MU-NLPC/Calc-aqua_rat huggingface dataset:
Surekha started a business investing Rs.25,000 in 1999. In 2000, he invested an additional amount of Rs. 10,000 and Rajesh joined him with an amount of Rs. 35,000. In 2001, Surekha invested another additional amount of Rs.10,000 and Jay joined them with an amount of Rs.35,000. What will be Rajesh's share in the profit of Rs.2,10,000 earned at the end of 3 years from the start of the business in 1999?	Choose the correct choice from the following answers.
A) Rs 45000  B) Rs 50000  C) Rs 70000  D) Rs 75000  E) None

Solution: Surekha:Rajesh:Jay= (25000×12+35000×12+45000×12):(35000×24) : (35000×12) = 1260000 : 840000 : 420000 = 3 : 2 : 1. Rajesh's share =Rs.(210000×2/6) = Rs.70000.   Answer Rs 70000
Answer: C
How many integers from 0 to 56, inclusive, have a remainder of 1 when divided by 3 ?
Choose the correct choice:	A) 15	B) 16	C) 17	D) 18	E) 19

Solution: My ans is also C.17.   Explanation:   1 also gives 1 remainder when divided by 3, another number is 4, then 7 and so on.   Hence we have an arithmetic progression: 1, 4, 7, 10,..... 55, which are in the form 3n+1.   Now we have to find out number of terms.   tn=a+(n-1)d, where tn is the nth term of an AP, a is the first term and d is the common difference.   so, 55 = 1+(n-1)3   or, (n-1)3 = 54   or, n-1 = 18   or, n = 19   19
Answer: E
How much interest can a person get on Rs. 8200 at 17.5% p.a. simple interest for a period of two years and six months? Pick one.
A) 3587.58	B) 3587.59	C) 3587.5	D) 3587.52	E) 3587.56

Solution: I = (8200 * 2.5 * 17.5)/100 = (8200 * 5 * 35)/(100 * 2 * 2) = Rs. 3587.50.Answer: 3587.5
Answer: C
N number of persons decide to raise 3 lakhs by equal contributions from each. If they contributed 50 each extra, the contribution would be 3.25 lakhs. How many persons are there? Choose the correct choice.
A) 600  B) 400  C) 450  D) Cannot be determined  E) None of these

Solution: Required persons = 325000−300000/50 = 500   Answer None of these
Answer: E
If the sales tax be reduced from 4 (1/3) % to 2 (1/2) %, then what difference does it make to a person who purchases a bag with marked price of Rs. 8000? Choose the correct choice:	A) 146.69	B) 146.66	C) 146.62	D) 146.61	E) 146.6

Solution: Explanation:   Required difference = (4 (1/3) of Rs. 8000) - (2 (1/2) of Rs. 8000)   = (13/3 – 5/2) % of Rs. 8000   = (11/6) x (1/100) x 8000   = Rs. 146.66   ANSWER: 146.66
Answer: B
In how many ways can you seat 8 people on a bench if one of them does not want to sit in one of the two middle seats or at either end?
Select the correct option
A) 17,540	B) 18,360	C) 19,320	D) 20,160	E) 21,480

Solution: One person can choose 4 possible chairs to sit. The remaining 7 people can sit in 7! ways.   The number of arrangements is 4*7! = 20,160.   The answer is 20,160.
Answer: D
Express 25 mps in kmph?	Pick
A) 22  B) 87  C) 90  D) 77  E) 22

Solution: 25 * 18/5= 
25 * 18/5 = 90
90 kmph   Answer: 90
Answer: C
How many odd factors does 250 have?	Select the correct option:	A) 3	B) 4	C) 5	D) 6	E) 8

