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mathematics

Adding two non multiples of R always results in a multiple of R; which of the following must be the value of R ?

NON- multiples of 2 would always be ODD and sum of two odd would be EVEN. so irrespective of value of non-multiples, sum of two them would always be even and thus multiple of 2.. A The answer is: A

A

mathematics

A salesperson gets a 15% commission on each sale he makes. How many sales of $270 each must he make in order to reach a salary of at least $1000?

Soln:- 10% of 270 = 27. 5% of 270 = 13.5. so, 15 % of 270 = 40.5 total salary required 1000 earning from single sale 40.5 # of sale = 1000/40.5 = 24.62 Approx 25 sale ANSWER:C The answer is: C

C

mathematics

The tax on a commodity is diminished by 20% and its consumption increased by 15%. The effect on revenue is?

Explanation: 100 * 100 = 10000 80 * 115 = 9200 ----------- 10000-----------800 100-----------? => 8% decrease ANSWER IS B The answer is: B

B

mathematics

Mary's income is 60% more Than Tim's income and Tim's income is 20% less than Juan's income.What % of Juan's income is Mary's income.

Even I got 96% J = 100 T = 100*0.8 = 80 M = 80*1.6 = 128 If Mary's income is x percent of J M = J*x/100 x = M*100/J = 128*100/100 = 128 Ans:A The answer is: A

A

mathematics

Three persons invested Rs.9000 in a joint business. The second person invested Rs.1000 more than the first and the third Rs.1000 more than second. After two years, they gained Rs.3600. How much third person will get?

First persons investment = x Second persons investment = x + 1000 Third persons investments = x + 2000 x + x + 1000 + x + 2000 = 9000 3x = 6000 x = 2000 Ratio = 2000 : 3000 : 4000 2:3:4 4/9 * 3600 = 1600 Answer: A The answer is: A

A

mathematics

What is the probability that the position in which the consonants appear remain unchanged when the letters of the word "Math" are re-arranged?

Explanatory Answer Step 1: Compute denominator In any probability question, the denominator represents the total number of outcomes for an event. The numerator represents the number of favorable outcomes. The total number of ways in which the word MATH can be re-arranged = 4! = 4*3*2*1 = 24 ways. Step 2: Compute numerator and the probability If the positions in which the consonants appear do not change, the first, third and the fourth positions are reserved for consonants and the vowel A remains at the second position. The consonants M, T and H can be re-arranged in the first, third and fourth positions in 3! = 6 ways so that the positions in which the positions in which the consonants appear remain unchanged. Therefore, the required probability 6/24=/14 Choice A The answer is: A

A

mathematics

In a graduating class of 232 students, 144 took geometry and 119 took biology. What is the difference between the greatest possible number P and the smallest possible number of students that could have taken both geometry and biology?

OFFICIAL SOLUTION: First of all, notice that since 144 took geometry and 119 took biology, then the number of students who took both geometry and biology cannot be greater than 119. {Total} = {geometry} + {biology} - {both} + {neither}; 232 = 144 + 119 - {both} + {neither}; {both} = 31 + {neither}. {both} is minimized when {neither} is 0. In this case {both} = 31. The greatest possible number of students P that could have taken both geometry and biology, is 119. Thus, the answer is 119 - 31 = 88. Answer: D. The answer is: D

D

mathematics

A retailer bought a machine at a wholesale price of $90 and later on sold it after a 10% discount of the retail price. If the retailer made a profit equivalent to 20% of the whole price, what is the retail price r of the machine?

Since the wholesale price was $90 and the profit was 20% of the wholesale price ([.2][90] = $18), the retail price would have to be above $108, but not that much greater than that. Let's start by TESTing Answer C: $120.... If..... Retail Price r= $120 10% discount off = $120 - (.1)(120) = 120 - 12 = 108 20% profit on wholesale price = 90 + (.2)(90) = 90 + 18 = 108 These two numbers MATCH, so this MUST be the answer! Final Answer: [Reveal]Spoiler: C The answer is: C

C

mathematics

10 men and 15 women together can complete a work in 8 days. It takes 100 days for one man alone to complete the same work. How many days will be required for one woman alone to complete the same work?

1 man's 1 day work = 1/100 (10 men + 15 women)'s 1 day work = 1/8 15 women's 1 day work = (1/8 - 10/100) = 1/40 1 woman's 1 day work = 1/600 1 woman alone can complete the work in 600 days. Answer:E The answer is: E

E

mathematics

Tom drives from town Q to town B, driving at a constant speed of 60 miles per hour. From town B Tom immediately continues to town C. The distance between Q and B is twice the distance between B and C. If the average speed of the whole journey was 36 mph, then what is Tom's speed driving from B to C in miles per hour?

Let's assume that it takes 4 hours to go from point Q to B. Then the distance between them becomes 240 which makes distance between B and C 120. (240+120)/(4+x) gives us the average speed which is 36. You find x=6. So the question simplifies itself to 120/6=20 Hence the answer is B. The answer is: B

B

mathematics

If 4 persons can do 4 times of a particular work in 4 days, then, 7 persons can do 7 times of that work in?

