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mathematics

A certain article of clothing was discounted during a special sale to 3/4 of its original retail price. When the clothing didn't sell, it was discounted even further to 1/3 of its original retail price during a second sale. By what percent did the price of this article of clothing decrease from the first sale to the second sale?

Say the original retail price of the item was $200. The price after the first sale = 3/4 * $200 = $150. The price after the second sale =1/3 * $200 = $200/3. The percent change from the first sale to the second = (150 - 200/3) / 150 = 1/3 = 55.55%. Answer: D. The answer is: D

D

mathematics

The ratio of two quantities is 5 to 6. If each of the quantities is increased by 3, what is the ratio of these two new quantities?

let the actual ratio be 5k/6k, increase numerator and denominator by 4=> 5k+3/6k+3 Until the value of k is unknown we can not determine the actual ratio. OR let the actual be 3/4. After increasing 3 => 6/7 let the actual be 6/8. After increasing 3 => 9/11 Therefore without actual quantities we cannot determine the actual ratio. Answer : D The answer is: D

D

mathematics

As x increases from 165 to 163, which of the following must increase? I. 2x - 5 II. 1 - 1/x III. 1/(x^2 - x)

I. 2x - 5 --> x increases from 165 to 163 --> 2x increases --> 2x - 5 increases. Correct. II. 1 - 1/x --> x increases from 165 to 163 --> 1/x decreases --> 1 -1/x increases. Correct. III. 1/(x^2 - x) --> x increases from 165 to 163 --> x^2-x increases --> 1/(x^2 - x) decreases. Answer: C. The answer is: C

C

mathematics

On selling 17 balls at Rs. 720, there is a loss equal to the cost price of 5 balls. The cost price of a ball is:

(C.P. of 17 balls) - (S.P. of 17 balls) = (C.P. of 5 balls) C.P. of 12 balls = S.P. of 17 balls = Rs.720. C.P. of 1 ball = Rs.720/12 = Rs. 60. Answer: Option D The answer is: D

D

mathematics

Find 96 ×× 98

Here both numbers are less than 100. So they are deficient of - 4 and - 2 compared with 100. So Answer: A The answer is: A

A

mathematics

What is the units digit of (147^17)^47 ?

The units digit of the exponents of 7 repeat in a cycle of four, which is {7,9,3,1}. The number 17 has the form 4n+1 so the units digit is 7 inside the bracket. The exponent 47 has the form 4n+3, so the units digit is 3. The answer is B. The answer is: B

B

mathematics

sue has 3 apples. Billy has 12 apples. If billy steals all of sues apples and eats 4 how many does he have left?

11 A The answer is: A

A

mathematics

A 25 cm wide path is to be made around a circular garden having a diameter of 4 meters. Approximate area of the path is square meters is?

Area of the path = Area of the outer circle - Area of the inner circle = ∏{4/2 + 25/100}2 - ∏[4/2]2 = ∏[2.252 - 22] = ∏(0.25)(4.25) { (a2 - b2 = (a - b)(a + b) } = (3.14)(1/4)(17/4) = 53.38/16 = 3.34 sq m Answer:A The answer is: A

A

mathematics

Two trains are running in opposite directions with the same speed. If the length of each train is 120 m and they cross each other in 12 sec, then the speed of each train is?

Let the speed of each train be x m/sec. Then, relative speed of the two trains = 2x m/sec. So, 2x = (120 + 120)/12 => x = 10 Speed of each train = 10 m/sec. = 10 * 18/5 =- 36 km/hr. ANSWER:D The answer is: D

D

mathematics

If the radius of a cylinder is doubled and height 5 times, what is the new volume of the cylinder divided by the old one?

let v and v' be the original and the changed volume now v=pir^2h v'=pi(2r)^2(5h) v'=20v D) 20 The answer is: D

D

mathematics

What is the ratio between perimeters of two squares one having 5 times the diagonal then the other?

d = 5d d = d a√2 = 5d a√2 = d a = 5d/√2 a = d/√2 => 5: 1 Answer:D The answer is: D

D

mathematics

The sides of a rectangular region measured to the nearest centimeter are 8 cm and 7 cm. Out of the following which is the largest possible value of actual area of rectangle ?

acan be anywhere between 7.5 and 8.4 andbcan be anywhere between 6.5 and 7.4. Hence max area can be 8.4*7.4 eq 62.16. largest value which is near to 62.16 is 61.07. Hence E. The answer is: E

E

mathematics

Two students appeared at an examination. One of them secured 9 marks more than the other and his marks was 56% of the sum of their marks. What are the marks obtained by them?

Let the marks secured by them be x and (x + 9) Then sum of their marks = x + (x + 9) = 2x + 9 Given that (x + 9) was 56% of the sum of their marks =>(x+9) = 56/100(2x+9) =>(x+9) = 14/25(2x+9) => 25x + 225 = 28x + 126 => 3x = 99 => x = 33 Then (x + 9) = 33 + 9 = 42 Hence their marks are 33 and 42 A) The answer is: A

A

mathematics

Let S be the set of permutations of the sequence 2, 3, 4, 5, 6 for which the first term is not 2. A permutation is chosen randomly from S. The probability that the second term is 5 is given by a/b (in lowest terms). What is a+b?

