MU-NLPC/Calc-aqua_rat huggingface dataset:
Set S has a mean of 10 and a standard deviation of 1.5. We are going to add two additional numbers to Set S. Which pair of numbers would decrease the standard deviation the most?  Choose the correct choice:
A) {2, 10}	B) {10, 18}	C) {7, 13}	D) {9, 11}	E) {16, 16}

Solution: Starting list has mean = 10 and standard deviation of 1.5.   (A) {2, 10} — these two don’t have a mean of 10, so adding them will change the mean; further, one number is “far away”, which will wildly decrease the mean, increasing the deviations from the mean of almost every number on the list, and therefore increasing the standard deviation. WRONG   B. {10, 18} — these two don’t have a mean of 10, so adding them will change the mean; further, one number is “far away”, which will wildly increase the mean, increasing the deviations from the mean of almost every number on the list, and therefore increasing the standard deviation. BTW, (A) & (B) are essentially the same change — add the mean and add one number eight units from the mean. WRONG   C. {7, 13} — centered on 10, so this will not change the mean. Both of these are a distance of 3 units from the mean, and this is larger than the standard deviation, so it increases the size of the typical deviation from the mean. WRONG   D. {9, 11} — centered on 10, so this will not change the mean. Both of these are a distance of 1 units from the mean, and this is less than the standard deviation, so it decreases the size of the typical deviation from the mean. RIGHT   E. {16, 16} — these are two values far away from everything else, so this will wildly increase the standard deviation. WRONG   Answer = {9, 11}
Answer: D
What is the greatest of 3 consecutive integers whose sum is 27? Pick:
A) 6  B) 7  C) 8  D) 9  E) 10

Solution: 27 / 3= 
27 / 3 = 9
9   The three numbers are 8, 9, and 10.   The answer is 10.
Answer: E
A is thrice as good as B in work. A is able to finish a job in 60 days less than B. They can finish the work in - days if they work together.  Options:
A) 18 days  B) 22 ½ days  C) 24 days  D) 26 days  E) 23 days

Solution: If A completes a work in 1 day, 22 ½ days completes the same work in 3 days   Hence, if the difference is 2 days, 22 ½ days can complete the work in 3 days   => if the difference is 60 days, 22 ½ days can complete the work in 90 days   => Amount of work 22 ½ days can do in 1 day= 1/90   Amount of work A can do in 1 day = 3 × (1/90) = 1/30   Amount of work A and 22 ½ days can together do in 1 day = 1/90 + 1/30 = 4/90 = 2/45   => A and 22 ½ days together can do the work in 45/2 days = 22 ½ days   Answer : 22 ½ days
Answer: B
The remainder obtained when a prime number greater than 5 is divided by 5 is Answers
A) a) 1 or 2
B) b) 1 or 5
C) c) 3 or 5
D) d) 4 or 5
E) e) 5

Solution: The easiest way to answer this question is probably to pick numbers. Use the next two prime numbers greater than 6, i.e. 7 and 11:   7/5 = 1 + remainder of 2   11 / 5 = 2 + remainder of 1   This is already sufficient to see that answer choice a) is correct.   a) 1 or 2
Answer: A
If x, y, and z are consecutive positive odd integers, not necessarily in that order, which of the following must be true? I. xy> z^4 II. (x + z)^4 > y III. x+y>z^4 Choose the correct option:	A) II only	B) I only	C) III only	D) I,II only	E) I,III only

Solution: Lets suppose that a,b,c can take any one of following three value 1,5,7. Most important point is that the options MUST BE TRUE under any condition.   x+y>z^4   Not necessarily true as 1+5<2401   xz>y^4   Not necessarily true as 1.7<625   We don't need to check option as all the options except A can be discarded.   Thus II onlynswer II only
Answer: A
A sum is sufficient to pay either George age for 15 days or marks wage to 10dayshow long together?	Choose the correct answer.
A) 4
B) 5
C) 6
D) 7
E) 8

Solution: George one day work is (1/15)   Marks one day work is (1/10)   G+M=(1/15)+(1/10)=(1/6)   6 is the answer   ANSWER:6
Answer: C
At what rate percent of simple interest will a sum of money double itself in 77 years?  Choose the correct choice from the following answers
A) 6.54 % B) 2.54 % C) 8 .2 % D) 4.94 % E) 1.29 %

