MU-NLPC/Calc-aqua_rat huggingface dataset:
In a throw of a coin probability of getting a head.  Choose the correct option:
A) 1/3 B) 2/3 C) 1/4 D) 2/5 E) 1/2

Solution: S= {H,T}   1/2= {H}   probability = n(1/2)/n(S) = 1/2   correct option is 1/2
Answer: E
What will come in place of the x in the following Number series? 12, 38, 116, 350, 1052, x Select the correct option:	A) 2450	B) 2560	C) 3200	D) 3400	E) 3158

Solution: 12   12 × 3 + 2 = 38   38 × 3 + 2 = 116   116 × 3 + 2 = 350   350 × 3 + 2 = 1052   1052 × 3 + 2 = 3158   3158
Answer: E
Find the angle between the hour and the minute hand of a clock when the time is 3.25. Choose the correct choice
A) 47 ½ B) 49 ½ C) 55 ½ D) 57 ½ E) None

Solution: Solution   Angle traced by the hour hand in 12 hours	= 360°.   Angle traced by it in 3 hrs 25 min	= 41 / 12 hrs   = (360 / 12 x 41 / 12)°   = 102 ½°.   Angle traced by minute hand in 60 min	= 360°.   Angle traced by it in 25 min.	= (360/ 60 x 25)°   = 150°   Required angle	= (150- 102 ½°)   = 47 ½°.   47 ½nswer 47 ½
Answer: A
A number when divided by 221 gives a remainder 43, what remainder will be obtained by dividing the same number 17?  Pick:
A) 11	B) 10	C) 9	D) 8	E) 7

Solution: 221 + 43= 
221 + 43 = 264
264/17= 9 (Remainder)   ANSWER:9
Answer: C
According to a 2010 census, males account for 51.27% of China's 1.34 billion people, while females made up 48.73% of the total. Which answer is closest to the ratio of male to female?
Choose the correct choice from the following options
A) 1.1 to 1	B) 2 to 1	C) 8 to 1	D) 0.5 to 1	E) 0.8 to 1

Solution: The ratio of A to B, where   A = the percent of males, and   B = the percent of females.   1.1 to 1 = 51.27   B = 48.73   1.1 to 1:B = 51.27:48.73 = 51.27/48.73:1   1.1 to 1:B nearly = 1.1:1   1.1 to 1nswer is 1.1 to 1
Answer: A
A salt manufacturing company produced a total of 2000 tonnes of salt in January of a particular year. Starting from February its production increased by 100 tonnes every month over the previous months until the end of the year. Find its ave66rage daily production for that year?
Choose the most appropriate option.
A) 80  B) 85  C) 83  D) 95  E) 00

Solution: Total production of salt by the company in that year = 2000 + 2100 + 2200 + .... + 3100 = 30600.   Average monthly production of salt for that year = 30600/365 â‰ˆ 84   ANSWER:83
Answer: C
Yesterday's closing prices of 1,980 different stocks listed on a certain stock exchange were all different from today's closing prices. The number of stocks that closed at a higher price today than yesterday was 20 percent greater than the number that closed at a lower price. How many of the stocks closed at a higher price today than yesterday?
Select the correct option:
A) 484 B) 1080 C) 1,100 D) 1,320 E) 1,694

Solution: Lets consider the below -   The number of stocks that closed at a higher price = H   The number of stocks that closed at a lower price = L   We understand from first statement -> H+L = 1980 ----(1)   We understand from second statement -> H = (120/100)L => H = 1.2L ----(2)   Solve eq (1)(2) to get H = 1080.   1080 is my answer.
Answer: B
On a weekend, 3 friends went skiing and evenly split the cost of their cabin. If the amount paid by each person was an integer, which of the following could not have been the cost of the cabin?
Select the correct option: A) $110 B) $150 C) $225 D) $54 E) $75

Solution: Each of the seven persons evenly splitting the cost is an integer amount, therefore check the divisibility by 3 for all answer choices.   110/3 = 36.67   150/3= 
150/3 = 50
50   225/3= 
225/3 = 75
75   54/3= 
54/3 = 18
18   75/3= 
75/3 = 25
25   A is not an integer amount.   $110nswer:$110
Answer: A
P and Q started a business investing Rs. 85,000 and Rs. 20,000 respectively. In what ratio the profit earned after 2 years be divided between P and Q respectively?	Choose the correct choice from the following options.
A) 17:6
B) 17:0
C) 17:4
D) 17:2
E) 17:3

