MU-NLPC/Calc-aqua_rat huggingface dataset:
In a certain game, a player begins with a bag containing tiles numbered 1 through 9, each of which has an equal probability of being selected. The player draws one tile. If the tile is even, the player stops. If not, the player draws another tile without replacing the first. If this second tile is even, the player stops. If not, the player draws a third tile—without replacing either of the first two tiles—and then stops. What is the probability that at the conclusion of the game, the sum of the tiles that the player has drawn is odd?
Choose the correct choice from the following answers.
A) 5/18 B) 13/36 C) 3/8 D) 5/8 E) 23/36

Solution: player begins with containing tiles 1 to 10 and have equal probability of selecting means   Proabability of selecting one number =1/10. here 5 even numbers and 5 odd numbers are there.   Next , player draws one title , if number is even player stops or otherwise title is odd without replacement   player draws second title.   If second title is even , player stops or title is odd without replacement player draws third title.   in third title , without replacement of first and second title, player draws and stops it.   the sum of tilte probability is odd. here two conditions are possible.   1st condition is   1st title is odd+ 2nd title is even stops= probability of selecting one title is 1/10*5c1.   Here are we are not selecting 1st condition as even stops because sum of tile is odd.   Here 5 odd numbers are there we can select 1out of 5 odd numbers.   without replacement of fist we select second tilte is even. is 5/10*5c1/9c1.   here we are selecting one number out of remaining 9 numbers. so probability is 5/18.   we are selecting 1 even number out of 5.   2nd condition is 1stodd without replacement,2nd odd without replacement and 3rd one also odd to get odd as sum of title.   Then probability is 5/10*4/9*3/8=1/12.   Finally sum of probability of two conditions is 5/18+1/12   =5/8.   so option 5/8 is correct.
Answer: D
The probability is 1/2 that a certain coin turns up heads on any given toss. If the coin is tossed seven times, what is the probability that the coin turns up tails on at least one of the tosses? Choose the correct choice from the following choices:
A) 7/8
B) 15/16
C) 31/32
D) 63/64
E) 127/128

Solution: P(7 heads)= 1/2*1/2*1/2*1/2*1/2*1/2*1/2=1/128.   P(at least one tail)=1-1/128=127/128.   The answer is 127/128.
Answer: E
5 goats’s and 10 hens are brought for Rs.2500. If the average price of a hen be Rs.50. What is the average price of a goat.
Choose one:
A) 425	B) 375	C) 350	D) 400	E) 500

Solution: Explanation:   Average price of a hen = Rs.50   total price of 10 hens = 10*50 = Rs.500   But total price of 5 goats and 10 hens = Rs. 2500   Total price of 5 goats is = 2500 - 500= 
2500 - 500 = 2_000
2000   Average price of a goat= 2000/5   = Rs. 400   Answer: 400
Answer: D
The price of sugar is increased by 4%. By how much percent should a home maker reduce her consumption of sugar to have no extra expenditure? Choices:  A) (300/103) %  B) (400/104) %  C) (100/107)%  D) (7/100)%  E) (100/700)%

Solution: Old price = $100 (assume);   Old consumption = 1 kg (assume).   New price = $104.   We want the spendings to remain at $100.   (New consumption)*104 = 100 --> (New consumption) = 100/104 kg.   Percent decrease = Change/Original *100 = (1 - 100/104)/1*100 = 400/104%.   Answer: (400/104) %.
Answer: B
What profit percent is made by selling an article at a certain price, if by selling at 2/3rd of that price, there would be a loss of 14%?	Select the correct option:  A) 20%  B) 26%  C) 42%  D) 29%  E) 22%

Solution: SP2 = 2/3 SP1   CP = 100   SP2 = 86   2/3 SP1 = 86   SP1 = 129   100 --- 29 => 29%   Answer: 29%
Answer: D
A reduction of 5% in the price of oil enables a house wife to obtain 10kgs more for Rs.5000, what is the reduced price for kg?  Choose the correct choice from the following:
A) 23  B) 27  C) 25  D) 35  E) 15

