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mathematics

There are 136 employees in Company X. If the number of employees who birth in June is the greatest, what is the least possible number of the employees in the company who birth in June?

IMO 15 Take each answer choice and substract it from 136 and the divided this with 11. A The answer is: A

A

mathematics

(4+√3+√5)^2-(√3+√5)^2=?

(4+√3+√5)^2-(√3+√5)^2 (4+√3)^2 + 5 +2 (4+√3) (√5) - ( 3 +5 + 2√3√5) 16+ 3+ 8√3 +5 +8 √5 + 2 √15 - 3-5 -2√15 16+8√3+8√5 B is the answer The answer is: B

B

mathematics

At the end of three years what will be the compound interest at the rate of 10% p.a. on an amount of Rs.15000?

A = 15000(11/10)^3 = 19965 = 15000 ---------- 4965 Answer:B The answer is: B

B

mathematics

A circular grass lawn of 35 metres in radius has a path 7 metres wide running around it on the outside. Find the area of path.

Radius of a circular grass lawn (without path) = 35 m ∴ Area = πr2 = π(35)2 Radius of a circular grass lawn (with path) = 35 + 7 = 42 m ∴ Area = πr2 = π(42)2 ∴ Area of path = π(42)2 – π(35)2 = π(422 – 352) = π( 42 + 35)(42 – 35) Answer A The answer is: A

A

mathematics

The present ages of three persons in proportions 4 : 7 : 9. Eight years ago, the sum of their ages was 56. Find their present ages (in years).

Explanation: Let their present ages be 4x, 7x and 9x years respectively. Then, (4x - 8) + (7x - 8) + (9x - 8) = 56 ⇒ 20x = 80 ⇒ x = 4. ⇒ Their present ages are 4x = 16 years, 7x = 28 years and 9x = 36 years respectively. Answer: B The answer is: B

B

mathematics

A cyclist rides a bicycle 8 km at an average speed of 11 km/hr and again travels 11 km at an average speed of 8 km/hr. What is the average speed for the entire trip?

distance = 19 km time = 8/11 + 11/8 = (64 + 121) / 88 = 185 / 88 hours average speed = (19 * 88) / 185 = 9.04 km/h The answer is C. The answer is: C

C

mathematics

Ramesh purchased a refrigerator for Rs. 12500 after getting a discount of 20% on the labelled price. He spent Rs. 125 on transport and Rs. 250 on installation. At what price should it be sold so that the profit earned would be 15% if no discount was offered?

Price at which the TV set is bought = Rs. 12,500 Discount offered = 20% Marked Price = 12500 * 100/80 = Rs. 15625 The total amount spent on transport and installation = 125 + 250 = Rs. 375\Total price of TV set = 15625 + 375 = Rs. 16000 The price at which the TV should be sold to get a profit of 15% if no discount was offered = 16000 * 115/100 = Rs. 18400.Answer: D The answer is: D

D

mathematics

A cricketer scored 142 runs which included 12 boundaries and 2 sixes. What percent of his total score did he make by running between the wickets.

Explanation : Number of runs made by running = 142 - (12 x 4 + 2 x 6) = 142 - (60) = 82 Now, we need to calculate 82 is what percent of 142. => 82/142 * 100 = 57.75 % Answer : A The answer is: A

A

mathematics

If x > 7, which of the following is equal to (x^2 + 4x + 4)/(x^2 - 4) ?

(x^2 + 4x + 4)/(x^2 - 4) = (x + 2)(x + 2) / (x + 2)(x - 2) =(x + 2)/(x - 2) E. (x + 2)/(x - 2) The answer is: E

E

mathematics

Four friends built a colony for themselves. They built their own houses at different distances from each other. Chris lived 60 km away from Alex. Darren lived 40 km away from Bill. Chris lived 10 km nearer to Darren than he lived to Bill. Can you find out how far was Darren's house from Alex?