Solution: P:Q = 85000 : 20000   = 17:4.   Answer: 17:4
Answer: C
For all numbers m and n, the operation @ is defined by m@n = m^2 - mn. If xy ≠ 0, then which of the following can be equal to zero?
I. x@y
II. (xy)@y
III. x@(x + y)
Choose the correct answer:
A) II
B) I and II
C) I and III
D) II and III
E) All of the above

Solution: m@n = m^2 - mn=m(m-n).... so m@n will be zero if m=n or m=0.. but a cannot be equal to 0.. as per Q, x and y can take any int value except 0...   now lets look at the choices..   when x=y, it will be 0... so ok...   when we put xy=y, it is possible when x=1 and y any integer... so ok again   when we put x=x+y.... only possibility when y=0 and it is given x and y cannot be 0....so not possible   only l and ll possible   answer:I and II
Answer: B
Two same glasses are respectively 1/4th 1/5th full of milk. They are then filled with water and the contents mixed in a tumbler. The ratio of milk and water in the tumbler is?	Choose the correct choice from the following answers: A) 9:36 B) 9:31 C) 9:35 D) 9:37 E) 9:32

Solution: 1/4 : 3/4 = (1:3)5 = 5:15   1/5 : 4/5 = (1:4)4 = 4:16   ------   9:31   Answer: 9:31
Answer: B
If Henry were to add 8 gallons of water to a tank that is already 3/4 full of water, the tank would be 7/8 full. How many gallons of water would the tank hold if it were full? Pick:
A) 25
B) 40
C) 64
D) 80
E) 96

Solution: 7/8x-3/4x=8galls   1/8*x=8gallons   x=64 gallons   Answer 64
Answer: C
a dealer buys 4 varieties of rice costing rs. 30,rs.40,rs.60 and rs.80 per kg in the ratio 4:5:4:3 and mixes all the four varieties and sells at 30% profit. What is the selling price per kg of rice?	Options
A) 62
B) 65
C) 66
D) 67
E) 69

Solution: CP = 30*4+40*5+60*4+80*3= 
30*4+40*5+60*4+80*3 = 800
800   SP= 1.3*800= 
1.3*800 = 1_040
1040   Total no.of kgs=4+5+4+3= 
4+5+4+3 = 16
16   SP per kg=1040/16= 
1040/16 = 65
65   ANSWER:65
Answer: B
A primitive village follows a strange custom. They have babies only to have a boy. Whenever a boy is born in a family, they stop having babies and whenever a girl is born, they have a baby again and again till a boy is born.
The probability of having a boy is same as the probability of having a girl. What will be the proportion of boys to girls in the village after some time?  Options:	A) 1:1	B) 1:2	C) 1:3	D) 1:4	E) 1:5

Solution: A   1:1 (approx)   We know that the probability of having a boy or having a girl is same and thus, half of the couples will stop after having a boy child. Half of the others will have a girl and will have a baby again. Out of those half of the couples, half will have a boy and will stop and half will have a girl again. This will keep on going like this.   Now, if there are X number of couples, there will be X boys.   1/2 have a boy and stop: 0 girls   1/4 have a girl, then a boy: X/4 girls   1/8 have 2 girls, then a boy: 2*X/8 girls   1/16 have 3 girls, then a boy: 3*X/16 girls   1/32 have 4 girls, then a boy: 4*X/32 girls   …   Total: X boys and   1X 2X 3X 4X   – + – + – + — +… = ~X
Answer: A
(3x + 2) (2x - 1) = ax^2 + kx + n . What is the value of a - n + k ? Choose the correct answer:
A) 5	B) 8	C) 9	D) 10	E) 11

Solution: Expanding we have 6x^2 - 3x + 4x -2   6x^2 + x - 2   Taking coefficients, a = 6, k= 1, n = -2   Therefore a - n + k = 6 - (-2) +1 = 8 + 1= 
8 + 1 = 9
9   The answer is 9.
Answer: C
On the first of the year, James invested x dollars at Proudstar bank in an account that yields 1.5% in interest every quarter year. At the end of the year, during which he made no additional deposits or withdrawals, he had y dollars in the account. If James had invested the same amount in an account which pays interest on a yearly basis, what must the interest rate be for James to have y dollars at the end of the year?  Choose the correct answer
A) 2.04%
B) 6.12%
C) 8%
D) 8.25%
E) 10%

Solution: If the interest were compounded annually instead of quarterly then in one year the interest would be 1.5*4= 
1.5*4 = 6
6%. Now, since the interest is compounded quarterly then there would be interest earned on interest (very small amount) thus the actual interest would be a little bit more than 6%.   Answer: 6.12%.
Answer: B
48.95-32.006=?
Pick one:	A) 16.089	B) 16.35	C) 16.89	D) 16.944	E) None of them

Solution: 48.950   - 32.006   ---------   16.944   Answer is 16.944
Answer: D
Joe bought a coffee maker for a 25% off the original price. If the coffee maker cost him $61.35, what is the original selling price of the coffee maker? Choose the correct choice from the following options
A) $76.69 B) $107.36 C) $83.45 D) $79.80 E) None of these.

