MU-NLPC/Calc-aqua_rat huggingface dataset:
A circle graph shows how the budget of a certain company was spent: 55 percent for salaries, 9 percent for research and development, 5 percent for utilities, 4 percent for equipment, 2 percent for supplies, and the remainder for transportation. If the area of each sector of the graph is proportional to the percent of the budget it represents, how many degrees of the circle are used to represent transportation?
Choose the correct choice from the following
A) 18° B) 36° C) 54° D) 72° E) 90°

Solution: The percent of the budget for transportation is 100 - (55+9+5+4+2)= 
100 - (55+9+5+4+2) = 25
25%   100% of the circle is 360 degrees.   Then (25%/100%)*360 = 90 degrees   The answer is 90°.  (25 /100 )*360= 
  (25 /100 )*360 = 90
90 degrees   The answer is 90°.
Answer: E
In a certain store, the profit is 320% of the cost. If the cost increases by 25% but the selling price remains constant, approximately what percentage of the selling price is the profit? Choices.
A) 23%	B) 56%	C) 70%	D) 35%	E) 20%

Solution: C   C.P. = Rs. 100. Then, profit = Rs. 320, S.P. = Rs. 420   New C.P. = 125% of Rs. 100 = Rs. 125.   New S.P. = Rs. 420   Profit = 420 - 125 = Rs. 295   Required percentage = 295/420 * 100 = 1475/21 = 70%
Answer: C
The digits of a two-digit number differ by six. Find the difference of the number and the number formed by reversing its digits?	Choose the correct answer:
A) 54
B) 45
C) 87
D) 78
E) 95

Solution: let the tens digit be x and ones digit be y   x-y =6   10x+y - (10y+x) = 9x-9y = 9 (x-y) = 9*6= 
9*6 = 54
54   54NSWER:54
Answer: A
A 12% stock yielding 10% is quoted at:  Choices: A) Rs. 83.33 B) Rs. 110 C) Rs. 112 D) Rs. 120 E) Rs. 140

Solution: Income of Rs 10 on investment of Rs 100   Income of Rs 12 on investment of ?   = (12*100)/10= 
(12*100)/10 = 120
120   ANSWER:Rs. 120
Answer: D
A fort had provision of food for 150 men for 45 days. After 10 days, 25 men left the fort. The number of days for which the remaining food will last, is:	Pick:
A) 34 B) 387 C) 42 D) 28 E) 71

Solution: Explanation:   After 10 days : 150 men had food for 35 days.   Suppose 125 men had food for x days.   Now, Less men, More days (Indirect Proportion)   {\color{Blue} \therefore } 125 : 150 :: 35 : x {\color{Blue} \Rightarrow } 125 x x = 150 x 35   {\color{Blue} \Rightarrow x=\frac{150\times 35}{125}}   {\color{Blue} \Rightarrow } x = 42.   Answer: 42) 42
Answer: C
The total car population in a Mumbai is 2,94,00 out of which 1,50,00 are made by Honda. Out of every 100 Honda cars, 98 are red in color, but only 53% of the total car population is red. Find the % of non-Honda cars that are red	Choose the correct choice from the following options:
A) 4%
B) 4.65%
C) 6.125%
D) 7.24%
E) 7.45%

Solution: Total Car.29.10 i.e., Honda +non Honda = 29400 Given: Whim. tractor .150W   Now,5346 of 2..00 = Honda +Red Non-Honda 29400 .:4 =15582 Thus...El Mall... 1.0 Now Honda 15582 flow, Non-. Honda =15582 - 15.582-14700=8B2 96 non-Honda =1=1.100 = 6.125%   6.125%
Answer: C
A reduction of 20% in the price of salt enables a lady to obtain 25 kgs more for Rs.100, find the original price per kg?	Choose the correct choice.
A) 6	B) 1	C) 5	D) 4	E) 7

