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The Wordsmiths 3

mathematics

Look at this series: 439,404, 369, 334, 299, 264 ... What number should come next?

229 This is a simple subtraction series. Each number is 35 less than the previous number. D The answer is: D

D

mathematics

A man can row three - quarters of a kilometer against the stream in 11¼minutes. The speed(in km/hr) of the man in still water is

Solution Rate upstream = (750 / 675)m/sec = (10 / 9) m/ sec. Rate downstream = (750 / 450) =(5 / 3) m/sec Rate in still water = 1/2(10 /9 + 5/3) = (25/18x18/5)km/hr = 5 km/hr. Answer D The answer is: D

D

mathematics

Amit Kumar invested an amount of 15,000 at compound interest rate of 10 pcpa for a period of two years. What amount will he receive at the end of two years?

Amount = 15000 (1 + 10⁄100)2 = 15000 × 11⁄10 × 11⁄10 = 18150 Answer E The answer is: E

E

mathematics

Out of 15 students in a class, 7 are from Maharashtra, 5 are from Karnataka, and 3 are from Goa. Four students are to be selected at random. What are the chances that at least one is from Karnataka?

Total possible ways of selecting 4students out of 15 = 15C4 = (15*14*13*12)/(4*3*2*1) =1365 The number of ways of selecting a 4 students in which no student belongs to Karnataka = 10C4 Number of ways of selecting atleast one student from Karnataka = 15C4-10C4 = 1155 Probability = 1155/1365 = 11/13 Answer is B The answer is: B

B

mathematics

In the last set of tests, a student scored marks in each of 5 subjects in the ratio 4:5:6:7:8 and got an overall average score of 54%. If a mark of 50% in a subject is a pass and the maximum marks of each subject is the same, how many subjects did the student pass?

The tests scores are 4k, 5k, 6k, 7k, and 8k. The sum of the test scores is 30k. The average test score is 30k/5 = 54. Then k = 9. The test scores are 36, 45, 54, 63, and 72. The student passed 3 subjects. The answer is C. The answer is: C

C

mathematics

Larry and Daniel are partners in a business, they invested Rs. 50,000 and Rs. 39,000 respectively.If the business yielded a total profit of Rs. 21,000, what is Daniel's share?

Explanation: Ratio of their shares = 50,000 : 39,000 = 50 : 39. Daniel's share = Rs. (21000 * 39/89) = Rs. 9202.25. Answer: E) 9202.25 The answer is: E

E

mathematics

Rs.385 were divided among X,Y,Z in such a way that X had Rs.20 more than Y and Z had Rs 15 more than X . How much was Y’s share?

Let Y gets Rs x. Then We can say X gets Rs (x + 20 ) and Y gets Rs ( x + 35) . x + 20 + x + x + 35 = 385 3x = 330 x = 110 . R’s share = Rs ( 110 + 35 ) = Rs.145 B The answer is: B

B

mathematics

If a, b, and c are consecutive integers such that a < b < c and a is an even prime number, which of the following is true? I. a × b × c < a^3 II. 5b > 5c III.a + b + c > a^3

Only 'A' is possible solution. If a is even prime number i.e 2, b is 3 and c is 4 Putting the values in the answers only 'A' seems valid. The answer is: A

A

mathematics

Kurt, a French painter, has 9 jars of paint: 4 jars of yellow paint, 2 jars of red paint, and 3 jars of brown paint. Kurt pours the contents of 3 jars of paint into a new container to make a new color, which he will name according to the following conditions: The paint will be namedBrun Yif it contains 2 jars of brown paint and no yellow. The paint will be namedBrun Xif the paint contains 3 jars of brown paint. The paint will be namedJaune Xif the paint contains at least 2 jars of yellow. The paint will be namedJaune Yif the paint contains exactly 1 jar of yellow. What is the probability Q that the new color will be one of theJaunecolors?