Solution: Let sum = x. Then, S.I. = x.   Rate = (100 * S.I.) / (P * T) = (100 * x) / (x * 77)   = 100/77 = 1.29 %   ANSW1.29 %R:1.29 %
Answer: E
The average age of seven persons sitting in a row facing east is 28 years. If the average age of the first three persons is 21 years and the average age of the last three persons is 34 years, then find the age of the person sitting in the middle of the row?	Answers.
A) 31 years  B) 78 years  C) 27 years  D) 11 years  E) 87 years

Solution: Total age seven persons = (28 * 7)years   Total age of the first three persons and the last three persons are (21 * 3) years and (34 * 3) years respectively.   Age of the person sitting in the middle of the row   = 28 * 7 - 21 * 3 - 34 * 3 = 196 - 63 - 102= 
196 - 63 - 102 = 31
31 years.   Answer: 78 years
Answer: B
The average (arithmetic mean) of the integers from 200 to 400, inclusive, is how much greater than the average of the integers from 100 to 200, inclusive?  Select the correct option.
A) 150 B) 175 C) 200 D) 225 E) 300

Solution: For an AP the mean or average of series is average of first and last term.   So, average of numbers between 200 to 400, inclusive = (200+400)/2= 
(200+400)/2 = 300
300   average of numbers between 100 to 200, inclusive= (100+200)/2= 
(100+200)/2 = 150
150   difference= 300 - 150= 
300 - 150 = 150
150   150nswer is 150
Answer: A
Several people are sitting around a round table playing a card game with a deck of 40 cards. Each person is dealt one card per deal, and the cards are dealt in a clockwise fashion. If Martin is dealt both the first card of the deck and the last card of the deck, which of the following could be the total number of people sitting at the table?	Pick:
A) 4 B) 5 C) 7 D) 11 E) 13

Solution: Let n be the number of people at the table.   If Martin gets the first and the last card, it means Martin got one more card than the others.   Thus 40/n has a remainder of 1 and so   40-1= 
  40-1 = 39
39 is a multiple of n.   The answer is 13.
Answer: E
Six computers, each working at the same constant rate, together can process a certain amount of data in 12 days. How many additional computers, each working at the same constant rate, will be needed to process the same amount of data in 6 days?
Choose the correct choice from the following
A) 3  B) 5  C) 6  D) 9  E) 12

Solution: Explanation: If six computers require 12 days to process the data, thats   a total of 72 computer-days the product of 6 and 12. If you change the number   of computers or the number of days, 72 will have to remain the product, whether   that means 72 days of one computer or one day with 72 computers.   In 6 days, the number of computers is:   6c = 72   c = 12   12 computers is 6 more than the 6 that it took to do the job in 12 days, so   the correct choice is (6).
Answer: C
If x and y are positive integers, which of the following CANNOT be the greatest common divisor of 5x and 20y?	Choose the correct choice from the following choices:
A) 5
B) 5(x-y)
C) 20x
D) 20y
E) 35x

Solution: We are looking for a choice that CANNOT be the greatest common divisor of 5x and 20y ...which means 5x and 20y when divided by the answer choice the quotient should not be a integer.   lets check   a. 5 5x/5 = x and 20y/5 = 4y both are integers so eliminate   b. 5(x-y) when x 20 /5= 
20 /5 = 4
4y both are integers so eliminate   b. 5(x-y) when x= 2 and y = 1 it could be be the greatest common divisor ..so eliminate   c. 20x when x = 1 its 20 and 20 cannot be the greatest common divisor of 5x and 20y ...   or 5x/20x = 1/4 which is not a integer.   20x
Answer: C
If two distinct positive divisors of 128 are randomly selected, what is the probability that their sum will be less than 32?	Answers:  A) 2/5  B) 3/7  C) 5/14  D) 11/28  E) 16/35

Solution: The positive divisors are 1, 2, 4, 8, 16, 32, 64, 128.   If any of the first five are chosen, the sum will be less than 32.   P(sum is less than 32) = 5/8 * 4/7 = 5/14   The answer is 5/14.
Answer: C
The average of 50 numbers is 38. If two numbers 45 and 55 are discarded, the average of the remaining set of numbers is  Choose the correct option
A) 38.5 B) 37.5 C) 37.0 D) 36.5 E) None of these

Solution: Average of the remaining set of numbers   [50 x 38 - (45 + 55)] / (50 - 2)   = (1900 - 100) / 48= 
(1900 - 100) / 48 = 75/2 = around 37.5
37.5   ANSWER:37.5
Answer: B
A man bought 40 shares of Rs. 60 at 5 discount, the rate of dividend being 1212%The rate of interest obtained is	Pick one:  A) 13.64%  B) 15.5%  C) 14%  D) 14.25%  E) 14.95%

