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mathematics

A man saves Rs. 200 at the end of each year and lends the money at 5% compound interest. How much will it become at the end of 3 years?

Amount = [200(1 + 5/100)3 + 200(1 + 5/100)2 + 200(1 + 5/100)] = [200 * 21/20(21/20 * 21/20 + 21/20 + 1)] = Rs. 662.02 Answer:C The answer is: C

C

mathematics

The annual interest rate earned by an investment increased by 10 percent from last year to this year. If the annual interest rate earned by the investment this year was 12.5 percent, what was the annual interest rate last year?

12.5=1.1*x X=11.36% Answer D) The answer is: D

D

mathematics

A,B,C invested the capitals in a business. If A invested Rs. 5000 more than B and C invested Rs.20,000 more than A, then how should a profit of Rs.36,000 be divided among A,B and C? Given : Capital of B is Rs.10,000

A==15,000 B==10,000 C==35,000 so, ration are 3:2:7 profit 14000 so,, 12000/12==1000 so,, A==3000, B==2000,, C==7000 ANSWER:D The answer is: D

D

mathematics

11, 13, 17, 19, 23, 29, 31, 37, 41, ?

The series consists of prime numbers. Answer : A. The answer is: A

A

mathematics

The number 95 can be written as the sum of the squares of 4 different positive integers in two ways. Of the following, which can be the sum of these 4 integers

The only possible sum for 4 different squares of an integer with total sum number is 95 are : 49 + 36 + 9 + 1 = 95 which are the square from numbers : 7, 6, 3, 1 (total sum number is 20) or 81 + 9 + 4 + 1 = 95 which are the square from numbers : 9, 3, 2, 1 (total sum number is 15) hence the answer is (E) The answer is: E

E

mathematics

30 ladies and 60 gentlemen are present at a party. There are 23 couples among them. If a lady and a gentleman is selected at random, what is the probability that they will be a couple?

In how many ways we can select a woman and a man from 30 women and 60 men? In 30*60 = 1800 ways. We have a total of 23 couples so, the probability of selecting a couple is 23/1800 = 23/1800. Ans- E The answer is: E

E

mathematics

There are 5 chess amateurs playing in Villa's chess club tournament. If each chess amateur plays with exactly 16 other amateurs, what is the total number of chess games possible to be played in the tournament?

Each person is one participant of 4 games. So there are in all 16*5 = 80 instances of one participant games. But each game has 2 participants so total number of games = 80/2 = 40 C The answer is: C

C

mathematics

A man's speed with the current is 18 km/hr and the speed of the current is 2.5 km/hr. The man's speed against the current is?

Man's speed with the current = 18 km/hr => speed of the man + speed of the current = 18 km/hr speed of the current is 2.5 km/hr Hence, speed of the man = 18 - 2.5 = 20.5 km/hr man's speed against the current = speed of the man - speed of the current = 20.5 - 2.5 = 18 km/hr Answer is B. The answer is: B

B

mathematics

Keats Library purchases a number of new books, all in the category of biography, and the library does not acquire any other books. With the addition of the new biographies, the biography collection of the library amounts to 55% of the total number of books in the library. If prior to the purchase, only 20% of the books in Keats Library were biographies, by what percent has the number of biographies in the library increased?

Let x be the number of new biographies added to the library. Let b be the original number of biographies, so the original number of books was 5b. 0.55(5b+x) = b+x 1.75b = 0.45x x = 3.9b The answer is D. The answer is: D

D

mathematics

Which of the following equations represents a line that is perpendicular to y=1/3*x+2?

For two lines to be perpendicular, the product of slopes should be equal to -1. Slope of line 1 = 1/2 Slope of the line perpendicular to line 1 must be -2. Option C can be rewritten as y = -2x + 4 --> Slope = -2 Answer: D The answer is: D

D

mathematics

Find the value of x in (x+1)/(x+3)=5

(x-1)/(x+3)=5 Multiplying both sides with x+3 gives x+1=5(x+3) = x+1=5x+15 Subtracting x from both sides gives 4x+15=1 Subtracting 15 from both sides gives 4x=-14 Dividing by 4 on both sides gives x=-3.5 Answer: E The answer is: E

E

mathematics

What is the probability that a leap year has 53 Sundays and 52 Mondays?

A leap year has 52 weeks and two days Total number of cases = 7 Number of favourable cases = 1 i.e., {Saturday, Sunday} Required Probability = 1/7 Answer:B The answer is: B

B

mathematics

Jisha walked for 3 days. She walked 18 miles on the first day, walking 3 miles per hour. On the second day she walked for one less hour but she walked one mile per hour, faster than on the first day. On the third day she walked the same number of hours as on the first day, but at the same speed as on the second day. How many miles in total did she walk?