The number of possible permutation without 2 in the first digit is 4X4X3X2X1=96 ways. The number of possible permutations with 5 in the second term is= 3X3X2X1=18 ways. 18c1/96c1 = 18/96= 3/16= > a+b=19. ANSWER:E The answer is: E

E

mathematics

A certain experimental mathematics program was tried out in 2 classes in each of 26 elementary schools and involved 32 teachers. Each of the classes had 1 teacher and each of the teachers taught at least 1, but not more than 3, of the classes. If the number of teachers who taught 3 classes is n, then the least and greatest possible values of n, respectively, are

One may notice that greatest possible values differ in each answer choice in contrast to the least values, which repeat. To find out the greatest value you should count the total classes (26*2=52), then subtract the total #of teachers since we know from the question that each teacher taught at least one class (52-32=20). Thus we get a number of the available extra-classes for teachers, and all that we need is just to count how many teachers could take 2 more classes, which is 20/2 = 10. So the greatest possible value of the # of teachers who had 3 classes is 10. Only answer C has this option. The answer is: C

C

mathematics

A boy has 11 trousers and 11 shirts. In how many different ways can he select a trouser and a shirt?

The boy can select one trouser in nine ways. The boy can select one shirt in 12 ways. The number of ways in which he can select one trouser and one shirt is 11 * 11 = 121 ways. Answer: A The answer is: A

A

mathematics

A single discount equivalent to the discount series of 12%, 10% and 5% is?

100*(88/100)*(90/100)*(95/100) = 75.24 100 - 75.24 = 24.76 Answer: D The answer is: D

D

mathematics

Q and R are two-digit positive integers that have the same digits but in reverse order. If the positive difference between Q and R is less than 30, what is the greatest possible value of Q minus R?

A two-digit integer "ab" can be expressed algebraically as 10a+b. Q-R=(10a+b)-(10b+a)=9(a-b)<30. The greatest multiple of 9 which is less than 30 is 27. The answer is E. The answer is: E

E

mathematics

In a box, there are 10 red, 6 blue and 5 green balls. One ball is picked up randomly. What is the probability that it is neither red nor green?

Total number of balls = 10+6+5 = 21 E = event that the ball drawn is neither red nor green = event that the ball drawn is red n(E) = 10 P(E) = 10/21 Answer is B The answer is: B

B

mathematics

In a group of 150 people, 90 have an age of more 30 years, and the others have an age of less than 20 years. If a person is selected at random from this group, what is the probability the person's age is less than 20?

Number of people whose age is less than 20 is given by 150 - 90 = 60 Probability P that a person selected at random from the group is less than 20 is given by 60 / 150 = 0.4 correct answer A The answer is: A

A

mathematics

Find the simple interest on Rs. 5000 at 6 % per annum for the period from 5th Feb to 19th April, 2015.

Explanation: Given: 1) Principal = Rs. 5000 2) Rate of interest = 6 % 3) Time = 5th Feb to 19th April, 2015 First find the time period 5th Feb to 19th April, 2015 Feb = 28 – 5 = 23 days March = 31 days April = 19 days Total days = 23 + 31 + 19 = 73 days Convert days into years, by dividing it by 365 Time = 73/365 = 1/5 Simple Interest = (P × R × T)/100 = [5000 × 6 × (1/5)]/100 =Rs.60 Simple Interest = Rs. 60 ANSWER IS C The answer is: C

C

mathematics

Two trains are running at 40 km/hr and 20 km/hr respectively in the same direction. Fast train completely passes a man sitting in the slower train in 5 sec. What is the length of the fast train?

Relative speed = (40 - 20) = 20 km/hr. = 20 * 5/ 18 = 50/9 m/sec. Length of faster train = 50/9 * 5 = 250/9 = 27 7/9 m. Answer:D The answer is: D

D

mathematics

What is the least positive integer X for which (X^2) + 164 is divisible by 2, 3, 4, 5, 6, 7, 8, 9, 10, and 11?

2 = 2 3 = 3 4 = 2 * 2 5 = 5 6 = 2 * 3 7 = 7 8 = 2 * 2 * 2 9 = 3 * 3 10 = 2 * 5 11 = 11 So (X ^ 2) + 164 = (2 * 2 * 2 * 3 * 3 * 5 * 7 * 11) = 27720. Then (X^2) = 27556. Then X = 166, which is option E. The answer is: E

E

mathematics

Due to 10% decrease in the price of sugar and John can buy 5kg more sugar in Rs.100, then find the CP of sugar?

Here r = 10 % ,x = 100 and A = 5 kg Actual price of sugar = 10*100/((100-10 )*5) = Rs. 2(2/9) B The answer is: B

B

mathematics

In how many V ways can the wordGMATbe arranged so that no such arrangement has A as the first letter?

Number of ways of arranging the word GMAT = 4! = 24 Number of ways of arranging the word GMAT so that A is always in the first = 3! = 6 Number of ways of arranging GMAT so that A is not in the beginning V= 24 - 6 = 18 Answer: C The answer is: C

C

mathematics

In a bag containing 5balls, a white ball was placed and then 1ball was taken out at random. What is the probability that the extracted ball would turn on to be white, if all possible hypothesis concerning the color of the balls that initiallyin the bag wereequally possible ?

Since, all possible hypothesis regarding the colour of the balls are equally likely, therefore these could be 3 white balls, initially in the bag. ∴ Required probability = 1/4 [1 + 3/4 + 1/2 + 1/4] = 1/4 [(4 + 3 + 2 + 1)/4] = 5/8 B The answer is: B

B

mathematics

Two trains, each 100 m long, moving in opposite directions, cross other in 8 sec. If one is moving twice as fast the other, then the speed of the faster train is?