I get B. Jaune Y = (4 choose 1)*(5 choose 2) = 4*10 = 40 Jaune X = (4 choose 2)*(5 choose 1) + (4 choose 3) = 6*5 + 4 = 34 Total combinations = 9 choose 3 = 84 Probability of Jaune Q= (40 + 34)/84 = 37/42 The answer is: B

B

mathematics

A can do a piece of work in 6days of 9 hours each and B alone can do it in 12 days of 9 hours each.how long will they take it to do working together 4 1/2 hours a day?

A's work per hour=1/54 B's work per hour=1/108 A & B's work per hour together=(1/54)+(1/108)=3/108=1/36 so A & B together complete the work in 36 hours... if they work 4 1/2=9/2 hours a day, it will take (36)/(9/2) days=8 days... ANSWER: A The answer is: A

A

mathematics

Which of the following is the Highest Common Factor of 49, 63 and 77?

THE HIGHEST COMMON FACTOR IS 7 Ans is :C The answer is: C

C

mathematics

In a dairy farm, 20 cows eat 20 bags of husk in 20 days. In how many days one cow will eat one bag of husk?

Explanation : One bag of husk = 20 cows per day ⇒ 20 × 1 × 20 = 1 × 20 × x For one cow = 20 days Answer : C The answer is: C

C

mathematics

In a survey of 340 employees, 104 of them are uninsured, 54 work part time, and 12.5 percent of employees who are uninsured work part time. If a person is to be randomly selected from those surveyed, what is the probability that the person will neither work part time nor be uninsured?

---------UI----------------NUI-------Total PT----(12.5/100)*104 = 13----------- --54 NPT---104-13-------------- x--------286 Total--104----------------------------340 we have to find not part time and not uninsured . in other words not part time and insured = x/340 = (286-104+13)/340 = 39/68 Answer is C. The answer is: C

C

mathematics

1. X and Y invest Rs.21000 and Rs.17500 respectively in a business. At the end of the year, they make a profit of Rs.26400. What is the share of X in the profit?

Explanation: Ratio of the investment =21000:17500=210:175=21000:17500=210:175 =42:35=6:5=42:35=6:5 Share of X in the profit =26400×611=2400×6=14400 ANSWER IS A The answer is: A

A

mathematics

A man started his journey from Lucknow to Kolkata, which is 200 km, at the speed of 40 kmph then he went to Banglore which is 300 km, at the speed of 20 kmph. Further he went to Ahmedabad which is 500 km, at the speed of 10 kmph. The average speed of the man is :

Solution: Average speed, = (Total distance /Total time) = [(200+300+500)/{(200/40)+(300/20)+(500/10)}] = 1000/70 = 14(2/7) kmph. Answer: Option A The answer is: A

A

mathematics

The age of the two friends were in the ration of 6:5. If the sum of their ages is 55. Then after how many years their ratio will become 8:7?

since given ratio is 6:5 of their ages. 6x+5x=55(given) 11x=55 x=5. so present ages are: 6*5=30 and 5*5=25 after few yrs ratio becomes 8:5. so,their ages will become 8x and 7x respectively, ie. 40 and 35 respectively. nw difference of their current ages and further ages is clear from above... ie. 10 yrs. ANSWER:C The answer is: C

C

mathematics

The sum of a number and its reciprocal is one-eighth of 34. What is the product of the number and its square root?

Let the number be x. Then, x + 1/x = 34/8 8x2 - 34x + 8 = 0 4x2 - 17x + 4 = 0 (4x - 1)(x - 4) = 0 x = 4 required number = 4 * √4 = 4 * 2 = 8. ANSWER:A The answer is: A

A

mathematics

A man can row 9 kmph in still water. When the river is running at 3.1 kmph, it takes him 1 hour to row to a place and black. What is the total distance traveled by the man?

M = 9 S = 3.1 DS = 12.1 US = 5.9 x/12.1 + x/5.9 = 1 x = 3.97 D = 3.97 * 2 = 7.94 Answer: E The answer is: E

E

mathematics

A, B, C, D, E are the five electronic shops in the Naza market, which have 20, 30, 60, 80 and 50 T. V . sets with them respectively, then the average number of T. V. sets in each shop is

Answer Average number of T. V. sets = ( 20 + 30 + 60 + 80 + 50 ) / 5 = 48 Correct Option: B The answer is: B

B

mathematics

A train 260 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?

