MU-NLPC/Calc-aqua_rat huggingface dataset:
Two trains are running in opposite directions with the same speed. If the length of each train is 120 metres and they cross each other in 12 seconds, then the speed of each train (in km/hr) is: Select the correct option:
A) 31 km/hr. B) 32 km/hr. C) 34 km/hr. D) 35 km/hr. E) 36 km/hr.

Solution: Let the speed of each train be x m/sec.   Then, relative speed of the two trains = 2x m/sec.   So, 2x = (120 + 120)/12   2x = 20   x = 10.   Speed of each train = 10 m/sec = 10 x 18/5 km/hr = 36 km/hr.   answer :36 km/hr.
Answer: E
By selling a bat for Rs.450/- a man loses 10% what is that bat cost price  Select
A) s.600/-	B) s.500/-	C) s.700/-	D) s.780/-	E) s.800/-

Solution: 90 % ------> 450 (90 * 5 = 450)   100 % ------>500 (100 * 5 = 500)   Cost price = Rs.500/-   s.500/-)
Answer: B
The sum of the first 40 positive even integers is 1,640. What is the sum of the first 40 odd integers? Pick:
A) 1500 B) 1600 C) 1400 D) 1200 E) 1000

Solution: Sum of first n even numbers = n(n+1) =1640   Sum of first n odd numbers = n^2 = 40*40= 
40*40 = 1_600
1600 (here n=40)   Answer : 1600
Answer: B
In a division sum, the divisor is ten times the quotient and five times the remainder. If the remainder is 42, the dividend is:  Choose the most appropriate option
A) 5330
B) 5336
C) 5343
D) 4452
E) 5350

Solution: Divisor = (5 * 42)= 
(5 * 42) = 210
210= 10 * Quotient = Divisor   => Quotient = 210/10= 
210/10 = 21
21   Dividend= (Divisor * Quotient) + Remainder   Dividend = (210 * 21) + 42= 
(210 * 21) + 42 = 4_452
4452.   4452
Answer: D
If a = (1/2)b and c = 8a, then which of the following represents the average (arithmetic mean) of a, b, and c, in terms of a ? Pick one:
A) a + 4 B) (11/3)a C) 4a D) (4 1/7)a E) (7 1/4)a

Solution: Official Answer: B   The average of the three variables isa + b + c/3. However, we need to solve in terms of a, which means we must convert b and c into something in terms of a.   Were told that a =1/2b, which is equivalent to b = 2a. We can plug that in and simplify the average to:a + 2a + c/3   We also know that c = 8a, which we can plug directly into the average expression:   a + 2a + 8a/3   = 11a/3=(11/3)a , choice(11/3)a.
Answer: B
An article is bought for Rs.675 and sold for Rs.900, find the gain percent? Select:  A) 33 1/9%  B) 33 1/2%  C) 33 1/3%  D) 33 5/3%  E) 35 1/3%

Solution: 675 ---- 225   100 ---- ? => 33 1/3%   Answer:33 1/3%
Answer: C
5358 x 56 = ?
Choose one: A) 272258 B) 272358 C) 300048 D) 274258 E) 274358

Solution: 5358 x 51	= 5358 x (50 + 6)   = 5358 x 50 + 5358 x 6   = 267900 + 32148= 
267900 + 32148 = 300_048
300048.   300048)
Answer: C
If @ is a binary operation defined as the difference between an integer n and the product of n and 5, then what is the largest positive integer n such that the outcome of the binary operation of n is less than 10?	Options.
A) 1  B) 2  C) 3  D) 4  E) 5

Solution: the product of n and 5 =5n..   the difference between an integer n and the product of n and 5=5n-n=4n..   the outcome of the binary operation of n is less than 10?   so 4n<10...   max value that n can take as an integer is 2   ANSWER:2
Answer: B
If 5x = 3y and xy ≠ 0, what is the ratio of 1/5*x to 1/6*y ?  Choose the correct option.
A) 25/6 B) 36/25 C) 18/25 D) 5/6 E) 25/36