Let the speed of the slower train be x m/sec. Then, speed of the train = 2x m/sec. Relative speed = ( x + 2x) = 3x m/sec. (100 + 100)/8 = 3x => x = 25/3. So, speed of the faster train = 50/3 = 50/3 * 18/5 = 60 km/hr. Answer:C The answer is: C

C

mathematics

A = {2, 3, 5, 7, 15} B = {2, 4, 6, 13} Two integers will be randomly selected from sets A and B, one integer from set A and one from set B, and then multiplied together. How many different products can be obtained?

Step 1: Find out the number of products you get. 5 distinct numbers in set A and 4 distinct in set B so number of products = 5*4 = 20 Step 2: Remove the products that appear more than once. Notice that 5, 7, 11 and 13 are primes and none of their multiples are in either set. So ignore them. We just need to focus on 2 and 3 of set A and 2, 4 and 6 of set B. 2, 3 2, 4, 6 The only product repeated when you take a number from each set is 12. (3*4 and 2*6) Rest all are distinct. Answer = 20 - 1 = 16 Note here that the second step will involve manual calculation since it will depend on the specific numbers you have in the two sets. B The answer is: B

B

mathematics

You have been given the task of transporting 3,000 apples 1,000 miles from Appleland to Bananaville. Your truck can carry 1,000 apples at a time. Every time you travel a mile towards Bananaville you must pay a tax of 1 apple but you pay nothing when going in the other direction (towards Appleland). What is highest number of apples you can get to Bananaville?

Step one: First you want to make 3 trips of 1,000 apples 333 miles. You will be left with 2,001 apples and 667 miles to go. Step two: Next you want to take 2 trips of 1,000 apples 500 miles. You will be left with 1,000 apples and 167 miles to go (you have to leave an apple behind). Step three: Finally, you travel the last 167 miles with one load of 1,000 apples and are left with 833 apples in Bananaville. The answer is: B

B

mathematics

In the reading room of a library, there are 24 reading spots. Each reading spot consists of a round table with 9 chairs placed around it. There are some readers such that in each occupied reading spot there are different numbers of readers. If in all there are 36 readers, how many reading spots do not have even a single reader?

1+2+3+4+5+6+7+8 = 36 so, 8 spots are occupied by users 24-8 = 16, ANSWER:B The answer is: B

B

mathematics

Rohit spends 40 % of his salary on food, 20% on house rent,10% on entertainment and 10% on conveyance. If his savings at the end of the month are Rs. 1500, Then his monthly salary is:

Saving = [100 – (40 + 20 +10 + 10)] % = 20 % Let the monthly salary be Rs. X Then, 20% of X = 1500 ¡ê 20X / 100 = 1500 X = 1500 x 5 = 7500 X = 7500 answer : C The answer is: C

C

mathematics

The simple interest on a sum of money will be Rs.600 after 10 years. If the principal is trebled after 5 years what will be the total interest at the end of the tenth year?

P --- 10 ---- 600 P --- 5 ----- 300 3P --- 5 ----- 900 ------ => 1200 Answer: C The answer is: C

C

mathematics

If you wanted to plant a certain number of flowers, but knew that 1 in 5 would not grow, how many flowers would you need to plant if you want a total of 20?

20 / (5-1) = 5 5 * 5 = 25 25 - (5-1) = 20 The correct answer is D The answer is: D

D

mathematics

Consider a set S = {2, 4, 6, 8, x, y} with distinct elements. If x and y are both prime numbers and 0 < x < 40 and 0 < y < 40, which of the following MUST be true? I. The maximum possible range of the set is greater than 33. II. The median can never be an even number. III. If y = 37, the average of the set will be greater than the median.

Solution Key Data from the Question Stem Set S has 6 elements. The elements of set S are distinct. x and y are prime numbers. Because 2 is already an element in S, both x and y have to be odd. 0 < x < 40 and 0 < y < 40 I. The maximum possible range of the set is greater than 33 The key word in this entire statement is maximum. We have to determine whether the maximum value possible for the range exceeds 33. We know x and y are prime numbers. The largest prime number less than 40 is 37. If either x or y is 37, the largest number in the set will be 37 and the smallest number is 2. Therefore, the maximum range of the set will be 37 - 2 = 35. It is greater than 33. Statement I is true. So, eliminate choices that donot contain I. Eliminate choice D II. The median can never be an even number There are 6 numbers in the set. Therefore, the median is the arithmetic mean of the 3rd and the 4th term when the numbers are written in ascending or descending order. The elements are {2, 4, 6, 8, x, y}, where x and y are prime numbers. If x and y take 3 and 5 as values, the median is 4.5 If x = 3, y = 7 or greater, the median is 5 If x = 5, y = 7 or greater, the median is 5.5 If x = 7, y = 11 or greater, the median is 6.5 If x = 11 or greater and y = 13 or greater, the median is 7. It is quite clear that the median is either an odd number or is not an interger. So, the median can never be an even integer. Statement II is true. Eliminate choices that do not contain II. Eliminate choices A and C as well. III. If y = 37, the average of the set will be greater than the median If y = 37, the set will be {2, 4, 6, 8, x, 37}, where x is a prime number greater than 2 and less than 37. The average will be 57+x657+x6 = 9.5 + x6x6 If x = 3, median = 5 and average = 10. Average > median. If x = 5, median = 5.5 and average = 10.33. Average > median If x = 7, median = 6.5 and average = 10.66. Average > medain If x = 11 or greater, the median = 7. Average will be definitely greater than 10. So, Average > Median. It is true that the average is greater than the median if y = 37. Statement III is also true. Statements I, II, and III are true. Choice E The answer is: E

E

mathematics

In a school of 850 boys, 44% of Muslims, 14% Hindus, 10% Sikhs and the remaining of other communities. How many belonged to the other communities?

