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mathematics

What will come in place of the x in the following Number series? 46080, 3840, 384, 48, 8, 2, x

46080 /12 = 3840 3840 /10 = 384 384 /8 = 48 48 /6 = 8 8/4 = 2 2 /2 = 1 A The answer is: A

A

mathematics

In an examination, 35% of the students passed and 455 failed. How many students appeared for the examiantion?

Solution Let the number of students appeared be x. Then, 65% of x = 455 ‹=›65 / 100 x = 455 ‹=› x= [455 x 100 / 65] = 700. Answer C The answer is: C

C

mathematics

Find the value of 1/(3+1/(3+1/(3-1/3)))

1/[3 + (1/(3+1/(3 - 1/3)))] => 1/[3 + 1/(3 + 1/(8/3))] => 1/[3 + 1/(3 + 3/8)] => 1/[3 + 8/27] => 1/(89/27) => 27/89 B The answer is: B

B

mathematics

For dinner at a restaurant, there are x choices of appetizers, y main courses, and z+ 1 choices of dessert. How many total possible choices are there if you choose 1 appetizer, 1 main course, and 1 dessert for your meal?

x appetizers, y main courses, z+ 1 dessert Required: 1 appetizer, 1 main course, and 1 dessert Number of ways possible = xC1*(z+1)C1*yC1 {NC1 = N! / (N-1)!*1! = N} Hence, number of ways = x(z+1)y = xyz + xy Correct Option: B The answer is: B

B

mathematics

If n is the smallest integer such that 108 times n is the square of an integer, what is the value of n?

108 can written as = 2 * 2 * 3 * 3 * 3 --> 2^2* 3^3 ---(1) so for 108 * n to be a square of an integer, the integer should have even powers to the prime numbers it composed of. here 2 already has even power -> So n has to be 2 to make the power of 2 in (1) even Option A is correct The answer is: A

A

mathematics

A man complete a journey in 10 hours. He travels first half of the journey at the rate of 20 km/hr and second half at the rate of 20 km/hr. Find the total journey in km.

0.5x/20 + 0.5x/20 = 10 --> x/20 + x/20 = 20 --> 2x = 20 x 20 --> x = (20x20)/2 = 200 km. Answer : E. The answer is: E

E

mathematics

Find the odd man out 3, 7, 15, 27, 63, 127, 255

1*2+1 = 3 3*2+1 = 7 7*2+1 = 15 15*2+1 = 31 31*2+1 = 63 63*2+1 = 127 127*2+1= 255 ANSWER:C The answer is: C

C

mathematics

A taxi charges p dollars for the first two miles and c cents per quarter mile for every mile after the first two. Which equation describes cost of a taxi ride of n miles in dollars.

This is about as complicated as these types of problems come, but it is essentially the same as any problem which has an initial cost which is added to a dependent additional cost. Looking at the problem, we notice that the cost p is added to the mile dependent cost, which is some combination of the other terms listed in the problem. With just that knowledge we can eliminate all but two of the answer choices! Choices (A), (B), and (E) either do some strange calculation with the initial cost p, or subtract the additional cost from p. Both of these circumstances would be next to impossible if there is an initial cost being added to another cost. Thus, we only have to choose between choice (C) and choice (D). We can easily find the right answer by plugging in real numbers and checking which choice yields a correct answer. We can also see that answer choice (D) seems to be multiplying the cost in cents by 100, which, if the trip was 6 miles and the charge per mile was 25 cents, would make the taxi cost an additional $3750! This seems impossible, and leaves only the correct answer choice, (C). The answer is: C

C

mathematics

A and B together do a work in 20 days.B and C together in 15 days and C and A in 12 days.then B alone can finish same work in how many days?

(A+B) work in 1 day= 1/20,(B+C) work in 1 days = 1/15.,(C+A) work in 1 days=1/12 (1) adding=2[A+B+C] in 1 day work = [1/20+1/15+1/12]=1/5 (A+B+C) work in 1 day= 1/10 B work in 1 days= [A+B+C] work in 1 days- work of (A+C) in 1 days =[1/10-1/12]=1/60 B alone finish work in 60 days Answer B The answer is: B

B

mathematics

A candidate got 30% of the votes polled and he lost to his rival by 4000 votes. How many votes were cast?

30%-----------L 70%-----------W ------------------ 40%----------4000 100%---------? => 10000 Answer:D The answer is: D

D

mathematics

A certain fruit stand sold orange for $0.70 each and bananas for $0.50 each. If a customer purchased both apples and bananas from the stand for a total of $6.30, what total number of apples and bananas did the customer purchase ?

Some multiple of 7 + Some multiple of 5 should yield 63. To get to a some multiple of 5, we should ensure that a 3 or 8 (5+3) should be a multiple of 7. 63 is a direct multiple of 7, however in this case there won't be any bananas. Hence the next option is to look for a multiple of 7 that has 8 as the unit digit. 28 satisfies this hence no. of apples is 4 and no of bananas is 7 D The answer is: D

D

mathematics

38, 52, 22,79, 31,47, 13, 82 Which of the following numbers is greater than three-fourth of the numbers but less than one-fourth of the numbers in the list above?