Solution: 5000*(5/100)= 
5000*(5/100) = 250
250 ---- 10   ? ---- 1=> Rs.25   Answer:25
Answer: C
If two numbers are in the ratio 2:3. If 10 is added to both of the numbers then the ratio becomes 5:6then find the smallest number?  Choose the correct choice from the following answers.
A) 22/3  B) 19/3  C) 20/3  D) 25/3  E) 24/3

Solution: 2:3   2x + 10 : 3x + 10 = 5 : 6   6[2x + 10] = 5[3x + 10]   12x + 60 = 15x + 50   15x -12x = 60 - 50   3x = 10, then X=10/3   Then the first number is = 2   2x = 10   Option 20/3
Answer: C
Solve the equation:
|(2x + 1)2 - 4x2 - 2| - 3|4x – 1| = - 6 Choices.
A) -1/2
B) 1/2
C) -3/4
D) 3
E) None

Solution: Solution:   |(2x + 1)2 - 4x2 - 2| – 3|4x -1| = - 6 <=>   |4x2 + 4x + 1 - 4x2 - 2 | - 3|4x - 1| = - 6 <=>   |4x – 1| - 3|4x – 1| = - 6 <=> -2|4x – 1| = - 6 <=>   |4x – 1| = 3 <=> 4x - 1 = 3 or 4x - 1 4  - 1= 
4  - 1 = 3
3 or 4x - 1= -3   Therefore x = 1 or x = -1/2   -1/2nswer -1/2
Answer: A
How many positive integers less than 500 can be formed using the numbers 1,2,3,and 5 for digits, each digit being used only once.
Options:
A) 22
B) 34
C) 73
D) 26
E) 11

Solution: Single digit numbers = 4   Double digit numbers = 4 x 3 = 12   Three digit numbers = 3 x 3 x 2 x 1 = 18   Total = 34   Answer:34
Answer: B
A, B and C enter into a partnership and their shares are in the ratio 1/2 : 1/3 : 1/4. After 2 months, A withdraws half of his capital and after 10 months, a profit of Rs. 378 is divided among them. What is B's share ? Select.
A) 144  B) 265  C) 177  D) 156  E) 199

Solution: Ratio of initial investments = 1/2 : 1/3 : 1/4 = 6 : 4 : 3.   Let their initial investments be 6x, 2x and 3x respectively.   A : B : C = (6x * 2 + 3x * 10) : (4x * 12) : (3x * 12) = 42 : 48 : 36 = 7 : 8 : 6.   B's share = Rs. (378 * 8/21) = Rs. 144.   144nswer: 144
Answer: A
The LCM of two numbers is 2310 and HCF is 61. If one of the numbers is 210. Then what is the other number ?  Select the correct option:
A) 715	B) 671	C) 330	D) 582	E) 465

Solution: First number * Second Number = LCM * HCF   Other number = 2310 * 61 / 210 = 11*61= 
11*61 = 671
671   ANSWER :671
Answer: B
Three integers are at random chosen between 0 and 9 inclusive. What is the probability Q that each number is different ? Pick:
A) A.18/25
B) B.4/5
C) C.81/100
D) D.9/10
E) E.1

Solution: Number of ways of choosing the 3 integers without restriction = 10 * 10 * 10   Number of ways of choosing the 3 integers so that the 3 integers are different = 10 * 9 * 8   Probability Q= 10 * 9 * 8/10 * 10 * 10 = 72/100 = 18/25   A.18/25nswer: A.18/25
Answer: A
If n = 3^10 – 2^10 which of the following is NOT a factor of n?  Choose the correct choice from the following options:
A) 43
B) 437
C) 23
D) 19
E) 373