Solution: 5x = 3y => x/y = 3/5   1/5*x to 1/6*y = x/y * 6/5 =(3/5)* (6/5)=18/25   Ans: 18/25
Answer: C
In a group of cows and chickes, the number of legs was 14 more than twice the number of heads . the number of cows was:  Choose the correct option:
A) 7	B) 5	C) 11	D) 12	E) 14

Solution: no of cows x and their legs 4x, no of chicke y and their legs 2y, total no of legs= 4x + 2y, total nof heads = x + y, the no of legs was 14 mor than twice the number of heads. 2x + 2y +14 = 4x + 2y, 14= 4x-2x+ 2y -2y, therefore, 14 = 2x , x = 7, correct answer : (7)
Answer: A
The circumferences of two circles are 264 meters and 352 meters. Find the difference between the areas of the larger and the smaller circles. Answers.
A) 3566	B) 5467	C) 4132	D) 3526	E) 3782

Solution: Let the radii of the smaller and the larger circles be s m and l m respectively.   2∏s = 264 and 2∏l = 352   s = 264/2∏ and l = 352/2∏   Difference between the areas = ∏l2 - ∏s2   = ∏{1762/∏2 - 1322/∏2}   = 1762/∏ - 1322/∏   = (176 - 132)(176 + 132)/∏   = (44)(308)/(22/7) = (2)(308)(7) = 4312 sq m   Answer: Option 4132
Answer: C
Arun obtained 76, 65, 82, 67 and 85 marks (out in 100) in English, Mathematics, Chemistry, Biology and Physics. What is his average mark?	Choose the correct answer:	A) 53	B) 54	C) 72	D) 75	E) 78

Solution: Explanation:   Average mark = 76+65+82+67+85/5=375/5= 
375/5 = 75
75   Answer: Option 75
Answer: D
How many 6 digit number contain number 4 ? Pick.
A) 317608	B) 327608	C) 337608	D) 427608	E) 357608

Solution: total 6 digit no. = 9*10*10*10*10*10= 
9*10*10*10*10*10 = 900_000
900000   not containing 4= 8*9*9*9*9*9= 
8*9*9*9*9*9 = 472_392
472392   total 6 digit number contain 4= 900000 - 472392= 
900000 - 472392 = 427_608
427608   ANSWER:427608
Answer: D
Baseball's World Series matches 2 teams against each other in a best-of-seven series. The first team to win four games wins the series and no subsequent games are played. If you have no special information about either of the teams, what is the probability w that the World Series will consist of fewer than 7 games?
Choose the correct answer:
A) 12.5%	B) 25%	C) 31.25%	D) 68.75%	E) 75%

Solution: In order to determine the probability that the World Series will last less than 7 games, we can first determine the probability w that the World Series WILL last exactly 7 games and then subtract this value from 1.   In order for the World Series to last exactly 7 games, the first 6 games of the series must results in 3 wins and 3 losses for each team.   Let's analyze one way this could happen for Team 1:   Game 1 Game 2 Game 3 Game 4 Game 5 Game 6   T1 Wins T1 Wins T1 Wins T1 Loses T1 Loses T1 Loses   There are many other ways this could happen for Team 1. Using the permutation formula, there are 6!/(3!)(3!) = 20 ways for Team 1 to win 3 games and lose 3 games in the first 6 games.   Logically, there are also 20 ways for Team 2 to win 3 games and lose 3 games in the first 6 games.   Thus, there are a total of 40 ways for the World Series to last the full 7 games.   The probability that any one of these 40 ways occurs can be calculated from the fact that the probability of a team winning a game equals the probability of a team losing a game = 1/2.   Given that 7 distinct events must happen in any 7 game series, and that each of these events has a probability of 1/2, the probability that any one particular 7 game series occurs is.   Since there are 40 possible different 7 game series, the probability that the World Series will last exactly 7 games is:   Thus the probability that the World Series will last less than 7 games is 100% - 31.25% = 68.75%.   The correct answer is 68.75%. 100  - 31.25= 
 100  - 31.25 = 68.75
68.75%.   The correct answer is 68.75%.
Answer: D
A mixture of 70 liters of wine and water contains 10% water. How much water must be added to make water 12 ½% of the total mixture?  Pick:
A) 6 liters
B) 8 liters
C) 4 liters
D) 2 liters
E) 1 liters