Solution: 75km Explanation: Distance between Bill and Darren = 40 km Distance between Bill and Chris + Distance between Chris and Darren = 40 km Distance between Bill and Chris + (Distance between Bill and Chris - 10) = 40 km 2 * Distance between Bill and Chris = 50 km Distance between Bill and Chris = 25 Distance between Chris and Darren = 15 km Therefore, distance between Darren's house and Alex's house = 60 + 15 = 75 km. Answer C The answer is: C

C

mathematics

A and B starts a business with Rs.8000 each, and after 7 months, B withdraws half of his capital . How should they share the profits at the end of the 18 months?

A invests Rs.8000 for 18 months, but B invests Rs.8000 for the first 7 months and then withdraws Rs.4000. So, the investment of B for remaining 11 months is Rs.4000 only. A : B 8000*18 : (8000*7) + (4000*11) 14400 : 100000 A:B = 36:25 Answer: A The answer is: A

A

mathematics

A monkey ascends a greased pole 10 meters high. He ascends 2 meters in the first minute and then slips down 1 meter in the alternate minute. If this pattern continues until he climbs the pole , in how many minutes would he reach at the top of the pole ?

The money is climbing 1meter in 2min. This pattern will go on till he reaches 10meters. I mean this will continue for first 8*2=16mins. he would have reached 8meters. After that he will climb 2meters and he will reach the pole. So total time taken = 16 + 1 = 17mins. So, asnwer will be C The answer is: C

C

mathematics

The Sum of first N consecutive odd integers is N^2. What is the sum of all odd integers between 9 and 39 inclusive.

We're dealing with a sequence of CONSECUTIVE ODD INTEGERS: 9 to 39, inclusive. We're asked for the SUM of this group. 1) Start with the sum of the smallest and the biggest: 9 + 39 = 48 2) Now look at the 'next smallest' and the 'next biggest': 11 + 37 = 48 Now we have proof that there is no middle term. We have 8 bunches of 48 8(48) = 384 B The answer is: B

B

mathematics

Number N is randomly selected from a set of all primes between 10 and 40, inclusive. Number G is selected from a set of all multiples of 5 between 10 and 40 inclusive. What is the probability that N+G is odd?

All primes except 2 are odd, thus N must be odd. For N + G = odd + G to be odd, G must be even. There are 7 multiples of 5 between 10 and 40, inclusive: 10, 15, 20, 25, 30, 35, and 40. Out of them 3 (15, 25, and 35) are odd. Therefore the probability that N + G is odd is 4/7. Answer: D. The answer is: D

D

mathematics

The list price of an article is Rs.70. A customer pays Rs.59.22 for it. He was given two successive discounts, one of them being 10%. The other discount is?

Option E Explanation: 70*(90/100)*((100-x)/100) = 59.22 x = 6% The answer is: E

E

mathematics

The ratio of pens to pencils is 5 to 6. There are 4 more pencils than pens. How many pencils are there?

Let the number of pens be 5x and the number of pencils be 6x. 6x - 5x = 4 x = 4 The number of pencils is 24. The answer is D. The answer is: D

D

mathematics

In how many different number of ways 4 boys and 3 girls can sit on a bench such that girls always sit together?

Option 'A' The answer is: A

A

mathematics

A vessel was filled with 10 ounces of liquid, and 0.008 ounce of the liquid evaporated each day during a 50-day period. What % of the original amount of liquid evaporated during this period?

Total amount of water evaporated each day during a 50-day period = .008 * 50 =.008 * 100/2 = .8/2 = .4 percent of the original amount of water evaporated during this period = (.4/10) * 100% = 4 % Answer B The answer is: B

B

mathematics

Chirag was conducting an experiment in which the average of 11 observation came to be 90. Average of first five observation was 87, and that of the last five was 84. What was the measure of the 6th observation?

Explanation : 11 * 90 - 5 * 87 - 5 * 84 = 900 - 435 - 420 = 135. Answer : D The answer is: D

D

mathematics

If the two-digit integers M and N are positive and have the same digits, but in reverse order, which of the following CANNOT be the sum of M and N?