Solution: 100*(20/100)= 
100*(20/100) = 20
20 --- 25   ? --- 1=> Rs.0.8   100 --- 80   ? --- 0.8 => Rs.1   Answer: 1
Answer: B
At a loading dock, each worker on the night crew loaded 3/4 as many boxes as each worker on the day crew. If the night crew has 2/3 as many workers as the day crew, what fraction of all the boxes loaded by the two crews did the day crew load?  Choose the correct choice from the following answers
A) 1/2
B) 2/3
C) 3/5
D) 4/5
E) 5/8

Solution: Let x be the number of workers on the day crew.   Let y be the number of boxes loaded by each member of the day crew.   Then the number of boxes loaded by the day crew is xy.   The number of boxes loaded by the night crew is (2x/3)(3y/4) = xy/2   The total number of boxes is xy + xy/2 = 3xy/2   The fraction loaded by the day crew is xy / (3xy/2) = 2/3   The answer is 2/3.
Answer: B
The cost to rent a small bus for a trip is x dollars, which is to be shared equally among the people taking the trip. If 10 people take the trip rather than 14, how many more dollars, in terms of x, will it cost per person?  Answers:
A) x/6  B) x/16  C) x/40  D) 3x/40  E) 3x/80

Solution: Choose x as a multiple of 16, I chose 64:   So for 10 people, that's 6.4 each and for 14 people it's 4 USD each... Pick one of the options that gives you 6.4 - 4 = 2.4... The answer is 3x/40.
Answer: D
If each side of a square is increased by 25%, find the percentage change in its area?
Choose one:
A) 56.29%  B) 56.25%  C) 56.95%  D) 53.25%  E) 36.25%

Solution: let each side of the square be a , then area = a x a   New side = 125a / 100 = 5a / 4   New area =(5a x 5a) / (4 x 4) = (25a²/16)   increased area== (25a²/16) - a²   Increase %= [(9a²/16 ) x (1/a² ) x 100]% = 56.25%   Answer: 56.25%
Answer: B
In how many ways can the letters of wordTREATMENTbe arranged such that all the Consonants always appear together?  Pick one: A) 9! B) 4!*6! C) 5!*5! D) 5!*4!*2! E) 6!*4!

Solution: Let the arrangment be: _ _ _ _ _ _ _ _ _ _ (9 letters, 3 vowels e, a, e and 6 consonant t, r, t, m, n, t)   For all consonants together, consider them as 1 group {t, r, t, m, n, t} E A E --> this gives us 4! arrangements with {} group considered as 1 . Now {} group can in itself be arranged in 6! ways   Thus total arrangements with all consonants together = 4!*6! --> 4!*6! is the correct answer.
Answer: B
In right triangle ABC, AC is the hypotenuse. If AC is 40 and AB + BC = 60, what is the area of the triangle ABC?  Choose the correct choice.
A) 225  B) 450  C) 25√2  D) 500  E) 200√2

Solution: Square AB + BC = 60:   (AB)^2 + 2*AB*BC + (BC)^2 = 3600. Since (AC)^2 = (AB)^2 + (BC)^2 = 40^2 = 1600, then (AB)^2 + 2*AB*BC + (BC)^2 = 1600 + 2*AB*BC = 3600.   1600 + 2*AB*BC = 3600.   AB*BC = 1000.   The area = 1/2*AB*BC = 500.   Answer: 500.
Answer: D
Ramu bought an old car for Rs. 42000. He spent Rs. 13000 on repairs and sold it for Rs. 64900. What is his profit percent? Pick:  A) 19%  B) 11%  C) 18%  D) 218%  E) 14%

Solution: Total CP = Rs. 42000 + Rs. 13000   = Rs. 55000 and SP = Rs. 64900   Profit(%) = (64900 - 55000)/55000 * 100= 
(64900 - 55000)/55000 * 100 = 18
18%   Answer:18%
Answer: C
The apartment on King-Williams street is an asset that its value is tramping about. From the year 1973 to 1983 it's value decreased by 16% and from 1983 to 1993 it's value increased by 16%. What is the value of the asset in 1993 if in 1973 it was worth $50,000?  Choose the correct answer:
A) $38,796. B) $48,720. C) $38,976. D) $39,679. E) $36,796.

