is located on line segment CD. If AB = CD and AX < CY, then Answers
A) XB > AB	B) XB < YD	C) AX > XB	D) AX < XB	E) YD < AB

Solution: A--X------B   C-----Y---D   YD < AB.   Answer: YD < AB.
Answer: E
The average weight of 10 person's increases by 2.5 kg when a new person comes in place of one of them weighing 50 kg. What might be the weight of the new person? Pick:
A) 76 kg  B) 76.5 kg  C) 75 kg  D) Data inadequate  E) None of these

Solution: Explanation:   Total weight increased = (10 x 2.5) kg = 25 kg.   Weight of new person = (50 + 25)= 
(50 + 25) = 75
75 kg.   Answer: 75 kg
Answer: C
how many terms are there in the G.P. 3,6,12,24,...,384? Pick.
A) 8  B) 9  C) 10  D) 11  E) 7

Solution: Here a=3 and r=6/3= 
6/3 = 2
2. let the number of items be n   then, t^n=384=> ar^n-1=384   = 3 x 2^n-1=384   =2^n-1=128 = 2^7   =n-1=7=>n=8   Therefore, number of terms is 8   8nswer is 8.
Answer: A
If the manufacturer gains 10 %, the wholesale dealer 15 % and the retailer 25 %, then find the cost of production of a table if the retail price was Rs 1265 Pick
A) 344 B) 800 C) 388 D) 377 E) 289

Solution: Explanation:   Let the cost of Production = Rs. P   Then, as per question,   \fn_jvn {\color{Black} \Rightarrow (\frac{125}{100}\times \frac{115}{100}\times \frac{110}{100}\times p)=1265}   \fn_jvn {\color{Black} \Rightarrow \frac{253}{160}\; p=1265}   \fn_jvn {\color{Blue} \Rightarrow p=800}   Answer: B) Rs. 800
Answer: B
A and B form a study group and divide a 75 question study guide. If A answer 7 questions per hour, while B answer 5 every hour, what fraction of the study guide is incomplete after 4 hours?
Choose one:
A) 48/75  B) 20/75  C) 27/75  D) 28/75  E) 16/75

Solution: Number of questions A can answer per hour: 7   Number of questions B can answer per hour: 5   Number of questions A and B can answer per hour:  7+5= 
 7+5 = 12
12   Number of questions A and B can answer in 4 hours: 4x12=48   Fraction of the study guide that is incomplete = 1-48/75=27/75   Answer is 27/75
Answer: C
15 lts of water containing 20% alcohol, then added 5 lts of water. What is % alcohol  Pick one:  A) 15%  B) 18%  C) 20%  D) 22%  E) 25%

Solution: in 15 ltr of mixure, 3 ltr alcohal and 12 ltr pure water.   when 5 ltr water is added, then   3 ltr alcohal in 20 ltr mixture means 15% alcohal in mixture.   15%NSWER:15%
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 40 years now, the son's age 10 years back was: Choose the correct option.
A) 10 years  B) 19 years  C) 33 years  D) 38 years  E) 39years

Solution: Let the son's present age be x years. Then, (40 - x) = x   2x = 40.   x = 20   Son's age 5 years back (20 - 10)= 
(20 - 10) = 10
10 years.   10 yearsnswer:10 years
Answer: A
What is the probability of getting a sum 9 from two throws of a dice? Choose the most appropriate option
A) 1/6 B) 1/8 C) 1/9 D) 1/12 E) 1/7

Solution: Explanation:   In two throws of a dice, n(S) = (6 x 6) = 36.   Let E = event of getting a sum ={(3, 6), (4, 5), (5, 4), (6, 3)}.   P(E) =n(E)/n(S)= 4/36 =	1/9	.   ANSWER : 1/9
Answer: C
Five years back, a father was 36 years older than his son. At present the father is 5 times as old as the son. How old will the son be three years from now?	Choose the correct choice from the following: A) 15 years B) 14 years C) 13 years D) 12 years E) 11 years