Solution: 70 * (10/100)= 
70 * (10/100) = 7
7   Wine Water   87 1/2% 12 1/2%   87 1/2% ------- 63   12 1/2% -------?=> 9-7= 
9-7 = 2
2   Answer: 2 liters
Answer: D
If x^2+(1/x^2)=7, x^4+(1/x^4)=? Choose the correct option:
A) 10  B) 47  C) 12  D) 14  E) 15

Solution: -> x^4+(1/x^4)=(x^2)^2+(1/x^2)^2=(x^2+1/x^2)^2-2x^2(1/x^2)=7^2-2=47.   Thus, the answer is 47.
Answer: B
A man ordered 4 pairs of black socks and some pair of brown socks. The price of a black socks is double that of a brown pair, while preparing the bill the clerk interchanged the number of black and brown pairs by mistake which increased the bill by 50%.The ratio of the number of black and brown pairs of socks in the original order was Choose the correct choice from the following options
A) 1:4
B) 1:2
C) 1:3
D) 1:5
E) 1:7

Solution: Let the price of a pair of brown socks=x, then price of a pair of black socks=2x   If in original order there are 'a' pairs of brown socks, then total price= 4*2x + a*x   With interchanging number of black and brown pairs, new price=a*2x + 4*x   Given new price is 50% more than the original, So a*2x+4*x= (150/100)(4*2x+a*x)   => 2ax+4x= (3/2)(8x+ax)   => 4ax - 3ax= 16x   => a=16 = original number of pairs of brown socks   So ratio of number of black and brown pairs of socks in original order= 4:16 =1:4   1:4NSWER:1:4
Answer: A
A can do a piece of work in 4 days. B can do it in 5 days. With the assistance of C they completed the work in 2 days. Find in how many days can C alone do it? Choose the correct choice from the following options:
A) 10
B) 20
C) 30
D) 40
E) 15

Solution: C= 1/2-1/4-1/5   =1/20   =20days   ANSWER 20
Answer: B
A alone can complete a work in 16 days and B alone can complete in 12 days. Starting with A they work on alternate days. The total work will be completed in?
Options: A) 12 B) 13 C) 13 5/7 D) 13 ¾ E) None of these

Solution: Explanation:   (A+B)’s 2 day work = 1/16 + 1/12 = 7/18   work done in 6 pairs of days=7/48 x 6 = 7/8   remaining work = 1/8   work done by A on 13th day =1/16 remaining work = 1/16   on 14th day its B turn 1/12 work is done by B in 1 day 1/16 work is done by B in 12 x 1/16 = 3/4 day   total time taken =13 ¾ days   Answer: Option 13 ¾
Answer: D
Of a group of people, 10 play piano, 11 play guitar, 14 play violin, 3 play all the instruments, 20 play only one instrument. How many play 2 instruments?	Choose the correct choice from the following answers:	A) 3	B) 6	C) 9	D) 12	E) 15

Solution: Let single piano players = p   Let single guitar players = g   Let single violin players = v   Given, p + g + v + 3 + 20 = 10 + 11 + 14.   Hence, p + g + v = 35 - 23= 
35 - 23 = 12
12   ANSWER:12
Answer: D
Jaya invests in a new mutual fund. The fund averages 10% growth annually for the first three years, but it loses 30% of its value in the fourth year. At the end of four years, the value of the mutual fund is approximately what percent of the amount Jaya originally paid?  Select the correct option:  A) 93%  B) 90%  C) 88%  D) 85%  E) 80%