Speed = 45 * 5/18 = 25/2 m/sec Total distance covered = 260 + 140 = 400 m Required time = 400 * 2/25 = 32 sec Answer:B The answer is: B

B

mathematics

What is the sixth digit to the right of the decimal point, in the decimal expansion of (3/5)^6?

Step 1 Convert fraction to decimal with two decimal places 3/5 = 0.60 then convert to scientific number = 6*10^-1 Step 2 Multiply 6^6 by 10^-6 Step 3 6 has the sequence 6, 36, 216 Answer is C The answer is: C

C

mathematics

Michelle deposited a certain sum of money in a savings account on July 1st, 2007. She earns an 14% interest compounded semiannually. The sum of money in the account on December 31st, 2009 is approximately what percent of the initial deposit?

Since Michelle earns 14% interest compounded semiannually, then she earns 7% interest every 6 months. Now, the simple interest earned in 5 periods (30 months = 5*6 months) would be 7%*5=35%. But, since the interest iscompoundedevery 6 months, then there would be interest earned on interest (very small amount) thus the actual interest earned would be a little bit more than 35%, only answer choice D fits. Answer: D The answer is: D

D

mathematics

Two people measure each other's height, the height of the taller person is H and the height of the other person is L. If the difference in their heights is equal to the average height, what is the Value of H/L

Difference = Average H - L = (H + L)/2, Solving for H/L gives 3. A quick check, H be 18 and L be 6, 18 - 6 = (18 + 6)/2 B The answer is: B

B

mathematics

A,B,C invested some money such that capital of C is half of B and capital of B is half of A. If they get a profit of Rs.7000 then profit share of B is

Ratio of their capital ie c:b:a=1:2:4 Hence b's share of profit =2/(7) *7000=2000 ANSWER:B The answer is: B

B

mathematics

Express a speed of 90 kmph in meters per second?

90 * 5/18 = 25 mps Answer: A The answer is: A

A

mathematics

John weighs twice as much as Susan. Susan's weight is 60% of Sam's weight. Mark weighs 50% of Lynn's weight. Lynn weighs 180% of John's weight. Which of these 5 people weighs the least?

John weighs twice as much as Susan --> J=2S --> John cannot weigh the least; Susan's weight is 60% of Sam's weight --> S=0.6*Sam --> Sam cannot weigh the least; Mark weighs 50% of Lynn's weight --> M=0.5*L --> Lynn cannot weigh the least; Lynn weighs 180% of John's weight --> L=1.8*J --> John cannot weigh the least (we already know that); As you can see the answer is either Susan (S) or Mark (M). To compare their weights we should express their weights in regards of the same person: M=0.5*L=0.5*(1.8*J)=0.9*J and from J=2S, S=0.5*J --> Susan weights the least: Susan's weight is 50% of that of John and Mark's weight is more than 50%of that of John. Answer: B. The answer is: B

B

mathematics

a survey of n people in the town of badaville found that 50% of them prefer brand A.another survey of 100 people in the town of Chotaville found that 60% prefer brand A.In total 55% of all the people surveyed prefer brand A.What is the total number of people surveyed?

.5*n+.6*100=.55*(n+100) n=100 total people surveyed=n+100 =100+100 =200 ANSWER:B The answer is: B

B

mathematics

Find the average of the first 20 natural numbers?

Average of the first 'n' natural numbers = (n + 1)/2 We get (20 + 1)/2 = 10.5.Answer: D The answer is: D

D

mathematics

A jar full of whiskey contains 40% alcohol. A part of this whisky is replaced by another containing 19% alcohol and now the percentage of alcohol was found to be 26%. The quantity of whisky replaced is

1 st jar (alchohol) = 40% 2nd jar = 19% after mix = 26% mean = 7:14=1:2=>2/1+2=2/3 ANSWER B The answer is: B

B

mathematics

A manufacturer of a certain type of screw rejects any screw whose length is less than 2.5 — 0.03 centimeters or greater than 2.53 centimeters. If k represents the length of a screw, in centimeters, which of the following inequalities specifies all the lengths of screws that are acceptable?