Solution: Start with the prime factorization: 250 = 2*5*7   For odd factors, we put aside the factor of two, and look at the other prime factors.   set of exponents = {1, 1}   plus 1 to each = {2, 2}   product = 2*2= 
2*2 = 4
4   Therefore, there are 4 odd factors of 250.   Answer: 4.
Answer: B
A mirror 2 inches wide is placed around a rectangular paper with dimensions 8 inches by 12 inches. What is the area of the frame, in square inches? Choose the correct choice from the following:  A) 96  B) 94  C) 28  D) 44  E) 18

Solution: This question is an example of a 'punch out' question - we have to find the area of EVERYTHING, then 'punch out' the part that we don't want.   We're told that a mirror 2 inches wide is placed around a rectangular paper with dimensions 8 inches by 12 inches. We're asked for the area of the mirror , in square inches.   Area of a rectangle = (length)(width)   So the area of the paper is... (8)(12) = 96   The mrror 'adds' 2 inches to the top, bottom, left and right 'sides' of the picture, so the area of EVERYTHING is...   (8+2+2)(12+2+2) = (12)(16) = 196   When we 'punch out' the area of the paper, we'll be left with the area of the FR96ME:   192 - 96= 
192 - 96 = 96
96   Final 96nswer:   96
Answer: A
If the perimeter of a rectangular garden is 700 m, its length when its breadth is 100 m is?  Choose the correct choice from the following.
A) 299 m
B) 777 m
C) 200 m
D) 250 m
E) 128 m

Solution: 2(l + 100) = 700 => l   = 250 m   Answer:250 m
Answer: D
The game of blackjack is played with a deck consisting of 13 cards (one of each of the numbers 2-10, one jack, one queen, one king, and one of ace) in each of four suits: clubs, diamonds, hearts, and spades.
In a game of blackjack, if your first card is a spade, what are the odds Q that it is an ace?  Answers.
A) 1/52
B) 1/26
C) 1/13
D) 1/4
E) 5/13

Solution: The question should ask about the probability not the odds.   There are 13 spades, the probability Q that the spade we already have is an ace is therefore 1/13.   Answer: 1/13.
Answer: C
A certain stock exchange designates each stock with a 1, 2 or 3 letter code, where each letter is selected from the 10 letters of the alphabet. If the letters may be repeated and if the same letters used in a different order, constitute a different code, how many diff stocks is it possible to designate with these codes?	Select the correct option
A) 1200
B) 996
C) 1110
D) 896
E) 1400

Solution: Pretty simple actually   Number of 1 letter symbols = 10   Number of 2 letter symbols = 10*10   Number of 3 letter symbols = 10*10*10   The answer is sum of the 3. = 10+100+1000= 
10+100+1000 = 1_110
1110   So the answer is 1110.
Answer: C
In a 1000 m race, A beats B by 200 meters or 25 seconds. Find the speed of B?
Pick one:
A) 8
B) 9
C) 7
D) 6
E) 2

Solution: Since A beats B by 200 m or 25 seconds, i   t implies that B covers 200 m in 25 seconds.   Hence speed of B = 200/25= 
200/25 = 8
8 m/s.   8nswer: 8
Answer: A
Boy purchased two flats for Rs.5,00,000. On one he gains 15 % while on the other he losses 15%. How much does he gain or lose?  Choose the most appropriate option:
A) 1.25% B) 2.1% C) 2.25% D) 2.65% E) 3%

Solution: Generally in such cases, there is always loss.   So always remember, when two materials are sold and if one material gets profit and the other gets a loss, then use the trick shown below to calculate the loss.   Loss% = 2.25%ommon loss and gain% 2 = x 2   10 10   Therefore, here common loss and gain % = 15%   Hence,   Loss% = 15 2 = 2.25%   2.25%
Answer: C
Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is: Answers.
A) 3 : 1	B) 3 : 2	C) 3 : 6	D) 3 : 7	E) 3 : 9

Solution: Let the speeds of the two trains be x m/sec and y m/sec respectively. Then, length of the first train = 27 x meters, and length of the second train = 17 y meters. (27 x + 17 y) / (x + y) = 23 ==> 27 x + 17 y = 23 x + 23 y ==> 4 x = 6 y ==> x/y = 3/2.   Answer: Option 3 : 2
Answer: B
A no.when divided by 222 gives a remainder 43, what remainder will beobtained by dividingthe same no.17? Choose the correct choice from the following options:	A) 2	B) 7	C) 9	D) 10	E) 15