Solution: 50,000 *1.16*.84=48,720   Answer $48,720.
Answer: B
Two boys starts from the same place walking at the rate of
5 kmph and 5.5 kmph respectively in the same direction. What time will they take to be 8.5 km apart?  Choose the most appropriate option:
A) 17hr
B) 14 hr
C) 12 hr
D) 20 hr
E) 22 hr

Solution: relative speed = 5.5 - 5= 
5.5 - 5 = 0.5
0.5 kmph   distance= 8.5 km   time = distance/speed = 8.5/0.5= 
8.5/0.5 = 17
17 hr   17hrNSWER 17hr
Answer: A
A train 400 m long can cross an electric pole in 20 sec and then find the speed of the train?  Choose the correct choice:
A) 72	B) 67	C) 28	D) 26	E) 27

Solution: Length = Speed * time   Speed = L/T   S = 400/20= 
400/20 = 20
20 M/Sec   Speed= 20*18/5 (To convert M/Sec in to Kmph multiply by 18/5)   Speed = 72 Kmph   72nswer:72
Answer: A
Rounded to three decimal places, 1.005^4 =	Select.
A) 1.004  B) 1.006  C) 1.008  D) 1.012  E) 1.02

Solution: As compared to 1, 0.005 is a very small quantity. Thus, we can write (1+0.005)^4 is nearly equal to (1+4*0.005) = 1.020.As the question asks for approximation to three decimal places, the further terms will anyways not come into picture.   1.02.
Answer: E
A solution of X pounds of water and sugar is boiled until 20% of the water content evaporates. Originally r% of sugar was present in the solution. After evaporation, what percentage of the solution is sugar? Pick one
A) 100r/(1-r)	B) 80r/(1-r)	C) 75r/(1-r)	D) 100r/(80-0.2r)	E) 100r/(80+0.2r)

Solution: We'll go for the ALTERNATIVE approach since there are variables in all the answers (which means that any number could work). Since the question deals with percents, the easiest number to use is X = 100. Now let's say that r = 10. Before the evaporation we had 10 pound of sugar and 90 pounds of water. Since only water evaporated, after the evaporation the 10 pounds of sugar remained the same, but the water reduced by 20% of 90 (18 pounds), so we have only 72 pounds of water. 10 out of 82 is the fraction of sugar, so if we multiply it by 100 we get the percents. The correct answer is 100r/(80+0.2r): 100r/(80+0.2r) >>> 100x10 / 82
Answer: E
In the coordinate plane a slope of the line K is 3/2 times the y-intercept of the line K. What is the x-intercept of the line K?  Pick
A) -2 B) 2/3 C) -2/3 D) 1/4 E) 3/2

Solution: As Y=3/2mx+m, from 0=3/2mx+m we get x=2/3. Hence, the correct answer choice is 2/3.
Answer: B
Rahul went to a shop and bought things worth Rs. 30, out of which 30 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?
Answers:
A) 25.7
B) 24.7
C) 23.7
D) 22.7
E) 26.7

Solution: Total cost of the items he purchased = Rs.30   Given that out of this Rs.30, 30 Paise is given as tax   => Total tax incurred = 30 Paise = Rs.30/100   Let the cost of the tax free items = x   Given that tax rate = 6%   ∴ (30−30/100−x)6/100 = 30/100   ⇒ 6(30 −0.3 −x) = 30   ⇒ (30− 0.3 − x) = 5   ⇒ x = 30 − 0.3 − 5 = 24.7   24.7)
Answer: B
Today is Wednesday. After 36 days, it will be :	Choose the correct choice from the following:
A) Thursday	B) Saturday	C) Monday	D) Sunday	E) Wednesday

Solution: Each day of the week is repeated after 7 days.   So, after 35 days, it will be Wednesday.   Thursdayfter 36 days, it will be Thursday   Thursdaynswer is Thursday
Answer: A
n May Mrs Lee's earnings were 60 percent of the Lee family's total income. In June Mrs Lee earned 20 percent more than in May. If the rest of the family's income was the same both months, then, in June, Mrs Lee's earnings were approximately what percent of the Lee family's total income ?  Choose the correct answer:
A) 64%
B) 68%
C) 72%
D) 76%
E) 80%