44 + 14 + 10 = 68% 100 – 68 = 32% 850 * 32/100 = 272 Answer:E The answer is: E

E

mathematics

The principal that amounts to Rs. 4913 in 3 years at 6 1/4 % per annum C.I. compounded annually, is?

Principal = [4913 / (1 + 25/(4 * 100))3] = 4913 * 16/17 * 16/17 * 16/17 = Rs.4096. Answer:D The answer is: D

D

mathematics

An book was sold after a discount of 20% and there was a gain of 20%. If the profit made on it was $6 less than the discount offered on it, find its selling price?

D $72 Let CP = $100x SP = $120x MP = 120x/80 * 100 = $150x D = $150x - $120x = $30x D - P = 30x - 20x = $6, 10x = $6 120x = 120/10 * 6 = $72 The answer is: D

D

mathematics

What positive number, when squared, is equal to the cube of the positive square root of 15?

Let the positive number be x x^2 = ((15)^(1/2))^3 =>x^2 = 4^3 = 36 => x = 6 Answer D The answer is: D

D

mathematics

Find the smallest four-digit number which is a multiple of 112

Explanation: The smallest four digit number is 1000. If 1000 is divided by 112, the remainder is 104. 112 - 104 = 8, if 8 is added to 1000, it will become the smallest four digit number and a multiple of 112. Answer: B The answer is: B

B

mathematics

In a single throw of a die, what is the probability of getting a number greater than 4?

S = {1,2,3,4,5,6} E = {5,6} Probability = 2/6 = 1/3 Answer is A The answer is: A

A

mathematics

Walking 9/8 of his usual rate, a boy reaches his school 4 min early. Find his usual time to reach the school?

Speed Ratio = 1:9/8 = 8:9 Time Ratio = 9:8 1 -------- 9 4 --------- ? 36 m.Answer:D The answer is: D

D

mathematics

A certain industrial machine requires 15 quarts (480 ounces) of oil every day, and it is given a mixture of oil A and oil B. Oil A consists of 5% special additives while oil B consists of 9% special additives. If the machine needs exactly 30 ounces of the special additives to ensure smooth operation, then how much of oil A, in ounces, should be in the mixture?

5%*x + 9% *(480-x)=30 13.2 = 4 %*x x=330 D The answer is: D

D

mathematics

Which of the following are/is prime? I. 143 II. 147 III. 145

1) 143 = 13*11 so we know it is not prime quickly eliminate all options having 1 as a choice which leaves us with 2 ) and 3) as possible answers From here on we find 147 = 3* 49 so we eliminate 147 which leaves us with 149 as the only possible solution D The answer is: D

D

mathematics

A room is 6 meters 24 centimeters in length and 4 meters 32 centimeters in Width. Find the least number of square tiles of equal size required to cover the entire floor of the room.

Let us calculate both the length and width of the room in centimeters. Length = 6 meters and 24 centimeters = 624 cm width = 4 meters and 32 centimeters = 432 cm As we want the least number of square tiles required, it means the length of each square tile should be as large as possible.Further,the length of each square tile should be a factor of both the length and width of the room. Hence, the length of each square tile will be equal to the HCF of the length and width of the room = HCF of 624 and 432 = 48 Thus, the number of square tiles required = (624 x 432 ) / (48 x 48) = 13 x 9 = 117 Answer: B The answer is: B

B

mathematics

What is the least number of digits (including repetitions) needed to express 10^600 in decimal notation?

10^n is a decimal number with a 1 followed by n zeros. So 10^600 will include 600 0's + 1 digit for 1 = 601 So the answer is B The answer is: B

B

mathematics

If -1<x<0, what is the median N of these six numbers listed below 1/x^3,1/x^2, 1/x,x, x^2,x^3

My approach: Put any value between -1 and 0. you will get the answer. lets say 0.5. so the list will be as follows: -8,-2,-0.5,-0.125 and last two numbers will be positive so need to see that. median will be between -0.5 and -0.125. So, (x^3+x)/2 (D). The answer is: D

D

mathematics

Three unbased coins are tossed. the probability of getting at most one head two tail is ?

S={TTT,TTH,THT,HTT,THH,HTH,HHT,HHH} E be the event of getting at least two head is {TTH,THT,HTT} P(E)=n(E)/n(S)=3/8 Answer(D) The answer is: D

D

mathematics

One pipe can fill a tank three times as fast as another pipe. If together the two pipes can fill tank in 36 min, then the slower pipe alone will be able to fill the tank in?

Let the slower pipe alone fill the tank in x min. Then, faster pipe will fill it in x/3 min. 1/x + 3/x = 1/36 4/x = 1/36 => x = 144 min ANSWER A The answer is: A

A

mathematics

A seven-digit phone number is divisible by 3. After adding the two digits of the area code the number is not divisible by 3, which of the following cannot be the area code?

Given that 7 digit number is divisible by 3 we know any number will not be divisible by 3 if the sum of all digits of the number is not the multiple of 3. Hence looking at the option we can say that the number that should be added to the seven digit number must be 06 as adding it will make it divisible by 3... hence answer is B The answer is: B

B

mathematics

There are 7 players in a bowling team with an average weight of 94 Kg. If two new players join the team, one weighs 110 Kg and the second weighs 60 Kg, what will be the new average weight?