Solution: 222 + 43= 
222 + 43 = 265
265/17= 10 (Remainder)   10
Answer: D
How many cuboids of length 5 m, width 4 m and height 3 m can be farmed from a cuboid of 16 m length, 10 m width and 12 m height.	Choose the correct choice:	A) 32	B) 28	C) 36	D) 40	E) 50

Solution: (16 Ã— 10 Ã— 12)/(5 Ã— 4 Ã— 3) = 32   32nswer is 32.
Answer: A
A school has received 50% of the amount it needs for a new building by receiving a donation of $400 each from people already solicited. People already solicited represent 40% of the people from whom the school will solicit donations. How much average contribution is requited from the remaining targeted people to complete the fund raising exercise?
Select the correct option
A) $400	B) $177.78	C) $320	D) $277	E) $200

Solution: Let us suppose there are 100 people. 40% of them donated $16000 ( 400 * 40 )   $16000 is 50% of total amount.   So total amount = 16000 * 100/50   Remaining amount is 50% of total amount.   50% of total amount = 16000 * (100/50) * (50/100)= 
16000 * (100/50) * (50/100) = 16_000
16000   This amount has to be divided by 50 ( remaining people are 50 )   So per head amount is  16000 / 50= 
 16000 / 50 = 320
320   ANSWER:$320
Answer: C
If a, b, and c are consecutive integers such that a < b < c and a is an even prime number, which of the following is true?
I. a × b × c < a^3
II. 5b < bc
III. a + b + c > a^3 Choose the correct choice.
A) I only  B) II only  C) III only  D) II and III  E) I, II, and III

Solution: Only 'C' is possible solution. If a is even prime number i.e 2, b is 3 and c is 4   Putting the values in the answers only 'III only' seems valid.
Answer: C
Jerome anticipated that the WebWeb.com stock price would fall and sold all his WebWeb.com stocks for $5 per stock. He paid $10,000 tax on the revenue. A week later, Jerome became convinced that the WebWeb.com stock price would rise, and he used the money that he had gotten from selling the WebWeb.com stocks to purchase them again, this time at $6 per stock. If Jerome ended up having 7000 WebWeb.com stocks fewer than the number he had before selling them, how many WebWeb.com stocks did he have originally?
Choose the correct answer:
A) 10,000	B) 11,600	C) 17,000	D) 14,000	E) 16,400

Solution: Let the number of shares be x.   5*x -10000(money paid in taxes) = 6(x- 7000)   Solving for x, we get the shares as 17000.   Ans :(Option 17,000)
Answer: C
72 hens cost Rs. __ 96.7__. Then what does each hen cost, where two digits in place of ‘__’ are not visible or are written in illegible hand?  Select the correct option
A) Rs. 3.23
B) Rs. 5.11
C) Rs. 5.51
D) Rs. 7.22
E) None

Solution: Explanation :   The best way to solve this question is to multiply the alternatives by 72 and find which one gives the middle three digits 96.7.   To cut time, you can choose to multiply 72 by integer values only, e.g. 72 × 3 = 216, 72 × 5 = 360 and 72 × 7 = 504.   It must be remembered that the decimal part of the answer will be multiplied by 72 and the actual answer will increase .   Let us now roughly multiply the decimal values of the options also by 72,   e.g. 72 x 0.2 = 14.4, 72 × 0.1 = 7.2 and 72 × 0.5 = 36.   So, option (1) will yield (216 + 14)= 
(216 + 14) = 230
230 (approximately),   option(2) will yield (360 + 7)= 
(360 + 7) = 367
367 (approximately),   option(3) will yield (360 + 36)= 
(360 + 36) = 396
396 (approximately),   and option(4) will yield (504 + 14)= 528 (approximately).   Of these only option (3) satisfies our requirement of 2nd and 3rd digits being 96.   Answer : Rs. 5.51
Answer: C
what is the nearest no. to 2304 which is divisible by 21?	Choose the correct answer.
A) 2289
B) 2310
C) 2333
D) 2456
E) 2309