Solution: Explanation :   Face Value of a share = Rs.60   He bought each share at Rs.60 - Rs.5 = Rs.55   Number of shares = 40   Dividend = 12 1/2%=25/2%   Dividend per share = 60×25/2×100=Rs.7.5   Total dividend = (40 × 7.5)   ie, He got a dividend of (40 × 7.5) for an investment of Rs.(40 × 55)   Interest obtained = 40×7.5×100/40×55=13.64%   13.64%nswer : Option 13.64%
Answer: A
If 42.30 = k(14 + m/50), where k and m are positive integers and m < 50, then what is the value of k + m ? Choose the most appropriate option:  A) 6  B) 7  C) 8  D) 9  E) 10

Solution: 42.30 = 14K + Km/50...we can rewrite the number as follows:   42+ 0.30= 14K + Km/50........Since K is integer, then 42=14K..........K=3   0.30=Km/50......40/100=3m/50......m=5   k+m=3+5= 
3+5 = 8
8   Answer: 8
Answer: C
There are 3 teams each with 5 basket players. How many combinations are there if we were to pick 2 players from the 3 teams such that no team was picked twice?  Choose the correct choice from the following choices
A) 50	B) 23	C) 75	D) 28	E) 45

Solution: There are altogether three arrangements, which are we can select two members each from team A and B, each from team A and C, and each from team B and C. For each arrangement, there are altogether 25 possibilities (5*5) since each team has 5 players. So there are a total of 75 possibilities (25*3).   ANSWER:75
Answer: C
If Jenee earns a raise of between 5% and 10%, non-inclusive, by what fraction could her salary have increased?  Pick:
A) 1/4
B) 1/5
C) 1/10
D) 3/50
E) 1/20

Solution: Perhaps it is also easy to just translate the % into fractions:   6%: 6/100 = 3/50   7%: 7/100   8%: 8/100 = 4/50 =2/25   9%: 9/100   Only 3/50 exists in the answer choices, so ANS 3/50
Answer: D
Two trains are running in opposite directions with the same speed. If the length of each train is 120 metres and they cross each other in 12 seconds, then the speed of each train (in km/hr) is:
Choose the most appropriate option.
A) 10	B) 18	C) 36	D) 72	E) 62

Solution: Let the speed of the train is x   Realtive speed between the trains =2x   time =12   distance=240   2x=240/12   2x=20   x=10 km/hr 10NSWER:10
Answer: A
The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is: Choices
A) 127 m
B) 277 m
C) 245 m
D) 217 m
E) 219 m

Solution: Speed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (130 + x)/30 = 25/2 => 2(130 + x) = 750 => x = 245 m.   Answer: 245 m
Answer: C
A Guava costs Rs 8 each and a apple costs Rs. 21 each. If I spend Rs 101 on total what is the number of guava I purchased?	Answers:
A) 5	B) 4	C) 3	D) 6	E) 10

Solution: 10 * 8+21= 
10 * 8+21 = 101
101   Answer : 10   Option : 10
Answer: E
How long does a train 165 meters long running at the rate of 54 kmph take to cross a bridge 660 meters in length Choose the most appropriate option:
A) 33	B) 44	C) 55	D) 77	E) 22

Solution: T = (660 + 165)/54 * 18/5= 
(660 + 165)/54 * 18/5 = 55
55   Answer: 55
Answer: C
Find the C.I. on a sum of Rs.1600 for 9 months at 20% per annum, interest being compounded quarterly?	Choose the correct answer
A) 2266	B) 7767	C) 2522	D) 1677	E) 2671

Solution: A = 1600(21/20)3 = 2522   Answer:2522
Answer: C
The speed of a boat in upstream is 40 kmph and the speed of the boat downstream is 90 kmph. Find the speed of the boat in still water and the speed of the stream?  Pick one: A) 25 kmph B) 76 kmph C) 12 kmph D) 97 kmph E) 15 kmph

Solution: Speed of the boat in still water   = (40+90)/2= 
(40+90)/2 = 65
65 kmph. Speed of the stream= (90-40)/2= 
(90-40)/2 = 25
25 kmph.   25 kmphnswer:25 kmph
Answer: A
How many integers from 101 to 1000, inclusive, remains the value unchanged when the digits were reversed? Answers
A) 50  B) 60  C) 70  D) 80  E) 90