Solution: Explanation:CP of Joe is 25% of the Original SP.:. Original SP = $61.35x100/75 = $81.80.Answer: Option None of these..
Answer: E
The length of a train and that of a platform are equal. If with a speed of 90 k/hr, the train crosses the platform in one minute, then the length of the train (in meters) is?
Choose one.
A) 227
B) 299
C) 276
D) 750
E) 211

Solution: Speed = [90 * 5/18] m/sec = 25 m/sec; Time = 1 min. = 60 sec.   Let the length of the train and that of the platform be x meters.   Then, 2x/60 = 25 è x = 25 * 60 / 2= 
25 * 60 / 2 = 750
750   Answer: 750
Answer: D
A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train? Choose the correct choice from the following answers
A) 120 metres  B) 180 metres  C) 324 metres  D) 150 metres  E) 180 metres

Solution: Speed=(60 x 5/18)/m/sec	=	50/3	m/sec.   Length of the train = (Speed x Time).   Length of the train =	50 x 9/3 m = 150 m.   ANSWER : OPTION 150 metres
Answer: D
On Saturday, the original price of a shirt was discounted by 20%. On Monday, the price of the shirt was marked up X percent so that the new price on Monday was 20% more than the original price before the discount. What is the value of X?	Choose the correct answer: A) 20% B) 30% C) 33 1⁄3% D) 40% E) 50%

Solution: Let the original price be 100   discounted Price = 80   New Price = 20 +100= 
20 +100 = 120
120   X=(40/80)*100   Ans:50%
Answer: E
At Company K, 15 percent of the employees are secretaries and 60 percent are salespeople. If there are 20 other employees of Company K, how many employees does Company K have? Select the correct option:  A) 80  B) 180  C) 190  D) 200  E) 400

Solution: Let the total number of employees in the company be x   % of secretaries = 15%   % of salespeople = 60%   % of of employees other than secretaries and salespeople = 100 - 75= 
100 - 75 = 25
25%   But this number is given as 20   so 25% of x= 20   x = 80   Therefore there a total of 80 employees in the company K   Correct answer - 80
Answer: A
What is the angle between the two hands of a clock when time is 8:30	Select:
A) 15 degree  B) 45 degree  C) 55 degree  D) 75 degree  E) 65 degree

Solution: Use the formula i.e   1/2(60h-11m) // h-hour and m-minute   1/2(60*8-11*30)   1/2(150)   75 degree   ANSWER:75 degree
Answer: D
During a sale, the price of a pair of shoes is marked down 12% from the regular price. After the sale ends, the price goes back to the original price. What is the percent of increase to the nearest percent from the sale price back to the regular price for the shoes?  Pick:
A) 9%  B) 10%  C) 11%  D) 14%  E) 90%

Solution: Assume the price = 100   Price during sale = 88   Price after sale = 100   Percent increase = 12/88*100 = 14% approx.   Correct Option: 14%
Answer: D
In how many ways can 5 boys be allotted four different wadrobe such that none of the wadrobe are empty and all the 5 boys are accommodated?	Select:
A) 300	B) 290	C) 240	D) 260	E) 280

Solution: 4 boys can be selected from 5 boys in 52404 ways = 5   4 boys can be arranged in 4 rooms in 4! ways   and since 1 boy has to share a room with one of the 4 boys, therefore total ways = 2! = 2   Hence total number of ways in which allocation can be done = 52404 * 4! * 2! = 5*2*4! =240   240
Answer: C
What is the remainder when 8^1 + 8^2 + 8^3 +...+ 8^9 is divided by 2?  Select the correct option
A) 4  B) 3  C) 2  D) None of the above  E) 5