Solution: remainder when 2304 is divided by 21=15   so,no. should added to make 15 to 21=6   no.=2304+6= 
2304+6 = 2_310
2310   answer 2310
Answer: B
A manufacturer of a certain type of screw rejects any screw whose length is less than 2.47 centimeters or greater than 2.53 centimeters. If k represents the length of a screw, in centimeters, which of the following inequalities specifies all the lengths of screws that are acceptable? Choose the correct choice from the following choices: A) |k + 0.03| > 2.5 B) |k — 0.03| <= 2.5 C) |k — 2.5| > 0.03 D) |k — 2.5| >= 0.06 E) |k — 2.5| <= 0.03

Solution: So, let's go through this step by step:   Any screw that is less than: 2.47 or greater than 2.53 will be rejected.   If k represents the length of a screw   In other words,Kis an acceptable screw that must fall within the acceptable range of 2.47 to 2.53, So:   2.47 ≤ K ≤ 2.53   You can rule out answers with < or > as opposed to ≤ or ≥ because the length cannot be LESS than 2.47 or GREATER than 2.53. In other words, 2.47 and 2.53 are acceptable lengths.   Let's look at (|k — 2.5| <= 0.03):   |k — 2.5| <= 0.03   For the positive case: k - 2.5 ≤ 0.03 ===>k ≤ 2.53   For the negative case: -(k - 2.5) ≤ 0.03 ===> -k +2.5 ≤ 0.03 ===> - k ≤ -2.47 ===>k ≥ 2.47   2.47 ≤ k ≤ 2.53   (|k — 2.5| <= 0.03)
Answer: E
A person's present age is two-fifth of the age of his mother. After 8 years, he will be one-half of the age of his mother. How old id the mother at present?	Choose the correct choice from the following:
A) 22	B) 77	C) 40	D) 26	E) 18

Solution: Let the mother's present age be x years. Then, the person's present age = 2/5 x years.   (2/5 x + 8) = 1/2 (x + 8)   2(2x + 40) = 5(x + 8) => x = 40   Answer: 40
Answer: C
The least perfect square, which is divisible by each of 21, 36 and 66 is
Choose the correct answer:
A) 213414
B) 213424
C) 213434
D) 213444
E) None of these

Solution: Explanation:   L.C.M. of 21, 36, 66 = 2772   Now, 2772 = 2 x 2 x 3 x 3 x 7 x 11   To make it a perfect square, it must be multiplied by 7 x 11.   So, required number = 2 x 2 x 3 x 3 x 7 x 7 x 11 x 11 = 213444   Option 213444
Answer: D
What is the perimeter of a triangle with sides 7 and 4 that has the maximum possible area?	Answers.
A) 11 + √5 B) 11 + √6 C) 11 + 4√7 D) 11 + √65 E) 11 + 3√17

Solution: We can maximize the area of the triangle by making these two sides the base and the height of a right angle triangle. Then the third side is the hypotenuse with a length of √(49+16)= 
(49+16) = 65
√65   The perimeter is 11 + √65   The answer is 11 + √65.
Answer: D
A certain collage has total of 700 seniors each majoring in exactly one of six subjects. A minimum of 20 seniors major in each six subjects. If three quarter of the seniors major in one of four subjects, what is the greatest possible number of seniors majoring in one of the other two subjects? Choose the correct answer:
A) 100
B) 80
C) 75
D) 155
E) 50

Solution: Answer 155   700 = 525 + 20 + x => x = 155   = 3/4 * 700 in 4 subjects + 20 min for 5th subject + x = 700
Answer: D
If 20% of a = b, then b% of 20 is the same as: Choices
A) 4% of a	B) 5% of a	C) 6% of a	D) 3% of a	E) 2% of a