Important:- Arrange the numbers in ascending order first. 13, 22, 31, 38, 47, 52, 79, 82 3/4th of the number list represents- 52 (6th number) remaining 1/4th list represents 79 (7 th number) 65.5 fits in between above 2 Answer:- B The answer is: B

B

mathematics

Rs.590 is divided amongst A, B, C so that 5 times A's share, six times B's share and eight times C's share are all equal. Find C's share?

A+B+C = 590 5A = 6B = 8C = x A:B:C = 1/5:1/6:1/8 = 24:20:15 15/59 * 590 = Rs.150 Answer: B The answer is: B

B

mathematics

What will be the compound interest on Rs. 50000 after 3 years at the rate of 12 % per annum

Explanation: (50000×(1+12/100)3) =>50000×28/25×28/25×28/25 =>70246.4 So Compound interest will be 70246.4 - 50000 = Rs 20246.4 Option B The answer is: B

B

mathematics

It takes Avery 3 hours to build a brick wall while Tom can do it in 4 hours. If the two start working together and after an hour Avery leaves, how much time will it take Tom to complete the wall on his own?

Avery's efficiency is 100/3 = 33% Tom's = 100/4= 25% they worked together for 1 hour and finished 58% of the job remaining =42 % Tom will complete 25% in 60 minutes , and 17% in 60*17/25 minutes = 40.8 minutes Time taken by Tom to finish the remaining on his own = 60+40.8 = 100.8 minutes (adjusting for 0.2) ~ 101 minutes ANSWER:C The answer is: C

C

mathematics

A is older than B by 5years. Seven years hence, thrice A's age shall be equal to four times that of B. Find their present ages.

Explanation: Let the present ages of A and B be 'a' and 'b' respectively. 3(a + 7)= 4( (b +7 ) --- (1) =>3a-4b=7 -------(1) a-b = 5 -------(2) Solving (1) and (2) we get b=8 Substituting b = 8 in second equation, we get a= 13. Answer : C => 2a = 32 => a = 16. Answer: C The answer is: C

C

mathematics

Kamal obtained 96, 65, 82, 67 and 85 marks(out of 100) in English, Mathematics, Physics, Chemistry and Biology. What are his average marks?

Sol. Average = 96 + 65 + 82 + 67 + 85 / 5) = (395 / 5) = 79. Answer D The answer is: D

D

mathematics

Suppose we have six marbles: 3 blue marbles, 2 yellow marbles, and one green marble. Suppose we are going to put them into three cups: a black cup, a white cup, and a purple cup. We could put all six in any cup and leave two cups empty; or we could put marbles in two cups and leave one cup empty; or we could put some marbles in each of the three cups. How many combinations are possible?

# ways to distribute Blue marbels(3) is : 1 in each cup= 1 2 in one cup and 1 in other=6 all 3 in one cup = 3 total 1+6+3=10 possibilities # ways to distribute yellow marbels(2) is : 1 in each cup = 3 ways all in one cup = 3ways total 6ways. # ways to distribute Green marbels(1) is : 3 ways total number of ways = 10*6 *3 = 180 B The answer is: B

B

mathematics

A committee of two people is to be chosen from 4 married couples. What is the number of different committees that can be chosen if two people who are married to each other cannot both serve on the committee?

One of the approaches: Each couple can send only onerepresentativeto the committee. Let's see in how many ways we can choose 2 couples (as there should be 2 members) out of 4 to send only onerepresentativesto the committee: 4C2=6. But each of these 2 couples can send two persons (husband or wife): 2*2=2^2=4. Total # of ways: 4C2*2^2=24. Answer: B. The answer is: B

B

mathematics

A survey reveals that the average income of a company’s customers is $45,000 per year. If 40 customers respond to the survey and the average income of the wealthiest 10 of those customers is $75,000, what is the average income of the other 30 customers? Is there a way to solve this using weighted average concept instead of doing tedious calculations?

let x be the average of 30 customers 30*x + 10* 75000 = 40*45000 solving this we have x= 35000 Answer is B. The answer is: B

B

mathematics

A positive number x is multiplied by 8, and this product is then divided by 3. If the positive square root of the result of these two operations equals x, what is the value of x ?

sq rt(8x/3) = x => 8x/3 = x^2 => x = 8/3 Ans - C The answer is: C

C

mathematics

A certain company retirement plan has arule of 70provision that allows an employee to retire when the employee's age plus years of employment with the company total at least 70. In what year could a female employee hired in 1990 on her 32nd birthday first be eligible to retire under this provision?

She must gain at least 70 points, now she has 31 and every year gives her two more points: one for age and one for additional year of employment, so 32 + 2*(# of years) = 70 --> (# of years) = 19 --> 1990+19=2009. Answer: B. The answer is: B

B

mathematics

20-3*5^2+15 = ?

20-3*5^2+15=-40 B The answer is: B

B

mathematics

70% of the employees in a multinational corporation have VCD players, 75 percent have microwave ovens, 80 percent have ACs and 85 percent have washing machines. At least what percentage of employees has all four gadgets?

