MU-NLPC/Calc-aqua_rat huggingface dataset:
a,b and c are three sides of a right angled triangle . a,b and c are all integers . Area of the triangle is T1. From all three sides a,b and c , we draw a square having areas as S1, S2 and S3 . Now, Total area ( T1+S1+S2+S3) is :  Choices:
A) a fractional value
B) may be even or odd
C) odd only
D) even only
E) None of these

Solution: Take any of the pythagorean triplets (3,4,5),(5,12,13),(7,24,25)..e.t.c   I will consider the first one.. a=3,b=4,c=5   then T1= 1/2*3*4= 
1/2*3*4 = 6
6(always be even for right angle triangle)   S1= 9(odd)   S2=16(even)   S3=25(odd)   Now T1+S1+S2+S3= 56(even).   also even+even=even, odd+odd=even   ANSWER:even only
Answer: D
How much space, in cubic units, is left vacant when maximum number of 3x3x3 cubes are fitted in a rectangular box measuring 6x9x11 ?  Choose the correct choice from the following answers:
A) 112
B) 111
C) 110
D) 109
E) 108

Solution: No of cubes that can be accommodated in box = (6*9*11)/(3*3*3)   6*9 in numerator can be perfectly divided by 3*3 in denominator.   side with length 11 can't be perfectly divided by 3 and hence is the limiting factor. Closet multiple of 3 less that 11 is 9. so vacant area in cube =   =6*9*(11-9)   =6*9*2= 
6*9*2 = 108
108   Ans - 108
Answer: E
A fair 2-sided coin is flipped 6 times. What is the probability that tails will be the result at least twice, but not more than 5 times?  Select:  A) 5/8  B) 3/4  C) 7/8  D) 57/64  E) 15/16

Solution: Total possible outcomes when coined is tossed 6 time=2^6=4*4*4= 
4*4*4 = 64
64   Total possible outcomes getting 2 or 3 or 4 or 5 tails= 67/82+67/83+67/84+67/85=(6*5)/2+(6*5*4)/(3*2)+(6*5)/2+6=15+20+15+6= 
15+20+15+6 = 56
56   Probability of getting at least 2 but not more than 5 times tails=56/64=7/8   Ans=7/8
Answer: C
Find the value of m from given 72519 x 9999 = m? Answers.
A) 455666576
B) 565476563
C) 567642887
D) 725117481
E) 658899003

Solution: 72519 x 9999 = 72519 x (10000 - 1)   = 72519 x 10000 - 72519 x 1   = 725190000 - 72519= 
725190000 - 72519 = 725_117_481
725117481   725117481
Answer: D
A tradesman by means of his false balance defrauds to the extent of 12%? in buying goods as well as by selling the goods. What percent does he gain on his outlay?	Select the correct option:
A) 26.4
B) 25.44
C) 27.5
D) 28.54
E) 27

Solution: Explanation:   g% = 12 + 12 + (12*12)/100= 
12 + 12 + (12*12)/100 = 636/25 = around 25.44
25.44%   Answer: 25.44
Answer: B
John was thrice as old as Tom 6 years ago. John will be 2 times as old as Tom in 4 years. How old is Tom today?  Select.
A) 12
B) 14
C) 16
D) 18
E) 20

Solution: J-6 = 3(T-6), so J = 3T-12   J+4 = 2(T+4)   (3T-12) + 4 = 2T + 8   T = 16   The answer is 16.
Answer: C
A train 900 m long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 min, then the length of the tunnel is?  Choose the correct choice:
A) 200m	B) 776 m	C) 400 m	D) 187 m	E) 1678 m

Solution: Speed = 78 * 5/18 = 65/3 m/sec.   Time = 1 min = 60 sec.   Let the length of the train be x meters.   Then, (900 + x)/60 = 65/3   x = 400 m.   Answer:400 m
Answer: C
there are sixty markings on a clock, minutes hand was exactly on one of those markings. nine markings away from the minutes hand was hours hand. what could be the time.
Select.
A) 5:14 B) 6:20 C) 7:48 D) 3:09 E) 3:19