Solution: Here, 20% of a=b i.e.,(20/100)a=b   then, b% 20 i.e.,(b/100)x20---I   then sub b=(20/100)a in I   we get,   =(20/100)a x (1/100) * 20   =(20/100)a x (20/100)   =(400/10000)a   =(4/100)a   = 4% of a   4% of aNSWER :4% of a
Answer: A
If (1+y)x=xwhich of the following must be true? Pick:
A) x=-1 or y=0
B) x=0 or y=-1
C) x=1 or y=1
D) x=-1 or y=-1
E) y=0 or x=0

Solution: We have (1+y)x=x   If x=0, y=y. True   If y=0, (1+x)*0=0 True   So, y=0 or x=0 will be the answer.
Answer: E
If −2≤e≤0 and n > 19, which of the following CANNOT be the value of en?  Answers:
A) -48
B) -38
C) -20
D) 0
E) 19

Solution: value of en not equal to -19=19 -19....Rest all are achievable
Answer: E
A women paid $1650 a year in interest on a loan with an annual rate of 11%. How w\much more money could she have borrowed for the same amount of interest if she had been able to get a loan amount with an annual rate of 10%? Choose the correct choice from the following answers:  A) $165  B) $1500  C) $1815  D) $ 15000  E) $16500

Solution: Let P = Principal amount   R1 = Interest Rate for case 1   R2 = Interest Rate for case 2   Time = T = 1year   Now Interest = (P * R1* T)/ 100   We have 1650 = (P*11*1)/100 => we get P = 15000$   now Case 2 : P = 15000 R2= 10% T= 1year   Interest Amount is $1650( Interest Amount Remains same)   Now on $15000 with 10% Interest Amount is $1500.   We get, Difference in Interest Amount's is $ 150   Solve for   150 = (P * 10 * 1)/100   P = $ 1500 . So the women can borrow $1500 more.   Answer: $1500
Answer: B
Train A left station T at 3:30 p.m. and traveled on straight tracks at a constant speed of 60 miles per hour. Train B left station T on adjacent straight tracks in the same direction that train A traveled on. Train B left station T 40 minutes after train A, and traveled at a constant speed of 75 miles per hour. Train B overtook train A on these straight tracks. At what time did train B overtake train A? Choose the correct choice from the following answers.
A) 4:10
B) 5:40
C) 6:10
D) 6:50
E) 7:30

Solution: Train A left 40 mins before Train B at a speed of 60 mph   So distance traveled by Train A in 40 mins= 40 miles   Let's say the total distance at the point of overtaking is x   So, the time taken for covering the remaining distance x-40 by Train A=x-40/60   Time taken for covering the distance x at 75 mph by Train B=x/75   Both Time should be equal which gives us,   x-40/60=x/75   x=160 mins=2 hr 40 mins   Time when train B overtake train A = 3:30+40 mins+ 2 hr 40 mins= 6:50   Correct Answer is 6:50.
Answer: D
An error 2% in excess is made while measuring the side of asquare. The % of error in the calculated area of the square is?	Answers.
A) 4.00%  B) 4.04%  C) 4.26%  D) 4.56%  E) 4.67%

Solution: 100 cm is read as 102 cm.   A1 = (100 x 100) cm2 and A2 (102 x 102) cm2.   (A2 - A1) = [(102)2 - (100)2]   = (102 + 100) x (102 - 100)   = 404 cm2.   Percentage error = 404 x 100 % = 4.04%   100 x 100   4.04%
Answer: B
Tough and Tricky questions: Mixture Problems.
A drink holding 6 ounces of an alcoholic drink that is 1 part rum to 2 parts coke is added to a jug holding 38 ounces of an alcoholic drink that is 1 part rum to 3 parts coke. What is the ratio of rum to coke in the resulting mixture? Choose the most appropriate option:
A) 2:5
B) 5:16
C) 3:5
D) 4:7
E) 14:5