Given a population where A% has a certain characteristic X and B% has another characteristic Y (assuming both aren't exclusive), then you get the minimum overlap by assuming that the entire population that doesn't have X has characteristic Y, therefore the minimum portion of the population that has both characteristics is: B-(100-A) % So given A=70 for employees with VCD players and B=75 for employees with microwave ovens, at least: 75-(100-70)=45% have both. Then take the output and repeat with the other appliances. A=45 for employees with both VCD players and microwaves, B=80 for ACs 80-(100-45)=25% A=25 for employees with VCD players, microwaves and ACs, B=85 for washing machines 85-(100-25)=10% Answer C The answer is: C

C

mathematics

A ranch has both horses and ponies. Exactly 5/7 of the ponies have horseshoes, and exactly 2/3 of the ponies with horseshoes are from Iceland. If there are 3 more horses than ponies, what is the minimum possible combined number of horses and ponies on the ranch?

5/7*P are ponies with horseshoes, so P is a multiple of 7. 2/3*5/7*P = 10/21*P are Icelandic ponies with horseshoes, so P is a multiple of 21. The minimum value of P is 21. Then H = P+3 = 24. The minimum number of horses and ponies is 45. The answer is D. The answer is: D

D

mathematics

The average of 10 numbers is calculated as 15. It is discovered later on that while calculating the average, one number namely 36 was wrongly read as 26. The correct average is?

Explanation: 10 * 15 + 36 – 26 = 160/10 = 16 C) The answer is: C

C

mathematics

What is the smallest positive integer K such that the product of 61347 x K is a perfect square?

A perfect square, is just an integer that can be written as the square of some other integer. For example 16=4^2, is a perfect square. Now, 61347 = 13^2 * 11^2 * 3, so if k=3 then 61347 k = (13 * 11 * 3)^2, which is a perfect square (basically the least positive value of k must complete only the power of 7 to even power as powers of other primes are already even). Answer: A. The answer is: A

A

mathematics

A company wants to spend equal amounts of money for the purchase of two types of computer printers costing $300 and $200 per unit, respectively. What is the fewest number of computer printers that the company can purchase?

The smallest amount that the company can spend is the LCM of 300 and 200, which is 600 for each, which is total 1200. The number of 1st type of computers which costing $300 = 600/300 = 2. The number of 2nd type of computers which costing $200 = 600/200 = 3. Total = 2+3 = 5 Answer is B. The answer is: B

B

mathematics

A goods train runs at the speed of 72 km/hr and crosses a 210 m long platform in 26 sec. What is the length of the goods train?

Speed = 72 * 5/18 = 20 m/sec. Time = 26 sec. Let the length of the train be x meters. Then, (x + 210)/26 = 20 x = 310 m. Answer: D The answer is: D

D

mathematics

How many numbers amongst the numbers 7 to 41 are there which are exactly divisible by 9 but not by 3?

9,18,27,36 are divisible by 9 and 3 also.So there are no numbers exactly divisible by 9 but not by 3 ANSWER:A The answer is: A

A

mathematics

If the average (arithmetic mean) of (2a+16) and (3a-8) is 79, what is the value of a?

((2a+16) + (3a-8)) / 2 = (5a+8)/2 = 79 a= 30 The answer is B. The answer is: B

B

mathematics

The average weight of a group of boys is 20 kg. After a boy of weight 36 kg joins the group, the average weight of the group goes up by 1 kg. Find the number of boys in the group originally ?

Let the number off boys in the group originally be x. Total weight of the boys = 20x After the boy weighing 36 kg joins the group, total weight of boys = 20x + 36 So 20x + 36 = 21(x + 1) = > x = 15 ANSWER:B The answer is: B

B

mathematics

The last day of a century cannot be :

100 years contain 5 odd days. So, last day of 1st century is ‘Friday’ 200 years contain (5 × 2) = 10 odd days = 3 odd days. So, last day of 2nd century is ‘Wednesday’. 300 years contain (5 × 3) = 15 odd days = 1 odd day. ∴ Last day of 3rd century is ‘Monday’. 400 years contain 0 odd day. ∴ Last day of 4th century is ‘Sunday’ Since the order is continually kept in successive cycles, we see that the last day of a century cannot be Tuesday,Thursday or Saturday. Answer D The answer is: D

D

mathematics

If the quantity 2^2+ 2^4 + 2^6 is written as (a + b)(a – b), in which both a and b are integers, which of the following could be the value of b?

(a+b)(a-b) = a^2 - b^2 2^2+ 2^4 + 2^6 = 2^2 (1+2^2+2^4) if the above expression is solved even then every term of the expression will remain a multiple of 2^2 which is out of parenthesis hence, b must be a multiple of 2^2 i.e. 4 Answer: option C The answer is: C

C

mathematics

The sum of the fourth and twelfth term of an arithmetic progression is 20. What is the sum of the first 15 terms of the arithmetic progression?

The sum of the first n terms of a G.P. is given by , where 'a' is the first term of the G.P., 'r' is the common ratio and 'n' is the number of terms in the G.P. Therefore, the sum of the first 6 terms of the G.P will be equal to And sum of the first 3 terms of the G.P. will be equal to Use the ratio between these two sums to find 'r' The ratio of the sum of the first 6 terms : sum of first 3 terms = 9 : 1 i.e. Or r3 + 1 = 9 r3 = 8 r = 2 The answer is C The answer is: C

C

mathematics

A and B together can do a work in 6 days. If A alone can do it in 15 days. In how many days can B alone do it?