Solution: given angle diff=9mins   we know   1min=6 deg   therefore 9mins=9*6= 
9*6 = 54
54 deg   so the angle diff must be 54 deg   better to go through the options   let us consider   A.5hrs 14mins   find angle   angle traced by hour hand=(5*30)+(14/2)= 
(5*30)+(14/2) = 157
157   angle traced by minute hand=(14*6)= 
(14*6) = 84
84   angle diff=157-84= 
157-84 = 73
73   similarly for option C.   angle traced by hour hand=(7*30)+(48/2)= 
(7*30)+(48/2) = 234
234   angle traced by minute hand=(48*6)= 
(48*6) = 288
288   angle diff=(288-234)= 
(288-234) = 54
54   ANSWER:7:48
Answer: C
The total cost of 100 paper plates and 200 paper cups is $8.00 At the same rates what is the total cost of 20 of the plates and 40 of the cups?	Choose the correct choice from the following:	A) $.90	B) $1.00	C) $1.20	D) $1.50	E) $1.60

Solution: U dont need to go through all this   What u have with u is   100 P + 200 C = $8.00   Just divide the equation by 5 and you will get what u are looking for   20P + 40 C = $1.60   Therefore OA is $1.60
Answer: E
In a certain city, 60 percent of the households have cable television, and 50 percent of the households have videocassette recorders. If there are 150,000 households in the city, then the number of households that have both cable television and videocassette recorders could be any number from:  Choose the correct answer.
A) 15,000 to 75,000 inclusive
B) 15,000 to 90,000 inclusive
C) 30,000 to 75,000 inclusive
D) 60,000 to 90,000 inclusive
E) 75,000 to 120,000 inclusive

Solution: The maximum percentage with both is 50% which is 75,000 households.   This means that every household with a recorder also has cable television.   The minimum percentage with both is 10% which is 15,000 households.   This means that 40% of households have only recorders but not cable television.   The other 10% of households with recorders have cable television.   The answer is 15,000 to 75,000 inclusive.
Answer: A
Rohit paid $4,000 for 100 shares of stock X and $2,000 for 100 shares of stock Y. He later sold the same shares of both stocks, gaining 3/5 the amount he paid for stock Y. If the prices he had paid for the stocks had been reversed and everything else remained the same, then the net result would have been:	Choose the correct option:
A) A Gain of 1.4 times as much  B) A Gain of 3 times as much  C) A Gain of 2 times as much  D) A Gain of 1.5 times as much  E) A Loss of 2 times as much

Solution: A = 4000; B = 2000; Profit = (3/5)*2000= 
(3/5)*2000 = 1_200
1200   After prices are reversed:   A= 2000; B =4000; Profit = (3/5)*4000= 
(3/5)*4000 = 2_400
2400   2400 --> Gain of 2 times 1200   Answer: A Gain of 2 times as much
Answer: C
A thief goes away with a SANTRO car at a speed of 40 kmph. The theft has been discovered after half an hour and the owner sets off in a bike at 50 kmph when will the owner over take the thief from the start?
Choose the correct choice from the following answers.
A) 2 hours	B) 6 hours	C) 8 hours	D) 9 hours	E) 3 hours

Solution: |-----------20--------------------|   50 40   D = 20   RS = 50 – 40 = 10   T = 20/10= 
20/10 = 2
2 hours   14. If I walk at 3 kmph, I miss   2 hoursnswer: 2 hours
Answer: A
Of the 60 researchers in a workgroup, 40 percent will be assigned to Team A and the remaining 60 percent to Team B. However, 70 percent of the researchers prefer Team A and 30 percent prefer Team B. What is the lowest possible number of researchers who will NOT be assigned to the team they prefer?  Choices.
A) 15
B) 18
C) 20
D) 25
E) 30

Solution: I solved it by assuming 100 people and then dividing my answer in two to save time on calculations. (percentage equals number of people) In that case   40 will be in team A   60 will be in team B   The larger diff is   70 want team A so diff is 70-40= 
70-40 = 30
30. At least 30 people will NOT get their wish, so for 60 researchers the same number is 18.   Answer choice 18
Answer: B
Last year the price per share of Stock X increased by k percent and the earnings per share of Stock X increased by m percent, where k is greater than m. By what percent did the ratio of price per share to earnings per share increase, in terms of k and m?	Options:	A) k/m %	B) (k – m) %	C) [100(k – m)] / (100 + k) %	D) [100(k – m)] / (100 + m) %	E) [100(k – m)] / (100 + k + m) %