Solution: Let the initial amount be 100.   Since it grew on constant basis as 10% for three years = 100*1.1^3 = 11*11*1.1 = 132 [Taking 1.1 as 1]   It eroded by 30% = 132 * .7 = 92.something approximated to 93%   So, The correct answer will be (93%) 93%
Answer: A
When 1/10 percent of 2,000 is subtracted from 1/10 of 2,000, the difference is	Choose the correct option
A) 0 B) 198 C) 450 D) 495 E) 500

Solution: We can break this problem into two parts:   1) What is 1/10 percent of 2,000?   2) What is 1/10 of 2,000?   To calculate 1/10 percent of 2,000 we must first remember to DIVIDE 1/10 BY 100.   So we have: (1/10)/(100)   To divide a number by 100 means to multiply it by 1/100, so we have:   1/10 x 1/100 = 1/1,000   Thus, 1/10 percent of 2,000 = 1/1,000 x 2,000 =2.   Now let's concentrate on part 2. We need to calculate 1/10 of 2,000. To do this we simply multiply 1/10 by 2,000.   1/10 x 2,000 = 200   The answer to part 1 is 2, and the answer to part 2 is 200. Their difference is 200 – 2 = 198.   Answer 198.
Answer: B
A corporation triples its annual bonus to 50 of its employees. What percent of the employees’ new bonus is the increase?
Choose the correct option
A) 50% B) 662⁄3% C) 100% D) 200% E) 300%

Solution: Let the annual bonus be X.   A corporation triples its annual bonus.   So new bonus = 3X.   Increase = 3X-X =2X   The increase is what percent of the employees’ new bonus   = (2X/3X)*100   = 66 2/3%   Hence 662⁄3%.
Answer: B
If the average (arithmetic mean) of a list of numbers is 12 and the standard deviation of that list of numbers is 1.3, then which of the following numbers is more than two standard deviations from the mean?
I. 13.5
II. 12.3
III. 9.3  Choose the correct option.
A) I only	B) I and II only	C) II only	D) III only	E) I and III only

Solution: Mean = 12   SIII only = 1.3   2 SIII only above mean = 12+2*1.3= 
12+2*1.3 = 14.6
14.6   2 SIII only below mean= 12-2*1.3= 
12-2*1.3 = 9.4
9.4   12.3 and 13.5 lies in the range of 2SIII only from mean   Answer: Option III only
Answer: D
If anangletis defined as 1 percent of 1 degree, then how many anglets are there in a quarter circle?	Choose the correct choice from the following
A) 0.36
B) 3.6
C) 9000
D) 3,600
E) 36,000

Solution: 1 degree * 1/100 = 1 anglet   So 1 degree = 100 anglets   => 90 degrees = 9000 anglets   Answer - 9000
Answer: C
the hiker walking at a constant rate of 4 miles per hour is passed by a bike traveling in the same direction along the same path at 20 miles per hour. the bike stops to wait for the hiker 5 minutes after passing her, while the hiker continues to walk at her constant rate, how many minutes must the bike wait until the hiker catches up? Options.
A) 16
B) 14
C) 10
D) 15
E) 20

Solution: After passing the hiker the cyclist travels for 5 minutes at a rate of 20 miles/hour.   In those 5 mins the cyclist travels a distance of 5/3 miles.   In those 5 mins the hiker travels a distance of 1/3 miles.   So the hiker still has to cover 4/3 miles to meet the waiting cyclist.   The hiker will need 1/3 hours or 20 mins to cover the remaining 4/3 miles.   So the answer is 20.
Answer: E
A box contains eight bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that at least one bulb is good?	Choose the correct choice from the following answers
A) 13/16
B) 1/2
C) 15/16
D) 11/16
E) 9/16

Solution: Required probability   = 1 - 1/16   = 15/16   Answer: 15/16
Answer: C
A tap can fill a tank in 14 hours. After half the tank is filled three more similar taps are opened. What is the total time taken to fill the tank completely?
Pick
A) 11 hrs 45 mins B) 12 hrs 45 mins C) 13 hrs 45 mins D) 14 hrs 45 mins E) 15 hrs 45 mins