1/6 – 1/15 = 1/10 => 10 Answer: A The answer is: A

A

mathematics

A number when divided successively by 4 and 5 leaves remainders 1 and 4 respectively. When it is successively divided by 5 and 4, then the respective remainders will be

4 | x y = (5 x 1 + 4) = 9 -------- 5 | y -1 x = (4 x y + 1) = (4 x 9 + 1) = 37 -------- | 1 -4 Now, 37 when divided successively by 5 and 4, we get 5 | 37 --------- 4 | 7 - 2 --------- | 1 - 3 Respective remainders are 2 and 3. Correct Option is B The answer is: B

B

mathematics

If C and D are non-zero integers, and C/D > 1, then which of the following must be true?

MULTIPLICATION OF TWO INTEGER IS OBIVIOUSLY GREATER THAN EACH ONE OF THEM. A The answer is: A

A

mathematics

9 men and 12 boys finish a job in 12 days, 12 men and 12 boys finish it in 10 days. 10 men and 10 boys shall finish it in how many days?

9M + 12B ----- 12 days 12M + 12B ------- 10 days 10M + 10B -------? 108M + 144B = 120M +120B 24B = 12M => 1M = 2B 18B + 12B = 30B ---- 12 days 20B + 10B = 30B -----? => 12 days Answer: C The answer is: C

C

mathematics

10 friends meet for movie 20 for picnic and 5 for games 4 for movie & picnic 2 for movie & games, 0 for picnic & games, 2 for all, how many are students are there in all?

n(A U B U C)=n(A) + n(B) + n(C) - n(A INTERSECTION B) - n(A INTERSECTION C) - n(C INTERSECTION B) + n(A INTERSECTION B - INTERSECTION C) Hence, Total no. of Students = 10 + 20 + 5 - 4 - 0 - 2 + 2 = 31. ANSWER:B The answer is: B

B

mathematics

In how many ways can a cricket eleven be chosen out of a batch of 15 players.

Required number of ways = 15C 11 = 15C (15-11) = 15 C 4 15C4 = 15 * 14 * 13 * 12 / 4 * 3 * 2 *1 = 1365 ANSWER B 1365 The answer is: B

B

mathematics

The ages of two persons differ by 16 years. 5 years ago, the elder one was 3 times as old as the younger one. What are their present ages of the elder person

Explanation: Let's take the present age of the elder person = x and the present age of the younger person = x � 16 (x � 5) = 3 (x-16-5) => x � 5 = 3x � 63 => 2x = 58 => x = 58/2 = 29 Answer: Option A The answer is: A

A

mathematics

It takes Avery 4 hours to build a brick wall while Tom can do it in 2 hours. If the two start working together and after an hour Avery leaves, how much time will it take Tom to complete the wall on his own?

Avery takes 4 hours Tom takes 2 hours Efficiency of Avery is 1/4 units/hr Efficiency of Tom is 1/2 units/hr Combined efficiency of Tom and Avery is 1/4 +1/2 = 3/4 units/hr Since they worked for 1 hour they completed 3/4 units of work and 1/4 units of work is left which is to be completed by Tom ( Since Avery left ) So Time taken by Tom to complete the remaining work will be 1/4/1/2 hours => 1/2*60 = 30 minutes... Answer will be (C) The answer is: C

C

mathematics

If x is real, find the maximum value of the expression -2x^2 + 9x + 11.

This is an equation of a downward facing parabola. The maximum value is the top point of the parabola. -2x^2+9x+11 = (-2x+11)(x+1) The roots are 11/2 and -1. The maximum value must be when x is halfway between these two points. x = 2.25 The maximum value is -2(2.25)^2+9(2.25)+11 = 21.125 The answer is D. The answer is: D

D

mathematics

If p is an even integer and q is an odd integer, which of the following must be an odd integer?

A. p/q p = 6, q = 3 => p/q is odd integer p = 4, q=3 =>p/q is not integer B. pq Must be even C. 2p+q 2p must be even, q is odd=> 2p+q must be ODD: CORRECT D. 2(p+q) must be even E. 3p/q Same A Answer: C The answer is: C

C

mathematics

A can finish a work in 24 days and B can do the same work in 15 days. B worked for 10 days and left the job. In how many days, A alone can finish the remaining work?

B's 10 day's work = ( 1 x 10 ) = 2 . 15 3 Remaining work = ( 1 - 2 ) = 1 . 3 3 Now, 1 work is done by A in 1 day. 24 Therefore 1 work is done by A in ( 24 x 1 ) = 8 days. E The answer is: E

E

mathematics

A pineapple costs Rs. 7 each. A watermelon costs Rs. 5 each. X spends Rs. 38 on these fruits. The number of pineapples purchased is

7P+5W= 38 As P and W are integers, only possible value of P is 4. ANSWER:C The answer is: C

C

mathematics

The length of a rectangular plot is 20 metres more than its breadth. If the cost of fencing the plot @ Rs. 26.50 per metre is Rs. 6360, what is the length of the plot in metres?