Solution: Using linear equations to convert the word problem:   ** F = fathers current ageS = sons current age   #1 Five years back, a father was 36 years older than his son: F-5 = 30 + (S - 5)   #2 At present the father is 5 times as old as the son: F = 5*S   How old will the son be three years from now?: S + 3 = ?   With two variables and two linear equations we are able to solve the problem:   (S*5) - 5 = 36 +S -5   4S=36   S = 9   S + 3 = 9 + 3= 
9 + 3 = 12
12   Answer: 12 years
Answer: D
The true discount on a bill due 9 months hence at 16% per annum is Rs. 189.The amount of the bill is :  Choices
A) Rs. 1386	B) Rs. 1764	C) Rs. 1575	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.189.   ∴ x 16x9/12x1/100= 189 or x = 1575.   ∴ P.W. = Rs. 1575.   ∴Sum due =P.W. + T.D. =Rs.(1575 + 189)=Rs.1764.   Answer Rs. 1764
Answer: B
What is the remainder when you divide 2^200-1 by 7?  Choose the most appropriate option.
A) 1	B) 2	C) 3	D) 4	E) 5

Solution: answer is C. this is very similar to the 32^32^32-1 divided by 7 question.
Answer: C
The average weight of 8 person's increases by 2.5 kg when a new person comes in place of one of them weighing 50 kg. What is the weight of the new person?	Choose the correct choice from the following answers.
A) 75 Kg
B) 50 Kg
C) 70 Kg
D) 80 Kg
E) 60 KG

Solution: Explanation:   Total increase in weight = 8 Ã— 2.5 = 20   If x is the weight of the new person, total increase in weight = xâˆ’50   => 20 = x - 50   => x = 20 + 50= 
20 + 50 = 70
70   Answer: Option 70 Kg
Answer: C
If x and y are positive integers and 11 + x + y + xy = 25, what is the value of x + y?  Pick one.
A) 3  B) 5  C) 6  D) 8  E) 9

Solution: Try each answer choices.   For A: 11 + 3 + xy = 25; xy = 11 (impossible, 11 prime number. 1 + 11 doesn't equal 3)   For B: 11 + 5 + xy = 25; xy = 9 (no combination of xy = 9 and x + y = 5)   For C: 11 + 6 + xy = 25; xy = 8 (x + y = 6; x = 2, y = 4 or x = 4, y = 2)   For D: 11 + 8 + xy = 25; xy = 6 (no combination of xy = 6 and x + y = 8)   For E: 11 + 9 + xy = 25; xy = 5 (impossible, 5 prime number. 1 + 5 doesn't equal 9)   Therefore, answer 6.
Answer: C
A basket contains 5 apples, of which 1 is spoiled and the rest are good. If Henry is to select 2 apples from the basket simultaneously and at random, what is the possibility that the 2 apples selected will include the spoiled apple?  Choose the correct choice from the following choices
A) 1/5 B) 3/10 C) 2/5 D) 1/2 E) 3/5

Solution: p (both apples are not spoiled) = 42/52/52/52 = 4*3/5*4 = 3/5   p (one of the apple spoiled) = 1-3/5 = 2/5   Answer is 2/5.
Answer: C
A boat can move upstream at 25 kmph and downstream at 45 kmph, then the speed of the current is? Choose the correct option
A) 5	B) 6	C) 7	D) 4	E) 10

Solution: US = 25   DS = 45   M = (45 - 25)/2= 
(45 - 25)/2 = 10
10   Answer: 10
Answer: E
At Bala's firm's annual revenue grows twice as fast as its costs. In 2007 it operated at a $1000 loss, it broke even in 2008, and in 2009 its revenues were 44% higher than in 2007. If the firm's revenues and costs grew at a constant rate over this period, what was its profit in 2009?
Choose one:  A) 700  B) 1000  C) 1300  D) 1600  E) 2000

Solution: At Bala's firm's annual revenue grows twice as fast as its costs. First solve for how much revenue is increasing each year:   R2008= R2007*(1+x)   R2009= R2007*(1+x)^2=1.44*R2007   (1+x)^2 = 1.44   1+x=1.2   x=0.2 aka revenue increases 20% each year and cost increases 10% annually   Next solve for R2007and 13002007:   R2007= 13002007- 1000   1.2*R2007- 1.1*13002007= 0   1.2*[13002007- 1000] - 1.1*13002007= 0   0.1*13002007= 1,200   13002007= 12,000   R2007= 11,000   Finally find 2009 profits:   Profit2009= 1.44*11,000 - 1.21*12,000   Profit2009= 15,840 - 14,520   Profit2009= 1320   Answer: 1300
Answer: C
If an object travels 90 feet in 2 seconds, what is the object’s approximate speed in miles per hour? (Note: 1 mile = 5280 feet)	Choose the correct choice from the following answers.
A) 30.68
B) 32.34
C) 34.56
D) 36.72
E) 38.95