Jisha walked 18 miles on the first day, walking 3 miles per hour i.e. total time of walk on Day-1 = 18/3 = 6 Hours Second day time of walk = 6-1 = 5 hours and Speed = 3+1=4 miles per hour i.e. Distance walked on second day = 5*4 = 20 miles Third day time of walk = 6 hours and Speed = 4 miles per hour i.e. Distance walked on second day = 6*4 = 24 miles Total Distance travelled on three days = 18+20+24 = 62 Answer: Option E The answer is: E

E

mathematics

Which of these must the factor F of the product of four consecutive even integers:- 1) 48 2) 64 3) 96 4) 192 5) 80

Let the four variables be a< b< c< d. Assume a worst case scenario where the a equal to a prime number (hence odd). therefore a = divisible by 1 b = a + 1 (divisible by 2) c = a + 3 (divisible by 3) d = a + 4 (divisible by 4) therefore each answer choice must be divisible by 2 x 3 x 4 = 24 only 80 is not divisible. Therefore answer = D The answer is: D

D

mathematics

3 buffaloes eat as much as 4 cows or 2 oxen. At a farm, there are 15 buffaloes, 8 oxen, and 24 cows. The fodder for these cattle is available for 48 days. If 60 more cows and 30 more buffaloes are brought in, how many days will the fodder last?

2 oxen = 3 buffaloes = 4 cows Also: 15 buffaloes + 8 oxen + 24 cows = 10 oxen + 8 oxen + 12 oxen = 30 oxen There is enough fodder for 1 oxen for 30*48 days. 60 cows + 30 buffaloes = 30 oxen + 20 oxen = 50 oxen The new total is equal to 80 oxen instead of 30 oxen. 30*48 / 80 oxen = 18 days The answer is B. The answer is: B

B

mathematics

here are 6 periods in each working day of a school. In how many ways can one organize 5 subjects such that each subject is allowed at least one period?

5 subjects can be arranged in 6 periods in 6P5 ways. Any of the 5 subjects can be organized in the remaining period (5C1 ways). Two subjects are alike in each of the arrangement. So we need to divide by 2! to avoid overcounting. Total number of arrangements = 6P5× 5C1 /2!=1800 Ans: D The answer is: D

D

mathematics

7 + 3 x 14 + 6 x 7^2 + 6 x 7^3 + 6 x 7^4 + 6 x 7^5 + 6 x 7^6 + 6 x 7^7 =

Let's see that 7 + 3 x 14 is 49 or 7^2, then: 7^2 + 6 x 7^2 becomes 7 x 7^2 that is 7^3. So we follow with the next element: 7^3 + 6 x 7^3 is equal to 7 x 7^3 that is 7^4. Then is assumed right before 6 x 7^7: 7^7 + 6 x 7^7 becomes 7 x 7^7 that is 7^8. Thus, the correct answer is the option D, 7^8. The answer is: D

D

mathematics

A river 2m deep and 45 m wide is flowing at the rate of 2 kmph the amount of water that runs into the sea per minute is?

Explanation: (2000 * 2 * 45)/60 = 3000 M3 Answer: Option A The answer is: A

A

mathematics

In how many ways can you seat 7 people on a bench if one of them does not want to sit at either end?

One person can choose 5 possible chairs to sit. The remaining 6 people can sit in 6! ways. The number of arrangements is 5*6! = 3600. The answer is B. The answer is: B

B

mathematics

A can give B 100 meters start and C 150 meters start in a kilometer race. How much start can B give C in a kilometer race?

Explanation: A runs 1000 meters while B runs 900 meters and C runs 850 meters. Therefore, B runs 900 meters while C runs 850 meters. So, the number of meters that C runs when B runs 1000 meters = (1000 x 850)/900 = 944.44 meters Thus, B can give C (1000 - 944.44) = 55.55 meters start Answer:D The answer is: D

D

mathematics

Raviraj invested an amount of 100000000 at compound interest rate of 10 pcpa for a period of three years. How much amount will Raviraj get after three years?

Amount = 100000000(1 + 10⁄100)3 = 100000000 × 11⁄10 × 11⁄10 × 11⁄10 = 133100000 Answer E The answer is: E

E

mathematics

Two trains are moving in opposite directions @ 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.9 km respectively. The time taken by the slower train to cross the faster train in seconds is:

Relative speed=60+90=150*5/18=(125/3)m/s Total Distance covered=(1.10+0.9)= 2 km = 2000m Required time = (2000*3/125) = 48sec ANSWER:C The answer is: C

C

mathematics

The mean of (54,822)^2 and (54,824)^2 =

54822^2 = (54823-1)^2 = 54823^2 + 1^2 - 2*54823*1 54824^2 = (54823+1)^2 = 54823^2 +1^2 + 2*54821*1 Taking the average of above 2 , we get (54823)^2 +1 hence the answer is D The answer is: D

D

mathematics

A jogger running at 9 km/hr along side a railway track is 270 m ahead of the engine of a 120 m long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger?

Speed of train relative to jogger = 45 - 9 = 36 km/hr. = 36 * 5/18 = 10 m/sec. Distance to be covered = 270 + 120 = 390 m. Time taken = 390/10 =39 sec. Answer: C The answer is: C

C

mathematics

If (n+2)!/n!=182, n=?

(n+2)!/n!= 182 Rewrite as:[(n+2)(n+1)(n)(n-1)(n-2)....(3)(2)(1)]/[(n)(n-1)(n-2)....(3)(2)(1)]= 132 Cancel out terms: (n+2)(n+1) = 132 From here, we might just TEST the answer choices. Since (14)(13) = 182, we can see that n = 12 E The answer is: E

E

mathematics

Company M produces two kinds of stereos: basic and deluxe. Of the stereos produced by Company S last month, 2/3 were basic and the rest were deluxe. If it takes 1.5 as many hours to produce a deluxe stereo as it does to produce a basic stereo, then the number of hours it took to produce the deluxe stereos last month was what fraction of the total number of hours it took to produce all the stereos?