Solution: One way of doing this is assuming some value for y. Say, y = 60. So x is greater than 20 but less than 30. Say x could be 25.   Not put y = 60 and x = 25 in the options:   (A) y < x < 2y -----> 60 < 25 < 2*120 ( does not hold)   (B) 2y < 6x < 3y ------> 2*60 < 6*25 < 3*60 (holds so could be the answer)   Mind you, you need to check every option to ensure that the relation holds for only one option. If it holds for more than one options, you will need to check for some other values too.   The point is that we assume values and then plug them in the options to see which relation works.   Last Year:   Price per share (PPS) increased by k%. Let's say k = 20. So if the price was 100, it increased by 20% to become 120 (New PPS).   Earnings per share increased by m%. Let's say m = 10 (m must be less than k). So if earnings per share was also 100, it increased by 10% to become 110 (New EPS).   By what percent did the ratio of price per share to earnings per share increase?   Ratio of PPS/EPS was   100/100= 
  100/100 = 1
1   New ratio= New PPS/ New EPS = 120/110 = 1.0909   %Increase = [(1.0909 - 1)/1] * 100 = 9.09%   Now, in the options, put k (1.0909 - 1)/1  * 100= 
(1.0909 - 1)/1  * 100 = 9.09
9.09%   Now, in the options, put k= 20, m = 10   Only (D) will give you 9.09%. Let me show you calculations of some of the options.   B. (k – m) %     (20 - 10)= 
  (20 - 10) = 10
10% (Not the answer)   C. [100(k – m)] / (100 + k) %   [100(20 - 10)]/(100 + 20) %= 1000/120 % = 8.3% (Not the answer)   D. [100(k – m)] / (100 + m) %   [100(20 – 10)] / (100 + 10) % = 1000/11 % = 9.09% (Answer) answer is [100(k – m)] / (100 + m) %
Answer: D
Line m lies in the xy-plane. The y-intercept of line m is -5, and line m passes through the midpoint of the line segment whose endpoints are (2, 4) and (6, -8). What is the slope of line m ? Choose the correct choice:
A) -3 B) -1 C) -1/3 D) 0 E) Undefined

Solution: Ans: A   Solution: line m goes through midpoint of (2, 4) and (6, -8). midpoint is (4,-2)   as we can see that the y axis of intercept point is (0,-5) means line m is parallel to x axis   slope M= -3   -3ns: -3
Answer: A
How many different subsets of the set {11, 14, 17, 24} are there that contain an odd number of elements?  Pick:
A) 3  B) 6  C) 10  D) 8  E) 12

Solution: Answer = 8 = 8   {11}   {14}   {17}   {24}   {11, 14, 17}   {14, 17, 24}   {11, 17, 24}   {11, 14, 24}
Answer: D
You need to print a document of the area 216 sq cm. Condition is 3 cm margin is to be left at both top & bottom and 2 cm at the sides. What is the optimized size of your paper? Options
A) 60sq.cm B) 70sq.cm C) 95sq.cm D) 80sq.cm E) 90sq.cm

Solution: let us consider it is a rectangle.   so area=24*9= 
24*9 = 216
216sq.cm   now (24-3*2)*(9-2*2)=18*5= 
18*5 = 90
90sq.cm   ANSW90sq.cmR:90sq.cm
Answer: E
A fair price shopkeeper takes 10% profit on his goods. He lost 20% goods during theft. His loss percent is:	Choose the correct choice from the following choices:	A) 72%	B) 42%	C) 32%	D) 12%	E) 22%

Solution: Explanation:   Suppose he has 100 items. Let C.P. of each item be Re. 1.   Total cost = Rs. 100. Number of items left after theft = 80.   S.P. of each item = Rs. 1.10   Total sale = 1.10 * 80 = Rs. 88   Hence, loss % = 12/100 * 100= 
12/100 * 100 = 12
12%   Answer:12%
Answer: D
Tom had 63 apples. He divides all apples evenly among 9 friends. How many apples did Tom give to each of his friends? Choose the correct answer:
A) 1	B) 2	C) 18	D) 7	E) 8

Solution: Total number of apples = 63   There are 9 friends of seats on the bus.   To find how many apples Tom gave to each of his friends, divide the total number of apples by the number of friends.   We get, divide 63 by 9   63 ÷ 9 = 7   Therefore, Tom gives 7 apples to each of his friends.   ANSWER IS 7
Answer: D
A cricket bat is sold for $850, making a profit of $230. The profit percentage would be	Select the correct option:
A) 24%	B) 25%	C) 30%	D) 37%	E) 40%