Solution: 90 feet/2 seconds = 45 feet/second   (45 feet/second)*(3600 seconds/hour)*(1 mile/5280 feet) = 30.68 (approximately)   The answer is 30.68.
Answer: A
Two dice are thrown simultaneously. What is the probability of getting two numbers whose product is even?
Select the correct option:
A) 2/7
B) 3/10
C) 3/4
D) 1/9
E) 7/9

Solution: In a simultaneous throw of two dice, we have n(S) = (6 x 6) = 36.   Then, E= {(1, 2), (1, 4), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 2), (3, 4),   (3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 2), (5, 4), (5, 6), (6, 1),   (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}   n(E) = 27.   P(E) =n(E)/n(S)=27/36=3/4.   hence:3/4
Answer: C
P, Q and R can do a piece of work in 20, 30 and 60 days respectively. In how many days can P do the work if he is assisted by Q and R on every third day?
Choose one
A) 15 days	B) 18 days	C) 20 days	D) 25 days	E) 10 days

Solution: P 2 days work = 1/20*2 = 1/10   (P + Q+ R)'s 1 day work ( 1/20 + 1/30 + 1/60) = 6/60 = 1/10   work done in 3 days = 1/5   so 1/5 work done in 3 days   whole work  ( 3* 5)= 
 ( 3* 5) = 15
15 days   15 daysNSWER 15 days
Answer: A
Sum of the squares of 3 no. is 276 and the sum of their products taken two at a time is 150. Find the sum?	Choose the correct answer:
A) 22
B) 18
C) 26
D) 24
E) 32

Solution: (a + b + c)2 = a2 + b2 + c2 + 2(ab +bc + ca) = 276 + 2* 150   a + b + c = âˆš576 = 24   Answer 24
Answer: D
From the starting point in a boat race, one competitor started to sail north at a speed of 1.6 Km/h, the other competitor started to sail west at a speed of 1.3 Km/h. What is the distance in Km between the two competitors after 5 hours?
Choose the correct choice from the following:
A) 10.3
B) 12.
C) 12.5.
D) 14.
E) 15.4.

Solution: Both competitors are sailing making angle of 90 degrees.   10.3fter 5 hrs one competitor will cover a distance of = 1.6 *5= 
1.6 *5 = 8
8 KM   10.3nd, other competitor will cover a distance of= 1.3*5= 
1.3*5 = 6.5
6.5KM   distance between them after 5 hrs= (8^2+ 6.5^2)^1/2= 10.3 KM   10.3 is the answer
Answer: A
If |x| = 9x-16, then x = ?	Choose the correct choice:
A) 1	B) 1/2	C) 2	D) 4	E) -1/2

Solution: Substituted option C i.e x=2. Inequality satisfied.   This eliminates all options except   Answer is 2
Answer: C
speed of a bus is 54kmph and including stoppages, it is 45kmph. For how many minsdoes the bus stop per hour?
Choose the correct choice:
A) 10 min
B) 20 min
C) 30 min
D) 50 min
E) 60 min

Solution: speed of the bus excluding stoppages = 54 kmph   speed of the bus including stoppages = 45 kmph   Loss in speed when including stoppages = 54 - 45= 
54 - 45 = 9
9kmph=> In 1 hour, bus covers 9 km less due to stoppages   Hence, time that the bus stop per hour = time taken to cover 9 km   =distancespeed=954 hour=16 hour = 606 min=10 min   10 min
Answer: A
On a certain scale of intensity, each increment of 10 in magnitude represents a tenfold increase in intensity. On this scale, an intensity corresponding to a magnitude of 165 is how many times an intensity corresponding to a magnitude of 135? Pick one:  A) 40  B) 100  C) 400  D) 1000  E) 10 000

Solution: Increase of 40 in magnitude corresponds to 10^4 increase in intensity:   If intensity for 135 is x then for 135 it'll be 10*x, for 145 it'll be 10*10*x=10^2*x, for 155 it'll be 10*10*10*x=10^3*x and for 165 it'll be 10*10*10*10*x=10^4*x.   Answer: 10 000.
Answer: E
Look at this series: 0.05, 0.2, ____, 3.2, 12.8, ... What number should fill the blank?  Choose one
A) 0.5
B) 0.6
C) 0.9
D) 0.7
E) 0.8