Let length of plot = L meters, then breadth = L - 20 meters and perimeter = 2[L + L - 20] = [4L - 40] meters [4L - 40] * 26.50 = 6360 [4L - 40] = 6360 / 26.50 = 240 4L = 280 L = 280/4= 70 meters. Answer: A The answer is: A

A

mathematics

John buys 100 shares of par value Rs. 5 each, of a company, which pays an annual dividend of 12% at such a price that he gets 10% on his investment. Find the market value of a share.

Face value of each share = Rs.5 Total dividend received by John = 100×5×12/100 = Rs.60 Let market value of 100 shares = Rs.x x×10/100=60 x = 600 ie, Market value of 100 shares = Rs.600 Hence, Market value of each share = Rs.6 Answer is D. The answer is: D

D

mathematics

Find the unit's digit in 264 ^102+264^103

Required unit's digit = unit's digit in 4102+4103.4102+4103. Now, 4242 gives unit digit 6. ⇒ 41024102 gives unit digit 6. ⇒ 41034103 gives unit digit of the product 6×46×4 i.e., 4. Hence, unit's digit in 264102+264103264102+264103 = unit's digit in (6+4)=0 A The answer is: A

A

mathematics

The first half of a 600-mile trip was travelled in x hours and the second half in y hours. Which of the following is equal to the average speed, in miles per hour, for the entire trip?

Time taken to cover first half i.e 300 miles of a 600 mile trip = x time taken to cover the second half i.e 300 miles of a 600 mile trip = y Total time taken = x+y Average speed for the entire trip =total distance /total time =600/(x+y) Answer B The answer is: B

B

mathematics

The difference between C.I. and S.I. on an amount of $20,000 for 2 years is $72. What is the rate of interest per annum?

$72 is the interest on the first year of interest. Let x be the interest rate. The interest after the first year is 20000*x. The interest on the first year's interest is 20000*x*x 20000*x^2 = 72 x = 0.06 The answer is B. The answer is: B

B

mathematics

Data sufficiency question: Is x has only '3' factors?

Only squares of primes has 3 factors. For example, 4 has three factors. 1, 2, 4. Now when we square 4, we get 16, which has 5 factors. 1, 2, 4, 8, 16. So Statement 1 is sufficient. Statement two says that one of the factor must be prime number. 10 has 4 factors. i.e., 1, 2, 5, 10 and one of which is prime. but we cannot say whether numbers of this format always have three factors or not. So statement 2 is insufficient. Answer:B The answer is: B

B

mathematics

In 1982 and 1983, Company B’s operating expenses were $13.0 million and $15.0 million, respectively, and its revenues were $15.6 million and $18.8 million, respectively. What was the percent increase in Company B’s profit (revenues minus operating expenses) from 1982 to 1983 ?

Profit in 1982 = 15.6 - 13 = 2.6 million $ Profit in 1983 = 18.8 - 15 = 3.8 million $ Percentage increase in profit = (3.8-2.6)/2.6 * 100 % = 46 1/6 % Answer B The answer is: B

B

mathematics

R is the set of positive even integers less than 101, and S is the set of the squares of the integers in R. How many elements does the intersection of R and S contain ?

R is the set of positive even integers less than 101, and S is the set of the squares of the integers in R. How many elements does the intersection of R and S contain? R=2,4,6,8,10,12... S=4,16,36,64... Numbers: 4, 16, 36, 64, and 100 are even integers (less than 101) that are in both sets. Solution: Five Answer: D The answer is: D

D

mathematics

Two trains are moving at 50 kmph and 70 kmph in opposite directions. Their lengths are 150 m and 100 m respectively. The time they will take to pass each other completely is?

70 + 50 = 120 * 5/18 = 100/3 mps D = 150 + 100 = 250 m T = 250 * 3/100 = 15/2 = 7 ½ sec ANSWER A The answer is: A

A

mathematics

A team of eight entered for a shooting competition. The best marks man scored 82 points. If he had scored 92 points, the average scores for. The team would have been 84. How many points altogether did the team score?

8 * 84 = 672 – 10 = 662 ANSWER:A The answer is: A

A

mathematics

A positive integer is divisible by 3 if and only if the sum of its digits is divisible by 3. If the six-digit integer is divisible by 3, and n is of the form 1k2,k42, where k represents a digit that occurs twice, how many values could n have?

1k2k42 Taking sum of the numericals = 1 + 2 + 4 + 2 = 9 We require the values of K such that they are also divisible by 3 102042 132342 162642 192942 Answer = 4 = D The answer is: D

D

mathematics

What value will replace the question mark in the following equation ? 5172.49 + 378.352 + ? = 9318.678

Let 5172.49 + 378.352 + x = 9318.678 Then , x = 9318.678 – (5172.49 + 378.352) = 9318.678 – 5550.842 = 3767.836 Answer is A. The answer is: A

A

mathematics

Calculate the percentage gain if a trader bought a bicycle for Rs 950 and sold it for Rs.1500?

C.P. = 950 S.P. = 1500 Gain = 1500-950 ---- 550 % Gain => 550/950*100 => 57.89% Answer:E The answer is: E

E

mathematics

Express a speed of 54 kmph in meters per second?