That is, 1 person can do one time of the work in 4 days. Therefore, 7 persons can do 7 times work in the same 4 days itself B) The answer is: B

B

mathematics

sue has 3 apples. Billy has 5 apples. If billy steals all of sues apples and eats 1 how many does he have left?

7 D The answer is: D

D

mathematics

If the sum of three consecutive positive odd integers is A, then the sum of the next three consecutive odd integers in terms of A is:

In Case of Consecutive Integers or Integers in Arithmetic Progression Mean = Median I.e. Median = A/3 = Mean = Second Integer First Integer = A/3 - 2 Second Integer = A/3 Third Integer = A/3 + 2 i.e. Fourth Integer = A/3 + 4 Fifth Integer = A/3 + 6 Sixth Integer = A/3 + 8 Now Mean of next 3 Integers = Median = A/3 + 6 i.e. Sum of Next 3 integers = (A/3 + 6)*3 = A+18 Answer: option C The answer is: C

C

mathematics

The effective annual rate of interest corresponding to a nominal rate of 6% per annum payable half-yearly is?

Amount of Rs. 100 for 1 year when compounded half-yearly = [100 * (1 + 3/100)2] = Rs. 106.09 Effective rate = (106.09 - 100) = 6.09% ANSWER:D The answer is: D

D

mathematics

Two different types of tea are mixed, at 6 Kg of type 1 and 4 Kg of type 2. One Kg of type 1 is Rs. 6 and that of type 2 is Rs. 7. The seller get 10% profit, by this action. Find at what price, he had sold the mixture/Kg?

CP of 6 kg tea of type 1= 6*6=36 Rs. CP of 4 kg tea of type 2= 4*7=Rs 28 CP of 10 kg mixed tea = Rs Rs 64 SP of mixture for 10% profit = 64*1.1= Rs 70.4 SP of 1kg mixed tea = Rs 7.04 ANSWER:B The answer is: B

B

mathematics

A train 640 meters long is running with a speed of 64 kmph. The time taken by it to cross a tunnel 140 meters long is?

D = 640 + 140 = 780 S = 64 * 5/18 = 17.7 mps T = 780/17.7 = 44 sec Answer: A The answer is: A

A

mathematics

The cost price of a radio is Rs.1800 and it was sold for Rs.1430, find the loss %?

1800 ---- 370 100 ---- ? => 20.5% Answer:B The answer is: B

B

mathematics

A and B walk around a circular track. They start at 8 a.m. from the same point in the opposite directions. A and B walk at a speed of 2 rounds per hour and 2 rounds per hour respectively. How many times shall they cross each other before 9.30 a.m. ?

Relative speed = 2 + 2 = 4 rounds per hour. So, they cross each other 4 times in an hour and 2 times in half an hour. Hence, they cross each other 6 times before 9.30 a.m. ANSWER:D The answer is: D

D

mathematics

A man bought 40 shares of Rs. 60 at 5 discount, the rate of dividend being 12%The rate of interest obtained is

Explanation : Face Value of a share = Rs.60 He bought each share at Rs.60 - Rs.5 = Rs.55 Number of shares = 40 Dividend = 12 % Dividend per share = 60×12×100=Rs.7 1/5 Total dividend = (40 × 7 1/5) ie, He got a dividend of (40 × 7 1/5) for an investment of Rs.(40 × 55) Interest obtained = 40×7 1/5×100/40×55=13.09% Answer : Option A The answer is: A

A

mathematics

Pipe A can fill a tank in 6 hours. Due to a leak at the bottom, it takes 9 hours for the pipe A to fill the tank. In what time can the leak alone empty the full tank?

Let the leak can empty the full tank in x hours 1/6 - 1/x = 1/9 => 1/x = 1/6 - 1/9 = (3 - 2)/18 = 1/18 => x = 18. Answer: C The answer is: C

C

mathematics

342

One day's work of A and B = 1/9 + 1/8 = (2+1)/18 = 1/6 So, the time taken to complete the work is 6 days. Answer: C The answer is: C

C

mathematics

In what ratio must rice at Rs.7.10 be mixed with rice at Rs.9.20 so that the mixture may be worth Rs.8 per Kg?

Explanation : By the rule of alligation, we have CP of 1 kg Rice of 1st kind CP of 1 kg Rice of 2nd kind 7.1 9.2 Mean Price 8 9.2 - 8 = 1.2 8 - 7.1 = .9 Required ratio = 1.2 : .9 = 12 : 9 = 4 : 3 Answer : Option D The answer is: D

D

mathematics

A tea expert claims that he can easily find out whether milk or tea leaves were added first to water just by tasting the cup of tea. In order to check this claims 12 cups of tea are prepared, 6 in one way and 6 in other. Find the different possible ways of presenting these 12 cups to the expert.