Solution: Answer = B) 5:16   ........................ Rum ..................... Coke ................. Total   First Drink ........... 2 ............................ 4 ..................... 6 (Ratio 1:2)   Second Drink ....... 8 ............................. 24 ................... 32 (Ratio 1:3)   Total .................. 10 ............................. 28 .................... 38   Ratio = 10:32= 5:16   5:16
Answer: B
If x and y are integers and x + y = 6, which of the following must be true?  Choose the correct choice from the following answers
A) x and y are consecutive integers.  B) If x < 0, then y > 0.  C) If x > 0, then y < 0.  D) Both x and y are even.  E) Both x and y are less than 5.

Solution: In option C if x > 0,then y<0 means x is +ve and y is -ve   In option B if x < 0, then y>0 means y is +ve and x is -ve, both are same and satisfying x+y = 5.   How option If x < 0, then y > 0. is right could you explain   If x < 0, then y > 0.
Answer: B
The greatest possible length which can be used to measure exactly the length 6m, 3m 85cm, 12 m 95 cm is
Choices.
A) 2	B) 7	C) 5	D) 8	E) 9

Solution: Explanation:   Required Length = H.C.F of 600 cm, 385 cm and 1295 c   = 5 cm.   Answer: 5) 5 cm
Answer: C
A and B can do a piece of work in 6 2/3 days and 5 days respectively. They work together for 2 days and then A leaves. In how many days after that B will complete the work alone.  Answers:
A) 1 ½ days	B) 2 ½ days	C) 3 ½ days	D) 4 ½ days	E) 5 ½ days

Solution: 1 ½ days   1 ½ days   3/20 * 2 + (2 + x)/5 = 1   x = 1 ½ days
Answer: A
The probability of having a girl is identical to the probability of having a boy. In a family with four children, what is the probability that all the children are of the same gender? Choose the correct answer
A) 1/8. B) 1/3 C) 1/4 D) 1/6 E) 1/2

Solution: There are two cases. All boys and all girls   case 1. all boys.   1/2*1/2*1/2*1/2= 1/16   case 2 .all girls.   1/2*1/2*1/2*1/2=1/16   We will add the cases to get 1/8
Answer: A
The sum of two consecutive number is 67. Which is the larger number?  Choose the correct choice from the following answers: A) 34 B) 43 C) 44 D) 45 E) 46

Solution: Let consecutive number be x, x+1   Therefore sum of the consecutive number is x + x+1=67   2x+1=67   2x=66   x=33   Therefore larger number is x+1=34   34NSWER:34
Answer: A
A train runs at the speed of 72 kmph and crosses a 250 m long platform in 26 seconds. What is the length of the train? Choose the correct choice from the following answers:
A) 270 m B) 210 m C) 340 m D) 130 m E) 140 m

Solution: Explanation:   Speed= 72 kmph = 72×10/36 = 20 m/s   Distance covered = 250+ x where x is the length of the train   Time = 26 s   (250+x)/26 = 20   250+x = 26×20 = 520 m   x = 520-250= 
520-250 = 270
270 m   270 mnswer: Option 270 m
Answer: A
A circular well with a diameter of 2 meters, is dug to a depth of 14 meters. What is the volume of the earth dug out.
Choose the most appropriate option
A) 40m3
B) 42m3
C) 44m3
D) 46m3
E) None of these

Solution: Explanation:   Volume=πr2hVolume=(22/7∗1∗1∗14)m3=44m3   Option 44m3
Answer: C
D and E are two points respectively on sides AB and AC of triangle ABC such that DE is parallel to BC. If the ratio of area of triangle ADE to that of the trapezium DECB is 144:25 and BC=13 cm, then find the length of DE. Choose the correct choice from the following options
A) 12 B) 13 C) 14 D) 11 E) 15

