MU-NLPC/Calc-aqua_rat huggingface dataset:
Anita, Indu and Geeta can do a piece of work in 18 days, 27 days and 36 days respectively. They start working together. After working for 4 days. Anita goes away and Indu leaves 7 days before the work is finished. Only Geeta remains at work from beginning to end. In how many days was the whole work done?	Select:
A) 16 days  B) 66 days  C) 77 days  D) 44 days  E) 33 days

Solution: :   4/18 + (x -7)/27 + x/36 = 1   x = 16 days   16 daysnswer: 16 days
Answer: A
The sides of a cube measures 6.5cm. If the surface area of the cube is the same as a ball, what is the radius of the ball? Round to the nearest whole number. Choices.
A) 9  B) 7  C) 4  D) 8  E) 6

Solution: First calculate the surface area of the cube. The cube is made of 6 squares with the sides measuring 6.5cm each. The surface area of 1 side of the cube is 42.25cm. Multiply the surface area of the 1 side by 6 will give you the cube's total surface area. The cubes surface area is 253.5cm. Now we know that the surface area of the ball is 253.5cm. To find out the surface area of a sphere you need to square the radius, then multiply by Pi, and multiply by the number 4. Going backwards to find the radius - you will need to dived the surface area by 4. Then divide by Pi. Then determine the square root of the answer. The radius is 4.460. Rounding to the nearest whole number the radius is 4. The correct answer is (4).
Answer: C
If the side length of Square B is four times that of Square A, the area of Square B is how many times the area of Square A? Select the correct option: A) 20 B) 16 C) 12 D) 8 E) 4

Solution: Let x be the side length of Square A.   Then the area of Square A is x^2.   The area of Square B is (4x)^2=16x^2.   The answer is 16.
Answer: B
W, X and Y invested Rs.8100, Rs.7200 and Rs.2700 respectively, in a partnership business. Find the share of Y in profit of Rs.60000 after a year? Choose the correct answer:
A) 3000
B) 6000
C) 9000
D) 12000
E) 15000

Solution: Explanation:   8100:7200:2700   9:8:3   3/20 * 60000= 
3/20 * 60000 = 9_000
9000   9000)
Answer: C
In a simultaneous throw of a pair of dice, find the probability of getting a total more than 10  Choose one
A) 5/13
B) 2/15
C) 1 by 12
D) 3/17
E) 6/19

Solution: Total number of cases = 6*6= 
6*6 = 36
36   Favourable cases= [(5,6)(6,5),(6,6)] = 3   So Probability = 3/36 = 1/12   Answer is 1 by 12
Answer: C
What is the sum of the first 24 natural numbers (starting from 1)?
Choices:
A) 250 B) 300 C) 350 D) 400 E) 450

Solution: The sum of n natural numbers = n*(n+1) / 2 = 24*25/2= 
24*25/2 = 300
300   The answer is 300.
Answer: B
The average of 11 results is 53, if the average of first six results is 49 and that of the last six is 52. Find the sixth result? Choose the correct choice from the following answers.
A) A)46	B) B)23	C) C)66	D) D)76	E) E)74

Solution: 1 to 11 = 11 * 53= 
11 * 53 = 583
583   1 to 6= 6 * 49= 
6 * 49 = 294
294   6 to 11= 6 * 52= 
6 * 52 = 312
312   6th= 294 + 312 – 583 = 23   Answer:23
Answer: B
Some ladies can do a piece of work in 12 days. Two times the number of such ladies will do half of that
work in :	Choose the correct choice from the following answers:
A) 6 days B) 4 days C) 12 days D) 3 days E) 2 days

Solution: Expl : Let x ladies can do the work in 12 days. More ladies, less days (Indirect)   Less work, less days (direct)   Ladies 2x : x Work 1 : ½   2x : x , 1 : ½ : : 12 : y   :. 2x * 1*y = x* ½ *12 or y = 3   Hence the required number of days = 3   Answer: 3 days
Answer: D
The smallest number which when diminished by 3 is divisible by 21,28,36 and 45 is... Choices:  A) 829  B) 869  C) 859  D) 4320  E) 427