Solution: Time taken by one tap to fill the tank = 7 hrs.   Part filled by the taps in 1 hour = 4 * 1/14 = 2/7   Remaining part = 1 - 1/2 = 1/2   2/7 : 1/2 :: 1 : x   x = 1/2 * 1 * 7/2 = 7/4 = 105 mins = 1 hr 45 mins   So, total time taken = 15 hrs 45 mins   ANSW15 hrs 45 minsR: 15 hrs 45 mins
Answer: E
A and B invests Rs.1500 and Rs.4000 respectively in a business. If A doubles his capital after 6 months. In what ratio should A and B divide that year's profit? Choose the correct choice from the following answers:
A) 9:5
B) 9:8
C) 9:2
D) 9:9
E) 9:16

Solution: (1.5*6 + 3*6): (4*12)   27:48 =>   9:16   Answer:9:16
Answer: E
In a factory there are three types of machine M1, M2 and M which produces 25%, 35% and 40% of the total products respectively. M1, M2 and M3 produces 2%, 4% and 5% defective products, respectively. what is the percentage of non-defective products ?
Choices
A) 89%	B) 97.1%	C) 96.1%	D) 86.1%	E) None of these

Solution: Solution: Non-defective products,   {[(25*0.98)+(35*0.96)+(40*0.95)]/100}*100   = 96.1%.   Answer: Option 96.1%  (25*0.98)+(35*0.96)+(40*0.95) /100 *100= 
  (25*0.98)+(35*0.96)+(40*0.95) /100 *100 = 96.1
96.1%.   Answer: Option 96.1%
Answer: C
A fruit juice is composed of pineapple, strawberry juice, and cherry juice. How many ml of cherry juice is required to make 6 liters of fruit juice containing twice as much pineapple juice as strawberry juice and three times as much strawberry juice as cherry juice? (1L=1000ml)  Choose the correct choice.
A) 1800 ml
B) 600 ml
C) 1000 ml
D) 200 ml
E) 50 ml

Solution: 1L=1000ml   6L=6000ml   pineapple=2 strawberry   strawberry=3 cherry   pineapple+strawberry+cherry=6,000   2 strawberry+strawberry+1/3 strawberry=6,000   10 strawberry=18,000   strawberry=18,00 ml   1800 mlnswer 1800 ml
Answer: A
Find the number of square tiles to cover the floor of a room measuring 6.5 m * 9.5 m leaving 0.25 m space around the room. A side of square tile is given to be 25 cms?  Choose the correct choice from the following:
A) 422
B) 476
C) 429
D) 864
E) 413

Solution: Floor area to be covered by tiles = 6 * 9= 
6 * 9 = 54
54   tiles area= 0.25 * 0.25= 
0.25 * 0.25 = 0.0625
0.0625   No. of tiles= 54/0.0625= 
54/0.0625 = 864
864   Answer : 864
Answer: D
The average of nine numbers is 14. The average of first four numbers is 11.5 and the average of last four numbers is 16.5. What is the middle number? Choose the correct choice from the following answers.
A) 14  B) 16  C) 15  D) 18  E) 17

Solution: The total of nine numbers = 9X14 = 126   The total of first 4 and last 4 numbers is = 4 X 11.5+4 X 16.5 = 112   So, the middle number is  (126 - 112 )= 
 (126 - 112 ) = 14
14   14
Answer: A
There are 8 balls in a bucket, 4 balls are blue and 4 balls are red. If two ball chosen randomly , how many chances there are at least one blue ball will present? Choose the correct choice from the following choices:
A) 21  B) 25  C) 16  D) 22  E) 20

Solution: Two ball will be chosen. At least 1 blue ball   Total ways = 8C2 = 28   Total without any blue ball = 4C2 = 6   Hence ways in which at least one blue will be present = 28 - 6= 
28 - 6 = 22
22   Correct option: 22
Answer: D
John bought a shirt on sale for 25% off the original price and another 25 % off the discounted price. If the final price was $16, what was the price before the first discount? Choose the correct choice from the following answers.
A) $28.44
B) $18.44
C) $48.44
D) $38.44
E) $68.44