So, let's go through this step by step: rejects any screw whose length is less than 2.5 — 0.03 centimeters or greater than 2.5 + 0.03 centimeters. In other words, any screw that is less than: 2.50 - 0.03 =2.47or greater than 2.53 will be rejected. If k represents the length of a screw In other words,Kis an acceptable screw that must fall within the acceptable range of 2.47 to 2.53, So: 2.47 ≤ K ≤ 2.53 You can rule out answers with < or > as opposed to ≤ or ≥ because the length cannot be LESS than 2.47 or GREATER than 2.53. In other words, 2.47 and 2.53 are acceptable lengths. Let's look at (D): |2k — 5| <= 0.06 or dividing by 2 |k — 2.5| <= 0.03 For the positive case: k - 2.5 ≤ 0.03 ===>k ≤ 2.53 For the negative case: -(k - 2.5) ≤ 0.03 ===> -k +2.5 ≤ 0.03 ===> - k ≤ -2.47 ===>k ≥ 2.47 2.47 ≤ k ≤ 2.53 (D) The answer is: D

D

mathematics

Divide $600 among A,B in the ratio 1:2. How many $ that A get?

Sum of ratio terms = 1+2 = 3 A = 600*1/3 = $200 Answer is E The answer is: E

E

mathematics

A recycling facility is staffed by 7 floor workers and one manager. All of the floor workers are paid equal wages, but the manager is paid n times as much as a floor worker. If the manager’s wages account for 1/7 of all wages paid at the facility, what is the value of n?

Say each floor worker is paid $x, then the manager is paid $xn. Total salary would be 7x+xn and we are told that it equals to 7xn: 7x+xn=7xn --> reduce by x: 7+n=7n -->6n= 7 n = 7/6 Answer: D The answer is: D

D

mathematics

How many such pairs of letters are there in the word EXPRESSION which have as many letters between them in the word as in the alphabet ?

(E,N) (P,S) (O.N) (X,S) ANSWER:A The answer is: A

A

mathematics

Amy’s retirement portfolio contains only stocks and bonds. At the beginning of 2016, her portfolio had an allocation of 60% stocks and 40% bonds. Over the course of 2016, the total value of her portfolio increased by 8%, with the value of her stock holdings increasing by 10%. By what percent did the value of her bond holdings increase?

Thus total value of Bond at the end of 2016 is 420 ( ie, 1080 - 660 ) So, Per unit value of Bond at the end of 2016 is 420/40=10.50 Hence, percentage increase is 0.50/10∗100=5%, answer will be (B) The answer is: B

B

mathematics

A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?

Explanation: Speed= 60 x 5/18 m/sec = 50/3 m/sec. Length of the train = (Speed x Time). Length of the train = 50/3 x 9 m = 150 m. ANSWER IS D The answer is: D

D

mathematics

Integers 3n+2 and 8n+6 are divisible by an integer p. If p is not equal to 1, then p equals to?

If p divides 3n+2, then p divides 24n+16. If p divides 8n+6, then p divides 24n+18. Then p must equal 2. The answer is A. The answer is: A

A

mathematics

Compound interest earned on a sum for the second and the third years are Rs.12000 and Rs.13800 respectively. Find the rate of interest?

Rs.13800 - 12000 = Rs.1800 is the interest on Rs.12000 for one year. Rate of interest = (1800/12000) * 100 = 15% p.a ANSWER:A The answer is: A

A

mathematics

By selling an article at Rs.1000, a shopkeeper makes a profit of 25%. At what price should he sell the article so as to make a loss of 25%?