Solution: 427   ANSW427R:427
Answer: E
A man on tour travels first 160 km at 64 km/hr and the next 160 km at 80 km/hr. The average speed for the first 380 km of the tour is:	Select.
A) 31.11 km/hr	B) 35.55 km/hr	C) 71.11 km/hr	D) 84.44 km/hr	E) 71 km/hr

Solution: Total time taken = 160/64 + 160/80 = 9/2 hours   --> Average speed = 380 x 2/9 = 84.44 km/hr.   Answer : 84.44 km/hr.
Answer: D
A sum of money becomes triple itself in 5 years at simple interest. How many years will it become eight times at the same rate?
Answers
A) 12 Â½ years
B) 16 Â½ years
C) 18 Â½ years
D) 72 Â½ years
E) 12 Â½ years

Solution: 100 ---- 200 ---- 5   200 ---- 5   100 ---- 2 1/2   ------------------   800 ---- 16 Â½ years   Answer:16 Â½ years
Answer: B
When the numerator of a fraction is decreased by 25% and its denominator is decreased by 20%, the new fraction obtained is 3/4. Find the original fraction?  Answers
A) 3/3	B) 7/2	C) 5/2	D) 3/4	E) None of these

Solution: Answer: Option E   Let the fraction be x/y.   When the numerator decreased by 25% and the denominator decreased by 20%.   (x * 3/4)/(y * 4/5) = 3/4 => x/y = 3/4 * (4/5)/(3/4) = 4/5
Answer: E
A, B, C subscribe Rs. 50,000 for a business. A subscribes Rs. 4000 more than B and B Rs. 5000 more than C. Out of a total profit of Rs. 30,000, C receives:
Choose the most appropriate option
A) s. 7,000
B) s. 7,200
C) s. 7,400
D) s. 7,700
E) s. 7,800

Solution: Let C = x.   Then, B = x + 5000 and A = x + 5000 + 4000 = x + 9000.   So, x + x + 5000 + x + 9000 = 50000   3x = 36000   x = 12000   A : B : C = 21000 : 17000 : 12000 = 21 : 17 : 12.   C's share = Rs. (30000 x 12/50) = Rs. 7,200.   s. 7,200
Answer: B
1240 men have provisions for 12 days. If 300 more men join them, for how many days will the provisions last now? Answers.
A) 12.9  B) 12.0  C) 9.7  D) 8.6  E) 12.1

Solution: 1240*12 = 1540*x   x = 9.7   Answer:9.7
Answer: C
All of the stocks on the over-the-counter market are designated by either a 3-letter or a 4-letter code that is created by using the 26 letters of the alphabet. Which of the following gives the maximum number of different stocks that can be designated with these codes?  Select the correct option:
A) a. 2(26^5)
B) b. 26(26^4)
C) c. 27(26^3)
D) d. 26(26^5)
E) e. 27(26^5)

Solution: no of different stocks for 3-letter code = 26^3   no of different stocks for 4-letter code = 26^4   total = 26^3 + 26^4 = 26^3(26+1) = 27(26^3)   [Reveal]Spoiler:   Option c. 27(26^3)
Answer: C
One ton has 2200 pounds, and one pound has 16 ounces. How many packets containing wheat weighing 16 pounds and 4 ounces each would totally fill a gunny bag of capacity 13 tons?  Choose the most appropriate option
A) 1760	B) 1700	C) 2350	D) 2500	E) 8000

Solution: 16 pounds and 4 ounces= 16*16 + 4= 
16*16 + 4 = 260
260 ounces.   13 tons= 13*2200 pound = 13*2200*16 ounces.   Hence the answer is   (13*2200*16)/260= 
  (13*2200*16)/260 = 1_760
1760.   1760nswer: 1760.
Answer: A
If m > 0 and z is m percent of y, then, in terms of m, y is what percent of z?  Choose the correct choice from the following answers.
A) a) 100m
B) b) 1/100m
C) c) 1/m
D) d) 10,000/m
E) e) 10/m