Solution: ABC and ADE are similar triangles.   So (side of AB14/side of ADE)^2=25/169   side of AB14/side of ADE = 5/13   So the length of DE = 5   Answer - 14
Answer: C
A box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that exactly three bulbs are good?  Answers:
A) 20/67  B) 20/63  C) 20/68  D) 20/28  E) 20/27

Solution: Required probability   = (⁵C₃ . ⁴C₁)/⁹C₄ = (10 * 4)/126   = 20/63   Answer:20/63
Answer: B
Which of the following inequalities is always true for any non-negative real number 'x' and 'y'? Choose the correct answer.
A) √(x+y) <= √x + √y	B) √(x-y) <= √x - √y	C) √(x+y) = √x + √y	D) √(x-y) >= √x - √y	E) √(x+y) >= √x + √y

Solution: Using the principle of subadditivity which we know applies with square roots, we know that evaluating the function for the sum of two elements will always produce something less than or equal to the sum of the function's values at each element. Therefore, the answer is √(x+y) <= √x + √y.
Answer: A
The number 83 can be written as the sum of the squares of 3 different positive integers. What is the sum of these 3 integers?  Answers.
A) 17  B) 16  C) 15  D) 14  E) 13

Solution: 7^2+5^2+3^2=49+25+9= 
49+25+9 = 83
83   7+5+3= 
7+5+3 = 15
15   Hence answer is 15
Answer: C
After replacing an old member by a new member, it was found that the average age of five members of a club is the same as it was 3 years ago. What is the difference between the ages of the replaced and the new member ?  Choose the correct choice from the following options
A) 37
B) 29
C) 11
D) 15
E) 12

Solution: Explanation:   i) Let the ages of the five members at present be a, b, c, d & e years.   And the age of the new member be f years.   ii) So the new average of five members' age = (a + b + c + d + f)/5 ------- (1)   iii) Their corresponding ages 3 years ago = (a-3), (b-3), (c-3), (d-3) & (e-3) years   So their average age 3 years ago = (a + b + c + d + e - 15)/5 = x ----- (2)   ==> a + b + c + d + e = 5x + 15   ==> a + b + c + d = 5x + 15 - e ------ (3)   iv) Substituting this value of a + b + c + d = 5x + 15 - e in (1) above,   The new average is: (5x + 15 - e + f)/5   Equating this to the average age of x years, 3 yrs, ago as in (2) above,   (5x + 15 - e + f)/5 = x   ==> (5x + 15 - e + f) = 5x   Solving e - f = 15 years.   Thus the difference of ages between replaced and new member = 15 years.   Answer: 15
Answer: D
Suppose you flip a fair coin 8 times. What is the probability that, in 8 flips, you get at least one head? Choose one:
A) 55/256
B) 255/256
C) 155/256
D) 5/256
E) 201/256

Solution: 255/256est way of solving an at least 1 type of question is to compute 1 - probability of flipping 0 heads   probability of flipping either a head or a tail = 1/2   probability of flipping 3 tails in a row (1/2)^5   probability of flipping at least 1 head = 1 - (1/2)^8 = 255/256   Answer : 255/256
Answer: B
If athul rows 16 km upstream and 24 km down steam taking 4 hours each, then the speed of the stream Choose the most appropriate option
A) 1kmph B) 2 kmph C) 1.5 kmph D) 12 kmph E) 15 kmph

Solution: Speed upstream = 16/4= 
16/4 = 4
4 kmph   Speed down stream= 24/4= 
24/4 = 6
6 kmph   Speed of stream= ½ (6-4) = 1 kmph   1kmphNSWER:1kmph
Answer: A
The breath of a rectangular landscape is 6 times its length. There is a playground in it whose area is 4200 square mtr & which is 1/7 th of the total landscape. What is the breath of the landscape?  Choose the correct answer:
A) 520  B) 420  C) 320  D) 550  E) 450

Solution: Sol. 6x * x =7* 4200   x = 70   Length = 6* 70= 
6* 70 = 420
420 420
Answer: B