SP = 1000 Profit = 25% CP = (SP)*[100/(100+P)] = 1000 * [100/125] = 800 Loss = 25% = 25% of 800 = Rs.200 SP = CP - Loss = 800 - 200 = Rs.600 ANSWER:A The answer is: A

A

mathematics

When a number is divided by 6 &then multiply by 12 the answer is 9 what is the no.?

if $x$ is the number, x/6 * 12 = 9 => 2x = 9 => x = 4.5 A The answer is: A

A

mathematics

Express of the following as a fraction: 4%

4% =4/100 =1/25. Answer is B. The answer is: B

B

mathematics

The smallest 3 digit prime number is

The smallest 3-digit number is 100, which is divisible by 2. 100 is not a prime number. 101 < 11 and 101 is not divisible by any of the prime numbers 2, 3, 5, 7, 11. 101 is a prime number. Hence 101 is the smallest 3-digit prime number. B) The answer is: B

B

mathematics

A tap can fill a tank in 4 hours. After half the tank is filled, two more similar taps are opened. What is the total time taken to fill the tank completely?

Explanation: 1 tap can fill the tank in 4 hours. Therefore 1 tap can fill half tank in 2 hours. 3 taps can fill the tank in 4/3 hour. Therefore 3 taps can fill half tank in 4/6 hour =40 minutes. Total time taken=2 hour 40 minutes Answer: Option D The answer is: D

D

mathematics

There are 5 boxes of different weights. They are weighed in pairs taken 2 at a time and the weights obtained are 110, 112, 113, 114, 115, 116, 117, 118, 120 and 121. What is the sum of the weights of the 5 boxes ?

Let the 5 boxes be a, b, c, d and e. The ten weights correspond to all the possible combinations of 2 weights out of 5. On adding all the given weights, each boxes weight gets added 4 times: a+b, a+c, a+d, a+e. Similarly for b: b+c, b+d, b+e and a+b (already included above) Similarly for c, d and e. Therefore, 110+112+113+114 .....+120+121 = 4* (a+b+c+d+e) or, 4* (a+b+c+d+e) = 1156 or, (a+b+c+d+e) = 1156/4 = 289 ANSWER:B The answer is: B

B

mathematics

If 5^r is a factor of 30!, which of the following is the maximum possible value of r?

5^r is a factor of 30! We need the maximum value of r Or in other words, we need the maximum power of 5 in 30! Powers of 5 in 30! = [30/5] + [30/25] = 7, where [x] is the integral part of x Other way is to calculate the number of 5's in 30! In the multiplication upto 30, we will encounter: 5, 10, 15, 20,25, 30 Each of 5, 10, 15, 20, 30 contain one power of 5 25 contains 2 powers of 5. Hence total powers of 5 in 30!= 5 + 2 = 7 Correct option: D The answer is: D

D

mathematics

Carrey rented a car for Rs.20 plus Rs.0.25 per kilometer driven. Samuel rented a car for Rs.24 plus Rs.0.16 per kilometer driven. If each drove d km. and each was charged exactly the same amount for the rental, then d equals ?

Explanation: 20 + 0.25 × d = 24 + 0.16d Solving we get d = 44.4 Answer:A The answer is: A

A

mathematics

Fresh grapes contain 85% water by weight and raisins obtained by drying fresh grapes contain 25% water by weight. How many kgs of fresh grapes are needed to get 20kgs of raisins?

The weight of non-water in 20 kg of dried grapes (which is 100-25=75% of whole weight) will be the same as the weight of non-water in x kg of fresh grapes (which is 100-85=15% of whole weight), so 20*0.75 = x*0.15 --> x =100. Answer: C The answer is: C

C

mathematics

Adding 30% of x to x is equivalent to multiplying x by which of the following?

130x/100= 1.3*x ANSWER:D The answer is: D

D

mathematics

How many different pairs of positive integers (a, b) satisfy the equation 1/a+1/b=34/57 ?