Solution: question is asking for palindrome   first digit possibilities - 1 through 9 = 9   second digit possibilities - 0 though 9 = 10   third digit is same as first digit   =>total possible number meeting the given conditions = 9 *10= 
9 *10 = 90
90   Answer is 90.
Answer: E
A pharmaceutical company received $5 million in royalties on the first $20 million in sales of and then $10 million in royalties on the next $108 million in sales. By approximately what percentage did the ratio of royalties to sales decrease from the first $20 million in sales to the next $108 million in sales?
Choices
A) 8%	B) 26%	C) 45%	D) 52%	E) 56%

Solution: (10/108)/(5/20) = 20/27 = 74% it means that 10/108 represents only 74%. Therefore a decrease of 26%.   Answer 26%
Answer: B
A driver goes on a trip of 70 kilometers, the first 35 kilometers at 48 kilometers per hour and the remaining distance at 24 kilometers per hour. What is the average speed of the entire trip in kilometers per hour?	Choose one:  A) 30  B) 32  C) 35  D) 36  E) 40

Solution: The time for the first part of the trip was 35/48 hours.   The time for the second part of the trip was 35/24 hours.   The total time fro the trip was 35/48 + 35/24 = 105/48 = 35/16 hours.   The average speed for the trip was   70 / (35/16)= 
  70 / (35/16) = 32
32 kph   The answer is 32.
Answer: B
How many 4 digit numbers can be formed using 0,1,2,3,4,5 and divisible by 4	Choose the correct choice from the following options:	A) 190	B) 200	C) 210	D) 220	E) 230

Solution: since a number cannot start with 0 so, 1st place of of 4 digit number can be filled in 5 ways i.e., 1,2,3,4,5.   second place of 4 digit number can be filled in 6 ways i.e., 0,1,2,3,4,5   since 4 digit numbers should be divisible by 4 so possibility of last 2 places are (04,12 20,24,32,40,52) i.e., 7 possibilities.   Therefore total number of 4 digut number divisible by 4 are- 5*6*7=210   ANSWER:210
Answer: C
For what value of x between − 7 and 7, inclusive, is the value of x^2 − 10x + 16 the greatest?
Choose the correct answer:
A) − 7
B) − 2
C) 0
D) 2
E) 7

Solution: we can see from the statement that two terms containing x, x^2 will always be positive and -10x will be positive if x is -ive..   so the equation will have greatest value if x is -ive, and lower the value of x, greater is the equation.   so -7 will give the greatest value..   ans − 7
Answer: A
The average (arithmetic mean) of a normal distribution of a school's test scores is 65, and standard deviation of the distribution is 6.5. A student scoring a 73 on the exam is in what percentile of the school?
Choices Answers.
A) 63rd percentile
B) 68th percentile
C) 84th percentile
D) 96th percentile
E) 98th percentile

Solution: (78-65)/6.5= 
(78-65)/6.5 = 2
2 sigmas or 95.5th percentile for +-2 sigma but in our case we need only upper tail, so it's 100 - (100 - 95.5)/2= 87th percentile   84th percentile
Answer: C
If c is 30% of a and 25% of b, what percent of a is b? Choices.
A) 2.5%	B) 15%	C) 120%	D) 35%	E) 250%

Solution: Answer = 120%   30a/100 = 25b/100   b = 30a/25 = 120a/100 = 120%
Answer: C
If the speed of a man is 57 km per hour, then what is the distance traveled by him in 30 seconds ? Choose the correct answer.
A) 275m B) 360m C) 475 m D) 420 m E) 440 m

Solution: The distance traveled in 30 sec = 57*(5/18) *30= 
57*(5/18) *30 = 475
475m   ANSWER:475 m
Answer: C
How many bricks, each measuring 25 cm x 11.25 cm x 6 cm, will be needed to build a wall of 7 m x 6 m x 22.5 cm?
Choices
A) 6400 B) 6410 C) 5600 D) 6500 E) 6800

Solution: Number of bricks = Volume of Wall/Volume of Bricks   =700x600x22.5/25x11.25x6= = 5600   answer :5600
Answer: C
If w, x, and y are consecutive odd positive integers and w < x < y, which of the following could be equal to x - y - w ?  Choose the correct answer:
A) -4
B) -2
C) -1
D) 0
E) -3