Solution: Notice that in the brackets we have the sum of 9 even multiples of 2, which yields remainder of 0 upon division by 2.   Answer : None of the above
Answer: D
A can run a kilometer race in 4 1/2 min while B can run same race in 5 min. How many meters start can A give B in a kilometer race, so that the race mat end in a dead heat? Choose the correct answer
A) 150
B) 100
C) 110
D) 140
E) 130

Solution: B   A can give B (5 min - 4 1/2 min) = 30 sec start.   The distance covered by B in 5 min = 1000 m.   Distance covered in 30 sec = (1000 * 30)/300= 
(1000 * 30)/300 = 100
100 m.   A can give 100 100 m start.
Answer: B
Bruce purchased 8kg of grapes at the rate of 70 per kg and 8 kg of mangoes at the rate of 55 per kg. How much amount did he pay to the shopkeeper? Choose the correct answer:
A) A)1040
B) B)1050
C) C)1000
D) D)1065
E) E)1075

Solution: Cost of 8 kg grapes = 70 × 8 = 560.   Cost of 8 kg of mangoes = 55 × 8 = 440.   Total cost he has to pay = 560 + 440= 
560 + 440 = 1_000
1000   1000
Answer: C
A certain pair of used shoes can be repaired for $10.50 and will last for 1 year. A pair of the same kind of shoes can be purchased new for $30.00 and will last for 2 years. The average cost per year of the new shoes is what percent greater than the cost of repairing the used shoes?  Choose the correct choice from the following choices:  A) 42.85  B) 44  C) 48  D) 38  E) 40

Solution: 1) Cost of repairing = 10.5 ( for one year ), Therefore for 2 years it would be$ 21.   2) Cost of new pair which will last for 2 years is$ 30.00   Percentage change formula =( Final value - Initial value ) / ( Initial Value ) * 100. In this case the final value would be the price of new shoe initial value would be the cost of repairing the old shoe.   I.e (30 - 21 ) / ( 21 ) * 100 = 42.85 %.   42.85ns is 42.85
Answer: A
Sujit incurred a loss of 45% on selling an article for Rs.3630/-. What was the cost price of the article?  Pick
A) Rs.5725/-
B) Rs.6600/-
C) Rs.6250/-
D) Rs.6750/-
E) None of these

Solution: Explanation:   45% loss means SP of Rs.3630/- is 55% of CP   :. CP = 3630x100/55 = Rs.6600/-   Answer: Option Rs.6600/-
Answer: B
AF + CD = AAA, where AF and CD are two-digit numbers and AAA is a three digit number; A, F, C, and D are distinct positive integers. In the addition problem above, what is the value of C?  Choose the correct choice from the following options:
A) 1  B) 3  C) 7  D) 9  E) Cannot be determined

Solution: Since AF and CD are two-digit integers, their sum can give us only one three digit integer of a kind of AAA: 111.   So, A=1 and we have 1F+CD=111   Now, C can not be less than 9, because no two-digit integer with first digit 1 (1F<20) can be added to two-digit integer less than 90, so that to have the sum 111 (if CD<90, so if C<9, CD+1F<111).   Hence C=9.   Answer: 9.
Answer: D
A volume of 10996 l water is in a container of sphere. How many hemisphere of volume 4l each will be required to transfer all the water into the small hemispheres?  Select the correct option:	A) 2812	B) 8231	C) 2734	D) 4222	E) 2749

Solution: a volume of 4l can be kept in 1 hemisphere   therefore, a volume of 10996l can be kept in (10996/4) hemispheres   ans.2749   ANSW2749R:2749
Answer: E
In an effort to plan out expenses, the Roberts family is representing its annual budget as a circle graph. Each sector of the graph is proportional to the amount of the budget it represents. If “clothes and shoes” takes up 45° of the chart, how much of the Roberts’s $20,000 annual budget is dedicated to clothes and shoes?	Choose the correct choice from the following:
A) $2,500	B) $3,000	C) $4,500	D) $5,000	E) $5,400

Solution: Given for clothes and shoes” takes up 45° of the circular chart.   Then clothes and shoes = 45/360 * 20000.= 
45/360 * 20000. = 2_500
> 2500.   IMO option $2,500 is correct answer...
Answer: A
In what time will a train 300 meters long cross an electric pole, if its speed is 90 km/hr
Choose the correct choice from the following answers:
A) 5 seconds B) 12 seconds C) 3 seconds D) 2.5 seconds E) None of these