M=10x+y N=10y+x M+N=11x+11y=11(x+y) In other words the answer is a multiple of 11. Now the question becomes " which of the following is NOT a multiple of 11?" Answer -181 ANSWER:A The answer is: A

A

mathematics

Dimitri weighs x pounds more than Allen weighs. Together, Allen and Dimitri weigh a total of 3y-y pounds. Which of the following represents Allen’s weight?

These type of multi-variable story problems are usually perfect for TESTing VALUES. Here, we're told that Dimitri weighs X pounds more than Allen weighs and that they weight a combined TOTAL of 3Y-2Y or Y pounds. IF.... Dimitri = 30 Allen = 20 X = 10 Y = 50 We're asked for Allen's weight, so we're looking for an answer that equals 20 when X = 10 and Y = 50. Answer A: 50 - (10/2) = 45 NOT a match Answer B: 20 - (50/2) = -5 NOT a match Answer C: (50-10)/2 = 20 This IS a match Answer D: 50 - 20 = 30 NOT a match Answer E: 20 - 50 = -30 NOT a match Final Answer: C The answer is: C

C

mathematics

For every positive even integer n, the function h(n) is defined to be the product of all the even integers from 4 to n, inclusive. If p is the smallest prime factor of h(100) +4, then p is?

h(100) will have 0 in its unit digit because while doing the calculation of the function we are multiplying by 10 (and 100). So h(100)+4 will have 4 in the units digit so smallest prime factor is 4. Answer: E The answer is: E

E

mathematics

For every positive integer n, the nth term of a sequence is the total sum of three consecutive integers starting at n. What is the total sum of terms 1 through 80 of this series?

Each term of the series has the form (n+n+1+n+2) = 3n+3 Since the series goes from 1 to 80, the sum of the series is: 3(1+2+...+80) + 80(3) = 3(80)(81)/2 + 80(3) = 120*81 + 240 = 9960 The answer is D. The answer is: D

D

mathematics

The LCM and HCF of two numbers are 8 and 48 respectively. If one of them is 24, Find the other ?

HCF x LCM = Product of Numbers 8 x 48 = 24 x the other number other number = (8 x 48) / 24 other number = 16 ANSWER : D The answer is: D

D

mathematics

The average of 6 no.'s is 2.5. The average of 2 of them is 1.1, while the average of the other 2 is 1.4. What is the average of the remaining 2 no's?

Sum of the remaining two numbers = (2.5 * 6) - [(1.1 * 2) + (1.4 * 2)] = 15 - (2.2 + 2.8) = 15 - 5 = 10 Required average = (10 / 2) = 5 Answer : E The answer is: E

E

mathematics

A tank is 25m long 12m wide and 6m deep. The cost of plastering its walls and bottom at 45 paise per sq m is

Explanation: Area to be plastered = [2(l + b) × h] + (l × b) = [2(25 + 12) × 6] + (25 × 12) = 744 sq m Cost of plastering = 744 × (45/100) = Rs.334.80 Answer: B The answer is: B

B

mathematics

A trader purchased two colour televisions for a total of Rs. 35000. He sold one colour television at 30% profit and the other 40% profit. Find the difference in the cost prices of the two televisions if he made an overall profit of 32%?

Let the cost prices of the colour television sold at 30% profit and 40% profit be Rs. x and Rs. (35000 - x) respectively. Total selling price of televisions = x + 30/100 x + (35000 - x) + 40/100 (35000 - x) => 130/100 x + 140/100 (35000 - x) = 35000 + 32/100 (35000) x = 28000 35000 - x = 7000 Difference in the cost prices of televisions = Rs. 21000 Answer: A The answer is: A

A

mathematics

Out of four numbers ,the average of first three is 16 and that of the last three is 15. If the last number is 22,the first number is :

Explanation: Let the numbers be a,b,c,d Given, a + b + c = 48, b + c + d = 45 Now, d = 22 thus, b + c + 22 = 45 ⇒ b + c = 23 Putting the value of b + c in a + b + c = 48 a + 23 = 48 ⇒ a = 25 Answer: E The answer is: E

E

mathematics

What profit percent is made by selling an article at a certain price, if by selling at 2/3rd of that price, there would be a loss of 30%?