Solution: Since, there are 6 cups of each kind, prepared with milk or tea leaves added first, are identical hence, total number of different people ways of presenting the cups to the expert is, [12!/(6!x 6!)]= 924 Answer: Option D The answer is: D

D

mathematics

All the students of class are told to sit in circle shape. Here the boy at the 10 th position is exactly opposite to 40 th boy. Total number of boys in the class?

As half the circle shape consist of 40-10=30 boys, So total number of boys in full circle=2*30=60 ANSWER: C The answer is: C

C

mathematics

Two trains each 190m in length each, are running on two parallel lines in opposite directions. If one goes at the speed of 65km/h while the other travels at 50km/h. how long will it take for them to pass each other completely.

Explanation: D = 190 m + 190 m = 380 m RS = 65 + 50 = 115 * 5/18 = 319/10 T = 380 * 10/319 = 11.9 sec Answer: Option C The answer is: C

C

mathematics

25 binders can bind 1400 books in 21 days. How many binders will be required to bind 1600 books in 20 days?

Binders Books Days 25 1400 21 x 1600 20 x/25 = (1600/1400) * (21/20) => x = 30 Answer:E The answer is: E

E

mathematics

The lenght of a room is 5.5 m and width is 4 m. Find the cost of paving the floor by slabs at the rate of Rs. 750 per sq. metre.

Area of the floor = (5.5 × 4) m2 = 22 m2. Cost of paving = Rs. (750 × 22) = Rs. 16500 . Answer: Option C The answer is: C

C

mathematics

The ratio of the length and the breadth of a rectangle is 4 : 3 and the area of the rectangle is 6912 sq cm. Find the ratio of the breadth and the area of the rectangle?

Let the length and the breadth of the rectangle be 4x cm and 3x respectively. (4x)(3x) = 6912 12x2 = 6912 x2 = 576 = 4 * 144 = 22 * 122 (x > 0) => x = 2 * 12 = 24 Ratio of the breadth and the areas = 3x : 12x2 = 1 : 4x = 1: 96. ANSWER:A The answer is: A

A

mathematics

9 - 3 ÷ 1/3 + 4 = ?

9 - 3 1/3 + 4 =9-3÷1/3+4 =9-(3X3) +4 =9-9+4 =4 CORRECT ANSWER : A The answer is: A

A

mathematics

The product of first twelve positive integers is divisible by all of the the following EXCEPT?

The product of the first twelve positive integers, 12!12! contains only the primes less than 12 (2, 3, 5, 7, 11), which means that the product won't be divisible by any number containing higher prime number. Now, you can notice that 34=2*17 --> 12! is not divisible by 17 (prime >11), thus 12! is not divisible by 2*17=34 too. Answer: E. The answer is: E

E

mathematics

Anil and suresh started a business with Rs.50,000 and 40,000 respectively. After 6 months Rakesh joined them with capital of Rs.60,000 They got a profit of Rs.6000, then profit of Rakesh is

Ratio of investments of Anil, Suresh & Rakesh=(50000*12) : (40000*12) : (60000*6)=5 : 4 : 3 Profit of Rakesh in Rs. 6000 = 3*6000/(5+4+3) =1500 ANSWER:A The answer is: A

A

mathematics

By selling 150 mangoes, a fruit-seller gains the selling price of 5 mangoes. Find the gain percent?

SP = CP + g 150 SP = 150 CP + 5 SP 145 SP = 150 CP 145 --- 5 CP 100 --- ? => 3.4% Answer:A The answer is: A

A

mathematics

Find the odd man out. 9,18,23,36,99

All except 23 are multiples of 9 Answer is C The answer is: C

C

mathematics

P, Q and R have $7000 among themselves. R has two-thirds of the total amount with P and Q. Find the amount with R?

A 2800 Let the amount with R be $ r r = 2/3 (total amount with P and Q) r = 2/3(7000 - r) => 3r = 14000 - 2r => 5r = 14000 => r = 2800. The answer is: A

A

mathematics

The jogging track in a sports complex is 726 m in circumference. Suresh and his wife start from the same point and walk in opposite direction at 4.5 km/hr and 3.75 km/hr respectively. They will meet for the first time in?

Let both of them meet after TT min 4500 m are covered by Suresh in 60 m. In TT min he will cover 4500T604500T60 Likewise, In TT min Suresh's wife will cover 3750T603750T60 Given, 4500T60+3750T60=7264500T60+3750T60=726 TT = 5.28 minutes Option(D) is correct The answer is: D

D

mathematics

If a fair coin is tossed six times, what is the probability of getting exactly five heads in a row?

P(HHHHHT) = 1/64 P(THHHHH) = 1/64 The sum of these probabilities is 2/64 = 1/32 The answer is B. The answer is: B

B

mathematics

At an election 2 candidates are participated and a candidate got 30% of votes and defeated by 1000. and 100 votes are invalid. Find the total polled votes?