The easiest way for me is to plug in numbers. Let the number of basic stereos produced be 40, and number of delux stereos produced be 20. Total of 60 stereos. If it takes an hour to produce a basic stereo then it will take 1.5 hours to produce a deluxe stereo. 40 basic stereos = 40 hours. 20 delux stereos = 30 hours. Total hours = 70. Then the fraction would be 30/70 = 3/7 Therefore answer C. The answer is: C

C

mathematics

8 men can dig a pit in 20 days.If a men work half as much again as a boy,then 4 men and 9 boys can dig a similar pit.Fint the days for 15 boys can dig?

1 man=3/2 boys (4 men+9 boys)=15 boys 8 men=[(3/2)+8]=12 boys now, 12 boys can dig the pit in 20 days. 15 boys can dig=16 days. Answer is option E The answer is: E

E

mathematics

Rahul went to a shop and bought things worth Rs. 25, out of which 30 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?

Total cost of the items he purchased = Rs.25 Given that out of this Rs.25, 30 Paise is given as tax => Total tax incurred = 30 Paise = Rs.30/100 Let the cost of the tax free items = x Given that tax rate = 6% ∴ (25−30/100−x)6/100 = 30/100 ⇒ 6(25 −0.3 −x) = 30 ⇒ (25 − 0.3 − x) = 5 ⇒ x = 25 − 0.3 − 5 = 19.7 A) The answer is: A

A

mathematics

What is the remainder when the number 14^2 * 15^8 is divided by 5?

14^2 has units digit 6 15^8 has units digit 5 Thus 14^2*15^8 has units digit 0 and will be divisible by 5. The remainder will be zero Answer: (A) The answer is: A

A

mathematics

A rabbit on a controlled diet is fed daily 300 grams of a mixture of two foods, food X and food Y. Food X contains 10% protein and food Y contains 15% protein. If the rabbit's diet provides exactly 40 grams of protein daily, how many grams of food X are in the mixture.

Let x be the amount of food X. 0.1x + 0.15(300-x) = 40 0.05x = 5 x = 100 The answer is A. The answer is: A

A

mathematics

Find the length of the longest pole that can be placed in a room 12 m long 8m broad and 9m high.

Length of longest pole = Length of the diagonal of the room = sqrt(12^2+8^2+9^2= sqrt(289)= 17 m. Answer is E. The answer is: E

E

mathematics

A man can row at 6 kmph in still water. If the velocity of current is 1 kmph and it takes him 1 hour to row to a place and come back, how far is the place?

Explanation: Speed in still water = 6 kmph Speed of the current = 1 kmph Speed downstream = (6+1) = 7 kmph Speed upstream = (6-1) = 5 kmph Let the required distance be x km Total time taken = 1 hour ⇒ x/7+x/5=1 ⇒5x+7x=35 ⇒12x=35 ⇒x=2.9 km Answer: Option C The answer is: C

C

mathematics

A crate measures 5 feet by 8 feet by 12 feet on the inside. A stone pillar in the shape of a right circular cylinder must fit into the crate for shipping so that it rests upright when the crate sits on at least one of its six sides. What is the radius, in feet, of the pillar with the largest volume that could still fit in the crate?

We can find the radius of all the three cases of cylinders. The only crux to find the answer faster is that: Voulme is pi*r^2*h. The volume is a function of r^2. so r has to be the highest to find the largest volume. So r=5 for the surface 8*12 face. Volume = 125pi Answer C The answer is: C

C

mathematics

The probability of two events A and B are0.25 and 0.40 respectively. The probability that both A and B occur is 0.20. The probability that neither A nor B occur is _________

we are apply that formula.............. P(AorB)=P(A)+P(B)-P(A AND B) =.25+.40-.20 =.45 but the probability of neither A nor B=1-.45 =0.55 ANSWER:C The answer is: C

C

mathematics

A rectangular box of volume x has width, depth and height in the ratio of 2:3:3 (in that order). What is the width as a function of x?

We are given width = 2, depth = 3, height = 3 Then Volume x = Width x Depth x Height = 2*3*3 = 18 i.e. x = 18 i.e. The correct option should result in 2 on substituting the value of x=18 Checking options with x=18 A) (2x/12)^(1/2) = (2*18/12)^(1/2) = 3^(1/2) INCORRECT ANSWER B) (x/2)^(1/2) = (18/2)^(1/2) = 9^(1/2) = 3 INCORRECT ANSWER C) (x/3)^(1/2) = (18/3)^(1/2) INCORRECT ANSWER D) (2x/9)^(1/2) = (2*18/9)^(1/2) = 4^(1/2) = 2 CORRECT ANSWER E) (x)^(1/2) = (18)^(1/2) INCORRECT ANSWER Answer: Option D The answer is: D

D

mathematics

A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?