The New average will be= (94*7+110+60)/9= 92 kgs E is the answer The answer is: E

E

mathematics

In a company, 54 percent of the employees are men. If 60 percent of the employees are unionized and 70 percent of these are men, what percent of the non-union employees are women?

The percent of employees who are unionized and men is 0.7*0.6 = 42% The percent of employees who are unionized and women is 60 - 42 = 18% 46% of all employees are women, so non-union women are 46%-18% = 28% 40% of all employees are non-union. The percent of non-union employees who are women is 28%/40% = 70% The answer is D. The answer is: D

D

mathematics

A man's speed with the current is 15 km/hr and the speed of the current is 2.5 km/hr. The man's speed against the current is:

Man's rate in still water = (15 - 2.5) km/hr = 12.5 km/hr. Man's rate against the current = (12.5 - 2.5) km/hr = 10 km/hr. Ans- C The answer is: C

C

mathematics

A sum is sufficient to pay either George age for 15 days or marks wage to 10dayshow long together?

George one day work is (1/15) Marks one day work is (1/10) G+M=(1/15)+(1/10)=(1/6) 6 is the answer ANSWER:C The answer is: C

C

mathematics

An order was placed for the supply of a carper whose length and breadth were in the ratio of 3 : 2. Subsequently, the dimensions of the carpet were altered such that its length and breadth were in the ratio 7 : 3 but were was no change in its parameter. Find the ratio of the areas of the carpets in both the cases?

Let the length and breadth of the carpet in the first case be 3x units and 2x units respectively. Let the dimensions of the carpet in the second case be 7y, 3y units respectively. From the data,. 2(3x + 2x) = 2(7y + 3y) => 5x = 10y => x = 2y Required ratio of the areas of the carpet in both the cases = 3x * 2x : 7y : 3y = 6x2 : 21y2 = 6 * (2y)2 : 21y2 = 6 * 4y2 : 21y2 = 8:7 Answer:C The answer is: C

C

mathematics

Five carpenters can individually complete a particular task in 3, 4, 5, and 7 hours, respectively. What is the maximum fraction of the task that can be completed in forty-five minutes if four of the carpenters work together at their respective rates ?

Farmer A, B, C, and D A's rate: 1/3 job/hour B's rate: 1/4 job/hour C's rate: 1/5 job/hour D's rate: 1/7 job/hour By intuition we know that the three fastest farmers are A B and C. As such (1/3 + 1/4 + 1/5)*(4/5) = ? 47/75 or (D) The answer is: D

D

mathematics

What is the sum of two consecutive even numbers, the difference of whose squares is 84?

Let the numbers be x and x + 2. Then, (x + 2)2 - x2 = 84 4x + 4 = 84 4x = 80 x = 20. The required sum = x + (x + 2) = 2x + 2 = 42. ANSWER A 42 The answer is: A

A

mathematics

Ten years ago, Kumar was thrice as old as Sailesh was but 10 years hence, he will be only twice as old. Find Kumar’s present age.

Let Kumar’s present age be x years and Sailesh’s present age be y years. Then, according to the first condition, x - 10 = 3(y - 10) or, x - 3y = - 20 ..(1) Now. Kumar’s age after 10 years = (x + 10) years Sailesh’s age after 10 years = (y + 10) (x + 10) = 2 (y + 10) or, x - 2y = 10 ..(2) Solving (1) and (2), we get x = 70 and y = 30 Kumar’s age = 70 years and Sailesh’s age = 30 years. ANSWER:C The answer is: C

C

mathematics

The output of a factory was increased by 10% to keep up with rising demand. To handle the holiday rush, this new output was increased by 10%. By approximately what percent would the output now have to be decreased in order to restore the original output?

The original output increases by 10% and then 10%. Total % change = a + b + ab/100 Total % change = 10 + 10 + 10*10/100 = 21% Now, you want to change it to 0, so, 0 = 21 + x + 21x/100 x = -21(100)/121 = 17% approximately Answer is E The answer is: E

E

mathematics

he population of a city is 140,000. If it increases at the rate of 6% per annum, then what will be its population 2 years hence?

Population after n years = P [1 + (R/100)]2 Population after 2 years = 140000 * [1 + 6/100]2 = (160000 x 53/50 x 53/50) = 157304 ANSWER: E The answer is: E

E

mathematics

The cost of 15 packets of sugar, each weighing 900 grams is Rs. 28. What will be the cost of 27 packets, if each packet weighs 1 kg?

Explanation : Let the required cost be Rs. x. Then, More packets, More cost (Direct Proportion) More weight, More cost (Direct Proportion) Packets 15 : 27 Weight 900 : 1000 :: 28 : x (15 x 900 x x) = (27 x 1000 x 28) x = (27 x 1000 x 28) /15 x 900 = 56 Answer B The answer is: B

B

mathematics

If the average (arithmetic mean) of x + 3, x + 4, and x + 5 is 0, then x =

(x+3 + x+4 + x+5)/3 = 0 =>3x + 12 = 0 =>x = -4 Answer A The answer is: A

A

mathematics

A certain company has records stored with a record storage firm in 15-inch by 12-inch by 10-inch boxes. The boxes occupy 1.08 million cubic inches of space. If the company pays $0.2 per box per month for the record storage, what is the total amount that the company pays each month for record storage?