Solution: let x be the price before the first discount. The price after the first discount is   x - 25%x (price after first discount)   $28.44 second discount of 25% of the discounted price after which the final price is 16   (x - 25%x) - 25%(x - 25%x) = 16   Solve for x   x = $28.44   correct answer $28.44
Answer: A
A salt manufacturing company produced a total of 4000 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 average monthly production for that year?  Choose the correct answer
A) 5520 B) 2789 C) 5550 D) 2889 E) 4550

Solution: Total production of salt by the company in that year = 4000 + 4100 + 4200 + .... + 5100 = 54600.   Average monthly production of salt for that year = 54600/12= 
54600/12 = 4_550
4550.   Answer: 4550
Answer: E
A can do a piece of work in 15 days and B in 20 days. They began the work together but 5 days before the completion of the work, A leaves. The work was completed in? Choose the correct choice from the following.
A) 11 2/3 days	B) 11 3/7 days	C) 8 days	D) 6 days	E) 5 days

Solution: A's 1 day's work =1/15   11 3/7 days's 1 day's work =1/20   5 days before the completion of the work, A leaves=X-5/15   (x â€“ 5)/15 + x/20 = 1   x = 11 3/7 days   Answer: Option 11 3/7 days
Answer: B
A man performs 3/5 of the total journey by rail, 17/20 by bus and the remaining 6.5km on foot. His total journey is? Choose the correct answer
A) 130	B) 152	C) 225	D) 260	E) 180

Solution: Let the total journey be x km   then, (3x/5)+(7x/20)+6.5 = x   12x+7x+20*6.5 = 20x   x = 130km   130nswer is 130
Answer: A
Stuart bought a sweater on sale for 30% off the original price and another 25% off the discounted price. If the original price of the sweater was $30, what was the final price of the sweater?  Choose the correct answer: A) $25.75 B) $35.75 C) $15.75 D) $ 45.75 E) $15.75

Solution: The price with 30% off   30 - 30% of 30 = 30 - (30 / 100) *30 = 30 - 9= 
30 - 9 = 21
21   The price with another 25% off   21 - 25% of 21= 21 - (25/100)* 21   = 21 - (525 / 100) = 21 - 5.25= 
21 - 5.25 = 15.75
$15.75   correct answer $15.75
Answer: C
Mr. Zimmer has 237 papers to hand out to his class. The class consists of 30 students, and each student will need 8 papers. How many more papers will he need to be able to give 8 papers to each 30 student?  Choose the correct choice from the following choices.
A) 3 B) 7 C) 21 D) 78 E) 4

Solution: 8*30= 
8*30 = 240
240, not 237.   Therefore 3 papers will need to be added in order for 30 students to get 8 papers each.   Therefore 3 is correct
Answer: A
x is what percent of y percent of z, in terms of x, y and z? p be the value expressed in terms of x,y and z.	Select the correct option:  A) xyz  B) 1/xyz  C) 10,000x/yz  D) 1000*xyz  E) 100x/yz

Solution: Algebraically, y% of z is just (y/100)*z, or yz/100. So we want to answer the question: x is what percent of yz/100? Say x is equal to p% of yz/100; then we have:   x = (p/100)*(yz/100)   10,000x/yz = p   10,000x/yz
Answer: C
A sells his goods 50% cheaper than B but 50% dearer than C. The cheapest is? Choose the correct choice from the following options.
A) 33.8  B) 32.3  C) 33.6  D) 33.3  E) 31.3

Solution: Let B = 100   A = 50   33.6 * (150/100) = 50   333.6 = 100   33.6 = 33.3 then '33.6' 33.6heapest   Answer: 33.6
Answer: C
A company wants to manufacture computer models of x% of a list of 10,000 models from the market. After a budget cut, the company finds it must reduce this selection by (x − 6)%. In terms of x, how many computer model will the group be able to manufacture?
Choose the correct answer
A) x*x – 6x
B) (x)(106 – x)
C) (100)(106 – x)
D) (100)(94 – x)
E) (x-6)/100