Speed = (54 * 5/18) m/sec = 15 m/sec. Length of the train = (15 x 20)m = 300 m. Let the length of the platform be x meters. Then, (x + 300)/36 = 15 ==> x + 300 = 540 ==> x = 240 m. Answer: B The answer is: B

B

mathematics

If two numbers are in the ratio 2:3. If 12 is added to both of the numbers then the ratio becomes 3:4 then find the smallest number?

2:3 2x + 12 : 3x + 12 = 3 : 4 4[2x + 12] = 3[3x + 12] 8x + 48 = 9x + 36 9x - 8x = 48 - 36 x = 12 Then smallest number is = 2 2x = 24 Correct Option D The answer is: D

D

mathematics

In Arun's company 60% of the employees earn less than $50,000 a year, 60% of the employees earn more than $40,000 a year, 11% of the employees earn $43,000 a year and 5% of the employees earn $49,000 a year. What is the median salary for the company?

In Arun's company 60% of the employees earn less than $50,000 a year, 50 and 51 employee will be each 43K. hence median = (43K+43k)/2 The answer is: A

A

mathematics

If a man can cover 32 metres in one second, how many kilometres can he cover in 3 hours 45 minutes?

32 m/s = 32 * 18/5 kmph 3 hours 45 minutes = 3 3/4 hours = 15/4 hours Distance = speed * time = 32 * 18/5 * 15/4 km = 432 km. Answer: D The answer is: D

D

mathematics

If a light flashes every 6 seconds, how many times will it flash in 1/2 of an hour?

In 1/2 of an hour there are 30*60 = 1800 seconds The number of 6-second intervals = 1800/6 = 300 After the first flash, there will be 300 more flashes for a total of 301. The answer is A. The answer is: A

A

mathematics

A river 5m deep and 35 m wide is flowing at the rate of 2 kmph, calculate the amount of water that runs into the sea per minute?

Rate of water flow-2kmph--2000/60--33.33 m/min depth of river--5m width of river--35m vol of water per min--33.33 *5*35---5832.75 Answer A The answer is: A

A

mathematics

The sector of a circle has radius of 21 cm and central angle 180o. Find its perimeter?

Perimeter of the sector = length of the arc + 2(radius) = (135/360 * 2 * 22/7 * 21) + 2(21) = 108 cm Answer: Option C The answer is: C

C

mathematics

A boy wants to go abroad by boat and return by flight. He has a choice of 4 different boat to go and 6 flight to return. In how many ways, can the boy perform his journey?

Ans.(D) Sol. Number of choices to go by ship = 4 Number of choices to return by airline = 6 From, fundamental principle, total number of ways of performing the journey = 4 x 6 = 24 ways The answer is: D

D

mathematics

Pipe A can fill a tank in 16 minutes and pipe B cam empty it in 24 minutes. If both the pipes are opened together after how many minutes should pipe B be closed, so that the tank is filled in 30 minutes?

Let the pipe B be closed after x minutes. 30/16 - x/24 = 1 => x/24 = 30/16 - 1 = 14/16 => x = 14/16 * 24 = 21. Answer:E The answer is: E

E

mathematics

If p is even and q is odd, which of the following is odd?

Just checking options (In case you have difficulty then choose values of r=2 and t=1) p = even q= Odd A. pq = Even*Odd = EvenINCORRECT B. 5pq = Odd*Even*Odd = EvenINCORRECT C. 6(pr^2)q = 6*(Even^2)*Odd = EvenINCORRECT D. 5p + 6q = 5*Even + 6*Odd = Even+Even = EvenINCORRECT E. 6p + 5q = 6*Even + 5*Odd = Even+Odd = OddCORRECT Answer: option E The answer is: E

E

mathematics

A sum of Rs.4800 is invested at a compound interest for three years, the rate of interest being 10% p.a., 20% p.a. and 25% p.a. for the 1st, 2nd and the 3rd years respectively. Find the interest received at the end of the three years.

Let A be the amount received at the end of the three years. A = 4800[1 + 10/100][1 + 20/100][1 + 25/100] A = (4800 * 11 * 6 * 5)/(10 * 5 * 4) A = Rs.7920 So the interest = 7920 - 4800 = Rs.3120 ANSWER:B The answer is: B

B

mathematics

If f(x) = 2x^2 + y, and f(2) = 100, what is the value of f(5)?

f(x) = 2x^2 + y f(2) = 100 => 2*(2)^2 + y = 100 => 8 + y = 100 => y = 92 f(5)= 2*(5)^2 + 92 = 142 Answer E The answer is: E

E

mathematics

Java House charges $3.25 for a cup of coffee that costs a total of $2.85 to make. Cup'O'Joe charges $2.80 for a cup that costs $2.65 to make. If Java House sells 24,000 cups of coffee, how many must Cup'O'Joe sell to make at least as much in total gross profit as its competitor does?