Solution: 3^10 - 2^10   = (3^5)^2 - (2^5)^2   =(3^5 + 2^5)(3^5- 2^4)   =(405+32(405-32)   =437*373   =19*23*373   Therefore, 43 is Not a factor of n.   43
Answer: A
A flagpole 18 meters high casts a shadow of length 45 meters. If a building under similar conditions casts a shadow of length 60 meters, what is the height of the building (in meters)?  Select.
A) 20  B) 24  C) 28  D) 32  E) 36

Solution: The height:length ratio will be equal in both cases.   18 / 45 = x / 60   x = 24   The answer is 24.
Answer: B
If the volume of two cubes are in the ratio 27:1, the ratio of their edges is: Choose the most appropriate option:	A) 3:1	B) 3:2	C) 3:5	D) 3:7	E) None of these

Solution: Explanation:   Let the edges be a and b of two cubes, then   a3/b3=27/1   =>(a/b)3=(3/1)3   a/b=3/1   =>a:b=3:1   Option 3:1
Answer: A
The length of a train and that of a platform are equal. If with a speed of 72 k/hr, the train crosses the platform in one minute, then the length of the train (in meters) is?  Choose the correct choice
A) 600
B) 799
C) 719
D) 750
E) 712

Solution: Speed = [72 * 5/18] m/sec = 20 m/sec; Time = 1 min. = 60 sec.   Let the length of the train and that of the platform be x meters.   Then, 2x/60 = 20 Ã¨ x = 20 * 60 / 2= 
20 * 60 / 2 = 600
600   600nswer: 600
Answer: A
Two boys starting from the same place walk at a rate of 5kmph and 5.5kmph respectively. What time will they take to be 11km apart, if they walk in the same direction? Choose the correct choice from the following:
A) 15 hours	B) 16 hours	C) 17 hours	D) 20 hours	E) 22 hours

Solution: The relative speed of the boys = 5.5kmph â€“ 5kmph   = 0.5 kmph   Distance between them is 11 km   Time = Distance/Speed   Time=11km / 0.5 kmph = 17 hrs   answer :22 hours
Answer: E
A certain kind of fuel is 1515high octane and 4545regular octane. If high octane costs three times as much as regular octane, what fraction of the cost of the fuel is due to the high octane?
Choose the correct choice from the following choices
A) 1/5 B) 2/3 C) 3/7 D) 3/5 E) 4/5

Solution: let x be the amount of fuel   high octane = x/5   regular = 4x/5   price of regular = y   price of high octante = 3y   cost of high octane in the fuel = 3y * x/5   total cost = 3y * x/5 + 4x/5 * y   % = cost of high octante / total cost   = 3/7   Answer is 3/7
Answer: C
One robot builds a robot in 1 hour, another one builds a robot in 2 hours. The 2 robots work together and when a new robot is complete, it joins the others, working at a constant rate of one robot in 2 hours. How much time will it take until there are 8 robots altogether, if the robots build only one robot at a time?
Pick one
A) 70 min  B) 94 min  C) 110 min  D) 131 1/7 min  E) 146 1/7 min

Solution: First the 2 robots work at the rate of   1 + 1/2 = 3/2   so they complete one robot in 2/3 rd of an hour = 40 minutes - (1)   Now the 3 robots work together at the rate of   1 + 1/2 + 1/2 = 4/2= 
4/2 = 2
2/1   so they complete one robot in 1/2 an hour,i.e 30 minutes - (2)   Now the 4 robots work together at the rate of   1 + 1/2 + 1/2 + 1/2= 5/2   so they complete one robot in 2/5th of an hour - (3)   Now the 5 robots work together at the rate of   1 + 1/2 + 1/2 + 1/2+1/2= 
1 + 1/2 + 1/2 + 1/2+1/2 = 3
3   so they complete one robot in 1/3th of an hour - (4)   Now the 6 robots work together at the rate of   1 + 1/2 + 1/2 + 1/2 + 1/2 + 1/2=7/2   so they complete one robot in 2/7th of an hour - (5)   Now the 7 robots work together at the rate of   1 + 1/2 + 1/2 + 1/2 + 1/2 + 1/2 + 1/2=9/2   so they complete one robot in 2/9th of an hour - (6)   And now we have 8 robots   So Total = (1) + (2) + (3)+(4)+(5) + (6) = 146 1/7minutes   Answer - 146 1/7 min
Answer: E
Rice weighing 35/2 pounds was divided equally and placed in 4 containers. How many ounces of rice were in each container? (Note that 1 pound = 16 ounces) Choose the most appropriate option:  A) 40  B) 50  C) 60  D) 70  E) 80