Winner votes = 100-30 = 70 polled votes = [(100*1000)/2*70-100]+100 = 2600 Answer is B The answer is: B

B

mathematics

Express 35 mps in kmph?

35 * 18/5 = 126 kmph Answer: C The answer is: C

C

mathematics

A batch of cookies was divided amomg 3 tins: 3/4 of all the cookies were placed in either the blue or the green tin, and the rest were placed in the red tin. If 1/4 of all the cookies were placed in the blue tin, what fraction of the cookies that were placed in the other tins were placed in the green tin

This will help reduce the number of variables you have to deal with: G + B = 3/4 R = 1/3 B = 1/4 We can solve for G which is 1/2 What fraction (let it equal X) of the cookies that were placed in the other tins were placed in the green tin? So.. X*(G+R)=G X*(1/2 + 1/3) = 1/2 X = 3/5 ANSWER: D The answer is: D

D

mathematics

The CI on Rs. 30,000 at 7% per year is Rs. 4347. The period is?

Amount = Rs. (30000 + 4347) = Rs. 34347. Let the time be n years. Then, 30000 1 + 7 n = 34347 100 107 n = 34347 = 11449 = 107 2 100 30000 10000 100 n = 2 years B The answer is: B

B

mathematics

A candidate got 30% of the votes polled and he lost to his rival by 1760 votes. How many votes were cast?

Let x be the total number of votes. 0.3x + 1760 = 0.7x 0.4x = 1760 x = 1760/0.4 = 4400 The answer is E. The answer is: E

E

mathematics

What is the units digit of 33^2 * 17^3 * 49^3?

The units digit of 33^2 is the units digit of 3*3 = 9 which is 9. The units digit of 17^3 is the units digit of 7*7*7 = 343 which is 3. The units digit of 49^3 is the units digit of 9*9*9 = 729 which is 9. The units digit of 9*3*9 = 243 is 3. The answer is B. The answer is: B

B

mathematics

M is 30% of Q. Q is 20% of P. N is 50% of P. Find M:N ratio

Let p be 100 N = 50% of 100 (P=100) = 50 Q= 20% of 100 (P=100) = 20 M = 30% of 20 (Q=20) = 6 M:N = 6:50 M:N = 3:25 ANSWER:C The answer is: C

C

mathematics

A sum was put at simple interest at a certain rate for 5 years Had it been put at 6% higher rate, it would have fetched 90 more. Find the sum.

Difference in S.I. = P×T/100(R1−R2) ⇒ 90 = P×5x6/100(∵ R1 - R2 = 2) ⇒ P = 90×100/5x6=300 Answer D The answer is: D

D

mathematics

The average salary of all the workers in a workshop is Rs. 8000. The average salary of 7 technicians is Rs. 12000 and the average salary of the rest is Rs. 6000. The total number of workers in the workshop is:

Let the total number of workers be x. Then, 8000x = (12000 * 7) + 6000(x - 7) = 2000x = 42000 = x = 21. ANSWER A The answer is: A

A

mathematics

The largest 5 digit number exactly divisible by 91 is:

Explanation: Largest 5-digit number = 99999 91) 99999 (1098 91 --- 899 819 ---- 809 728 --- 81 --- Required number = (99999 - 81) = 99918. Answer:D The answer is: D

D

mathematics

If y > 0, (2y)/5 + (3y)/10 is what percent of y?

can be reduced to 2y/5+3y/10 =2y/5=70% D The answer is: D

D

mathematics

There are n cities. What is the number of airlines that connected 4 different cities (airline from city A to city B is different with airline from city B to city A)?

First of all, the possible number of airlines is n. Then, the possible number of airlines departing from one city to another becomes (n-3). Hence, the answer is n(n-3), which makes A an answer choice. B The answer is: B

B

mathematics

A certain basketball team that has played 2/3 of its games has a record of 18 wins and 2 losses. What is the greatest number of the remaining games that the team can lose and still win at least 3/4 of all of its games?

18 wins, 2 losses - total 20 games played. The team has played 2/3rd of all games so total number of games = 30 3/4th of 30 is 22.5 so the team must win 23 games and can afford to lose at most 7 total games. It has already lost 2 games so it can lose another 5 at most. Answer (C) The answer is: C

C

mathematics

In August,a cricket team that played 120 matches won 24% of the games it played.After a continuous winning streak,this team raised its average to 52%.How many matches did the team win to attain this average?

let the no of matches played more=x so, (120+x)*52/100=28.8+x by solving we get x=70 ANSWER:D The answer is: D

D

mathematics

In how many ways can 6 people be seated at a round table if one of those seated cannot sit next to 2 of the other 5?