There is no certain way to solve 2 unknown with 1 equation. The best way is to look at the question and retrospect the most efficient way. In this question, a and b are only positive integers. So that is a big relief. Now, we can start with putting a=1,2,.. and so on till the time we are confident about one of the options. So, we start with a=1, we get b as -ve. out a=2, we get b as 6. Yes (Now (a,b) = (2,6). We can directly see that (a,b)=(6,2) will also satisfy. So we have 2 possible solutions) a=3, we get b as 3. Yes (Now we have 3 possible solutions) a=4, we get b as fraction. Out a=5, we get b again as some fraction. Out a=6 already taken. We have A,B options left. C,D,E are out. A is 6. To have 6 as the answer, we will need one more pair like2,6and one more solution where a=b. When a=b, we have only 1 solution = 5. So, one more solution, where a=b is not possible. So, answer will be E. The answer is: E

E

mathematics

The cost price of a radio is Rs.1500 and it was sold for Rs.1230, find the loss %?

1500 ---- 270 100 ---- ? => 18% Answer:A The answer is: A

A

mathematics

if m>0 and a is m percent of b, then, in terms of m, b is what percent of a?

Given (m*b)/100=a to find (b/a)*100 Rearranging first equation b/a*100 = 100*100/m =10000/m Answer B The answer is: B

B

mathematics

When a number is divided by 13, the remainder is 11. When the same number is divided by 17, then remainder is 9. What is the number ?

x = 13p + 11 and x = 17q + 9 13p + 11 = 17q + 9 17q - 13p = 2 => q = 2+13p/17 least value of p for which q = 2+13p/17 is whole no is p = 26 x = (13*26+11) = 349 ANSWER B The answer is: B

B

mathematics

A woman has two blouses of different colors, three skirts of different colors, and two different pairs of shoes. She refuses to wear her pink blouse with her green skirt. How many different blouseskirt-shoe combinations could she wear?

total ways = 2*3*2=12.. now its better to find the ways in which the pink blose and green skirty are together and subtract from total to get the answer.. the ways in which the pink blose and green skirty are together=1*1*2=2.. total ways =12-2=10.. B The answer is: B

B

mathematics

A number when divided by a divisor leaves a remainder of 24. When twice the original number is divided by the same divisor, the remainder is 11. What is the value of the divisor?

Let the original number be 'a' Let the divisor be 'd' Let the quotient of the division of aa by dd be 'x' Therefore, we can write the relation as a/d = x and the remainder is 24. i.e., a=dx+24 When twice the original number is divided by d, 2a is divided by d. We know that a=dx+24. Therefore, 2a = 2dx + 48 The problem states that (2dx+48)/d leaves a remainder of 11. 2dx2dx is perfectly divisible by d and will therefore, not leave a remainder. The remainder of 11 was obtained by dividing 48 by d. When 48 is divided by 37, the remainder that one will obtain is 11. Hence, the divisor is 37. A The answer is: A

A

mathematics

Two trains 300 m and 450 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is?

Relative speed = 60 + 40 = 100 km/hr. = 100 * 5/18 = 250/9 m/sec. Distance covered in crossing each other = 300 + 450 = 750 m. Required time = 700 * 9/250 = 27 sec. Answer: B The answer is: B

B

mathematics

If 3 and 5 are prime numbers, which of the following CANNOT be the sum of 3 and 5?

ans : A The answer is: A

A

mathematics

A tradesman by means of his false balance defrauds to the extent of 20%? in buying goods as well as by selling the goods. What percent does he gain on his outlay?

g% = 20 + 20 + (20*20)/100 = 44% Answer: C The answer is: C

C

mathematics

In measuring the sides of a rectangle, one side is taken 6% in excess, and the other 5% in deficit. Find the error percent in the area calculated from these measurements.

Let x and y be the sides of the rectangle. Then, Correct area = xy. Calculated area = (53/50) x (19/20) y = (144/143)(xy) Error In measurement = (144/143)xy- xy = (1/143)xy Error percentage = [(1/143)xy (1/xy)100] % = (7/10) % = 0.7%. Answer is B. The answer is: B

B

mathematics

What percent of 120 are 90?