Java: Profit/Cup = 3.25-2.85 = 0.4 : No of Cups = 24,000 : Gross Profit = 24,000*0.4 = 9,600 Joe: Profit/Cup = 0.15 : Gross Profit = 9,600 : No of Cups = 9,600/0.15 = 64000 Answer D The answer is: D

D

mathematics

22 people are there, they are shaking hands together, how many hand shakes possible,if they are in pair of cyclic sequence.

in case of cycle no of handshakes = no of persons hence ans = 22 ANSWER:D The answer is: D

D

mathematics

A metallic sheet is of rectangular shape with dimensions 48 m x 36 m. From each of its corners, a square is cut off so as to make an open box. If the length of the square is 8 m, the volume of the box (in m3) is:

EXPLANATION Clearly, l = (48 – 16)m = 32 m, b = (36 -16)m = 20 m, h = 8 m. Volume of the box = (32 x 20 x 8) m3 = 5120 m3. Answer B The answer is: B

B

mathematics

Find the value of (1/(2*3))+(1/(3*4))+(1/(4*5))+(1/(5*6))+…..+ ((1/(9*10)).

Given expression=((1/2)-(1/3))+((1/3)-(1/4))+((1/4)-(1/5))+ ((1/5)-(1/6))+….+ ((1/9)-(1/10)) =((1/2)-(1/10))=4/10 = 2/5. Answer is A. The answer is: A

A

mathematics

45% of the employees of a company are men. 60% of the men in the company speak French and 40% of the employees of the company speak French. What is % of the women in the company who do not speak French?

No of employees=100(say) Men=45 Women=55 Men speaking french=0.6*45=27 Employees speaking french=0.55*100=55 Therefore women speaking French=55-42=13 And women not speaking French=55-13=42 % of women not speaking French=42/55*100=76.36% Answer C The answer is: C

C

mathematics

A certain board game has a row of squares numbered 1 to 100. If a game piece is placed on a random square and then moved 7 consecutive spaces in a random direction, what is the probability T the piece ends no more than 7 spaces from the square numbered 49?

OA is E required prob is 7 spaces any side of 49. so total 14 spaces are required in 7 moves which can be achieved by max 7 move on any side so total spaces = 28 probability T= 28%.E The answer is: E

E

mathematics

Find compound interest on Rs. 7500 at 4% per annum for 2 years, compounded annually

Explanation: Please apply the formula Amount=P(1+R100)nC.I. = Amount - P Answer: D The answer is: D

D

mathematics

If the average of 744, 745, 747, 748, 749, 752, 752, 753, 755 and x is 750, what is the value of x?

Sum of the deviations of the numbers in the set from the mean is always zero 744, 745, 747, 748, 749, 752, 752, 753, 755 mean is 750 so the list is -6-5-3-2-1+2+2+3+5... this shud total to zero but this is -5 , hence we need a number that is 5 more than the mean to get a +5 and make it zero hence the answer is 750 + 5 =755 D The answer is: D

D

mathematics

A four-character password consists of one letter of the alphabet and three different digits between 0 and 7, inclusive. The letter must appear as the second or third character of the password. How many different passwords are possible?

4 character password: DLDD First digit can be chosen in 8 ways. The letter can be chosen in 26 ways. Next digit can be chosen in 7 ways. Next digit can be chosen in 6 ways. This gives us 8*26*7*6ways Now, the letter can also be DDLD so there will be another 8*26*7*6 ways Total = 8*26*7*6*2 = 17,472 ways C The answer is: C

C

mathematics

Find the smallest number which should be multiplied with 36963 to make it a perfect square.

36963 = 111*111*3 Required smallest number = 3 3 is the smallest number which should be multiplied with 36963 to make it a perfect square. ANSWER:D The answer is: D

D

mathematics

Find the compound interest and the amount on Rs.8000 at 5% per annum for 3 years when C.I is reckoned yearly?

A = 8000(21/20)3 = 9261 = 8000 --------- 1261 Answer: A The answer is: A

A

mathematics

The distance light travels in one year is approximately 5,870,000,000,000 miles. the distance light in 100 year is

the distance of the light travels in 100 years is 5,870,000,000,000 x 100 miles= 587,000,000,000,000=587 x 10 power12 miles, correct answer will be (B) The answer is: B

B

mathematics

Due to construction, the speed limit along an 9-mile section of highway is reduced from 55 miles per hour to 30 miles per hour. Approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ?

Old time in minutes to cross 9 miles stretch = 9*60/55 = 9*12/11 = 9.81 New time in minutes to cross 9 miles stretch = 9*60/30 = 9*2/1 = 18 Time difference = 8.19 Ans:E The answer is: E

E

mathematics

A boat goes 8 km upstream in 24 minutes. The speed of stream is 4 km/hr. The speed of boat in still water is:

Speed upstream =8(24/60) = 20 km/hr Speed of the stream = 4 km/hr speed of boat in still water = (20+4) = 24 km/hr Answer: A The answer is: A

A

mathematics

Machine A can do a certain job in 8 hours. Machine B can do the same job in 10 hours. Machine C can do the same job in 12 hours. All three machines start the job at 9:00 a.m. Machine A breaks down at 11:00 a.m., and the other two machines finish the job. Approximately what time Q will the job be finished?

Ans: C (1:00pm) From 9:00-11:00c(2 hrs) A can do 1/8 Job/hr. so in 2 hours he can do 1/4 job. B can do 1/10 job/hr so in 2 hrs. he can do 1/5 Job. C can do 1/12 job/hr so in 2 hours he can do 1/6 job. Total = 1/4+1/5+1/6 = 37/60 Job Now balance work needs to be done by B and C. Balance Work= 23/60 Job Combined rate of B and C = 1/10+1/12 = 11/60 job/hr. So they will do 22/60 work in 2 hrs (approx. to the balance work of 23/60) Hence the Job will be completed 2hrs. after 11:00 i.e. @ 1:00pm=Q Ans: C (1:00pm) The answer is: C

C

mathematics

Shekar scored 76, 65, 82, 67 and 55 marks in Mathematics, Science, Social studies, English and Biology respectively. What are his average marks?