6 People in a round table can be seated in (6 - 1) ! ways = 120. Now we need to subtract the number of cases when one of those is sitting next to 2 of the other 5. We can consider as if 5 people are sitting in a row because it is round table. Again consider 3 people, those who can not sit together, as a single unit – So the possible arrangements among remaining people 5 – 3 + 1 Unit are = 3 ! And the 3 people unit can arrange among themselves in 3 ! ways. So the possible cases when one of those is sitting next to 2 of the other 5 = 3 ! * 3 ! = 36 Total possible cases = 120 -36 = 84 ANS:D The answer is: D

D

mathematics

A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 38 years now, the son's age five years back was:

Let the son's present age be x years. Then, (38 - x) = x 2x = 38. x = 19. Son's age 5 years back (19 - 5) = 14 years. Answer : A The answer is: A

A

mathematics

How many kg of pure salt must be added to 100kg of 10% solution of salt and water to increase it to a 35% solution?

Amount salt in 100kg solution = 10*100/100 = 10 kg Let x kg of pure salt be added then(10+x)/(100+x)=35/100 200+20x=700+7x 13x = 500 x = 28.5 Answer is B The answer is: B

B

mathematics

Lagaan is levied on the 60 percent of the cultivated land. The revenue department collected total Rs. 3,84,000 through the lagaan from the village of Mettur. Mettur, a very rich farmer , paid only Rs.480 as lagaan. The percentage of total land of Mettur over the total taxable land of the village is:

Total land of Sukhiya = \inline \frac{480x}{0.6} = 800x \therefore Cultivated land of village = 384000x \therefore Required percentage = \inline \frac{800x}{384000}\times 100 = 0.20833 A The answer is: A

A

mathematics

A sum of money is divided among A, B, C & D in the ratio 3:5:8:9 respectively. If the share of D Rs.1872 more than the share of A, then what is the total amount of money of B & C together?

Sol. Share of B + C = -3 x (5 + 8) = Rs. 4056 B The answer is: B

B

mathematics

A father said his son , " I was as old as you are at present at the time of your birth. " If the father age is 38 now, the son age 5 years back was

Let the son's present age be x years .Then, (38 - x) = x x= 19. Son's age 5 years back = (19 - 5) = 14 years Answer: A The answer is: A

A

mathematics

1/2, 1/4, 1/8, 1/16, 1/32, .... In the sequence above each term after after the first one-half the previous term. If x is the FOURTH term of the sequence, then x satisfies which of the following inequalities?

In the Sequence notice that the sequence is just the 1/(2^n) ... so for 1st term=1/2^1=1/2 2nd term=1/(2^2)1/4, 3rd term=1/(2^3)=1/8 and so on... Thus the 4th term will be 1/(2^4)=1/16 =0.0625 A The answer is: A

A

mathematics

When positive integer B is divided by 6 the remainder is 3. Which of the following CANNOT be an even integer?

When positive integer B is divided by 6 the remainder is 3 So, B could equal 3, 9, 15, 21, etc let's TEST B =3 a.3+ 1 = 4 (EVEN) b.3-11 = -8 (EVEN) c. 4(3) + 2 = 14 (EVEN) d. (3-3)/3 +2 = 2 (EVEN) At this point, we can already see the answer must be E. Let's check E forfun e.3/3 = 1 (ODD) Great! Answer: E The answer is: E

E

mathematics

A store reduced the price of all items in the store by 8% on the first day and by another 10% on the second day. The price of items on the second day was what percent of the price before the first reduction took place?

consider price of the all items as $100 after a initial reduction of 8% price becomes = 0.92 *100 = $ 92 after the final reduction of 10% price becomes = 0.9* 92 = $ 82.8 price of all items on second day is 82.8% of price on first day correct answer option E The answer is: E

E

mathematics

A machine puts c caps on bottles in m minutes. How many R hours will it take to put caps on b bottles?

The machine puts c caps in m minutes or c caps in m/60 hours. Rate = c/m/60 = 60c/m. To put b caps the machine will take:- Time = Work/Rate T = b/60c/m = bm/60c Answer is B. The answer is: B

B

mathematics

A pipe can fill a cistern in 20 minutes whereas the cistern when fill can be emptied by a leak in 28 minutes. When both pipes are opened, find when the cistern will be full?

1/20 - 1/28 = 1/70 70 minutes Answer:C The answer is: C

C

mathematics

The product of two numbers is 4107. If the H.C.F of these numbers is 37, then the greater number is?

Let the numbers be 37a and 37b. Then, 37a * 37 b = 4107 => ab = 3 Now, co-primes with product 3 are (1, 3). So, the required numbers are (37 * 1, 37 * 3) i.e., (1, 111). Greater number = 111. Answer:C The answer is: C

C

mathematics

A carpenter worked alone for 1 day on a job that would take him 6 more days to finish. He and another carpenter completed the job in 6 more days. How many days would it have taken the second carpenter to do the complete job working alone?