SP2 = 2/3 SP1 CP = 100 SP2 = 70 2/3 SP1 = 70 SP1 = 105 100 --- 5 => 5% Answer: A The answer is: A

A

mathematics

Find the number of ways in which 4 different beads can be arranged to form a necklace.

Since in forming a necklace clockwise and anticlockwise arrangements are not different, therefore,4 beads can be arranged to form a necklace in(4-1)! /2ways = 3*2/2 = 3 ways Answer is C The answer is: C

C

mathematics

What is the are of an equilateral triangle of side 16 cm?

36 * 5/18 = 10 mps Answer: A The answer is: A

A

mathematics

A policeman noticed a criminal from a distance of 180 km. The criminal starts running and the policeman chases him. The criminal and the policeman run at the rate of 8 km and 10 km per hour respectively. What is the distance between them after 3 minutes ?

Explanation : Solution: Relative speed = (10 - 8) = 2 km/hr. Distance covered in 3 minutes = (2 * 3/60) km = 1/10 km = 100 m. .'. Distance between the criminal and policeman = (180 - 100) m = 80 m. Answer : B The answer is: B

B

mathematics

If a function f is defined by f(x)= 3/(x-1) for all non zero numbers x. If f(a) = 3 and f(ab) = 9 then b= ?

Given that f(x) = 3/(x-1) and f(a) = 3, then f(a) =3/(x-1)=3 ===> x-1=1 ==> x =2, then backsolve using the answer choices: f(ab) = f(2b) = 3/(2b-1) A) 1/3 ===> f(2*1/3) = f(2/3) = 3/((2*2/3)-1) = 9 WINS B) 1/2 ===> f((2*1/2) = f(1) = 3/1-1 = undefined C) -1/2 ===> f(2*-1/2) = f(-1) = 3/1+1 = 3/2 D) -1/3 ===> f(2*-1/3) = f(-2/3) = 3/(2*-2/3 -1) = -9/7 E) -2 ===> f(2*-2) = f(-4) = 3/(2*-4 -1) = -1/3 Answer: A The answer is: A

A

mathematics

If 3<x<6<y<8, then what is the greatest possible positive integer difference of x and y?

3 < x < 6 < y < 8; 3 < x y < 8 3 + y < x + 8 y - x < 5. Positive integer difference is 4 (for example y = 7.5 and x = 3.5) Answer: B. The answer is: B

B

mathematics

A 300 meter long train crosses a platform in 39 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform?

Speed = [300 / 18] m/sec = 50/3 m/sec. Let the length of the platform be x meters. Then, x + 300 / 39 = 50/3 3(x + 300) = 1950 è x = 350m. Answer: C The answer is: C

C

mathematics

What is the cost of leveling the field in the form of parallelogram at the rate of Rs.40/10 sq.metre, whose base & perpendicular distance from the other side being 24m & 34m respectively?

Area of the parallelogram = Length of the base * Perpendicular height = 24 * 34 = 816 m. Total cost of levelling = Rs.816 E The answer is: E

E

mathematics

An inspector rejects 0.08% of the meters as defective. How many will he examine to reject 2?

Let the number of meters to be examined be x Then, 0.08% of x = 2 (8/100)*((1/100)*x = 2 x = 2500 Answer is C The answer is: C

C

mathematics

For any numbers w and z, w#z = w^3z(8 - w^2). If both z and w#z are positive numbers, which of the following could be a value of w?

Since w#Z and w are positive, we need to take the value of w such that w#z or w^3z(8 - w^2) is positive. ANSWER:E The answer is: E

E

mathematics

If 25% of x is 30 less than 15% of 1500, then x is?

25% of x = x/4 ; 15% of 1500 = 15/100 * 1500 = 225 Given that, x/4 = 225 - 30 => x/4 = 195 => x = 780. Answer:D The answer is: D

D

mathematics

Tough and Tricky questions: Mixture Problems. A drink holding 6 ounces of an alcoholic drink that is 1 part rum to 2 parts coke is added to a jug holding 30 ounces of an alcoholic drink that is 1 part rum to 3 parts coke. What is the ratio of rum to coke in the resulting mixture?