Volume Per Box: 15x12x10 = 1,800 Total Volume: 1,080,000 Number of Boxes: Total Volume / Volume Per Box = 1,080,000 / 1,800 = 600 Price Per Month: Number of Boxes * Price Per Box = 600 * 0.2 = 120 Answer: D The answer is: D

D

mathematics

Insert the missing number. 3, 9, 6, 6, 9, 3, 12, 0, 15, (....)

Explanation: There are two series, beginning respectively with 3 and 9. In one 3 is added and in another 3 is subtracted. The next number is 0 - 3 = -3. Answer: C) -3 The answer is: C

C

mathematics

A man buys s cycle for $1400 and sells it at a loss of 15%. What is the selling price of the cycle?

S.P. = 85% of the $1400 = 85/100 * 1400 = $1190 Answer is C The answer is: C

C

mathematics

It costs $3 for the first 1/3 hour to use the laundry machine at the Laundromat. After the first ¼ hour it costs $12 per hour. If a certain customer uses the laundry machine for 2 hours and 35 minutes, how much will it cost him?

2 hrs 35 min = 155 min First 20 min ------> $3 Time left is 135 min... Now, 60 min costs $ 12 1 min costs $ 12/60 155 min costs $ 12/60*155 => $ 31 So, Total cost will be $31 + $3 => $ 34 Hence answer will be C The answer is: C

C

mathematics

The H.C.F. and L.C.M. of two numbers are 12 and 5040 respectively If one of the numbers is 144, find the other number

Explanation: Solve this question by using below formula. Product of 2 numbers = product of their HCF and LCM 144 * x = 12 * 5040 x = (12*5040)/144 = 420 Option D The answer is: D

D

mathematics

A person buys an article at Rs.650. At what price should he sell the article so as to make a profit of 10%?

Cost price = Rs.650 profit = 10% of 650 = Rs.65 Selling price = Cost price + Profit = 650 + 65 = Rs.715 Answer: B The answer is: B

B

mathematics

Excluding stoppages, the speed of a train is 45 kmph and including stoppages it is 36 kmph. Of how many minutes does the train stop per hour?

T = 9/45 * 60 = 12 Answer: C The answer is: C

C

mathematics

If two of the four expressions x+y, x+5y, x-y, and 5x-y are chosen at random, what is the probability W that their product will be of the form of x^2-(by)^2, where b is an integer?

Only (X+y)(x-y) pair will give the form x^2-(by)^2 The probability of selecting these two pairs are 1/4 * 1/3 = 1/12, assuming x+y is picked first, then x-y, but x-y can be picked first followed by x+y. So the probability W= 1/12 * 2 = 1/6 Ans E The answer is: E

E

mathematics

Two pipes can fill a tank in 20 and 24 minutes respectively and a waste pipe can empty 3 gallons per minute. All the three pipes working together can fill the tank in 15 minutes. The capacity of the tank is?

Work done by the waste pipe in 1 minute = 1/15 - (1/20 + 1/24) = - 1/40 Volume of 1/40 part = 3 gallons\ Volume of whole = 3 * 40 = 120 gallons. Answer: C The answer is: C

C

mathematics

A, B, C together started a business. A invested Rs.5000 for 5 months B invested Rs.3000 for 6 months and C Rs.7000 for 3 months. If they get a total profit of Rs.7600. Find the share of A?

5*5:3*6:7*3 25 : 30 : 21 25/76 * 7600 = 2500 Answer:B The answer is: B

B

mathematics

The population of a town is 10000. It increases annually at the rate of 25% p.a. What will be its population after 2 years?

Formula : 10000 × 125/100 × 125/100 = 15625 Answer : D The answer is: D

D

mathematics

In a hostel, the number of students decreased by 8% and the price of food increased by 20% over the previous year. If each student consumes the same amount of food then By how much should the consumption of food be cut short by every student, so that the total cost of the food remains the same as that of the previous year?

Cost of food (C) = Food consumed per student (F) * Number of students (N) * Price of food (P) Originally, C = FNP When number of students decrease by 8%, and the price of food increases by 20%, C = F(new) * (0.92N) * (1.2P) => F(new) = F/(0.92*1.2) => F(new) = 0.906F Therefore the new cost of food must be 90.6% of the old cost, or the cost of food must decrease by 9.4% ANSWER:E The answer is: E

E

mathematics

A started a business with an investment of Rs. 70000 and after 6 months B joined him investing Rs. 120000. If the profit at the end of a year is Rs. 39000, then the share of B is?

Ratio of investments of A and B is (70000 * 12) : (120000 * 6) = 7 : 6 Total profit = Rs. 39000 Share of B = 6/13 (39000) = Rs. 18000 Answer:E The answer is: E

E

mathematics

The positive difference between Sam and Lucy’s ages is a, and the sum of their ages is z. If Lucy is older than Sam, then which of the following represents Lucy’s age?

let Lucy's age be L and sam's age be S as given, L-S=a -- 1 L+S=z --2 adding both the equations 2L=a+z L= (a+z)/2 answer is D The answer is: D

D

mathematics

If 2^(2w) = 8^(w−1), what is the value of w?

2^(2w) = 8^(w−1) 2^(2w) = 2^(3*(w−1)) 2^(2w) = 2^(3w-3) Let's equate the exponents as the bases are equal. 2w = 3w-3 w = 3 The answer is A. The answer is: A

A

mathematics

Lucy's personal library had 1/20 the capacity as the town library. Lucy decided to donate 1/2 of her book collection to the town library. What fraction of the town library's capacity would Lucy's book donation fill?