A carpenter worked only 1 day on something that takes him 6 MORE days. Means; Carpenter finishes his work in 7 days. Let his buddy finish the same task in x days. Respective rates per day: 1/7 AND 1/x To complete 1 work: First guy worked for 5 days @ rate=1/7 per day. Second one worked for 6 days @ rate=1/x per day Expression: Days*Rate=Work 5*1/7+6*1/x=1 5x+42=7x 2x=42 x=21 days. Ans:E The answer is: E

E

mathematics

How many ways can you arrange 16 people into 4 rows of 4 desks each?

for 1st person there are 16 places for 2nd person there are 15 places for 3rd ..... 14 places no. of ways will be = 16*15*14......3*2*1 = 16! ANSWER:C The answer is: C

C

mathematics

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

The distance of the light travels in 100 years is: 5,870,000,000,000 × 100 miles. = 587,000,000,000,000 miles. = 587 × 1012 miles. Answer :E The answer is: E

E

mathematics

50% of the population of a village is 23040. The total population of the village is ?

Answer ∵ 50% of P = 23040 ∴ P = (23040 x 100) / 50 = 46080 Correct Option: D The answer is: D

D

mathematics

The cost price of an article is 55% of the marked price. Calculate the gain percent after allowing a discount of 15%.

Sol. Let marked price = Rs. 100. Then, C.P. = Rs. 55. S.P = Rs. 85. ∴ Gain % = [30/55 * 100]% = 54.5%. Answer C The answer is: C

C

mathematics

What two-digit number is less than the sum of the square of its digits by 13 and exceeds their doubled product by 5?

Let the digits be x and y. The number would be 10x + y. We are given that 2xy + 5 = 10x +y = x^2 y^2 -13 Thus 2xy +5 = x^2 + y^2 - 13 x^2 + y^2 -2xy = 16 (x-y)^2 = 16 (x-y) = 4 or -4 Substituting the values of (x-y) in the equation 2xy +5 = 10x + y x comes out to be 1 or 9... thus the two numbers can be 15 or 99 Thus the answer is B The answer is: B

B

mathematics

David obtained 70, 60, 78, 60 and 65 marks (out of 100) in English, Mathematics,Physics, Chemistry and Biology What are his average marks ?

Explanation: Average = (70+ 60+ 78+ 60+ 65 )/ 5 = 333/5 = 66.6. Answer:C The answer is: C

C

mathematics

The cost of Type 1 material is Rs. 15 per kg and Type 2 material is Rs.20 per kg. If both Type 1 and Type 2 are mixed in the ratio of 2 : 3, then what is the price per kg of the mixed variety of material?

Type 1 cost = 15 type 2 cost = 20 =>2:3 hence cost the mixture= (15*2)+(20*3) /(2+3) = 18 ANSWER A The answer is: A

A

mathematics

The speed of a boat in upstream is 45 kmph and the speed of the boat downstream is 90 kmph. Find the speed of the boat in still water and the speed of the stream?

Speed of the boat in still water = (45+90)/2 = 67.5 kmph. Speed of the stream = (90-45)/2 = 22.5 kmph. Answer:B The answer is: B

B

mathematics

In a St.Johns college students, 50 percent are third year students and 80 percent are not second-year students. What fraction of those students who are not third-year students are second-year students?

= 20/50. = 2/5 my answer is B too The answer is: B

B

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

The speed of a boat in upstream is 50 kmph and the speed of the boat downstream is 90 kmph. Find the speed of the boat in still water and the speed of the stream?

Speed of the boat in still water = (50+90)/2 = 70 kmph. Speed of the stream = (90-50)/2 = 20 kmph. Answer:B The answer is: B

B

mathematics

From the given equation find the value of c: c²-3c-10

(c - 5)(c + 2) C = -2 or 5 Answer is C The answer is: C

C

mathematics

Solution X is 10 percent alcohol by volume, and solution Y is 30 percent alcohol by volume. How many milliliters of solution Y must be added to 200 milliliters of solution X to create a solution that is 25 percent alcohol by volume?

we know that X is 10% , Y is 30% and W.Avg = 25% . what does this mean with respect to W.Avg technique ? W.Avg is 1 portion away from Y and 3 portion away from X so for every 1 portion of X we will have to add 3 portions of Y. If X = 200 then Y = 600 ANSWER:E The answer is: E

E

mathematics

How many three letter words are formed using the letters of the word THREE?

The number of letters in the given word is five. The number of three letter words that can be formed using these four letters is 5P4 = 5 * 4 * 3*2 = 120. Answer:D The answer is: D

D

mathematics

The least number which when divided by 5, 6, 7 and 8 leaves a remainder 3, but when divided by 9 leaves no remainder, is

Explanation: L.C.M of 5, 6, 7, 8 = 840 therefore Required Number is of the form 840k+3. Least value of k for which (840k+3) is divisible by 9 is k = 2 therefore Required Number = (840 x 2+3)=1683. Answer: B The answer is: B

B

mathematics

If (2)^n=(1/2)^2, what is the value of n?