Solution: 35/2 ÷ 4 = 35/8 pounds in each container   35/8 pounds * 16 ounces / pound = 70 ounces in each container   The answer is 70.
Answer: D
Oil cans x and y are right circular cylinders and the height and radius of y are each twice those of x. If the oil in can x filled to capacity sells for $3, how much does the oil in y sell for if y is only half filled? Choose the correct answer:
A) $11	B) $12	C) $13	D) $14	E) $18

Solution: formula for vol of a cyl is PI*r^2*h   so Vy = 8*Vy   y when half filled will cost 4 times x so ans is $12
Answer: B
What is the area of a square field whose diagonal of length 22 m? Select:	A) 287	B) 269	C) 270	D) 242	E) 230

Solution: d2/2 = (22 * 22)/2= 
(22 * 22)/2 = 242
242   Answer:242
Answer: D
If the average of t, b, c, 14 and 15 is 12. What is the average value of t, b, c and 29	Options
A) 12  B) 13  C) 14  D) 15  E) 16

Solution: t+b+c+14+15 = 12*5= 
12*5 = 60
60=>t+b+c = 60-29= 
60-29 = 31
31   t+b+c+29= 31+29= 
31+29 = 60
60   Average= 60/4= 
60/4 = 15
15   Answer 15
Answer: D
Two sides of a triangle have length 6 and 8. Which of the following are possible areas of the triangle?
I. 2
II. 22
III. 24  Choose the correct option:
A) I, II, and III  B) I and II only  C) II and III only  D) I and III only  E) I only

Solution: Answer = A. I, II, and III   With dimensions of only 2 sides given (for a triangle), this becomes an open ended question   I, II, and IIIny area is possible out of the three
Answer: A
A table is bought for Rs.400/- and sold at Rs.500/- find gain or loss percentage?  Choose the correct option:
A) 25%	B) 30%	C) 35%	D) 43%	E) 45%

Solution: Formula = (Selling price ~ Cost price)/Cost price * 100   = (500 - 400)/400 = 25% gain   25%)
Answer: A
y = 100 - 398x
Which of the following values of x gives the greatest value of y in the equation above? Choose the correct option:  A) 200  B) -4  C) 0.5  D) 0  E) 1

Solution: Clearly, the negative value of x will result in maximum value of y.   Answer is -4
Answer: B
Two pipes P and Q can fill a cistern in 12 and 10 minutes respectively. Both are opened together, but at the end of 3 minutes the first is turned off. How much longer will the cistern take to fill? Choose the correct choice from the following
A) 1/8	B) 1/2	C) 2/4	D) 1/4	E) 1/4

Solution: 3/12 + x/10   = 1   x= 8 1/2   Answer: 1/2
Answer: B
25 percent of the women in a college class are science majors, and the non-science majors make up 80% of the class. What percentage of the men are science majors if 40% of the class are men?
Choose the correct choice from the following.
A) 2% B) 12.5% C) 28% D) 30% E) 45%

Solution: 2.5/k + 2/m = 6/t   Assuming total # is 100 :   [Science - Women] will have - 0.25 * 60 = 15   [Non-Science-Women] will have - 45   [Science-Men] will have = 20-15= 
20-15 = 5
5   S0 5/40 * 100= 12.5%   Answer - 12.5%
Answer: B
The number of new words that can be formed by rearranging the letters of the word 'TOO' is
Choose the correct choice from the following: A) 5 B) 10 C) 11 D) 2 E) 3