54 * 5/18 = 15 mps Answer:C The answer is: C

C

mathematics

When tossed, a certain six-sided die has an equal probability of landing on any of the six sides. If the die is tossed 4 times, what is the probability that it will land on the same side each time?

On the first toss, the die will land on one of the sides. On the second toss, the probability of landing on the same side is 1/6. On the third toss, the probability of landing on the same side is 1/6. On the fourth toss, the probability of landing on the same side is 1/6. P(same side four times)=1/6*1/6*1/6=1/216. The answer is D. The answer is: D

D

mathematics

Antony has s pairs of shoes, which is 1/2 as many as Steve and thrice as many as Stephen. In terms of s, how many pairs of shoes do the three of them have combined?

== s +2s + s/3 ==> 3s + 1/3 s = 10/3*s Ans .B The answer is: B

B

mathematics

A merchant marks his goods up in such a way that the profit made on selling 30 articles is equal to the cost price of 20 articles. What is the R % profit made by the merchant?

C.P of 1 article= $30(say) C.P of 20 articles=30*20=$600 Now, C.P of 20 articles=Profit on 30 articles Therefore, profit on 1 article=$600/30=$20 Profit R%=(20/30)*100=66.67% Answer A The answer is: A

A

mathematics

A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 sec. The speed of the train is?

Speed of the train relative to man = 125/10 = 25/2 m/sec. = 25/2 * 18/5 = 45 km/hr Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 45 => x = 50 km/hr. Answer: Option B The answer is: B

B

mathematics

To mail a package, the rate is 10 cents for the first pound and 5 cents for each additional pound. Two packages weighing 5 pounds and 10 pounds, respectively can be mailed seperately or combined as one package. Which method is cheaper and how much money is saved?

5 pounds = 1*10+4*5 = 30 10 pounds = 1*10+9*5 =55 total = 85 15 pound = 1*10+14*5 = 80 dif. 5 Answer : D The answer is: D

D

mathematics

3 candidates in an election and received 1136, 7636 and 11628 votes respectively. What % of the total votes did the winningcandidate got in that election?

Total number of votes polled = (1136 + 7636 + 11628) = 20400 So, Required percentage = 11628/20400 * 100 = 57% C The answer is: C

C

mathematics

On average, Machine A will produce a completed item once every two minutes, and Machine B will produce a completed item once every eleven minutes. The number of items Machine A produces in a 24-hour period is approximately what percent greater than the number of items Machine B would produce in that same period?

Machine A: 1 item in 2 minutes --> 1/2 items in 1 minute; Machine B: 1 item in 11 minutes --> 1/11 items in 1 minute. In the same time period, Machine A produces (1/2-1/11)/(1/11)*100=~450% more items than machine B. Answer:D The answer is: D

D

mathematics

I chose a number and divide it by 8. Then I subtracted 100 from the result and got 6. What was the number I chose?

Solution: Let x be the number I chose, then x/8−100=6 x/8=106 x=848 Answer E The answer is: E

E

mathematics

In traveling from a dormitory to a certain city, a student went 1/5 of the way by foot, 2/3 of the way by bus, and the remaining 11 kilometers by car. What is the distance, in kilometers, from the dormitory to the city?

I believe there is a better way to do it. Basically one of the options should satisfy the given criteria. 60 did 1/5 *60 =12 2/3*60=40 so total distance 52 + remaining 11 =63 Answer E The answer is: E

E

mathematics

In a certain math department, students are required to enroll in either Calculus or Trigonometry, each of which is offered in beginner and advanced courses. The number of students enrolled in Trigonometry is 50% greater than the number of students enrolled in Calculus, and 70% of Calculus students are enrolled in the beginner course. If 4/5 of students are in the beginner courses, and one student is selected at random, what is the probability that an advanced Trigonometry student is selected?

Let x be the number of students in calculus. Then the number of students in trigonometry is 1.5x The number of students on beginner calculus is 0.7x The number of students in beginner trigonometry is 4/5*(2.5x) - 0.7x = 1.3x The number of students in advanced trigonometry is 0.2x The percentage in advanced trigonometry is 0.2x / 2.5x = 8% The answer is A. The answer is: A

A

mathematics

A basket has 5 apples and 4 oranges. Three fruits are picked at random. The probability that at least 2 apples are picked is?

Total fruits = 9 Since there must be at least two apples, (⁵C₂ * ⁴C₁)/⁹C₃ + ⁵C₃/⁹C₃ = 25/42. Answer: A The answer is: A

A

mathematics

A computer manufacturer produces a certain electronic component at a cost of $80 per component. Shipping costs for delivering the components are $3 per unit. Further, the manufacturer has costs of $16,500 a month related to the electronic component regardless of how many it produces. If the manufacturer produces and sells 150 components a month, what is the lowest price it can sell them for such that the costs don't exceed the revenues?

by the question, the equation would be 150 p - 83*150 - 16500 = 0 p being the price we want to find and equation resulting zero means revenue and costs are equal so we can get the minimum price of the component. solving the equation, we get p = $ 193. Answer E for me. The answer is: E

E

mathematics

Which of the following is a divisible by 3 number ?