(2)^n = (1/2)^2 = (2)^-2 n = -2 (Answer = A) The answer is: A

A

mathematics

Average of money that group of 4 friends pay for rent each month is $800.After one persons rent is increased by 20% the new mean is $860.What was original rent of friend whose rent is increased?

0.2X = 4(860-800) 0.2X = 240 X = 1200 Answer E The answer is: E

E

mathematics

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

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

B

mathematics

A cube of edge 16cm is immersed completely in a rectangular vessel containing water. If the dimensions of the base of vessel are 20cm * 15cm , find the rise in water level?

Increase in volume = volume of the cube = 16*16*16 cm^3 Rise in water level = volume / area = 16*16*16/20*15 = 13.65cm Answer is C The answer is: C

C

mathematics

If P represents the product of the first 14 positive integers, then P is NOT a multiple of

Answer is E. Since prime factor of 57 is 2x17. 17 is a prime number and not part of the first 14 positive integers. A) 9 x 11 B) 12 x 7 C) 12 x 6 D) 13 x 5 E) 2 x 17 The answer is: E

E

mathematics

A certain kind of necklace is made from 9 yellow, 6 blue, and 3 silver beads. What is the maximum number of these necklaces that can be made from 63 beads of each color ?

Atleast 9 yellow breads are needed to make a necklace, so irrespective of the combinations of blue and silver beads, the number of necklaces that can be formed will be 63/9 =7 Answer:- A The answer is: A

A

mathematics

A single discount equivalent to the discount series of 20%, 10% and 5% is?

100*(80/100)*(90/100)*(95/100) = 68.4 100 - 68.4 = 31.6 Answer: C The answer is: C

C

mathematics

A grocer has a sale of Rs. 5400, Rs. 9000, Rs. 6300, Rs. 7200 and Rs.4500 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 5600?

Total sale for 5 months = Rs. (5400 + 9000 + 6300+ 7200 + 4500) = Rs. 32400. Required sale = Rs. [ (5600 x 6) - 32400 ] = Rs. (33600 - 32400) = Rs.1200. Option A The answer is: A

A

mathematics

How many positive integers less than 256 are multiple of 4 but NOT multiples of 6?

248/4=64 Multiples of 4 which are a multiple of 6 will be of the form 2*2*3=12n where n>0 240/12=20 64-20=44 Answer: E The answer is: E

E

mathematics

The area of a base of a cone is 30 cm2. If the height of the cone is 6cm, find its volume?

πr2 = 30 h = 6 1/3 * 30 * 6 = 60 Answer: D The answer is: D

D

mathematics

A bullet train leaves Kyoto for Tokyo traveling 240 miles per hour at 12 noon. Ten minutes later, a train leaves Tokyo for Kyoto traveling 160 miles per hour. If Tokyo and Kyoto are 400 miles apart, at what time will the trains pass each other?

Train A: going from K to T Train B: going from T to K First I calculated how far Train A will have travelled by the time Train B starts at 12:10: 10 minutes at 240 mph 1/6*240=40miles They have 400-40=360 miles to travel to meet each other. I found the combined rate of the two trains Rate(A) + Rate(B) = 400mph Divide Distance/Rate to find total time each will travel: 360/400>>> 54 Minutes to meet 12:10+54 minutes = 01:04 or Answer E The answer is: E

E

mathematics

The product of all the prime numbers less than 22 is closest to which of the following powers of 10?

Quickly approximate 2, 3, 5, 7, 11, 13, 17, 19 =2.1x10^2*1.3*1.7*1.9 =9.69* 10^6 =1*10^7 C The answer is: C

C

mathematics

A retailer buys a radio for Rs 225. His overhead expenses are Rs 20. He sellis the radio for Rs 300. The profit percent of the retailer is

Explanation: cost price = (225 + 20) = 245 sell price = 300 gain = (55/245)*100 = 22.4%. Answer: A The answer is: A

A

mathematics

TATA company plans to assign identification numbers to its employees. Each number is to consist of four different digits from 0 to 9, inclusive, except that the first digit cannot be 0. How many different identification numbers are possible?

TATA company plans to assign identification numbers to its employeeS.The first digit can take 9 values from 1 to 9 inclusive; The second digit can also take 9 values (9 digits minus the one we used for the first digit plus 0); The third digit can take 8 values; The fourth digit can take 7 values. Total = 9*9*8*7 = something with the units digit if 6. Answer: B. The answer is: B

B

mathematics

Of the 20,210 employees of the anvil factory, 2/7 are journeymen. If half of the journeymen were laid off, what percentage of the total remaining employees would be journeymen?