Solution: z= m/100 * y   So y= 100/m * z   So y= (10000/m)/100 * z   d) 10,000/m
Answer: D
The number of new words that can be formed by rearranging the letters of the word 'can' is?  Choose the correct answer.
A) 3	B) 6	C) 10	D) 8	E) 5

Solution: Number of words which can be formed   = 3! - 1 = 6 - 1= 
6 - 1 = 5
5.   Answer: 5
Answer: E
The largest 4 digit number exactly divisible by 88 is?
Choose the most appropriate option
A) 9935  B) 9939  C) 9944  D) 9954  E) 9960

Solution: Largest 4-digit number = 9999   88) 9999 (113   88   ----   119   88   ----   319   264   ---   55   ---   Required number = (9999 - 55)= 
(9999 - 55) = 9_944
9944.   9944)
Answer: C
Find the L.C.M of 2^3 * 3^2* 5 *7^3*11^3, 2^4 * 3^2* 5^3* 7^3*11, 2^2* 3* 5^3* 7^3*11
Select the correct option: A) 2^4 * 3^2 * 5^3 * 7^3 * 11^3 B) 2^2*3^3*5^2 * 7^4 * 11 C) 2^2*3^4*5^3 * 7^4 * 11 D) 2^2*3^3*5^3 * 7^4 * 11^3 E) 2^3*3^3*5^3 * 7^4 * 11^2

Solution: L.C.M= product of the highest powers of 2,3,5,7 and 11=2^4 * 3^2 * 5^3 * 7^3 * 11^3   2^4 * 3^2 * 5^3 * 7^3 * 11^3nswer (2^4 * 3^2 * 5^3 * 7^3 * 11^3)
Answer: A
When processing flower-nectar into honey bees' extract, a considerable amount of water gets reduced. How much flower-nectar must be processed to yield 1kg of honey, if nectar contains 50% water, and the honey obtained from this nectar contains 20% water? Select the correct option:
A) 1.2 kg
B) 1.5 kg
C) 1.7 kg
D) 1.6 kg
E) None of these

Solution: Explanation :   Flower-nectar contains 50% of non-water part.   In honey this non-water part constitutes 80% (100-20).   Therefore 0.5 X Amount of flower-nectar = 0.80 X Amount of honey = 0.80 X 1 kg   Therefore amount of flower-nectar needed =   (0.80/0.51)kg=1.6 kgs   Answer : 1.6 kg
Answer: D
Find the area of trapezium whose parallel sides are 20 cm and 18 cm long, and the distance between them is 12 cm  Choose the correct choice:  A) 178 cm2  B) 179 cm2  C) 285 cm2  D) 167 cm2  E) 228 cm2

Solution: Area of a trapezium = 1/2 (sum of parallel sides) * (perpendicular distance between them)   = 1/2 (20 + 18) * (12)   = 228 cm2   Answer: 228 cm2
Answer: E
P alone can complete a piece of work in 6 days. Work done by Q alone in one day is equal to one-third of the work done by P alone in one day. In how many days can the work be completed if P and Q work together?	Options.
A) 7
B) 4(1/2)
C) 65
D) 9
E) 1

Solution: Work done by P alone in one day = 1/6th of the total work done by Q alone in one day = 1/3(of that done by P in one day) = 1/3(1/6 of the total) = 1/18 of the total.   Work done by P and Q, working together in one day = 1/6 + 1/18 = 4/18 = 2/9 of the total   They would take 9/2 days = 4 (1/2) days to complete the work working together.   Answer: 4(1/2)
Answer: B
A division of a company consists of four men and eight women. If two of these twelve employees are randomly selected as representatives of the division, what is the probability that both representatives will be female?  Pick one:
A) 7/11	B) 7/33	C) 14/33	D) 7/66	E) 14/66

Solution: The total number of ways to choose two representatives is 12C2=66.   The number of ways to choose two females is 8C2=28.   P(choosing two female representatives)=28/66=14/33   The answer is 14/33.
Answer: C
15 Java programmers, working in a constant pace, finish a web page in 3 days. If after one day, 9 programmers quit, how many more days are needed to finish the
remainder of the job?	Options
A) 5. B) 2. C) 8. D) 4. E) 6.