Assuming that the town library has space for 100 books, that would mean that Lucy's personal library had 20 books. If Lucy donated a 1/2 of her books, that would mean she donated 10 books. Those 10 books would make 10/100 of the town library's collection. 10/100 simplifies to 1/10. (Answer: B) The answer is: B

B

mathematics

Each student is given a four-character identification code. The first character is a number from 0 to 9 inclusive, and the last three characters are selected from the 26 letters of the alphabet. If characters may be repeated and the same characters used in a different order constitute a different code, how many different identification codes can be generated following these rules?

The number of possible codes is 10*26*26*26=175,760. The answer is A. The answer is: A

A

mathematics

A sum of money becomes double itself in 8 years at simple interest. How many times will it become 10 years at the same rate?

P ---- 2P ---- 8 years 2 1/4 P ---- 10 years ANSWER A The answer is: A

A

mathematics

A person purchased a TV set for Rs. 1600 and a DVD player for Rs. 625. He sold both the items together for Rs. 31150. What percentage of profit did he make?

The total CP = Rs. 1600 + Rs. 625= Rs. 2225 and SP = Rs. 31150 Profit(%) = (31150 - 2225)/2225* 100 = 1300% ANSWER:C The answer is: C

C

mathematics

Population of a city in 20004 was 1000000. If in 2005 there isan increment of 15% , in 2006 there is a decrements of 35 % and in 2007 there is an increment of 30%, then find the population of city atthe end of the year 2007

Required population = P (1 + R1/100)(1 - R2/100)(1 + R3/100) = P (1 + 15/100)(1 - 35/100)(1 + 30/100) = 971750 B The answer is: B

B

mathematics

From a seven-member dance group, three will be chosen at random to volunteer at a youth dance event. If Kori and Jason are two of the seven members, what is the probability that both will be chosen to volunteer?

Total number of ways to choose 3 out of 7 = 7C3 = 420. Number of ways to choose 2 (any but Kori and Jason) out of 5 (excluding Kori and Jason) = 5C2 = 10. P = favorable/total = 10/420 = 1/42. Answer: A. The answer is: A

A

mathematics

Ravi can do a piece of work in 30 days while Prakash can do it in 40 days. In how many days will they finish it together?

Explanation: 1/30 + 1/40 = 7/120 120/7 = 17 1/7 days So, both together will finish the work in 17 1/ 7 days. Answer:A The answer is: A

A

mathematics

Two pipes A and B can separately fill a cistern in 20 min and 30 min respectively. There is a third pipe in the bottom of the cistern to empty it. If all the three pipes are simultaneously opened, then the cistern is full in 60 min. In how much time, the third pipe alone can empty the cistern?

Work done by the third pipe in 1 min = 1/60 - (1/20 + 1/30) = - 1/15. [-ve sign means emptying] The third pipe alone can empty the cistern in 15 min. ANSWER:D The answer is: D

D

mathematics

The first train leaves the station at 6:00 am with a speed of 60 km/hr. The second train leaves at 7:00 am, in the same direction from the same station, with a speed of 75 km/hr. What time will the second train catch the first train?

In sixty minutes, the first train travels 60 km. The second train catches the first train with a relative speed of 15 km/h. The second train will catch the first train in 4 hours. The second train will catch the first train at 11:00 am. The answer is B. The answer is: B

B

mathematics

On a certain number line, conditions are a<b<c<d<e and abcd>0. Which of the following must be true? I ab>0 II cd>0 III de>0 ,IV e+ve =ve

Givena<b<c<d<e and abcde>0. Suppose, for the product to be greater than 0, we can two variables as -ve or four variables can be -ve. We are given : I ab>0 II cd>0 III de>0 case 1: a and b can be negative/positive and if they are... we get greater than 0. case 2: we have cd , then c and d both can be negative/positive and if they are... we get greater than 0. case 2: we have de , then c and d both can be negative/positive and if they are... we get greater than 0. if cd both negative , then de both have to negative in order to get greater than 0. In order to abcde>0 , cde can't be negative else we get -ve value, then we need to have either a or b as negative then ab can't be greater than 0. so cde have to be positive. ab > 0 , cd > 0 obviouly e will be positive , since we have information de> 0 . ( Here we have relationship between cd and de , where d is common). So cases 1 and 2 are fine. OptionE The answer is: E

E

mathematics

In a division sum, the divisor is ten times the quotient and five times the remainder. If the remainder is 46, the dividend is:

Divisor = (5 * 46) = 230 = 10 * Quotient = Divisor => Quotient = 230/10 = 23 Dividend = (Divisor * Quotient) + Remainder Dividend = (230 * 23) + 46 = 5336. B The answer is: B

B

mathematics

P can do a work in 24 days. Q can do the same work in 9 days and R can do the same in 12 days. Q and R start the work and leave after 3 days. P finishes the remaining work in --- days.

Explanation : Work done by P in 1 day = 1/24 Work done by Q in 1 day = 1/9 Work done by R in 1 day = 1/12 Work done by Q and R in 1 day = 1/9 + 1/12 = 7/36 Work done by Q and R in 3 days = 3×7/36 = 7/12 Remaining work = 1 – 7/12 = 5/12 Number of days in which P can finish the remaining work = (5/12) / (1/24) = 10 Answer : Option D The answer is: D

D

mathematics

Sujal covers a distance in 40 min , if she drives at a speed of 60 km/h on an average. Find the speed at which she must drive at to reduce the time of the journey by 25%.