Solution: Let total earning be 100$ then Mrs. Lee earns 60$.   If this increased by 20% in June then Mrs.Lee new income is 72$, and the family income is 112$.   % of mrs lee = 72*100/112 = ~64%   64%NSWER:64%
Answer: A
A man can row a boat at 20 kmph in still water. If the speed of the stream is 6 kmph, what is the time taken to row a distance of 60 km downstream? Select the correct option.
A) 30/20 hours	B) 39/28 hours	C) 30/32 hours	D) 30/13 hours	E) 32/34 hours

Solution: Speed downstream = 20 + 6= 
20 + 6 = 26
26 kmph.   Time required to cover 60 km downstream= d/s = 60/26 = 30/13 hours.   Answer:30/13 hours
Answer: D
A man rows down stream 32km and 14 km upstream. if he takes 6 hrs to covereach distance, then the velocity of the current is  Choose the correct choice from the following:
A) 1/2kmph
B) 1.5kmph
C) 1 3/2kmph
D) 2kmph
E) 4kmph

Solution: Rate down stream=(32/6)kmph;   Rate up stream=(14/6)kmph;   velocity of the current =1/2(32/6-14/6)kmph   =1.5kmph   Answer(1.5kmph)
Answer: B
A large box contains 20 small boxes and each small box contains 25 chocolate bars. How many chocolate bars are in the large box?
Choices.
A) 250	B) 500	C) 450	D) 550	E) 650

Solution: The number of chocolate bars is equal to   20 * 25= 
20 * 25 = 500
500   correct answer 500
Answer: B
The average of 9 numbers is 8 and the average of 7 other numbers is 6. What is the average of all 16 numbers?
Choose the correct choice from the following
A) 9  B) 8  C) 7 1⁄8  D) 7 1⁄2  E) 7 1⁄4

Solution: The average of 9 numbers is 8....   The sum of those numbers is (9)(8) = 72.   The average of 7 other numbers is 6....   The sum of those numbers is (7)(6) = 42   The sum of ALL 16 numbers is 72+42= 
72+42 = 114
114. The average of those numbers is 114/16= 57/8 = 7 1/8.   Final Answer:   [Reveal]Spoiler:   7 1⁄8
Answer: C
A trader sold an article on a certain price with 40% profit. If he sold double of previous selling price then find its profit % Choose one:
A) 140% B) 180% C) 120% D) 100% E) 150%

Solution: let cost price = 100%   selling price = 140%   new s.p. = 280%   p% = 280-100= 
280-100 = 180
180%   Answer is 180%
Answer: B
length =9 feet
breadth =37−9/2=14 feet
Area =9×14=126 square feet	Choose the correct answer:
A) 126 sq. ft
B) 156 sq. ft.
C) 216 sq. ft.
D) 145 sq. ft.
E) 122 sq. ft.

Solution: A   126 sq. ft.   length =9 feet   breadth =37−9/2=14 feet   126 sq. ftrea =9×14=126 square feet
Answer: A
A certain shade of gray paint is obtained by mixing 3 parts of white paint with 5 parts of black paint. If 2 gallons of the mixture is needed and the individual colors can be purchased only in one gallon or half gallon cans, what is the least amount Q of paint, in gallons, that must be purchased in order to measure out the portions needed for the mixture?
Options:
A) 2
B) 2 1/2
C) 3
D) 3 1/2
E) 4

Solution: Given W:B = 3:5   That means say 3 gallons of white paint + 5 gallons of black paint = 8 gallons of paint mixture.   But we want least amount of whiteblack paints for minimum of 2 gallons of mixture, so lets reduce keeping same ratio,   1.5 : 2.5 gives  1.5 + 2.5= 
 1.5 + 2.5 = 4
4 gallons of mixture, but we want only 2 gallons, lets further reduce   0.75: 1.25 gives  1+1.5= 
 1+1.5 = 2.5
2.5 gallons of mixture. This looks ok, but lets reduce further just to be sure   0.375: 0.625 gives  0.5 + 1= 
 0.5 + 1 = 1.5
1.5 gallons of mixture, thats less than 2 gallons of mixture Q, so not acceptable.   So correct ans is 2.5 gallons. 2 1/2
Answer: B
If log 27 = 1.497, then the value of log 9 is: Answers:  A) 0.934  B) 0.945  C) 0.954  D) 0.958  E) 0.998