Explanation : C is divisible by 3 with out integers. Answer : Option C The answer is: C

C

mathematics

In a six-sided polygon CQRSTV ∠C measures 48° less than the average (arithmetic mean) of the remaining five angles. What does ∠C equal to, in degrees?

The sum of interior angle in a polygon is (n-2)*180 so for a six sided figure, (6-2)*180 = 720 let the A.M of the other 5 angles be 'm' --> m*5 + ∠C = 720, we know ∠C=m-48 --> m*5 + m - 48 = 720, solving we get m=128 hence ∠C= 128-48 = 80 Ans B. The answer is: B

B

mathematics

Mr. Karan borrowed a certain amount at 6% per annum simple interest for 9 years. After 9 years, he returned Rs. 8510/-. Find out the amount that he borrowed.

Explanation: Let us assume Mr. Karan borrowed amount is Rs. A. (the principal) By formula of simple interest, S.I. = PRT / 100 Where P = The principal, R = Rate of interest as a %, T = Time in years S.I. = (P * 6 * 9)/100 = 54 P/100 Amount = Principal + S.I. 8510 = P + (54P/100) 8510 = (100P + 54P)/100 8510 = 154P/100 P = (8510 * 100)/154 = Rs. 5525.974 ANSWER: E The answer is: E

E

mathematics

The distance from Steve's house to work is 20 Km. On the way back Steve drives twice as fast as he did on the way to work. Altogether, Steve is spending 6 hours a day on the roads. What is Steve's speed on the way back from work?

Time is in the ratio 2:1 :: to: fro office Therefore, 2x+1x=6 hrs Time take to come back - 2 hrs, distance travelled - 20km => Speed = 10kmph B The answer is: B

B

mathematics

A bag contains 6 red, 5 blue and 2 green balls. If 2 ballsare picked at random, what is the probability that both are red?

P(Both are red), =6C213C2=6C213C2 =5/26 C The answer is: C

C

mathematics

In country Z, 12% of the people do not have a university diploma but have the job of their choice, and 25% of the people who do not have the job of their choice have a university diploma. If 40% of the people have the job of their choice, what percent of the people have a university diploma?

Setting up a matrix is how I solve this one. Diploma No Diploma Totals Job of Choice w/Diploma Job of Choice w/o Diploma = 12% Job of Choice Total = 40% Not Job of Choice with Diploma =.25X Not Job of Choice w/o Diploma= .75X Total Not Job of Choice = X Total with Diploma Total without Diploma Total citizen = 100 If 40% of people have their job of choice, then 60% of people do NOT have their job of choice. 25% of 60% = 15%. We can also see that 28% of the people have their job of choice and a diploma (40%-12%=28%). 28% + 15% = 43%. Therefore 43% of the people in Country Z have a diploma. Ans B The answer is: B

B

mathematics

A goes 8 km East, then 3 km South, 4km West. How far is he from starting point and in which direction?

8E, 3S,4W Subtract opposite direction 8E-4W,3S=> 4E, 3S Square root of(4^2+ 3^2)= 5 Km South East. ANSWER:B The answer is: B

B

mathematics

32% of employees are women with fair hair. 40% of fair-haired employees are women. What percent of employees have fair hair?

I came up with (E) 80 Think of 100 people total: From the first fact, 32 of these are women with fair hair. From the second fact, these 30 women make up 40% of the total fair haired population. We can then make a ratio of 60:40 fair haired men to fair haired women. This means that (60/40)*32 equals the number of fair haired men, which is 48 men with fair hair. Add this 48 to the 32 women and get 80 fair haired men and women out of 100 total men and women. 80% E The answer is: E

E

mathematics

A table is bought for Rs.800/- and sold at Rs.600/- find gain or loss percentage

Formula = (Selling price ~ Cost price)/Cost price * 100 = (600 - 800)/800 = 25% loss D The answer is: D

D

mathematics

For which of the following “n” is the number 2^74 +2^2058+2^2n is a perfect square?

2^74 +2^2058+2^2n = K2K2 2^74 +2^2058+2^2n = (237)2+22058+(2n)2(237)2+22058+(2n)2 We try to write this expression as (a+b)2=a2+2ab+b2(a+b)2=a2+2ab+b2 Now a = 237237, 2ab = 2205822058 and b = 2n2n Substituting the value of a in 2ab, we get b = 2020 Ans: D The answer is: D

D

mathematics

James has a total of 560 balls. 140 balls are yellow, 250 balls are blue, and 170 balls are red. What percentage of the balls are yellow ?

Explanation : Yellow Percentage = (140/560 x 100)% = 25% Answer : C The answer is: C

C

mathematics

To mail a package, the rate is u cents for the first pound and v cents for each additional pound, where u>v. Two packages weighing 3 pounds and 5 pounds, respectively can be mailed seperately or combined as one package. Which method is cheaper and how much money is saved?

This means it costs x cent for the first pound in weight for example, 20 cents for the first pound. It costs y cents for the every pound in weight above this, for example 10 cents for pound 2 and 10 cents for pound 3. x is more than y. for example 20 cents vs. 10 cents 3 pounds: x+2y 5 pounds:x+4y Total: 2x+6y 8 pounds: x+7y So we are saving: (2X+6y) - x+7y = x-y cents Combined is cheaper as we maximise y and minimize x. Answer is: 1) Combined, with a saving of x-y cents The answer is: A

A

mathematics

In expressing a length 81.479 km as nearly as possible with three significant digits, find the percentage error?