Solution: Explanation:   Number of words which can be formed = 3! - 1 = 6 - 1= 
6 - 1 = 5
5.   5nswer: 5
Answer: A
A train 110 m long is running with a speed of 60 km/hr. In what time will it pass a man who is running at 6 km/hr in the direction opposite to that in which the train is going?	Choose the correct choice from the following
A) 4
B) 6
C) 7
D) 4
E) 2

Solution: Speed of train relative to man = 60 + 6= 
60 + 6 = 66
66 km/hr.= 66 * 5/18 = 55/3 m/sec.   Time taken to pass the men = 110 * 3/55= 
110 * 3/55 = 6
6 sec.   Answer: 6
Answer: B
If "BEACH" is given a code of 19, then what is the difference between "SANDCASTLE" and "WAVES"?	Pick: A) 15 B) 28 C) 30 D) 168 E) 22

Solution: Case – Codes : A - 1, 28 - 2, C - 3, D - 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   SANDCASTLE: 98   WAVES: 70   Answer: 28
Answer: B
Bag A contains red, white and blue marbles such that the red to white marble ratio is 1:3 and the white to blue marble ratio is 2:3. Bag B contains red and white marbles in the ratio of 1:4. Together, the two bags contain 50 white marbles. How many red marbles could be in bag A?
Answers:
A) 1
B) 5
C) 4
D) 6
E) 8

Solution: 6 is the answer.   5ag A-   R:W:5 = 2:6:9   Let W in bag A be 6K   5ab 5 -   R:W = 1:4   Let W in bag 5 be 4k   W =50 = 6K+4k   => k= 5   Total Red's in bag A will be 2K = 10   5
Answer: B
How much time is required to cover the distance of 910 Km by a car driver, if he start with the initial speed of 40 Km/hr. and increases the speed by 5 Km/hr for every next hour ? Choose the correct choice from the following choices:  A) 11 hours  B) 12 hours  C) 13 hours  D) 14 hours  E) 15 hours

Solution: IT is AP series problem where   a= 40, d=5 , sum = 910   and n=?   910 = (n/2)*(2*40+(n-1)*5)   5n^2+75n-1820=0   n^2+15n-364=0   solving it, we get   n=13   so 13 hours   ANSWER:13 hours
Answer: C
Sandy purchased 20 dozen toys at the rate of $360 per dozen. Sandy sold each toy at the rate of $31.50. What was the percentage profit? Choices:
A) 3%
B) 5%
C) 7%
D) 9%
E) 11%

Solution: A dozen toys cost $360, so each toy cost $30.   selling price / cost price = 31.50 / 30= 
31.50 / 30 = 1.05
1.05   The percentage profit is 5%.   The answer is 5%.
Answer: B
Two trains are moving in the same direction at 72 kmph and 36 kmph. The faster train crosses a man in the slower train in 25 seconds. Find the length of the faster train?  Choose the correct choice:
A) 270
B) 250
C) 187
D) 257
E) 271

Solution: Relative speed = (72 - 36) * 5/18 = 2 * 5= 
2 * 5 = 10
10 mps.   Distance covered in 25 sec= 25 * 10= 
25 * 10 = 250
250 m.   The length of the faster train= 250 m.   Answer: 250
Answer: B
A departmental store charges the commission of 15 percent on the first sale of items worth $50,000 and then an additional 10 percent on any sale price that exceeds the initial $50,000. If the department store earned $24,000 in commissions for the sale of a series of diamonds, what was the sale price of the diamond set?	Options.
A) $215,000 B) $365,000 C) $115,000 D) $240,000 E) $160,000