Solution: log 27 = 1.497   log (3cube ) = 1.497   3 log 3 = 1.497   log 3 = 0.499   log 9 = log(3square ) = 2 log 3 = (2 x 0.499) = 0.998.   Answer: Option 0.998
Answer: E
A man rides at the rate of 50km/hr. But stops 30minutes to change horses at the end of every 25th kilometer. How long will he take to go a distance of 250 kilometers?  Choose the correct choice from the following:
A) 5hr
B) 6hr 30min
C) 8hr 10min
D) 7hr 20min
E) 8hr

Solution: speed of man = 50km/hr   number of rests = (250/25)-1= 
(250/25)-1 = 9
9   time taken for the man= (250/50)+9*(20/60)= 
(250/50)+9*(20/60) = 8
8 hr   Answer is 8hr
Answer: E
The average of marks obtained by 120candidates was 35. If the avg of marks of passed candidates was 39 and that of failed candidates was 39 and that of failed candidates was 15, the no.of candidates who passed the examination is?
Pick one:	A) 80	B) 90	C) 100	D) 120	E) 130

Solution: Let the number of candidate who passed = y   Then, 39y + 15(120 - y) =120 x 35   ⇒ 24y= 4200 -1800= 
4200 -1800 = 2_400
2400 / 24= 
2400 / 24 = 100
100   100
Answer: C
Peter invests a sum of money and gets back an amount of $ 815 in 3 years . David invests an equal amount of money and gets an amount of $870 in 4 years. If both amounts were invested at the same rate (simple interest ) What was the sum of money invested ?	Options:
A) 670  B) 650  C) 698  D) 744  E) 700

Solution: Since both Peter and David invested the same amount of money at the same rate, they would earn same interest per year.   David invested for one year more than Peter and hence he got interest amount for one more year.   Interest earned per year = Amount received by David - Amount received by Peter = 870 - 815= 
870 - 815 = 55
55   Interest earned for 3 years= 55*3= 
55*3 = 165
165   Amount invested= 815 - 165= 
815 - 165 = 650
650   Answer: 650
Answer: B
A metallic sheet is of rectangular shape with dimensions 48 m x 36 m. From each of its corners, a square is cut off so as to make an open box. If the length of the square is 8 m, the volume of the box (in m cube) is:
Choose the correct choice.
A) 4120 m cube  B) 4140 m cube  C) 5140 m cube  D) 5120 m cube  E) None of these

Solution: Explanation:   l = (48 - 16)= 
(48 - 16) = 32
32 m, [because  8+8= 
 8+8 = 16
16]   b= (36 -16)= 
(36 -16) = 20
20 m,   h= 8 m.   Volume of the box = (32 x 20 x 8) m cube   = 5120 m cube.   Option 5120 m cube
Answer: D
The average of first five multiples of 5 is Choose the correct choice:
A) 3	B) 6	C) 9	D) 12	E) 15

Solution: Solution   Average	= 5(1+2+3+4+5) / 5   = 75 / 5.= 
75 / 5. = 15
15   Answer 15
Answer: E
At what rate of CI per year will a sum of Rs. 1200 become Rs. 1348.32 in 2 years?	Choose the correct choice from the following choices.
A) 3%
B) 6%
C) 7%
D) 8%
E) 9%

Solution: Let the rate be R% p.a.   Then, 1200 x 1 +	R 2	= 1348.32   100   1 +	R 2	=	134832	=	11236   100	120000	10000   1 +	R 2	= 106 2   100	100   1 +	R	=	106   100	100   R = 6%   6%
Answer: B
40 percent of the ducks included in a certain side effects study were male. If some of the ducks had side effects during the study and 10 percent of the ducks who had side effects were male, what was the ratio of the side effect rate for the male ducks to the side effect rate for the female ducks?
Choose the correct choice from the following choices:  A) 1/4  B) 9/14  C) 2/3  D) 7/8  E) 1/6