Solution: Since W, X and Y are CONSECUTIVE ODD POSITIVE INTEGERS and W < X < Y, we can start with the easiest set of values that comes to mind:   W = 1   X = 3   Y = 5   The question asks for what COULD be the value of X - Y - W.   In this case, the value would be...   3 - 5 - 1 = -3   -3 IS among the answer choices, so we're done.   -3
Answer: E
The cash difference between the selling prices of an article at a profit of 4% and 6% is Rs. 3. The ratio of the two selling prices is: Select
A) 51:52 B) 52:53 C) 51:53 D) 52:55 E) 50:51

Solution: Explanation:   Let C.P. of the article be Rs. x.   Then, required ratio = 104% of x / 106% of x   = 104/106 = 52/53 = 52:53   ANSWER IS 52:53
Answer: B
X and Y started a business by investing Rs.36000 and Rs.42000 respectively after 4 months Z joined in the business with an investment of Rs.48000, then find share of Z in the profit of Rs.14190 ?	Choose the correct choice from the following answers:  A) 3200  B) 4000  C) 3250  D) 4128  E) 3985

Solution: Ratio of investment, as investments is for different time.   Investment x Number of units of time.   Ratio of investments X : Y : Z = 36000 : 42000 : 48000 => 6 : 7 : 8.   X = 6 x 12 Months = 72, Y = 7 x 12 = 84, Z = 8 X 8 = 64 => 18 : 21 : 16.   Ratio of investments => X : Y : Z = 18 : 21 : 16.   Investment Ratio = Profit sharing Ratio.   Z = 14190 Ã— 16/55 = Rs.4128.   Share of Z in the profit is Rs.4128.   Option 4128
Answer: D
An outlet pipe can empty 2/3 of a cistern in 12 minutes. In 4 minutes, what part of the cistern will be emptied?  Choose the correct choice from the following:	A) 1/3	B) 2/5	C) 2/7	D) 2/9	E) 3/10

Solution: 4/12 * 2/3 = 2/9   The answer is 2/9.
Answer: D
Find large number from below question The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder  Choose the correct choice from the following options:
A) 1209
B) 1324
C) 1245
D) 1300
E) 1635

Solution: Let the smaller number be x. Then larger number = (x + 1365).   x + 1365 = 6x + 15   5x = 1350   x = 270   Large number = 270+1365= 
270+1365 = 1_635
1635   1635
Answer: E
A certain company consists of 4 managers and 8 non-managers. How many different teams of 3 employees can be formed in which at least one member of the team is a manager and at least one member of the team is not a manager? (Two groups are considered different if at least one group member is different)	Choose the correct answer.
A) 84
B) 108
C) 160
D) 270
E) 990

Solution: Total # of teams of 3 possible is 12C3=220   # of teams with only managers or only non-managers is: 4C3+8C3=4+56= 
4+56 = 60
60;   # of teams of 3 with at least one manager or at least one non-manager is: 220-60= 
220-60 = 160
160.   ANSWER:160
Answer: C
6) A marketing firm determined that , of 240 households surveyed, 80 used neither Brand A nor Brand B soap.60 used only Brand A soap and for every household that used both brands of soap, 3 used only brand B soap.how many of the 200 household surveyed used both brands of soap?	Answers.
A) a) 15
B) b) 20
C) c) 25
D) d) 40
E) e) 45

Solution: 160 = At least one of Soap A or B   Both brands = x   Brand B = 3x   => 60 + x + 3x = 160   => 4x = 100   => x = 25   Answer - c) 25
Answer: C
If a person walks at 14 km/hr instead of 10 km/hr, he would have walked 20 km more. The actual distance travelled by him is :  Choose the most appropriate option
A) 52 km	B) 62 km	C) 55 km	D) 50 km	E) None

Solution: Sol.   Let the actual distance travelled be x km. Then,   x/10 = (x+20)/14   ⇔ 14x = 10x + 200   ⇔ 4x = 200   ⇔ x = 50 km.   Answer 50 km
Answer: D
A child must place 7 different toys in 4 different bins. If any of the toys can go in any of the bins, in how many ways can the child place the toys into the bins?	Choose the correct choice from the following: A) 6^6 B) 6^4 C) 4^7 D) 4^4 E) 6^4-4^6