Solution: Lets start with looking at the options. All options are above 50,000 -> Thus the total commission will be the sum of 15% of 50,000 and 10% of the rest of the amount.   Let's start with calculating 15% of 50,000 = 7,500.   So out of the total commission of 24000, 7500 was earned on the first 50,000. Commission remaining = 24,000 - 7500 = 16,500   16,500 is actually the 10% of the rest of the amount => 165,000   So total sales = 50,000 + 165,000 = 215,000   $215,000NSWER:$215,000
Answer: A
Two trains of equal length 120 metres move in the same direction. The faster train completely
overtakes the slower one in 15 seconds. If the slower train were to move at half its speed, the over
taking would take in 10 seconds. At what speeds are the 2 trains moving (faster and slower respectively
in m/s) Select:
A) 24, 22
B) 32, 16
C) 30, 18
D) 28, 14
E) None of these

Solution: The total distance covered for over taking = length of the two trains = 120 +120= 
120 +120 = 240
240   Speed of faster train be x m/s and slower train be y m/s   In the first case Relative speed= x-y   Relative Speed = Distance / Time taken = x-y = 240/15= 
240/15 = 16
16 m/s………(1)   In the second case, the slower train moves at half its speed   Relative Speed= x-0.5y = 240/10= 
240/10 = 24
24 m/s …………………..(2)   Solving equation 1 & 2 we get x= 32 and y = 16 .   :. The speed of the faster and slower trains are 32 m/s and 16 m/s respectively   Answer: 32, 16
Answer: B
35 percent of the women in a college class are science majors, and the non-science majors make up 70% of the class. What percentage of the men are science majors if 40% of the class are men?	Choose the most appropriate option:
A) 20%
B) 25%
C) 22.5%
D) 30%
E) 45%

Solution: 3.5/k + 2/m = 6/t   Assuming total # is 100 :   [Science - Women] will have -> 0.35 * 60 = 21   [Non-Science-Women] will have -> 39   [Science-Men] will have = 30-21= 
30-21 = 9
9   S0 9/40 * 100= 22.5%   Answer -22.5%
Answer: C
Ratio of Rani's and Kamal's age is 3:5. Ratio of Kamal's and Pooja's age is 2:3.If Rani's age is two-fifth of Pooja's age, what is Rani's age?
Pick one:	A) 10 years	B) 15 years	C) 24 years	D) Cannot be determined	E) None of these

Solution: Solution:Here in this question only ratio is given.No other information like sum ,difference or product is given.So given data is inadequate to find a solution.   Answer Cannot be determined
Answer: D
If the operation @ is defined for all a and b by the equation a@b =(a^b)/2,then (3@2)=?  Choose the correct answer:
A) 4
B) 2
C) 9/2
D) -9/2
E) -8/2

Solution: work within the parenthesis first so solve (3@2) first   (3@2)=(3^2)/2=9/2   so 9/2 is the answer....this question is merely testing order of operations   remember PEMDAS   Answer:9/2
Answer: C
The length of the bridge, which a train 180 metres long and travelling at 45 km/hr can cross in 30 seconds, is?  Pick one.
A) 876 m
B) 157 m
C) 195 m
D) 156 m
E) 167 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, (180 + x)/30 = 25/2   => 2(180 + x) = 750 => x   = 195 m.   Answer: 195 m
Answer: C
Albert invested Rs. 8000 in a scheme for 2 years at compound interest rate 5% p.a. How much amount will Albert get on maturity of the fixed deposit?
Choose the correct choice from the following options:  A) Rs.8829  B) Rs.8820  C) Rs.8822  D) Rs.8289  E) Rs.8820

Solution: Amount = [8000 * (1 + 5/100)2]   = 8000 * 21/20 * 21/20   = Rs.8820   Answer:Rs.8820
Answer: E
The average age of a husband and a wife is 25 years when they were married nine years ago but now the average age of the husband, wife and child is 23 years(the child was born during the interval). What is the present age of the child?
Choose the correct answer
A) 2 years
B) 5 years
C) 9 years
D) 4 years
E) 1 years