The exam gives us a number that is easily divisible by 7 to pique our curiosity and tempt us into calculating actual numbers (also because otherwise the ratio would be incorrect). Since the question is about percentages, the actual numbers will be meaningless, as only the ratio of that number versus others will be meaningful. Nonetheless, for those who are curious, each 1/7 portion represents (14210/7) 2,030 employees. This in turn means that 4,060 employees are journeymen and the remaining 10,150 are full time workers. If half the journeymen were laid off, that would mean 1/7 of the total current workforce would be removed. This statistic is what leads many students to think that since half the journeymen are left, the remaining journeymen would represent half of what they used to be, which means 1/7 of the total workforce. If 1/7 of the workforce is journeymen, and 1/7 is roughly 14.3%, then answer choice A should be the right answer. In this case, though, it is merely the tempting trap answer choice. What changed between the initial statement and the final tally? Well, you let go of 1/7 of the workforce, so the total number of workers went down. The remaining workers are still 1/7 of the initial workers, but the group has changed. The new workforce is smaller than the original group, specifically 6/7 of it because 1/7 was eliminated. The remaining workers now account for 1/7 out of 6/7 of the force, which if we multiply by 7 gives us 1 out of 6. This number as a percentage is answer choice B, 49.67%. Using the absolute numbers we calculated before, there were 4,060 journeymen employees out of 14,210 total. If 2,030 of them are laid off, then there are 2,030 journeyman employees left, but now out of a total of (14,210-2,030) 12,180 employees. 2,030/12,180 is exactly 1/6, or 16.67%. The answer will work with either percentages or absolute numbers, but the percentage calculation will be significantly faster and applicable to any similar situation. The underlying principle of percentages (and, on a related note, ratios) can be summed up in the brainteaser I like to ask my students: If you’re running a race and you overtake the 2nd place runner just before the end, what position do you end up in? The correct answer is 2nd place. Percentages, like ratios and other concepts of relative math, depend entirely on the context. Whether 100% more of something is better than 50% more of something else depends on the context much more than the percentages quoted. When it comes to percentages on the GMAT, the goal is to understand them enough to instinctively not fall into the traps laid out for you.E The answer is: E

E

mathematics

The length of the bridge, which a train 130 meters long and travelling at 45 km/hr can cross in 30 seconds, is?

Speed = (45 * 5/18) m/sec = (25/2) m/sec. Time = 30 sec. Let the length of bridge be x meters. Then, (130 + X)/30 = 25/2 ==> 2(130 + X) = 750 ==> X = 245 m. Answer: C The answer is: C

C

mathematics

If 2x + y = 7 and x + 2y = 5, then 5xy/3 =?

2*(x+2y = 5) equals 2x+4y=10 2x+4y=10 - 2x + y= 7 = 3y=3 Therefore Y = 1 Plug and solve... 2x + 1 = 7 2x=6 x=3 (5*3*1)/3 = 15/3 =5 A The answer is: A

A

mathematics

On the xy-plane, each point on circle C has coordinates such that x 0 and y 0. If the center of circle C is the point (3; 12), what is the maximum possible area of C?

I think that theintentof this question is that the circle will have NO CO-ORDINATES that fit the following 2 forms: (0, Y) or (X, 0). In real basic terms, this circle will NEITHER touch (nor cross) the X-axis NOR will it touch (nor cross) the Y-axis. With a center at (3,8), the longest possible radius would ALMOST touch the X-axis, so the radius would be a little less than 3. If the radius WAS 3 exactly, then the area would be 9pi, which is approximately 28.26 Since the circle CAN'T touch the X-axis, the area has to be LESS than approximately 28.26 As it's written, none of the answers is clearly the correct one. D The answer is: D

D

mathematics

A rectangular room has the rectangular shaped rug shown as above figure such that the rug’s area is 160 square feet and its length is 6 feet longer than its width. If the uniform width between the rug and room is 6 feet, what is the area of the region uncovered by the rug (shaded region), in square feet?

Rug's area = 160 which is (x) x (6+x) = 160 so x= 10 rug maintains a uniform distance of 6 feet so room has dimension 10+12 and 16+12 i.e. 22 and 28 area of room 22x28 = 616 area covered is 160 so uncovered area is 616-160=456 (ANSWER B) The answer is: B

B

mathematics

A merchant gains or loses, in a bargain, a certain sum. In a second bargain, he gains 550 dollars, and, in a third, loses 120. In the end he finds he has gained 300 dollars, by the three together. How much did he gain or lose bv the first ?

In this sum, as the profit and loss are opposite in their nature, they must be distinguished by contrary signs. If the profit is marked +, the loss must be -. Let x = the sum required. Then according to the statement x + 550 - 120 = 300 And x = -130. Answer A The answer is: A

A

mathematics

What is the greatest possible (straight line) distance, between any two points on a hemisphere of radius 5?

Maximum distance straight line is diameter d = 2r = 10.. ANS option B. The answer is: B

B

mathematics

Five drainage pipes, each draining water from a pool at the same constant rate, together can drain a certain pool in 16 days. How many additional pipes, each draining water at the same constant rate, will be needed to drain the pool in 4 days?

This is an inverse proportional problem...... 5 pipes in 16 days; So for 4 days, it will be = 16 x 5 / 4 = 20 So, 20-5 = 15 Answer E The answer is: E

E