Answer = E) 5:10 ........................ Rum ..................... Coke ................. Total First Drink ........... 2 ............................ 4 ..................... 6 (Ratio 1:2) Second Drink ....... 8 ............................. 24 ................... 32 (Ratio 1:3) Total .................. 10 ............................. 28 .................... 38 Ratio = 10:20 = 5:10 E The answer is: E

E

mathematics

If −y ≥ x, and −x < −7, then which of the following must be true?

−y ≥ x, and −x < −7 y <= -x < -7 As '-x' is less than '-7' and Y is less than or equal to '-x' we have y < -7 which is similar to -y > 7. C) -y > 7 The answer is: C

C

mathematics

What is the ratio of y to x if (x + 3y) / ( x - y) = 7/4?

Solving for y/x gives, 3/19 (E) The answer is: E

E

mathematics

If a number is 40% more than the another, how much % is the smaller number less than the first ?

Take a number 100, Then the other number is 140 % the smaller number is less than the first = [(40/(140)) x 100]% = 28(4/7)%. ANSWER:C The answer is: C

C

mathematics

x and y are integers. x + y < 11 , and x > 6. What is the smallest possible value of x - y ?

Because x & y are integers, the two equations can be simply written as : x+y<= 10 --- eq. 1 x>= 7 ---- eq. 2 For smallest value of x-y, x has to be the smallest whereas y has to be the largest. From the above eq. 2, smallest value of x = 7 Plugging it in eq. 1: 7+y<=10, or y<=3 Therefore, largest value of y=3 & smallest values of x=7 x-y = 7 - 3 = 4 Answer is C The answer is: C

C

mathematics

A clothing manufacturer has determined that she can sell 100 suits a week at a selling price of Rs. 200 each. For each rise of Rs. 4 in the selling price she will sell 2 less suits a week. If she sells the suits for Rs. x each, how many rupees a week will she receive from the sales of the suits?

Explanatory Answer Assume that she sells the suits at Rs.204; then she will sell two suits lesser or 98 suits. Substitute x = 204 in each of the answer choices and check where the answer is 98. For choice (2), the answer is 98 and this is the quickest way to find the answer. Answer B The answer is: B

B

mathematics

An amount of money is to be divided between P, Q and R in the ratio of 3:7:12. If the difference between the shares of P and Q is Rs.3600, what will be the difference between Q and R's share?

4 --- 3600 5 --- ? => 4500 Answer:B The answer is: B

B

mathematics

Choose the missing terms out of the given alternatives. AZ, BY, CX, ?

D DW The first letter moves one step forward. The second letter moves one step backward. The answer is: D

D

mathematics

Round off the given number to nearest hundreds 4765

the given number is 4765 its tens digit is 6. so replace each of the tens and ones digit by 0 and increase the hundreds digit by 1 to get the rounded off number to the nearest hundred. correct answer (A) The answer is: A

A

mathematics

In a certain apartment building, there are one-bedroom and two-bedroom apartments. The rental prices of the apartment depend on a number of factors, but on average, two-bedroom apartments have higher rental prices than do one-bedroom apartments. Let M be the average rental price for all apartments in the building. If M is $2,000 higher than the average rental price for all one-bedroom apartments, and if the average rental price for all two-bedroom apartments is $8,000 higher that M, then what percentage of apartments in the building are two-bedroom apartments?

Ratio of 2 Bedroom Apartment: 1 Bedroom Apartment = 2000 : 8000 -----> 1 : 4 Let total number of Apartments be X No. of 2 Bedroom Apartment = (1 / 5) * X percentage of apartments in the building are two-bedroom apartments ----> (1/5) * 100 ---> 20% Answer : A The answer is: A

A

mathematics

If a certain number is divided by 12, the quotient, dividend, and divisor, added together, will amount to 64. What is the number?