Solution: Say total male = 40   Total female =60   Required ratio =( .1/40)/ (.9/60) = 1/6 1/6 is the answer
Answer: E
John had a stock of 900 books in his bookshop. He sold 75 on Monday, 50 on Tuesday, 64 on Wednesday, 78 on Thursday and 135 on Friday. What percentage of the books were not sold? Pick one:	A) 50.4%	B) 23.8%	C) 66.5%	D) 34.9%	E) 55.3%

Solution: Let N be the total number of books sold. Hence   N = 75 + 50 + 64 + 78 + 135= 
75 + 50 + 64 + 78 + 135 = 402
402   Let M be the books NOT sold   M= 900 - N = 900 - 402= 
900 - 402 = 498
498   Percentage   Books not sold / total number of books= 498/900 = 0.553 = 55.3%   correct answer 55.3%
Answer: E
If (x - 1)(x - 2) = x^2 + x, what is a possible value of x?  Select:
A) 1/2
B) 2
C) -1
D) 1
E) -2

Solution: Rearranging the given expression:   (x - 1)(x - 2) = x^2 + x   i.e. x^2 - 3x + 2 = x^2 + x   i.e. -4x = -2   i.e. x = -4/-2= 
-4/-2 = 2
2   Answer: Option 2   Had it been a difficult expression to solve further, then we could have used options to check which on esatisfies the expression after solving it as further as possible
Answer: B
A pump can fill a tank with water in 2 hours. Because of a leak, it took 2 1/6 hours to fill the tank. The leak can drain all the water of the tank in?
Choose the correct choice:
A) 17 hr
B) 19 hr
C) 10 hr
D) 24 hr
E) 26 hr

Solution: Work done by the tank in 1 hour   = (1/2 - 2 1/6)   = 1/26 Leak will empty the tank in 26 hrs.   Answer:26 hr
Answer: E
6, 11, 21, 36, 56, 81, 111, 146, 186, ?  Answers:  A) 511  B) 711  C) 811  D) 231  E) 911

Solution: The pattern is + 5, + 10, + 15, + 20, + 25, + 30, + 35, + 40, + 45, + 50,....   Answer : 231.
Answer: D
How many ways are there for 4 males and 3 females to sit (around a circular table) if no male should sit next to a male (and no female next to female) and Mary wants to sit with her back on the wall?
Pick:	A) 48	B) 12	C) 72	D) 100	E) 720

Solution: So Mary has her own chair, fixed position. Other two females around the table can sit in 2 ways: the first to the left of Mary and the second to the right or vise-versa. Now, if 4 males will sit between them then no two female or two male will sit next to each other (female-male-female-male-female-male). But these males on their spots can also sit in different ways, namely in 4! different ways, so total 2*4!=48.   48nswer 48.
Answer: A
A completes a work in 12 days and B complete the same work in 18 days. If both of them work together, then the number of days required to complete the work will be  Choose the correct choice from the following answers.
A) 8 days	B) 9 days	C) 10 days	D) 12 days	E) 7.2 days

Solution: If A can complete a work in x days and B can complete the same work in y days, then, both   of them together can complete the work in x y/ x+ y days   Therefore, here, the required number of days = 12 × 18/ 30 = 7.2 days.   7.2 days
Answer: E
On Saturday morning, Malachi will begin a camping vacation and he will return home at the end of the first day on which it rains. If on the first three days of the vacation the probability of rain on each day is 0.4, what is the probability that Malachi will return home at the end of the day on the following Monday? Pick one:
A) 0.008  B) 0.144  C) 0.488  D) 0.512  E) 0.64

Solution: Re-phrasing the question:   What is the probability of: Saturday: No rain, Sunday: No rain, Monday: Rain   Probablity of rain = 0.4   Therefore, probability of no rain = 0.6   0.6*0.6*0.4= 
0.6*0.6*0.4 = 0.144
0.144   Hence 0.144
Answer: B
If "YELLOW" is given a color code of 92, what is the difference between "BROWN" and "RED"?	Choices
A) 40  B) 52  C) 119  D) 45  E) 32