Solution: there are 4 different bins and each of the toy can go to any of these bins..   so answer 7âˆ—7âˆ—7âˆ—7âˆ—7âˆ—7âˆ—7=4^7   ANSWER:4^7
Answer: C
At the beginning of 2011, Company X created a list of n charities, and committed to donating 10% of its prots for the year to these charities, donating an equal amount to each charity. However, during the year, Company X removed a charities from this list, and donated 10% of its prot in equal amounts to each of the remaining charities on the list. If the Wesley Homeless Shelter was one of the charities on the list which received a donation from Company X, which of the following represents, in terms of n and a, the percent increase in the amount the Wesley Homeless Shelter received because the a charities were removed from the list?	Choose the correct choice from the following choices:  A) 100n/a  B) 100a/(n-a)  C) 100(n-a)/n  D) 100n/(n-a)  E) "100(n-a)" divided by "a"

Solution: Sol:   Let profit be "P"   for n charities - each get p/n   when a charities are removed - each get p/(n-a)   increase will be (p/(n-a)) - (p/n) = pa/(n-a)*n   Increase % will be (pa/(n-a)*n) / (p/n) multiplied by 100.   result will be 100a/(n-a)   ANSW"100(n-a)" divided by "a"R:"100(n-a)" divided by "a"
Answer: E
After 4 games, team B had an average of 61.5 points per game. If it got only 47 points in game 5, how many more points does it need to score to get its total above 500? Choose the correct choice from the following options:
A) 85 B) 74 C) 67 D) 53 E) 207

Solution: (4*61.5) + 47 +x >500   246+47+x > 500   293+x >500   => x>207   Option 207
Answer: E
In an increasing sequence of 8 consecutive even integers, the sum of the first 4 integers is 268. What is the sum of all the integers in the sequence?
Choose the correct choice from the following answers
A) 552	B) 568	C) 574	D) 586	E) 590

Solution: In an increasing sequence of 8 consecutive even integers, the sum of the first 4 integers is 268. What is the sum of all the integers in the sequence?   x+x+2+x+4+x+6=268   x=64   64+66+68+70+72+74+76+78= 
64+66+68+70+72+74+76+78 = 568
568   ANSWER:568
Answer: B
In each series, look for the degree and direction of change between the numbers. In other words, do the numbers increase or decrease, and by how much
Look at this series: 1.2, 2.4, 3.6, 4.8, ... What number should come next?	Options:
A) 4.7 B) 3.6 C) 4.9 D) 6.0 E) 4.4

Solution: 6.0   In this simple addition series, each number increases by 1.2   Answer : 6.0
Answer: D
At a certain fruit stand, the price of each apple is 40 cents and the price of each orange is 60 cents. Mary selects a total of 20 apples and oranges from the fruit stand, and the average (arithmetic mean) price of the 20 pieces of fruit is 56 cents. How many oranges must Mary put back so that the average price of the pieces of fruit that she keeps is 52 cents?	Options:
A) 6
B) 7
C) 8
D) 9
E) 10

Solution: Let number of Apples = A   number of oranges = B   A+B=20 --- 1   .56 =(.4A + .6 B)/20   => 56 = 4A + 6B ----2   Solving 1 and 2, we get   A= 4   B= 16   Let the number of oranges put back = C   52*(20-c) = 40*4 + 60(16-C)   => C= 10   Answer 10
Answer: E
A 25 cm wide path is to be made around a circular garden having a diameter of 4 meters. Approximate area of the path is square meters is?	Choose the correct answer:
A) 3.34
B) 3.37
C) 3.35
D) 3.76
E) 3.31

Solution: 3.34rea of the path = 3.34rea of the outer circle - 3.34rea of the inner circle   = ∏{4/2 + 25/100}2 - ∏[4/2]2   = ∏[2.252 - 22] = ∏(0.25)(4.25) { (a2 - b2 = (a - b)(a + b) }   = (3.14)(1/4)(17/4) = 53.38/16 = 3.34 sq m   3.34nswer: 3.34
Answer: A
39 persons can repair a road in 12 days, working 5 hours a day. In how many days will 30 persons, working 6 hours a day, complete the work? Answers:
A) 16
B) 19
C) 13
D) 14
E) 18

Solution: Let the required number of days be X.   Less persons, More days (Indirect Proportion)   More working hours per day, Less days (Indirect Proportion)   Persons 30	:	39   Working hours/day	6	:	5 :: 12 : X   THEREFORE 30 x 6 x X = 39 x 5 x 12   X =(39 x 5 x 12)/(30 x 6)   X = 13.   ANSWER:13
Answer: C