Solution: Explanation:   First convert speed into m/sec   Speed = 90*(5/18)= 
90*(5/18) = 25
25 m/sec   Time= Distance/speed   = 300/25= 
300/25 = 12
12 seconds   Answer: 12 seconds
Answer: B
A river 3m deep and 55 m wide is flowing at the rate of 1 kmph the amount of water that runs into the sea per minute is?	Choose the correct choice from the following choices.
A) 2338.9 B) 2748.9 C) 2148.9 D) 2745.9 E) 2718.9

Solution: Rate of water flow-1kmph--1000/60--16.66 m/min   depth of river--3m   width of river--55m   vol of water per min--16.66 *3*55---2748.9   Answer 2748.9
Answer: B
For a light that has an intensity of 60 candles at its source, the intensity in candles, S, of the light at a point d d feet from the source is given by the formula S=60k/d^2 60, where k is a constant. If the intensity of the light is 30 candles at a distance of 2 feet from the source, what is the intensity of the light at a distance of 10 feet from the source?
Choose the correct answer:
A) 3/10 candles	B) 1/2 candles	C) 1 1/3 candles	D) 6/5 candles	E) 3 candles

Solution: ANS = 3/10   S= 60k/d^2   At 2 feet   30 = 60k/4 so k = 2   At 10 feet   S = 60 *2/10^2 = 6/5   6/5 candles
Answer: D
A mixture of 70 litres of milk and water contains 10% water. How many litres of water should be added to the mixture so that the mixture contains 12 1/2% water?	Answers:
A) 17	B) 22	C) 58	D) 2	E) 69

Solution: Explanation:   Quantity of milk in the mixture = 90/100 (70) = 63 litres.   After adding water, milk would form 87 1/2% of the mixture.   Hence, if quantity of mixture after adding x liters of water, (87 1/2) / 100 x = 63 => x = 72   Hence 72 - 70= 
72 - 70 = 2
2 litres of water must be added   Answer:2
Answer: D
A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for Rs.7000. With the help of C, they completed the work in 3 days. How much is to be paid to C? Choose the correct choice from the following answers
A) s. 375  B) s. 400  C) s. 600  D) s. 800  E) s. 875

Solution: C's 1 day's work = 1/3 - (1/6 + 1/8) = 1/3 - 7/24 = 1/24   A's wages : B's wages : C's wages = 1/6 : 1/8 : 1/24 = 4: 3 : 1   C's share (for 3 days) = Rs.	(3 * 1/24 * 7000) =Rs.875   Answer = s. 875
Answer: E
Maxwell leaves his home and walks toward Brad's house. One hour later, Brad leaves his home and runs toward Maxwell's house. If the distance between their homes is 34 kilometers, Maxwell's walking speed is 4 km/h, and Brad's running speed is 6 km/h. What is the total time it takes Maxwell before he meets up with Brad?	Options:
A) 3
B) 4
C) 5
D) 6
E) 8

Solution: Total Distance = 34 kms   Maxwell Speed = 4 kms/hr   Maxwell travelled for 1hour before Brad started , therefore Maxwell traveled for 4 kms in 1 hour.   Time taken = Total Distance / Relative Speed   Total Distance after Brad started = 30 kms   Relative Speed (Opposite side) (As they are moving towards each other speed would be added ) = 6+ 4= 
6+ 4 = 10
10 kms/hr   Time taken to meet Brad after Brad Started= 30 / 10= 
30 / 10 = 3
3 hrs   Distance traveled by Maxwell= Maxwell's speed * time taken = 4 * 3= 
4 * 3 = 12
12+4= 
12+4 = 16
16 kms...   Therefore Total Time taken by Maxwell to meet Brad= Distance travelled by Maxwell / Maxwell's Speed = 16 /4= 
16 /4 = 4
4 hrs ... Answer 4
Answer: B
If (1+a)y=y, which of the following must be true?
Choose the correct choice from the following answers:
A) a=-1 or y=0 B) a=0 or y=0 C) a=1 or y=1 D) a=-1 or y=-1 E) a=0 or y=1

Solution: We have (1+a)y=y.   If a=0, y=y. True   If y=0, (1+a)*0=0 True   So, a=0 or y=0 will be the answer.
Answer: B
The area of a parallelogram is 128sq m and its altitude is twice the corresponding base. Then the length of the base is?  Choose the correct choice from the following answers
A) 8 B) 9 C) 6 D) 4 E) 2

Solution: 2x * x = 128 => x   = 8   8nswer: 8
Answer: A
A woman sold 200 oranges at $12.10, some at the rate of 3 for 35 cents and the rest at 4 for 85 cents. How many were sold at the first rate?  Pick:
A) 45 B) 21 C) 9 D) 15 E) 12