Explanation : Average= (76+65+82+67+55)/5 = 375/5 =69 Hence average=69 Answer : B The answer is: B

B

mathematics

Water consists of hydrogen and oxygen, and the approximate ratio, by mass, of hydrogen to oxygen is 2:16. Approximately how many grams of oxygen are there in 126 grams of water?

(16/18)*126 = 112 grams The answer is B. The answer is: B

B

mathematics

What is 30% of 210?

X/210 = 30/100 100X = 210X30 X =(210X30)/100 X =6300/100 = 63 ANSWER = B = 63 The answer is: B

B

mathematics

A and B start a business with investments of Rs. 5000 and Rs. 4500 respectively. After 4 months, A takes out half of his capital. After two more months, B takes out one-third of his capital while C joins them with a capital of Rs. 7000. At the end of a year, they earn a profit of Rs. 5080. Find the share of each member in the profit.

Explanation: A:B:CA:B:C =(5000×4+2500×8)=(5000×4+2500×8) :(4500×6+3000×6):(4500×6+3000×6) :(7000×6):(7000×6) =40000:45000:42000=40000:45000:42000 =40:45:42=40:45:42. A's share = Rs. 5080×401275080×40127 = Rs. 1600. B's share = Rs. 5080×451275080×45127 = Rs. 1800. C's share = Rs. 5080×421275080×42127 = Rs. 1680. ANSWER IS A The answer is: A

A

mathematics

A circle in the coordinate plane passes through points (-3, -2) and (2, 4). What is the smallest possible area of that circle?

The distance between the two points is sqrt(61). radius = sqrt(61)/2 Area= pi*(sqrt(61)/2)^2 B. 15.25π The answer is: B

B

mathematics

If a and b are consecutive integers (b>a), which of the following statements could be false? 1. a^4+b is always even number. 2. a^2*b is always even number 3. (a + b) is always an odd number.

2^4+3 =16+3 = 19 Option I false 2^2 * 3 = 4+3 =7 (odd number). Option II is false odd + even = odd. Option III is true Answer : C The answer is: C

C

mathematics

If the length of a rectangle is increased by 20% and the breadth is reduced by 20%, what will be the effect on its area?

Percentage change = x - y - xy⁄100 = 20 – 20 – 20×20/100=−4%=4%decrease Answer D The answer is: D

D

mathematics

On multiplying a numberZ by 153, the result obtained was 102325. However, it is found that both the 2's are wrong. Find the correct result.

The only thing you actually know about the correct number Z is that it is divisible by 153 and has 5 as a factor. You should immediately try to find the factors of 153 and look for them in the options. 153 = 9*17 Divisibility by 9 is easy to check. Only (D) satisfies. The answer is: D

D

mathematics

Find the area of circle whose radius is 21m?

22/7 * 21 * 21 = 1386 Answer: E The answer is: E

E

mathematics

A batsman scored 125 runs which included 5 boundaries and 5 sixes. What percent of his total score did he make by running between the wickets?

Explanation : Number of runs made by running, =>125−(5×4+5×6). =>125-50 =>75 Hence, the required percentage is:- =>75/125*100 =>60% Answer : E The answer is: E

E

mathematics

A car traveled 480 miles per tankful of gasoline on the highway and 336 miles per tankful of gasoline in the city. If the car traveled 6 fewer miles per gallon in the city than on the highway, how many miles per gallon did the car travel in the city?

Let the speed in highway be h mpg and in city be c mpg. h = c+6 h miles are covered in 1 gallon 462 miles will be covered in 462/h. Similarly c miles are covered in 1 gallon 336 miles will be covered in 336/c. Both should be same (as car's fuel capacity does not change with speed) => 336/c = 480/h => 336/c = 480/(c+6) => 336c+336*6=480c =>c=336*6/144 =14 Answer A. The answer is: A

A

mathematics

If Henry were to add 4 gallons of water to a tank that is already 3/4 full of water, the tank would be 7/8 full. How many gallons of water would the tank hold if it were full?

7/8x-3/4x=4galls 1/8*x=4gallons x=32 gallons Answer A The answer is: A

A

mathematics

Jerry’s average (arithmetic mean) score on the first 3 of 4 tests is 81. If Jerry wants to raise his average by 2 points, what score must he earn on the fourth test?

Total score on 3 tests = 81*3 = 243 Jerry wants the average to be = 83 Hence total score on 4 tests should be = 83*4 = 332 Score required on the fourth test = 332 - 243 = 89 Option B The answer is: B

B

mathematics

A random 10-letter code is to be formed using the letters A, B, C, D, E, F, G, H, I and I (only the “I” will be used twice). What is the probability that a code that has the two I’s adjacent to one another will be formed?