Solution: 230/(850 - 230) = 230/620 = 23/62 =37%   Answer: 37%.
Answer: D
You play the following game with a friend. You share a pile of chips, and you take turns
removing between one and four chips from the pile. (In particular, at least one chip must be
removed on each turn.) The game ends when the last chip is removed from the pile; the one
who removes it is the loser.
It is your turn, and there are 2014 chips in the pile. How many chips should you remove to
guarantee that you win, assuming you then make the best moves until the game is over? Choose the correct choice:
A) 1
B) 2
C) 3
D) 4
E) there is no way to guarantee a win, even with the best play

Solution: The key to winning this game is that if you leave your opponent with 5k +1 chips,   for any integer k 0, then you win. When your opponent removes r chips, you remove 5-r,   and so there are now 5(k- 1) + 1 chips left, and you keep using this strategy until there is   only one chip left, at which point your opponent takes it and loses.   So, you should take 3 chips to leave 2011 = 5 402 + 1.   correct answer 3
Answer: C
36 men can complete a piece of work in 18 days. In how many days will 108 men complete the same work ?
Choose the correct choice
A) 24 B) 77 C) 6 D) 29 E) 21

Solution: Explanation:   Less Men, means more Days {Indirect Proportion}   Let the number of days be x   then,   108 : 36 :: 18 : x   x = 6   Answer: 6) 6 days
Answer: C
A bag contains one rupee, 50 paisa and 10 paisa coins in the ratio of 3:2:1. How many 50 paisa coins are there, if the total number of money in the bag is Rs 820?	Pick
A) 400 coins	B) 40 coins	C) 100 coins	D) 4100 coins	E) 4200 coins

Solution: Let the number of 100p, 50p and 10p coins be 3x ,2x and x .   The ratio of the values of coins = 100 p: 50p :10 p = 10:5:1   Total amount = (10 x 3x ) + (5 x 2x) +( 1 x x) = 30x+10x+x=41x   The ratio of their values in rupees= 30x:10x:x   Given total amount is Rs 820 => 41x = 820 => x=Rs 20   Total value of 50p coins (in rupees) = 10 x 20 =Rs 200   Total 50 paisa coins are = 200 x 2 = 400 coins   400 coinsnswer:400 coins
Answer: A
It was a beautiful sunny morning. The air was fresh and a mild wind was blowing against my wind screen. I was driving from Bangalore to Brindavan Gardens. It took me 1 hour and 30 minutes to complete the journey.
After lunch I returned to Bangalore. I drove for 90 rhinutes. How do you explain it ?  Choose the correct option
A) 75 min	B) 60 min	C) 90 min	D) 80 min	E) 88 min

Solution: C   90 min   Jansi went out for shopping. She had in her handbag approximately Rs. 15/- in one rupee notes and 20 p. coins. When she returned she had as many one rupee notes as she originally had and as many 20 p. coins as she originally had one rupee notes. She actually came back with about one-third of what she had started out with.   How much did she spend and exactly how much did she have with her when she started out ?   There is nothing to explain here. The driving time there and back is absolutely the same because 90 minutes and 1 hour and 30 minutes are one and the same thing.   This problem is meant for inattentive readers who may think that there is some difference between 90 minutes and 1 hour 30 minutes.
Answer: C
How many positive 5-digit integers have the odd sum R of their digits? Select the correct option:  A) 9*10^2  B) 9*10^3  C) 10^4  D) 45*10^3  E) 9*10^4

Solution: We are looking at numbers between 10000 and 99999 both inclusive.   There are 90000 numbers.   Now for   10000 : sum of digits is odd;   10001 :sum of digits is even;   10002 : sum of digits is odd ; so on and so forth. So every alternate number is such that the sum of digit is odd.   (Exception for the above statement :   When it is 10009 the sum is even and for 10010 again the sum is even; But if you look at 10019 :sum is odd; 10020 : sum is odd   and this pattern continues so basically the number of odd sum of digits and even sum of digits are equal)   This means exactly half of the numbers will have odd sum of their digits. i.e 45000   Answer :45*10^3
Answer: D
The price of 2 sarees and 4 shirts is Rs. 1600. With the same money one can buy 1 saree and 6 shirts. If one wants to buy 12 shirts, how much shall he have to pay ?	Choose the correct option:
A) Rs. 1200 B) Rs. 2400 C) Rs. 4800 D) Cannot be determined E) None of these