Solution: Given:   3 day's work : x   1 day's work : x/3   Given:   15 people complete the work in 3 days .   After 1 day's work (x/3), 9 people left.   Remaining work = x - x/3 =2x/3   Now ,   1 day's work of 15 persons= x/3   1 day's work of 1 person = x/45.   1 day's work of 6 persons(15-9)= 2x/15.   2x/15 work completed in 1 day.   2x/3 work completed in = 5 days   Question asks how many more days needed to complete the remaining work,therefore 5 more days needed to complete the remaining work.   5.nswer is 5..
Answer: A
If x^2 = 141, which of the following is closest to a potential value of x?	Choose the correct choice from the following answers:
A) -127
B) -11
C) 12
D) 13
E) 131

Solution: Here the thing we must not forget is that X^even has two potential solutions   => x =+- √141 => +- 12 (approx)   this value is closer to 12   Hence 12 is correct.
Answer: C
How many two-digit whole numbers yield a remainder of 2 when divided by 12 and also yield a remainder of 2 when divided by 6?
Choose the most appropriate option:
A) None	B) Five	C) Six	D) Seven	E) Eight

Solution: The possible number N can be written as follow:   N = Multiple of LCM(12,6) + 1st such number   N = 12x + 2   Possible values =2,26,38,50,62,86,98   Answer : 6 such 2 digit number. Six.
Answer: C
Of the 150 employees at company X, 50 are full-time, and 100 have worked at company X for at least a year. There are 20 employees at company X who aren’t full-time and haven’t worked at company X for at least a year. How many full-time employees of company X have worked at the company for at least a year?	Choose the correct answer.
A) 20 B) 30 C) 50 D) 80 E) 100

Solution: 150 employees   50 are full-time   100 have worked at company X for at least a year   20 employees at company X who aren’t full-time and haven’t worked at company X for at least a year.   How many full-time employees of company X have worked at the company for at least a year?   150-50= 
150-50 = 100
100 employees not full time   100-20= 
100-20 = 80
80 employees not full time who worked over a year   100 employees have worked at company X for at least a year-80 employees not full time who worked over a year= 20 full-time employees of company X have worked at the company for at least a year   ans 20
Answer: A
Set S contains exactly 10 numbers and has an average (arithmetic mean) of 6.2. If one of the numbers in Set S is increased by 3, while all other numbers remain the same, what is the new average of Set S? Answers:
A) 6.5	B) 6.7	C) 6.8	D) 6.85	E) 6.9

Solution: Old set S - Total is avg * no of elements = 6.2*10= 
6.2*10 = 62
62   If one number is increased by 3 then total increased to  62+3= 
 62+3 = 65
65   New avg - 65/10= 6.5.   Hence answer is 6.5.
Answer: A
Each shelf of a bookcase contained 12 books. If the librarian took out 22 books and rearranged the remaining books so that all shelves but one contained 8 books and the last shelf contained 10 books, how many shelves does the bookcase have?	Choose the correct choice from the following choices: A) 8 B) 6 C) 7 D) 5 E) 4

Solution: Let x be the number of shelves.   No of books in the beginning =12*x   After taking out 21 books No of remaining books = 12x -21   when the remaining books are rearranged, each shelf except the last shelf has 8 books and the last shelf has 11 books. So No of remaining books is also equal to 8*(x-1)+10   12x-22=8(x-1)+10   4x=24   x=6. Answer 6
Answer: B
The average of first five prime numbers greater than 5 is?  Choices:
A) 13.4  B) 12.26  C) 12.3  D) 32.8  E) 32.4