Solution Let x = the number sought. Then x/12 + x + 12 = 64. And x - 624/13 = 48. Answer B The answer is: B

B

mathematics

A retailer buys 40 pens at the market price of 36 pens from a wholesaler ,if he sells these pens giving a discount of 1% ,what is the profit % ?

let the market price of each pen be Rs 1 then,C.P of 40 pens = Rs 36 S.P of 40 pens =99% of Rs 40=Rs 39.60 profit %=((3.60*100)/36) %=10% Ans: E The answer is: E

E

mathematics

If the speed of X meters per minute is equivalent to the speed of Y kilometers per hour, what is Y in terms of X? (1 kilometer=1000 meters)

x=1000y/60 y = 0.06x Answer : D The answer is: D

D

mathematics

How many three digit even numbers M can be formed that are divisible by 9 such that both M and M^2 have the same units digits?

For an even number to have the same units digit as its square, it must have the units digit of 0 (0^2 = 0) or 6 (6^2 = 6). Thus the units digit of M must be 0 or 6. For a number to be divisible by 9, the sum of its digit must be divisible by 9. If the units digit of M is 0, then M could be: 900; 810, 180; 720, 270; 630, 360; 540, 450; 990. 10 numbers. If the units digit of M is 0, then M could be: 306; 216, 126; 936, 396; 846, 486; 756, 576; 666. 10 numbers. Total = 10 + 10 = 20. Answer: A. The answer is: A

A

mathematics

In the third grade of Windblown School there are 78 students, one third of them failed the math test and 1/6 failed that literature test. At least how many students failed both tests?

Total = 78 failed in math = 78/3=26 failed in literature=78/6=13 the least failed in both can be 0 while max can be 13 Answer A The answer is: A

A

mathematics

The cost of 20 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 20 : 27 Weight 900 : 1000 :: 28 : x (20 x 900 x x) = (27 x 1000 x 28) x = (27 x 1000 x 28) /20 x 900 =42 Answer A The answer is: A

A

mathematics

A monkey start climbing up a tree 19 ft tall.Each hour it hops 3 ft and slips back 2 ft. How much time would it take the monkey to reach the top.

if monkey hops 3ft and slips back 2ft in a hour, it means the monkey hops (3ft-2ft)= 1ft/hr. similarly in 16hrs it wil be 16ft. Bt since the height of the tree is 19ft, so if the monkey hops up the tree in the next hr i.e 17th hr then it reaches at the top of the tree. hence it takes 17 hrs for monkey to reach at the top ANSWER:D The answer is: D

D

mathematics

At the moment there are 54,000 tagged birds in a certain wildlife refuge. If exactly 20 percent of all birds in the refuge are tagged, what percent of the untagged birds must be tagged so that half of all birds in the refuge are tagged?

All birds = 54000 Currently Tagged = 54000 * 20/100 = 10800 So Untagged birds = 54000 - 10800 = 43200 Half of all birds = 27000 The number of birds to be tagged to make half of all birds tagged = 27000 - 10800 = 16200 So now the question remains - 16200 is how much percentage of untagged birds (43200) = 16200 * 100 /43200 = 37.5 % Answer (B) The answer is: B

B

mathematics

A farming field can be ploughed by 6 tractors in 4 days. When 6 tractors work together, each of them ploughs 120 hectares a day. If two of the tractors were moved to another field, then the remaining 4 tractors could plough the same field in 5 days. How many hectares a day would one tractor plough then?

If each of 6 tractors ploughed 120 hectares a day and they finished the work in 4 days, then the whole field is: 120*6*4=720*4=2880hectares. Let's suppose that each of the four tractors ploughed x hectares a day. Therefore in 5 days they ploughed 5*4*x=20*x hectares, which equals the area of the whole field, 2880 hectares. So, we get 20x=2880 x=2880/20=144. Hence, each of the four tractors would plough 144 hectares a day. Answer is D. The answer is: D

D

mathematics

A salesman’s terms were changed from a flat commission of 5% on all his sales to a fixed salary of Rs.1000 plus 2.5% commission on all sales exceeding Rs. 4,000. If his remuneration as per new scheme was Rs. 600 more than that by the previous schema, his sales were worth?