Solution: Let the price of a saree and a shirt be Rs. x and Rs. y respectively.   Then, 2x + 4y = 1600 .... (i)   and x + 6y = 1600 .... (ii)   Divide equation (i) by 2, we get the below equation.   => x + 2y = 800. --- (iii)   Now subtract (iii) from (ii)   x + 6y = 1600 (-)   x + 2y = 800   ----------------   4y = 800   ----------------   Therefore, y = 200.   Now apply value of y in (iii)   => x + 2 x 200 = 800   => x + 400 = 800   Therefore x = 400   Solving (i) and (ii) we get x = 400, y = 200.   Cost of 12 shirts = Rs. (12 x 200) = Rs. 2400.   Answer: Option Rs. 2400
Answer: B
What is the 4 digit number in which the 1st digit is 1/3 of the second, the 3rd is the sum of the 1st and 2nd, and the last is three times the second? Choose the correct choice from the following.
A) 1100	B) 1200	C) 1349	D) 1400	E) 1450

Solution: First digit is 1/3 second digit => The numbers can be 1 & 3, 2& 6, 3 & 9.   First + second = third => we can eliminate 3 & 9 since  3 + 9= 
 3 + 9 = 12
12.   Last is 3 times the second=> we can eliminate option 2 & 6 since  3 * 6= 
 3 * 6 = 18
18.   Hence the number is 1349   1349
Answer: C
Two cars are driving toward each other. The first car is traveling at a speed of 75 km/h, which is 25% slower than the second car's speed. If the distance between the cars is 1050 km, how many hours will it take until the two cars meet?	Choose the most appropriate option:	A) 4	B) 4.5	C) 5	D) 5.5	E) 6

Solution: The speed of the first car is 75 km/h.   The speed of the second car is  75 / 0.75= 
 75 / 0.75 = 100
100 km/h.   The two cars complete a total of 175 km each hour.   The time it takes the cars to meet is   1050 / 175= 
  1050 / 175 = 6
6 hours.   The answer is 6.
Answer: E
The dimensions of a room are 25 feet * 15 feet * 12 feet. What is the cost of white washing the four walls of the room at Rs. 5 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each?  Select the correct option:	A) 3887	B) 2689	C) 2678	D) 4530	E) 3780

Solution: Area of the four walls = 2h(l + b)   Since there are doors and windows, area of the walls   = 2 * 12 (15 + 25) - (6 * 3) - 3(4 * 3)   = 906 sq.ft.   Total cost = 906 * 5 = Rs. 4530   Answer: 4530
Answer: D
Machine A produces 100 parts twice as fast as Machine B does. Machine B produces 100 parts in 40 minutes. If each machine produces parts at a constant rate, how many parts does Machine A produce in 10 minutes?	Choose the correct option.
A) 20
B) 50
C) 60
D) 40
E) 30

Solution: Machine B produces 100 part in 40 minutes. Machine A produces 100 parts twice as fast as B, so Machine A produces 100 parts in  40/2= 
 40/2 = 20
20 minutes.   Now, Machine A produces 100 parts in 20 minutes which is 100/20= 
100/20 = 5
5 parts/minute.   5 parts X a total of 10 minutes= 50   50
Answer: B
After 6 games, team B had an average of 65 points per game. If it got only 47 points in game 7, how many more points does it need to score to get its total above 500?	Choose the correct option
A) 85  B) 74  C) 67  D) 63  E) 28

Solution: (6*65) + 47 +x >500   390+47+x > 500   437+x >500   => x>63   Option 63
Answer: D
There are 23 distinct numbers in set M, there are 28 distinct numbers in set N, and there are 12 distinct numbers that are in both sets M and N. Set H is the set containing the elements that are in at least one of sets M and N. How many elements are in set H? Options:
A) 39
B) 40
C) 51
D) 58
E) 63

Solution: {Total} = {M} + {N} - {Both}   {Total} = 23 + 28 - 12= 
23 + 28 - 12 = 39
39.   39nswer: 39.
Answer: A
A fruit seller had some apples. He sells 40% apples and still has 420 apples. Originally, he had	Choose the correct option.
A) 588 apples
B) 600 apples
C) 672 apples
D) 700 apples
E) None

Solution: Solution   Suppose originally he had x apples.   Then,(100-40)% of x = 420.   ‹=› 60/100×x = 420   x ‹=› (420 ×100 / 60   ‹=› 700.   Answer 700 apples
Answer: D
A man can row 30 km downstream and 20 km upstream in 4 hours. He can row 45 km downstream and 40 km upstream in 7 hours. Find the speed of man in still water?  Choose the correct choice from the following options
A) 12.9  B) 12.6  C) 12.4  D) 12.5  E) 12.1