Solution: This is a simple multiplication series. Each number is 4 times greater than the previous number.   Answer: 0.8
Answer: E
Two persons start running simultaneously around a circular track of length 200 m from the same point at speeds of 15 km/hr and 25 km/hr. When will they meet for the first time any where on the track if they are moving in opposite directions ?
Options
A) 27 sec B) 17 sec C) 18 sec D) 22 sec E) 37 sec

Solution: Explanation:   Time taken to meet for the first time anywhere on the track   = length of the track / relative speed   = 200 / (15 + 25)5/18 = 200x 18 / 40 x 5 = 18 seconds.   Answer: 18 sec
Answer: C
Two pipes A and B can fill a cistern in 8 and 12 minutes respectively, and a third pipe C can empty it in 15 minutes. How long will it take to fill the cistern if all the three are opened at the same time?
Choose the correct choice from the following choices
A) 17 1/17 min  B) 28 1/7 min  C) 17 1/7 min  D) 17 1/8 min  E) 17 5/7 min

Solution: 1/8 + 1/12 - 1/15 = 17/120   120/17 = 7 1/17   17 1/17 minnswer:17 1/17 min
Answer: A
Forty five percent of a number is 21 less than four fifth of that number. What is the number ?  Choose the correct answer
A) 60  B) 140  C) 230  D) 130  E) 125

Solution: Let the number be x.   Then, 4*x/5 â€“(45% of x) = 21   4x/5 â€“ 45x/100 = 21   x = 60.   60nswer 60.
Answer: A
The number of ways in which six boys and six girls can be seated in a row for a photograph so that no two girls sit together is	Select the correct option:
A) 8! * â·Pâ‚†  B) 6! * â·Pâ‚†  C) 4! * â·Pâ‚†  D) 2! * â·Pâ‚†  E) 3! * â·Pâ‚†

Solution: Explanation:   We can initially arrange the six boys in 6! ways.   Having done this, now three are seven places and six girls to be arranged. This can be done in â·Pâ‚† ways.   Hence required number of ways = 6! * â·Pâ‚†   Answer:6! * â·Pâ‚†
Answer: B
A rectangular farm has to be fenced one long side, one short side and the diagonal. If the cost of fencing is Rs.10 per meter. The area of farm is 1200 m2 and the short side is 30 m long. How much would the job cost?  Answers
A) 1218
B) 1200
C) 1688
D) 6996
E) 2791

Solution: l * 30 = 1200 è l = 40   40 + 30 + 50= 
40 + 30 + 50 = 120
120   120 * 10= 
120 * 10 = 1_200
1200   Answer: 1200
Answer: B
A train 90m long is running at 20kmph. In how much time will it pass a platform 80m long?  Choose the correct answer
A) 15.6 seconds	B) 24.6 seconds	C) 28.6 seconds	D) 13.6 seconds	E) 35.6 seconds

Solution: 13.6 secondsistance travelled = 90 + 80= 
90 + 80 = 170
170mSpeed= 20 * 5/8 = 25/2mTime = 170 * 2/25= 
170 * 2/25 = 68/5 = around 13.6
13.6 SecondsAnswer : 13.6 seconds.
Answer: D
A can do a piece of work in 9 days. When he had worked for 2 days B joins him. If the complete work was finished in 8 days. In how many days B alone can finish the work?  Pick one
A) 18	B) 77	C) 66	D) 54	E) 12

Solution: 8/9 + 6/x = 1   X = 54 days   Answer:54
Answer: D
The distance from Steve's house to work is 10 Km. On the way back Steve drives twice as fast as he did on the way to work. Altogether, Steve is spending 6 hours a day on the roads. What is Steve's speed on the way back from work? Choose the correct answer.
A) 5.
B) 10.
C) 14.
D) 15.
E) 20.

Solution: Time is in the ratio 2:1 :: to: fro office   Therefore, 2x+1x=6 hrs   Time take to come back - 2 hrs, distance travelled - 10km => Speed = 5kmph   5.
Answer: A
A developer has land that has x feet of lake frontage. The land is to be subdivided into lots, each of which is to have either 80 feet or 120 feet of lake frontage. If 1/9 of the lots are to have 80 feet of frontage each and the remaining 40 lots are to have 120 feet of frontage each, what is the value of x ?  Choose the correct choice from the following answers.
A) 400 B) 3,200 C) 3,700 D) 4,400 E) 5,200