Solution: This can be solved like a classical mixture problem but numbers are awkward to deal with.   It's easier to just look at the answer choices. You know that a multiple of 3 oranges has to be sold at the first rate, and a multiple of 4 at the second rate. You simple subtract the answer choices for the first rate from 100 and check whether the remainder (i.e. the number of oranges sold at the second rate) is a multiple of 4.   200 - 45= 
200 - 45 = 155
155=> not a multiple of 4 so exclude     200 - 21= 
  200 - 21 = 179
179=> not a multiple of 4 so exclude     200 -9= 
  200 -9 = 191
191=> not a multiple of 4 so exclude     200 - 15= 
  200 - 15 = 185
185=> not a multiple of 4 so exclude     200 - 12= 
  200 - 12 = 188
188=> a multiple of 4 so keep   Hence, answer choice 12 is correct.   12
Answer: E
What will come in place of the x in the following Number series? 75, 225, x, 2025, 6075	Choose the correct choice:
A) 675	B) 752	C) 300	D) 400	E) 1200

Solution: (675)   25 x 3 = 75, 75 x 3 = 225 , 225 x 3 = 675, 1675 x 4 = 2025.
Answer: A
Graph G has a line of symmetry of x = –5/2. Graph G passes through the point (2, 2). What is the x-coordinate of another point that must have a y-coordinate of 2?  Choose the correct choice from the following answers: A) –8 B) –7 C) –5 D) –4 E) 2

Solution: Line of symmetry is X=-2.5; one point is (2,2)   Right side distance =2.5+2(distance from origin) = 4.5; therefore Left side distance should be same from line of symmetry =4.5;   therefore left side co-ordinate=4.5+ 2.5(distance from origin) =7; as the X coordinate is in 2nd quadrant hence -7   Therefore answer is –7
Answer: B
There are 30 socks in a bag. 30% is in blue color. What is the probability to take two blue socks?
Choose one:
A) 11/145
B) 12/145
C) 13/145
D) 14/145
E) 22/145

Solution: out of 30% 30 socks are blue => out of 30 9 socks are blue in color.   probability of selecting two blue socks out of 9 socks is 9C2.   so the required answer is :   (probability of selecting two blue socks out of 9 socks) /(Probability of selecting 2 socks out of 30 socks)   => (9C2) / (30C2)   => 36 / 435   => 12/145   ANSWER:12/145
Answer: B
A merchant sells an item at a 20% discount, but still makes a gross profit of 20 percent of the cost. What percent R of the cost would the gross profit on the item have been if it had been sold without the discount?  Options
A) 20%	B) 40%	C) 50%	D) 60%	E) 75%

Solution: Let the Market Price of the product is MP.   Let the Original Cost Price of the product is CP.   Selling Price (Discounted Price) = 100%of MP - 20%MP   = 80% of MP. ---------------- (1)   Profit made by selling at discounted price = 20% of 50%P -------------- (2)   Apply the formula:   Profit R= Selling Price - Original 50%ost Price   => 20% of 50%P = 80% of MP - 100% 50%P   => MP = 12050%P/80 = 3/2 (50%P)   Now if Product is sold without any discount, then,   Profit = Selling Price (without discount) - Original 50%ost Price   = Market Price - Original 50%ost Price   = MP - 50%P   = 3/2 50%P - 50%P   = 1/2 50%P   =50%of 50%P   Thus, Answer should be50%.
Answer: C
One train is traveling 54 kmph and other is at 10 meters a second. Ratio of the speed of the two trains is?	Choose one
A) 5:4
B) 3:2
C) 5:0
D) 5:4
E) 5:1

Solution: 54 * 5/18 = 10   15:10 => 3:2   Answer: 3:2
Answer: B
How many ways are there to award a gold, silver and bronze medal to 14 contending teams?  Choose the most appropriate option.
A) 14 x 13 x 12 B) 10!/(3!7!) C) 10!/3! D) 360 E) 300

Solution: we clearly know that there can be only one winning team which deserves the gold medal. we can do the selection in 14 ways   if gold medal is given to 1 of the teams then only possible 13 teams can be considered for silver medal. we can do selection in 13 ways   similarly if gold and silver medals are awarded then only remaining 12 teams can be considered for a bronze medal. we can do the selection in 12 ways   Total number of ways to select the 3 possible medal winners = 14 * 13 * 12   Correct answer - 14 x 13 x 12
Answer: A