Total number of combinations possible = 10!/2!10!/2! Total favorable combinations = 9!9! - We have considered the two Is as one element. Since we have two Is, they can interchange their positions, without affecting the code. Probability = 9!/(10!/2!)=9!∗2!/10!=1/59!/(10!/2!)=9!∗2!/10!=1/5 ANS:C The answer is: C

C

mathematics

The sum of 3 hours 45 minutes and 1 hours 55 minutes is approximately what percent of a day?

Since the question is asking for an approximate percentage 3:45+1:55 ~ 6 hours % of day = 6*100/24 ~ 6*100/25= 24% Answer is D. The answer is: D

D

mathematics

A cycle is bought for Rs.900 and sold for Rs.1260, find the gain percent?

900 ---- 360 100 ---- ? => 40% Answer:C The answer is: C

C

mathematics

An order was placed for the supply of a carpet whose breadth was 6 m and length was 1.44 times the breadth. What be the cost of a carpet whose length and breadth are 40% more and 25% more respectively than the first carpet. Given that the ratio of carpet is Rs. 45 per sq m?

Length of the first carpet = (1.44)(6) = 8.64 cm Area of the second carpet = 8.64(1 + 40/100) 6 (1 + 25/100) = 51.84(1.4)(5/4) sq m = (12.96)(7) sq m Cost of the second carpet = (45)(12.96 * 7) = 315 (13 - 0.04) = 4095 - 12.6 = Rs.4082.40 Answer:D The answer is: D

D

mathematics

A person covers a distance in 21 minutes. If runs at a speed of 12 km per hour on an average. Find the speed at which he must run to reduce the time of journey to 5 minutes.

Explanation: T = 21 m Spees = 12 kmph = 12 x 5/18 = 10/3 m/s Let new speed be "x" 21 x (10/3) = 5x x = 14 m/s Answer: Option C The answer is: C

C

mathematics

Let Tn be the number of all possible triangles formed by joining vertices of an n-sided regular polygon. If Tn+1−Tn=10Tn+1−Tn=10, then the value of n is

We are given that Tn+1−Tn=C3n+1−C3n=10 --> C3n+1−C3n=(n+1)!/3!(n−2)!−n!3!(n−3)!=10 --> (n−1)n(n+1)/6−(n−2)(n−1)n/6=10 (n−1)n=20 --> n=5n=5. Answer: A. Or: one additional point gives 10 more triangles, so when we add one point there are 10 different pairs of points which make triangles with that additional point --> C2n=10--> (n−1)n=20 --> n=5 Answer: A. The answer is: A

A

mathematics

Let the sides of a rectangular prism are consecutive multiples of 5. Which among the following could be the base area

Length=5*a breadth=5*(a+1) or 5*(a+2) Base area -> multiple of 25 450=25*18 Answer:B The answer is: B

B

mathematics

If the position of the first, sixth digits of the number 2796543018 are interchanged, similarly the positions of the the second and seventh digits are interchanged and so on, which of the following will be the left of seventh digit from the left end?

Explanation: The new number formed is 4 3 0 1 8 2 7 9 6 5 The seventh digit from the left is 7, the 3rd digit from the left of 7 is 1 Answer: A) 1 The answer is: A

A

mathematics

A work crew of 4 Men takes 5 days to complete one-half of a job. If 11 men are then added to the crew and the men continue to work at the same rate, how many days will it take the enlarged crew to do the rest of the job?

Suppose 1 man can do work in X days.. so 4 men will do in .. 4/X=1/5*1/2 as half job is done X=40 now 11 more are added then 15/40=1/2*1/d for remaining half job d=1 1/3 Number of days C The answer is: C

C

mathematics

Mira’s expenditure and sayings are in the ratio 3: 2. Her income increases by 10 percent. Her expenditure also increases by 12 percent. By how much per cent does her saving increase?

We get two values of x ,7 and 13. But to get a viable answer we must keep in mind that the central value(10)must lie between x and 12. Thus the value of x should be 7 and not 13 Thus, Required %increase = 7% ANSWER:A The answer is: A

A

mathematics

There arr 4 prime numbers in ascending order. The multiplication of 1st 3 is 385 and that of last 3is 1001. what is the last number is

Explanation: abcbcd=3851001=>ad=513 abcbcd=3851001=>ad=513 So d = 13 D The answer is: D

D

mathematics

A train 110 m long is running with a speed of 30 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?

Speed of train relative to man = 30 + 6 = 36 km/hr. = 36 * 5/18 = 10 m/sec. Time taken to pass the men = 110 /10 =11 sec. Answer:D The answer is: D

D

mathematics

In a kilometer race, A can give B a 100 m start and C a 150 m start. How many meters start can B give to C?

A can give B a 100 m start and C a 150m. Start means when A runs 1000m, B runs 900m and C runs 850m. When B runs 1000m, C will run 1000 x (850/900) m (i.e. 8500/9 m) Thus, B can give C a start of - 1000 - (8500/9), i.e. 500/9 m. Answer: D The answer is: D

D

mathematics

For which of the following functions f is f(y) = f(1-y) for all y?

I remember seeing this problem in a GMATprep test. I think choice D should be F(y)=(y^2) (1-y)^2. If that is true then substituting (1-y) for will give us the same function back and the answer choice is D, where the function is multiplicative The answer is: D

D

mathematics

Among 250 viewers interviewed who watch at least one of the three TV channels namely A, BC. 116 watch A, 127 watch C, while 107 watch B. If 70 watch exactly two channels. How many watch exactly one channel?