Solution: Based on the answer choices and the question, this question begs the use of x=6 as a sample number.   Initial = 6%*10000 = 600   Reduction = 6-6= 
6-6 = 0
0%, so no math required here to calculate the reduction; just make sure that you can calculate 600 in your answer.   A. x*x – 6x= 0; No   B. (x)(106 – x) = 600; Winner!   C. (100)(106 – x) > 600; No   D. (100)(94 – x) > 600; No   E. (x-6)/100 = 0; No   (x)(106 – x)
Answer: B
If 10 typists can type 30 letters in 30 minutes, then how many letters will 40 typists working at the same rate complete in 1 hour?  Choose the correct choice from the following answers
A) 200  B) 210  C) 205  D) 225  E) 240

Solution: No. of letters typing by 10 typists in 30 minutes = 30   No. of letters typing by 10 typists in 60 minutes = 30*2= 
30*2 = 60
60   No. of letters typing by 40 typists in 60 minutes= 60/10*40= 
60/10*40 = 240
240   Answer : 240
Answer: E
Two cards are drawn at random from a pack of 52 cards. What is the probability that either both are black or both are queen? Choose the correct choice from the following answers:
A) 4/26 B) 55/221 C) 56/221 D) 55/220 E) 57/220

Solution: Probability of taking 2 from 52 cards = 52C2 = 52 * 51/2*1= 
52 * 51/2*1 = 1_326
1326   There r 26 black cards   There r 4 queens   prob that both r black cards P(A)= 26C2/1326 = 26 * 25/2 * 1= 
26 * 25/2 * 1 = 325
325/1326   prob that both r queens P(55/221)= 4C2/1326 = 4 * 3/2 * 1= 
4 * 3/2 * 1 = 6
6/1326   P(A n 55/221)= 2C2/1326 = 1/1326   P(A U 55/221) = P(A) + P(55/221) - P(A n 55/221) = 325/1326 + 6/1326 - 1/1326   => 55/221   ANSWER:55/221
Answer: B
workers decided to raise Rs.3 lacs by equal contribution from each. Had they contributed Rs.50 eachextra, the contribution would have been Rs.3.50 lacs . How many workers were they?	Choose the correct option
A) 220  B) 230  C) 500  D) 560  E) 1000

Solution: N * 50 = (350000 - 300000)= 
(350000 - 300000) = 50_000
50000   N= 50000 / 50= 
50000 / 50 = 1_000
1000   1000
Answer: E
A Cuban cigar would cost 5 dollar less than 1.5 times a French cigar, had the French cigar cost 0.7 dollar less than it does now. An Arabian cigar costs 50 cents more than 1.5 times the Cuban cigar. The three cigars together cost 74.7 dollars. What is the price of the French cigar? Answers:	A) 92.7$.	B) 23$.	C) 25.5$.	D) 12.7$.	E) 37.4$.

Solution: The three cigars together cost 74.7 dollars. If each cost the same , they would have cost a little less than 25 dollars each.   From the given data we know French cigar < Cuban cigar < Arabic cigar   and each is more expensive 1.5 times. Therefore eliminate options C,A,E straightaway . Since French cigar is at least 1.5 times cheaper we know B cannot be the answer.   Therefore 12.7$. is the answer.
Answer: D
Two trains of equal length, running with the speeds of 60 and 20 kmph, take 50 seconds to cross each other while they are running in the same direction. What time will they take to cross each other if they are running in opposite directions? Choose the correct choice from the following answers:
A) 12.5	B) 8.01	C) 7.5	D) 26	E) 22

Solution: RS = 60 -40= 
60 -40 = 20
20 * 5/18= 100/18   T = 50   D = 50 * 100/18 = 2500/9   RS = 60 + 20= 
60 + 20 = 80
80 * 5/18   T= 2500/9 * 18/400= 
2500/9 * 18/400 = 25/2 = around 12.5
12.5 sec.12.5nswer: 12.5
Answer: A