Solution: Case – Codes : A - 1, B - 2, C - 3, 45 - 4, E - 5, F - 6, G - 7, H - 8, I - 9, J - 10, K - 11, L - 12, M - 13, N - 14, O - 15, P - 16, Q - 17, R - 18, S - 19, T - 20, U - 21, V - 22, W - 23, X - 24, Y - 25, Z - 26   BROWN- 72   RE45- 27   Answer: 45
Answer: D
What is the sum of the integers from -170 to 171, inclusive?  Choose the correct choice from the following choices:
A) 181
B) 171
C) 191
D) 201
E) 202

Solution: in an arithmetic progression,   the nth term is given by tn=a+(n-1)d   here tn=171, a=-170, d=1   hence, 171=-170+(n-1)   or n=342   Sum of n terms can be calculated by sn=n/2(a+l)   a=first term, l=last term, n=no. of terms   sn=342*(-170+171)/2   sn=342*1/2= 
342*1/2 = 171
171   Answer : 171
Answer: B
The interior surfaces of a children's room (including ceiling, floor and 4 faces) are to be painted by 6 different colors. In how many ways can be this be done?  Choose the correct answer:
A) A.720	B) B.256	C) C.1	D) D.12	E) E.36

Solution: If I have to paint 6 faces with 6 different colour...   First face can have 6c1 options,   2nd would have 5c1, and subsequent ones would have 4c1, 3c1, 2c1 and 1 options respectively.   Total options = 6c1 X 5c1 x 4c1 x 3c1 x 2c1 x 1 = 720 distinct ways   Correct answer - A.720
Answer: A
If the probability that the Detroit Lions win the Super Bowl is 1/20 and the probability that the Detroit Tigers win the World Series is 1/6, what is the probability that either the Bears win the Super Bowl or the Cub win the World Series (but not both)?  Pick one:
A) 1/2	B) 2/7	C) 1/3	D) 1/4	E) 1/5

Solution: 19/20*1/6 + 1/20*5/6 = 24/120 = 1/5   The answer is 1/5.
Answer: E
What is the difference between the biggest and the smallest fraction among 2/3 , 3/4 , 4/5 and 5/6?
Select the correct option:
A) 1/6  B) 1/12  C) 1/20  D) 1/30  E) None of these

Solution: Explanation:   Converting each of the given fractions into decimal form, we get   Since 0.833>0.8>0.75>0.66   So,   Required Difference = 5/6-2/3=1/6   1/6NSWER IS 1/6
Answer: A
The ratio of the length and the breadth of a rectangle is 4 : 3 and the area of the rectangle is 6912 sq cm. Find the ratio of the breadth and the area of the rectangle?	Choose one
A) 1:96 B) 1:98 C) 1:26 D) 1:97 E) 1:56

Solution: Let the length and the breadth of the rectangle be 4x cm and 3x respectively.   (4x)(3x) = 6912   12x2 = 6912   x2 = 576 = 4 * 144 = 22 * 122 (x > 0)   => x = 2 * 12= 
2 * 12 = 24
24   Ratio of the breadth and the areas= 3x : 12x2 = 1 : 4x = 1: 96.   1:96nswer:1:96
Answer: A
The volume of a rectangular swimming pool is 840 cubic meters and water is flowing into the swimming pool. If the surface level of the water is rising at the rate of 0.5 meters per minute, what is the rate W, in cubic meters per minutes, at which the water is flowing into the swimming pool?
Select.
A) 0.125	B) 0.25	C) 0.5	D) 0.75	E) Not enough information to determine the rate

Solution: The correct answer is E.   There are not enough info to answer the question.   A 840 cubic meters rectangle is built from: height*length*width.   From the question we know the volume of the pool and the filling rate.   A pool can have a height of 10*width8.4*length10 and have a volume of 840 cubic meters, and it can have a height of 1 meter, width of 100 meters and length of 8.4. In both cases the pool will fill up in a different rate = Not enough information to determine the rate
Answer: E