[1000 + (X-4000) * (2.5/100)] - X * (5/100) = 600 X = 12000 Answer: B The answer is: B

B

mathematics

5, 9, 17, 29, 45, ?

The pattern is + 4, + 8, + 12, + 16, .... Answer : A. The answer is: A

A

mathematics

It costs a man 75 dollars to buy the things that he needs to make hotdogs. The city allows him to sell his hotdog somewhere near the city hall. However, the city hall charges him 1 dollar for each hotdog sold Calculate the break even point if the price he charges for 1 hotdog is $1.50

Let x be the number of hotdogs sold Let C be the cost of buying and selling x hotdogs Let R be the revenue made for selling x hotdogs R = selling price of 1 hotdog × number of hotdogs sold R = 1.50x C = fixed cost + variable cost variable cost = fee charged for 1 hotdog × number of hotdogs sold variable cost = 1x C = 75 + 1x R = C 1.50x = 75 + 1x 1.50x - 1x = 75 + 1x - 1x 0.5x = 75 x = 150 since 0.5 × 150 = 75 The break even point is to sell 150 hotdogs. Answer B The answer is: B

B

mathematics

In Town P, 60 percent of the population are employed, and 45 percent of the population are employed males. What percent of the employed people in Town P are females?

The percent of the population who are employed females is 60-45 = 15% The percent of employed people who are female is 15% / 60% = 25%. The answer is B. The answer is: B

B

mathematics

X and Y started a business with capitals Rs. 20000 and Rs. 25000. After few months Z joined them with a capital of Rs. 30000. If the share of Z in the annual profit of Rs. 50000 is Rs. 14000, then after how many months from the beginning did Z join?

Investments of X, Y and Z respectively are Rs. 20000, Rs. 25000 and Rs. 30000 Let investment period of Z be x months. Ratio of annual investments of X, Y and Z is (20000 * 12) : (25000 * 12) : (30000 * x) = 240 : 300 : 30x = 8 : 10 : x The share of Z in the annual profit of Rs. 50000 is Rs. 14000. => [x/ (18 + x)] 50000 = 14000 => [x/ (18 + x)] 25 = 7 => 25x = 7x + (18 * 7) => x = 7 months. Z joined the business after (12 - 7) months. i.e., 5 months.Answer: B The answer is: B

B

mathematics

A new savings account offers 9 percent annual interest compounded every 6 months. What would be the total balance in an account after 1 year, if the initial amount in the account were $6000?

The interest is compounded every 6 months. To calculate interest, you must take the principal and multiply it by the interest and the length of time (using the unit used in the interest, typically years). At the end of the first 6 months the interest earned is $6,000(.09) (1/2) = $270. (Note: the 6 months are “1/2” in the equation since 9% is a yearly rate, not a bi-yearly one). Since the interest is compounded, the second six months of the year are not earning interest on just the original $6,000, but on the interest as well, so they are actually earning interest on $6,270. The interest earned during the final 6 months of the year is $6,270(.09)(1/2) = $282.15. Therefore, the total balance is the original amount ($6000) + $270 + $282.15 = $6,552.15. The correct answer is E. The answer is: E

E

mathematics

The average age of 18 students of a class is 18 years. Out of these, the average age of 5 students is 14 years and that of the other 9 students is 16 years, The age of the 18th student is

Explanation: Age of the 18th student = [18 * 18 - (14 * 5 + 16 * 9)] = (324-214) = 110 years. Answer: C The answer is: C

C

mathematics

A man complete a journey in 10 hours. He travels first half of the journey at the rate of 21 km/hr and second half at the rate of 24 km/hr. Find the total journey in km.

0.5x/21 + 0.5x/24 = 10 x/21 + x/24 = 20 15x = 168 x 20 x = (168 x 20)/15 = 224 km. answer B The answer is: B

B

mathematics

The average of seven numbers is 18. The average of first three numbers is 14 and the average of last three numbers is 19. What is the middle number?

The total of seven numbers = 7X18 = 126 The total of first 3 and last 3 numbers is = 3 X 14+3 X 19 = 99 So, the middle number is (126 - 99 ) = 27 B The answer is: B

B