Solution: 34 * 2= 
34 * 2 = 68
68   23 * 3= 
23 * 3 = 69
69   -----------   1 years   Answer:1 years
Answer: E
An alchemist discovered that the formula expressing the correct proportions needed to turn ordinary metal into gold is G = 3/2M + 25, where G is the number of gold bars and M is the number of metal bars. If a metal bar weighs twice as much as a gold bar, how many metal bars will yield an equal weight of gold?  Options: A) a.	A - 10 B) b.	B - 15 C) c.	C – 22.5 D) d.	D – 30 E) e.	E – 67.5

Solution: A --- 30/2 + 15 = 40 --- wrong   B --- 45/2 + 15 = not an integer --- wrong   C --- 22.5(3/2) + 15 = not an integer --- wrong   D --- 90/2+15 = 70 --- CORRECT   This is one of those problems that will probably be easiest to solve by plugging in numbers. The algebra is do-able, but it's not worth the effort (in my opinion). I was able to solve it in under 30 seconds total with this method.   a.	A - 10
Answer: A
How many seconds will a 500 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?  Select the correct option:
A) 176 sec
B) 30 sec
C) 766 sec
D) 165 sec
E) 186 sec

Solution: Speed of train relative to man = 63 - 3= 
63 - 3 = 60
60 km/hr.= 60 * 5/18 = 50/3 m/sec.   Time taken to pass the man = 500 * 3/50= 
500 * 3/50 = 30
30 sec.   Answer:30 sec
Answer: B
Sum of 24 odd numbers is? Select the correct option:
A) 572  B) 573  C) 574  D) 575  E) 576

Solution: sum of 1st n odd no.s = 1+3+5+7+... = n^2   so, Sum of 1st 24 odd numbers = 24^2 = 576   ANSW576R:576
Answer: E
A rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered.If the area of the field is 680 sq.ft, how many feet of fencing will be required ?
Choose one:  A) 88 feet  B) 86 feet  C) 84 feet  D) 82 feet  E) None of these

Solution: Explanation:   We are given with length and area, so we can find the breadth.   as Length * Breadth = 88 feetrea   => 20 * Breadth = 680   => Breadth = 34 feet   88 feetrea to be fenced = 2B + L = 2*34 + 20= 
2*34 + 20 = 88
88 feet   Option 88 feet
Answer: A
In a dance competition the points in each round for the first,second,third and fourth position were 1000,500,200,100 . No other points were given. Reney participated in several rounds in the competition and the product of her score was 100000. In How many rounds did she participate?
Choose the correct choice from the following answers:  A) 4  B) 2  C) 5  D) Cannot be determined  E) 20

Solution: Correct answer is D because we are given that there won't be any points awarded for rounds other than 1st four position.   Thus, it may happen that she played 50 rounds out of only 7 rounds were there in which she was awarded some points.
Answer: D
What is the area of square field whose side of length 8 m?	Select the correct option
A) 225  B) 64  C) 772  D) 882  E) 21

Solution: 8 * 8= 
8 * 8 = 64
64 sq m   Answer:64
Answer: B
What distance will be covered by a bus moving at 54 kmph in 30 seconds?	Choose the most appropriate option:
A) 287  B) 900  C) 289  D) 276  E) 207

Solution: 54 kmph = 54 * 5/18   = 30 mps   D = Speed * time = 30 * 30= 
30 * 30 = 900
900 m.   Answer:900
Answer: B
A man can row downstream at 18 kmph and upstream at 10 kmph. Find the speed of the man in still water and the speed of stream respectively?  Options
A) 8 B) 9 C) 6 D) 4 E) 2

Solution: Let the speed of the man in still water and speed of stream be x kmph and y kmph respectively.   Given x + y = 18 --- (1)   and x - y = 10 --- (2)   From (1) & (2) 2x = 28 => x = 14, y = 4.   Answer:4
Answer: D