Given Speed = 60 Kmph. It means Sujal covered 60 km in 60 min (1 hour). So, in 40 min he will cover 40 km. 25% time reduced = 40 - 25% of 40 = 30 min. Thus, Sujal needs to cover 40 km in 30 min (0.5 hour). Speed * Time = Distance. Speed * 0.5 = 40 Speed = 80 kmph. ANSWER : OPTION D The answer is: D

D

mathematics

Two bus stations are 600 km apart. if two separate buses depart from both stations and travel towards each other, at what time will they meet each other, given that the first bus left at 12 p.m. and travels at a speed of 60 kmph while the second bus left at 1 p.m. and travels at a speed of 40 kmph.

Suppose they meet x hours after 12 p.m. Distance moved by first bus in x hours + distance moved by 2nd bus in x-1 hrs = 600 60x+40(x-1) =600 60x+40x-40= 600 100x= 640 x = 6.4 So they meet 6.4 hr after 12 p.m. which is at 6.40 p.m. Answer is E The answer is: E

E

mathematics

Last year a certain bond yielded 5 percent of its face value in interest. If that interest was approximately 4 percent of the bonds selling price of $8,000, what is the bonds face value?

Interest = 0.05*face value = 0.04*8,000 --> face value = 0.04*8,000/0.05 = 6,400. Answer: C. The answer is: C

C

mathematics

John can complete a given task in 16 days. Jane will take only 12 days to complete the same task. John and Jane set out to complete the task by beginning to work together. However, Jane was indisposed 5 days before the work got over. In how many days did the work get over from the time John and Jane started to work on it together?

In such questions, you need to start from the end. Last 5 days John works alone and completes 5 * (1/16) = 5/16 of the work. So 11/16 of the work should have been completed by the two of them together before Jane left. Their combined rate of work is 1/16 + 1/12 = 7/48 Time taken to complete 11/16 of the work = (11/16)/(7/48) = 33/7 days. So total number of days taken to complete the work =33/7 + 5 = 68/7 days. E The answer is: E

E

mathematics

Two squares are chosen on a chessboard at random. What is the probability that they have a side in common?

In 64 squares, there are: (1) 4 at-corner squares, each has ONLY 2 squares each having a side in common with... (2) 6*4 = 24 side squares, each has ONLY 3 squares such that each has a side in common with... (3) 6*6 = 36 inner squares, each has 4 squares such that each has a side in common with... So we have the calculation: P = (4/64)*(2/63) + (24/64)*(3/63)+ (36/64)*(4/63) P = 1/18 ANSWER:A The answer is: A

A

mathematics

The 8 spokes of a custom circular bicycle wheel radiate from the central axle of the wheel and are arranged such that the sectors formed by adjacent spokes all have different central angles, which constitute an arithmetic series of numbers (that is, the difference between any angle and the next largest angle is constant). If the largest sector has a central angle of 83.5°, what fraction of the wheel’s area is represented by the smallest sector?

The largest angle is 83.5. Let d be the difference between any two angles in the progression. The sum of all the angles will be: 83.5 + (83.5-d) + (83.5-2d) + ... + (83.5-7d) = 668 - 28d The sum of all the central angles in a circle = 360 668 - 28d = 360 d = 308/28 = 11 The smallest sector is (83.5-7d) = 83.5-7*11 = 6.5 The fraction of the area covered is 6.5/360 = 13/720. The answer is E. The answer is: E

E

mathematics

In covering distance,the speed of A & B are in the ratio of 3:4.A takes 30min more than B to reach the destion.The time taken by A to reach the destinstion is.

Ratio of speed = 3:4 Ratio of time = 4:3 let A takes 4x hrs,B takes 3x hrs then 4x-3x = 30/60 hr x = ½ hr Time taken by A to reach the destination is 4x = 4 * ½ = 2 hr Answer is E. The answer is: E

E

mathematics

The length of a rectangle is increased by 25% and its breadth is decreased by 20%. What is the effect on its area?

100 * 100 = 10000 125 * 80 = 10000 Answer:A The answer is: A

A

mathematics

A committee has 6 men and 6 women. What are the number of ways of selecting 2 men and 3 women from the given committee?

The number of ways to select two men and three women = 6C₂ * ⁶C₃ = (6*5)/(2 * 1) * (6 * 5 * 4)/(3 * 2) = 300 Answer: B The answer is: B

B

mathematics

In a 200 m race,A covers the distance in 45 seconds and B in 60 second.In this race A beats B by :

Solution Distance covered by B in 15 sec. = (200/60x15)m =50m. ∴ A beats B by 50 metres. Answer B The answer is: B

B

mathematics

How long does a train 165 meters long running at the rate of 36 kmph take to cross a bridge 660 meters in length?

Explanation: T = (660 + 165)/36 * 18/5 T = 82.5 Answer: Option D The answer is: D

D

mathematics

A, B and C enter into a partnership with a capital in which A's contribution is Rs. 10,000. If out of a total profit of Rs. 1000, A gets Rs. 500 and B gets Rs. 300, then C's capital is?

A : B : C = 500 : 300 : 200 = 5 : 3 : 2. Let their capitals be 5x, 3x and 2x respectively. Then, 5x = 10000 => x = 2000. C's capital = 2x = Rs. 4000. Answer: D The answer is: D

D