Solution: 7 + 11 + 13 + 17 + 19= 
7 + 11 + 13 + 17 + 19 = 67
67/5= 
67/5 = 67/5 = around 13.4
13.40   13.4nswer: 13.4
Answer: A
Find the average of all prime numbers between 30 and 50
Choose the correct choice from the following:
A) 35	B) 39.8	C) 41.2	D) 50.9	E) 62

Solution: Prime numbers between 30 and 50 are 31,37,41,43,47   Required average = (31+37+41+43+47)/5 = 199/5= 
199/5 = 199/5 = around 39.8
39.8   Answer is 39.8
Answer: B
Of all the homes on Gotham Street, 1/3 are termite-ridden, and 5/8 of these are collapsing. What fraction of the homes are termite-ridden, but NOT collapsing?
Answers
A) 1/3
B) 1/4
C) 1/5
D) 1/6
E) 1/8

Solution: The fraction of homes which are termite-infested but not collapsing is 3/8*1/3 = 1/8   The answer is 1/8.
Answer: E
The compound interest on a certain sum for 2 years at 10% per annum is $525. The simple interest on the same sum for double the time at half the rate percent per annum is:  Choose the correct choice.
A) $400 B) $500 C) $600 D) $800 E) $900

Solution: Let the sum be $. P.   Then,[P(1+10/100)^2 - P] = 525   ->P[(11/10)^2 - 1] = 525   P = (525*100/21)= 
(525*100/21) = 2_500
2500   SUM= $2500   SO SI = $(2500*5*4/100)= 
(2500*5*4/100) = 500
$ 500   ANSWER : $500 $500
Answer: B
Alex takes a loan of $8,000 to buy a used truck at the rate of 9 % simple Interest.Calculate the annual interest to be paid for the loan amount.  Options:
A) 680
B) 700
C) 720
D) 730
E) 750

Solution: From the details given in the problem Principle = P = $8,000 and R = 9% or 0.09 expressed as a decimal.   As the annual Interest is to be calculated, the time period T =1.   Plugging these values in the simple Interest formula,   I = P x T x R   = 8,000 x 1 x 0.09   = 720.00   Annual Interest to be paid = $720   answer :720
Answer: C
A shopkeeper sold an article offering a discount of 5% and earned a profit of 23.5%. What would have been the percentage of profit earned if no discount was offered?	Choose the correct choice from the following choices:	A) 17%	B) 18%	C) 30%	D) 17%	E) 12%

Solution: Let C.P. be Rs. 100.   Then, S.P. = Rs. 123.50   Let the marked price be Rs. x. Then, 95/100 x = 123.50   x = 12350/95 = Rs. 130   Now, S.P. = Rs. 130, C.P. = Rs. 100   Profit % = 30%.   Answer: 30%
Answer: C
617 + 6.017 + 0.617 + 6.0017 = ?  Pick
A) 6.2963
B) 62.9635
C) 629.6357
D) 0.62963
E) None of them

Solution: 617.00   6.017   0.617   + 6.0017   --------   629.6357   ---------   Answer is 629.6357.
Answer: C
Pipe A fills a tank in 20 minutes. Pipe B can fill the same tank 4 times as fast as pipe A. If both the pipes are kept open when the tank is empty, how many minutes will it take to fill the tank?  Choices
A) 2 B) 3 C) 4 D) 5 E) 6

Solution: A's rate is 1/20 and B's rate is 1/5.   The combined rate is 1/20 + 1/5 = 1/4   The pipes will fill the tank in 4 minutes.   The answer is 4.
Answer: C
John invests $x at the semi-annual constant compounded rate of 2 percent and also does $15,000 at the quarterly constant compounded rate of 4 percent. If the interests are the same after 1 year, what is the value of x??	Select the correct option:
A) 20000  B) 30000  C) 40000  D) 30301.5  E) 50000