Solution: Total number of plots,be T   Plots with 80ft is (1/9)th of total plots.   Plots with 120ft frontage = (8/9) X total number of plots   i.e 8/9 X T = 40 T = 45   Total lake frontage = 40X120 + 5X80 = 5200   Answer : 5,200
Answer: E
10% people of a village in Sri Lanka died by bombardment, 20% of the remainder left the village on account of fear. If now the population is reduced to 4500, how much was it in the beginning? Choose the correct choice from the following:  A) 5999  B) 6788  C) 6250  D) 4559  E) 6989

Solution: X * (90/100) * (80/100) = 4500   X = 6250   Answer: 6250
Answer: C
A committee is to be formed by randomly choosing 3 people from 7 candidates. If Alice and Bob are candidates, what is the probability that Alice will be selected but Bob will not?  Pick one:
A) 2/7 B) 3/7 C) 2/35 D) 3/35 E) 4/35

Solution: The total number of ways to form a committee is 7C3=35.   The number of committees which include Alice but not Bob is 5C2=10.   The probability that Alice is selected but Bob is not selected is 10/35=2/7.   The answer is 2/7.
Answer: A
Find the average of all the numbers between 11 and 21 which are divisible by 2.  Choose the correct option.
A) 15
B) 18
C) 16
D) 22
E) None

Solution: Sol.   Average = (12 + 14 + 16+ 18+ 20 / 5) = 80 / 5= 
80 / 5 = 16
16.   Answer 16
Answer: C
For any positive number x, the function [x] denotes the greatest integer less than or equal to x. For example, [1] = 1, [1.267] = 1 and [1.999] = 1. If k is a positive integer such that k^2 is divisible by 45 and 80, what is the units digit of k^3/4000 ?	Pick.
A) 0  B) 0  C) 27  D) 54  E) Cannot be determined

Solution: K=[lCM of 80 and 45] * (any integer)   however minimum value of k is sq.rt of 3^2*4^2*5^2 = 60 * any integer   for value of k(60) * any integer unit value will be always zero .   0
Answer: B
A circular path of 13 m radius has marginal walk 2 m wide all round it. Find the cost of leveling the walk at 25p per m2? Choose the correct choice from the following answers.
A) Rs.45	B) Rs.48	C) Rs.44	D) Rs.43	E) Rs.41

Solution: π (152 - 132) = 176   176 * 1/4   = Rs.44   Answer:Rs.44
Answer: C
Two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 16 kmph and 20 kmph respectively. When they meet, it is found that one train has traveled 60 km more than the other one. The distance between the two stations is?  Choose the correct choice from the following choices:  A) 565  B) 444  C) 676  D) 767  E) 432

Solution: 1h ----- 4   ? ------ 60   12 h   RS = 16 + 20= 
16 + 20 = 36
36   T= 12   D = 36 * 12= 
36 * 12 = 432
432   Answer: 432
Answer: E
Set E consists of all even integers between 2 and 100, inclusive. Set X is derived by reducing each term in set E by 50, set Y is derived by multiplying each term in set E by 1.5, and set Z is derived by dividing each term in set E by -4. Which of the following represents the ranking of the three sets in descending order of standard deviation?	Choose the correct choice from the following options
A) X, Y, Z  B) X, Z, Y  C) Y, Z, X  D) Y, X, Z  E) Z, Y, X

Solution: Set E - {2, 4, ..., 100};   Set X - {-48, -46, ..., 50};   Set Y - {3, 6, ..., 150};   Set Z - {-2/4, -4/4, ..., -100/4} = {-1/2, -1, -3/2, ..., -25}.   If we add or subtract a constant to each term in a set the SD will not change, so sets E and X will have the same SD.   If we increase or decrease each term in a set by the same percent (multiply by a constant) the SD will increase or decrease by the same percent, so set Y will have 1.5 times greater SD than set E and set Z will have 4 times less SD than set E (note SD can not be negative so SD of Z wil be SD of E divided by 4 not by -4).   So, the ranking of SD's in descending order is: Y, E=X, Z.   Answer: Y, X, Z.
Answer: D
The average age of a husband and a wife is 30 years when they were married ten years ago but now the average age of the husband, wife and child is 30 years(the child was born during the interval). What is the present age of the child? Choose the correct choice.
A) 2 years  B) 5 years  C) 10 years  D) 4 years  E) 1 years

Solution: 40 * 2= 
40 * 2 = 80
80   30 * 3= 
30 * 3 = 90
90   -----------   10 years   Answer:10 years
Answer: C