250 = n(Exactly 1 channel) + n(Exactly 2 channels) + n(Exactly 3 channels) 250 = n(Exactly 1 channel) + 70 + n(Exactly 3 channels) Let's find the value of n(Exactly 3 channels) = x 250 = n(A) + n(B) + n(C) - n(A and B) - n(B and C) - n(C and A) + n(A and B and C) Note that each of n(A and B) is the sum of 'number of people watching exactly two channels A and B' and 'number of people watching all three channels'. 250 = 116 + 127 + 107 - n(Exactly 2 channels) - 3x + x 250 = 116 + 127 + 107 -70 - 2x x = 25 250 = n(Exactly 1 channel) + 70 + 25 n(Exactly 1 channel) = 165 Answer (C) The answer is: C

C

mathematics

If 6 (A's capital) = 8 (B's capital) = 10 (C's capital). Then the ratio of their capitals is?

6A = 8B = 10 C A:B:C = 1/6:1/8:1/10 = 20:15:12 Answer: C The answer is: C

C

mathematics

A hat company ships its hats, individually wrapped, in 8-inch by 10-inch by 12-inch boxes. Each hat is valued at $7.50. If the company’s latest order required a truck with at least 336,000 cubic inches of storage space in which to ship the hats in their boxes, what was the minimum value of the order?

Number of boxes= Total volume/volume of one box= 336,000/ (8*10*12)= 350 One box costs 7.50, so 350 box will cost= 350*7.5= 2625 D is the answer The answer is: D

D

mathematics

On a dinner date, a couple is sitting around a circular table. Their seating arrangement is considered different only when the position of the couple is different relative to each other. what is the total number of possible seating arrangement for the couple?

for 2 people seating arrangement around a circular table = (2-1)! = 1! = 1 OA is D The answer is: D

D

mathematics

A sum of money is to be distributed among A, B, C, D in the proportion of 5 : 2 : 4 : 3. If C gets Rs. 1000 more than D, what is B's share?

Let the shares of A, B, C and D be Rs. 5x, Rs. 2x, Rs. 4x and Rs. 3x respectively. Then, 4x - 3x = 1000 x = 1000. B's share = Rs. 2x = Rs. (2 x 1000) = Rs. 2000. Answer: Option C The answer is: C

C

mathematics

The banker’s gain on a sum due 3 years hence at 10% per annum is Rs. 120. The banker’s discount is

Solution T.D =(B.G x 100 / R x T) = Rs.(120x100/10 x 3) = Rs.400. B.D =Rs(400+ 120) = Rs.520. Answer C The answer is: C

C

mathematics

In a certain aquarium, the number of red fish is three times the number of the green fish, and the number of blue fish is half the number of the red fish. If the ratio of green fish to red fish were to be doubled, and the ratio of red fish to blue fish were to be doubled, then the ratio of blue fish to green fish in that aquarium would be

Lots of little places to make a mistake or panic here. =) R = 3G B = R/2 G/R = 1/3 ----> Doubled G/R = 2/3 R/B = 2 ----> Doubled R/B = 4 B/G = (B/R)*(R/G) = (1/4)*(3/2) = 3/8 ANSWER:E The answer is: E

E

mathematics

Which of the following options represents an approximate value for the question mark (?) in the following equation? 662.4 + 15.2 × 4.1 + ? = 672.951

662.4 + 15.2 × 4.1 + ? = 672.951 or, ? = 672.951 – 662.4 + 15.2 × 4.1 ? = 672.951 – 662.4 + 62.32 ≈ 72.9 Answer E The answer is: E

E

mathematics

A deck of 9 cards contains 2 red cards, 3 blue cards, and 4 green cards. 3 cards are randomly drawn with replacement from the deck. What is the probability that all three cards are the same color?

Note that cards are drawn with replacement. So every time we draw from 9 cards and it's possible to draw 3 red cards, 3 blue cards or 3 green cards: P=(2/9)3+(3/9)3+(4/9)3=11/81 Answer: A. The answer is: A

A

mathematics

To asphalt 1km road, 30 men spent 12 days working 8 hours per day. How many days, 20 men will spend to asphalt a road of 2km working 9 hours a day?

Man-hours required to asphalt 1 km road=30*12*8=2880 Man-hours required to asphalt 2 km road=2880*2=5760 Man-hours available per day=20*9=180 Therefore number of days=5760/180=32 days Ans=C The answer is: C

C

mathematics

At 9 am a car (A) began a journey from a point, traveling at 40 mph. At 10 am another car (B) started traveling from the same point at 60 mph in the same direction as car (A). At what time will car B pass car A?

After t hours the distances D1 traveled by car A is given by D1 = 40 t Car B starts at 10 am and will therefore have spent one hour less than car A when it passes it. After (t - 1) hours, distance D2 traveled by car B is given by D2 = 60 (t-1) When car B passes car A, they are at the same distance from the starting point and therefore D1 = D2 which gives 40 t = 60 (t-1) Solve the above equation for t to find t = 3 hours Car B passes car A at 9 + 3 = 12 pm Answer A The answer is: A

A