Solution: A = P(1+r/n)^nt   A= total amount accrued   P = principal deposited   r = rate of interest in decimal form   n = number of times per year, interest compounded   t = time in number of years.   .   x(1+0.02/2)^2 - x = 15,000(1+0.04/4)^4 - 15,000 [ when the principal is subtracted from the total amount accrued , the resulting difference is the interest portion and question states interests are equal)   => x[(1.01)^2 - 1] = 15,000[(1.01)^4 - 1]   => x[(1.01)^2 - 1] = 15,000[(1.01)^2+1][(1.01)^2-1] --> Using a^2-b^2 = a+b X a-b formula and cancel common expression on both sides   => x = 15,000(1.0201+1) =30301.5   Hence answer is 30301.5.
Answer: D
In a function they are distributing noble prize. In how many ways can 3 prizes be distributed among 4 boys when a boy gets any no. of prizes? Pick one:  A) 25  B) 43  C) 64  D) 78  E) 98

Solution: Ans.(C)   Sol. In this case, repetitions are allowed, so all the three prizes can be given in 4 ways, i.e. (4 x 4 x 4) ways = 43 ways = 64 ways Or nr ways = 43 ways = 64 ways
Answer: C
The function g(j) is defined for integers j such that if j is even, g(j) = j/2 and if j is odd, g(j) = j + 5. Given that g(g(g(g(g(j))))) = 19, how many possible values for j would satisfy this equation?  Choose the correct choice from the following answers.
A) 1	B) 5	C) 7	D) 8	E) 11

Solution: Let me define terms:   in g(j) = R   j is argument, R is result, g() is function,   in g(g(g(g(g(j))))), g1 is inner most, g5 is outermost for identification.   From definition of function g, we can deduce that:   If Result is even then two possibilities for argument = 1 Even 1 Odd   If Result is odd then one possibility for argument = 1 Even   Since final result = 19 = Odd   Possibilities:   g1:1 Even   g2: 1*(Even,Odd ) =1 Even 1 Odd   g3: 1*(Even,Odd) + 1 Even =2 Even 1 Odd   g4: 2*(Even, Odd) + 1 Even =3 Even 2 Odd   g5: 3*(Even, Odd) + 2 Even =5 Even 3 Odd = Total 8   Ans 8 it is!
Answer: D
13 buckets of water fill a tank when the capacity of each bucket is 42 litres. How many buckets will be needed to fill the same tank, if the capacity of each bucket is 6 litres?	Answers
A) 91
B) 80
C) 96
D) 98
E) 90

Solution: Capacity of the tank = (13 Ã— 42) litre   Number of buckets required of capacity of each bucket is 17 litre = 13Ã—42/6=13Ã—7=91   91nswer is 91
Answer: A
A certain lab experiments with white and brown mice only. In one experiment, 2/3 of the mice are white. If there are 14 white mice in the experiment, how many brown mice are in the experiment? Choose the correct choice from the following answers
A) 12
B) 8
C) 28
D) 7
E) 27

Solution: Let total number of mice = M   Number of white mice = 2/3 M=14 M =21   Number of brown mice = 1/3 M = 1/3*21   =>brown mice = 7   Answer 7
Answer: D
During a Thanksgiving weekend, a car rental company rented seven-tenths of their vehicles, including two-fifths of the 4WDs that it had. If 40% of the vehicles are 4WDs, then what percent of the vehicles that were not rented were not 4WDs? Options
A) 20%
B) 30%
C) 40%
D) 60%
E) 25%

Solution: 3/10 of all the vehicles were not rented.   (3/5)(2/5) = 6/25 of all the vehicles are 4WDs that were not rented.   (6/25) / (3/10) = 4/5 is the fraction of non-rented vehicles that were 4WDs   1 - 4/5 = 20% of non-rented vehicles were not 4WDs.   The answer is 20%.
Answer: A
People standing in a straight line are wearing alternating colored shirts. The pattern of shirts begins with red, followed by green, blue, white and yellow. This pattern continues (red, green, blue, white and yellow) until it ends with a blue shirt. If there are more than 5 people in line, which of the following cannot be the number of people in the line?  Answers:
A) 27	B) 38	C) 53	D) 63	E) 78