Solution: Let the speed of the man in still water be a kmph and let the speed of the stream be b kmph.   Now 30/(a + b) + 20/(a - b) = 4 and 45/(a + b) + 40/(a - b) = 7   Solving the equation, the speed of man in still water is 12.5 kmph.   Answer:12.5
Answer: D
What is the probability that when a hand of 6 cards is drawn from a well shuffled deck of 52 cards, It contains 2 Queen? Options:
A) 1/23445	B) 113/22434	C) 29187/1017926	D) 1017926/29187	E) None of these

Solution: nCr = n!/(n-r)!r!   Total number of possible hands = 52C6   52C6 = (52!)/((52-6)! × 6!)   52C6 = 61075560.   Number of hands with 2 Queen and 4 non-Queen cards = 4C2 × 48C4   4C2 = (4!)/(2! × 2!) = 6.   4829187/10179264 = (48!)/(44! × 4!) = 3 × 47 × 46 × 45 = 291870   (other 2 cards must be chosen from the rest 48 cards)   P (2 Queen) = (429187/10179262 × 4829187/10179264)/5229187/10179266 = 29187/1017926   29187/1017926
Answer: C
In the following sequence of alphabets, if the second half is reversed, which letter would be the fifth to the right of the letter which is twelveth from the left ?
A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
Choose one
A) J	B) W	C) T	D) G	E) K

Solution: Explanation:   Case 1 : A B C D E F G H I J K L M N O P Q R S T U V W X Y Z   After reversal of the second half of the sequence of alphabet, we get,   Case 2 : A B C D E F G H I J K L M Z Y X W V U T S R Q P O N   The twelveth letter from the left end of the above sequence of alphabet Case 2 is L. The letter which is 5th to the right of L is W.   ANSWER: W
Answer: B
If the price of a certain computer increased 30 percent from d dollars to 364 dollars, then 2d =	Choose the most appropriate option.
A) 540
B) 570
C) 619
D) 649
E) 560

Solution: Before Price increase Price = d   After 30% Price increase Price = d+(30/100)*D = 1.3d = 364 (Given)   i.e. d = 364/1.3= 
364/1.3 = 280
$280   i.e. 2d= 2*280= 
2*280 = 560
560   Answer: option 560
Answer: E
Tom opened a shop investing Rs.30000. Jose joined him 2 months later, investing Rs.45000. They earned a profit of Rs.36000 after completion of one year. What will be Jose's share of profit? Choose the correct choice from the following choices:
A) 20000  B) 10000  C) 25000  D) 34000  E) 30000

Solution: SoL = ~s- So 20000nju’s share = [5/9] x 36000 = 20000   20000
Answer: A
There were two candidates in an election. Winner candidate received 60% of votes and won the election by 288 votes. Find the number of votes casted to the winning candidate?  Choices:
A) 776	B) 864	C) 299	D) 257	E) 125

Solution: W = 60% L = 40%   60% - 40% = 20%   20% -------- 288   60% -------- ?  60  - 40= 
 60  - 40 = 20
20%   20% -------- 288   60% -------- ?=> 864   Answer:864
Answer: B
The sum of two numbers is 50 and their product is 375. What will be the sum of their reciprocals?
Select the correct option: A) 1/40 B) 8/75 C) 2/15 D) 75/8 E) 75/6

Solution: (1/a)+(1/b)=(a+b)/ab=50/375=2/15   ANSWER:2/15
Answer: C
A couple has two children, one of whom is a girl. If the probability of having a girl or a boy is 50%, what is the probability that the couple has two daughters?
Choose the most appropriate option
A) 1/8
B) 1/4
C) 1/3
D) 1/2
E) 2/3

Solution: First child ---- Second child:   B ---------------------------- B;   B ---------------------------- G;   G ---------------------------- B;   G ---------------------------- G.   We know that one if the kids is a girl. So, we have one of the three cases in red. Each case there is equally likely (each has the probability of 1/2*1/2=1/4). So, the probability of GG is 1/3.   Answer: 1/3.
Answer: C
Find the expenditure on digging a well 14m deep and of 3m diameter at Rs.18 per cubic meter?
Choices:
A) 2998 B) 2799 C) 1782 D) 1485 E) 2780

Solution: 22/7 * 14 * 3/2 * 3/2= 
22/7 * 14 * 3/2 * 3/2 = 99
99 m2   99 * 18= 
99 * 18 = 1_782
1782   Answer:1782
Answer: C