Error = 81.5-81.479 = 0.021 Required percentage = (0.021/81.479)*100 = 0.026% Answer is C The answer is: C

C

mathematics

A batsman scored 120 runs whichincluded 3 boundaries and 8sixes. What % of his total score did he make by running between the wickets

Number of runs made by running = 110 - (3 x 4 + 8 x 6) = 120 - (60) = 60 Now, we need to calculate 60 is what percent of 120. => 60/120 * 100 = 50% B The answer is: B

B

mathematics

A fair die is rolled once and a fair coin is flipped once. What is the probaility that either the die will land on 3 or that the coin will land on heads?

Event A = Fair die is rolled once Event B = Fair coin is flipped once. P(A or B) = P(A) + P(B) - P(A and B) = 1/6 + 1/2 - (1/6)(1/2) = 7/12 ANSWER B The answer is: B

B

mathematics

In filling a lot with sand, that is 40 m * 20 m * 2m the volumes of the sand filled will be?

40 * 20 * 2 = 1600 ANSWER:D The answer is: D

D

mathematics

The cross-section of a cannel is a trapezium in shape. If the cannel is 8 m wide at the top and 2 m wide at the bottom and the area of cross-section is 770 sq m, the depth of cannel is?

1/2 * d (8+2) = 770 d = 154 Answer: C The answer is: C

C

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: Option B The answer is: B

B

mathematics

What was the day on 15th august 1947 ?

Explanation: 15 Aug, 1947 = (1946 years + Period from 1.1.1947 to 15.8.1947) Odd days in 1600 years = 0 Odd days in 300 years = 1 46 years = (35 ordinary years + 11 leap years) = (35 x 1 + 11 x 2)= 57 (8 weeks + 1 day) = 1 odd day Jan. Feb. Mar. Apr. May. Jun. Jul. Aug ( 31 + 28 + 31 + 30 + 31 + 30 + 31 + 15 ) = 227 days = (32 weeks + 3 days) = 3 odd days. Total number of odd days = (0 + 1 + 1 + 3) = 5 odd days. Hence, as the number of odd days = 5 , given day is Friday. Answer: A The answer is: A

A

mathematics

The rate of a certain chemical reaction is directly proportional to the concentration of chemical A present and inversely proportional to the concentration of chemical B present. If the concentration of chemical B present is increased by 50 percent, which of the following is closest to the percent change in the the concentration of chemical A required to keep the reaction rate unchanged.

Let's say here is the formula of how A and B affects the reaction speed: rate = A/B After the concentration B is increased by 50%, the percentage of B become 1.5B, to keep 'rate' the same, need to have 1.5A. Which means A increased by 50% Answer : B The answer is: B

B

mathematics

24 men working at 8 hours a day can finish a work in 10 days. Working at the rate of 10 hours a day, the number of men required to finish the same work in 6 days is?

Using Using the chain rule, M1 x T1 = M2 x T2 Therefore, 24 x 8 x 10 = 10 x X x 6 X= 32 Hence, the number of men required to finish the work = 32. ANSWER:B The answer is: B

B

mathematics

The speed at which a man can row a boat in still water is 15 kmph. If he rows downstream, where the speed of current is 3 kmph, what time will he take to cover 30 metres?

Speed of the boat downstream = 15 + 3 = 18 kmph = 18 * 5/18 = 5 m/s Hence time taken to cover 60 m = 30/5 = 6 seconds. Answer:B The answer is: B

B

mathematics

Find the value of 72514 x 9999 = m?

72514 x 9999 = 72514 x (10000 - 1) = 72514 x 10000 - 72514 x 1 = 725140000 - 72514 = 725067486 A The answer is: A

A

mathematics

Tom opened a shop investing Rs.30000. Jose joined him 2 months later, investing Rs.45000. They earned a profit of Rs.54000 after completion of one year. What will be Jose's share of profit?

SoL = ~s- So Anju’s share = [5/9] x 54000 = 30000 E The answer is: E

E

mathematics

If {h} denote the remainder when 3h is divided by 2 then which of the following is equal to 1 for all positive integers h? I. {2h+1} II. {2h}+1 III. 2{h+1}

C - I and II 3h/2 = 0 or 1 I just substituted 1 in the equations and solved. The answer is: C

C

mathematics

Raju and Reenu are standing in a row there are 9 peoples. what is the probability that at least 3 people will stand between Raju and Reenu

9C2=36 3 people between Raju and Reena 7+5+3=15 15/36=5/12 ANSWER:A The answer is: A

A

mathematics

A began a business with Rs. 85,000. He was joined afterwards by B with Ks. 42,500. For how much period does B join, if the profits at the end of the year are divided in the ratio of 3 : 1 ?

Suppose B joined for x months . Then, ( 85000 * 12 )/(42500 * x) = 3. or x = (85000 * 12) / (42500 * 3) = 8. So, B joined for 8 months. Answer: D The answer is: D

D