Solution: The correct answer should not take the form: 5x + 3. Hence, it is 27
Answer: A
The area of one square is x^2 + 10x + 25 and the area of another square is 4x^2 − 12x + 9. If the sum of the perimeters of both squares is 32, what is the value of x?  Select the correct option:
A) 0 B) 2 C) 2.5 D) 4.67 E) 10

Solution: spotting the pattern of equations both are in form of (X+C)^2 so   A1= (x+5)^2 & A2= (2x-3)^2   L1= x+5 & L2= 2x-3   P1 = 4( x+5) & P2=4(2x-3)   P1+P2=32   4( x+5) +4(2x-3)=32..............> X=2   Answer: 2
Answer: B
he number of sequences in which 10 players can throw a ball, so that the youngest player may not be the last is? Select.
A) 4328883 B) 2377110 C) 3265920 D) 2882124 E) 2782000

Solution: x Not younger_______ ↑   The last ball can be thrown by any of the remaining 9 players. The first 6 players can throw the ball in 9p9 ways.   The required number of ways = 9(9!) = 4320   Answer:3265920
Answer: C
100 kg of a mixture containing milk and water in the ratio 11:5. How much more water is to be added to get a new mixture containing milk and water in the ratio 3:2?	Choose the correct choice from the following choices.
A) 2.49kg B) 5.78kg C) 3.45kg D) 4.17kg E) 6kg

Solution: Milk in 100kg of mix = 100*10/16 = 125/2 kg   Water in it= 100-125/2 = 75/2 kg   Let x kg of water be added to it.   (125/2)/(75/2 + x) = 3/2   x=4.17kg   Answer is 4.17kg
Answer: D
In how many ways can the integer 48 be expressed as a product of two different positive integers? Options:  A) 10  B) 8  C) 5  D) 4  E) 2

Solution: Method 1: Listing all multiples since given number is small   48 = 1*48, 2*24, 3*16, 4*12, 6*8 => 5 ways   Method 2: Express given number as prime factors   48 = 6*8 = 2*3 * 2^3 = 2^4 * 3   Total number of factors = (4+1)(1+1) = 5*2= 
5*2 = 10
10   Since the given number is not a perfect square, there will be exact 5 pairs possible of the given 10 factors=> 5 ways   Option 5
Answer: C
In a 500 m race, the ratio of the speeds of two contestants A and B is 3 : 4. A has a start of 140 m. Then, A wins by: Select the correct option:
A) 20 m  B) 40 m  C) 60 m  D) 45 m  E) 55 m

Solution: To reach the winning post A will have to cover a distance of (500 - 140)m, i.e., 360 m.   While A covers 3 m, B covers 4 m.   while 20 m covers 360 m B covers (4/3*360)= 
(4/3*360) = 480
480 m   when 20 m reaches the winning post B covers 480 m and 20 m behind   20 mNSWER 20 m
Answer: A
A manufacturer of a certain product can expect that between 0.2 percent and 0.5 percent of the units manufactured will be defective. If the retail price is $2,500 per unit and the manufacturer offers a full refund for defective units, how much money can the manufacturer expect to need to cover the refunds on 20,000 units?  Select the correct option.
A) Between $15,000 and $25,000  B) Between $30,000 and $50,000  C) Between $60,000 and $100,000  D) Between $100,000 and $250,000  E) Between $300,000 and $500,000

Solution: Number of defective units is between = .2 % of 20000 and .5% of 20000   = 40 and 100   Retail Price per unit = 2500 $   Expected price of refund is between = 2500 x 40 and 2500 x 100   =1,00,000 and 2,50,000 dollars   Answer Between $100,000 and $250,000
Answer: D
The difference of the areas of two squares drawn on two line segments in 32 sq. cm. Find the length of the greater line segment if one is longer than the other by 2 cm	Choose the correct choice.
A) 9 cm B) 8 cm C) 7 cm D) 6 cm E) 5 cm

Solution: Explanation:   Let the lengths of the line segments be x and x+2 cm   then,   (x+2)2−x2=32x2+4x+4−x2=324x=28x=7cm   Option 7 cm
Answer: C