(?% /100) * 120 = 90 ? = 75% Answer: 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

An error 4% in excess is made while measuring the side of a square. The percentage of error in the calculated area of the square is:

Explanation: 100 cm is read as 104 cm. A1 =(100 × 100)cm2 = 10000 and A2= (104 × 104)cm2= 10816 (A2 - A1) = 10816-10000 = 816 => 816/10000*100 =8.16 Answer : D The answer is: D

D

mathematics

Two unbiased coins are tossed. What is probability of getting at most one tail ?

Explanation: Total 4 cases = [HH, TT, TH, HT] Favourable cases = [HH, TH, HT] Please note we need atmost one tail, not atleast one tail. So probability = 3/4 Answer: D The answer is: D

D

mathematics

The slant height of a cone is 13 cm and radius of the base is 9 cm, find the curved surface of the cone?

π * 13 * 9 = 367 Answer:A The answer is: A

A

mathematics

The perimeter of a semi circle is 144 cm then the radius is?

36/7 r = 144 => r = 28 Answer:B The answer is: B

B

mathematics

A box contains 12 mangoes out of which 4 are spoilt. If four mangoes are chosen at random, find the probability that A number is selected at random from first thirty natural numbers. What is the chance that it is a multiple of either 3 or 13?

The probability that the number is a multiple of 3 is 10/30. (Since 3*10 = 30). Similarly the probability that the number is a multiple of 13 is 2/30. {Since 13*2 = 26). Neither 3 nor 13 has common multiple from 1 to 30. Hence these events are mutually exclusive events. Therefore chance that the selected number is a multiple of 3 or 13 is (10+2)/30 = 2/5. ANSWER:B The answer is: B

B

mathematics

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

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

B

mathematics

The average weight of 8 girls increases by 3 kg when a new girl comes in place of one of them weighing 70 kg. What might be the weight of the new girl?

Total weight increased = 8 x 3 kg = 24 kg. Weight of new person = 70 + 24 kg = 94 kg Answer : A The answer is: A

A

mathematics

seven balls of different colors are to be placed in three different boxes such that any box contains at least 1 ball . What is the maximum number of different ways in which this can be done?

Since the balls are all of different colors, let's permute them and then decide how many balls we put in each box. For example, arrange in a row the balls, then decide: two balls go into the first box, next two in the second box, and the last ball goes to the third box. Since in each box there must be at least one ball, we have the possibilities of (2,2,1), (2,1,2), (1,2,2) OR (3,1,1), (1,3,1), (1,1,3) balls in the three boxes. For the 2,2,1 type arrangements, we have [5!/(2!2!1!)]*3 = 90 possibilities. Inside a box, it doesn't matter the order of the balls. For the 3,1,1 type arrangements, we have [5!/(3!1!1!)]*3 = 60 possibilities. Total of 150 + 90 =240 possibilities. Answer C. The answer is: C

C

mathematics

The time it took car P to travel 900 miles was 2 hours less than the time it took car R to travel the same distance. If car P’s average speed was 10 miles per hour greater than that of car R, what was car R’s average speed, in miles per hour?

Let speed of car R be=x Then speed of car P= x+10 A/Q, (900/x)-(900/(x+10))=2 Solving for x=62 miles\hr. C The answer is: C

C

mathematics

Which of the following statements must be true? I)The product of first 100 prime numbers is even II)The sum of first 100 prime numbers is odd. III)The sum of first five non-negative even numbers is divisible by both 4 and 5

First look at some Odd & Even Rules:- Multiplication E x E = E O x O = O E x O = E = O x O Addition E + E = E E + O = O = O + E O + O = E Now coming to the statements:- I. The product of first 100 prime numbers is even First 100 prime nos. includes 2 which is the ONLY even no. Hence, any no. multiplied by even no will give an Even No. II. The sum of first 100 prime numbers is odd We can figure this out through Cyclicity Rule. Ignore the First TWO Prime Nos. and let us start with 5, which is Odd. O + O = E (Sum of two primes) E + O = O (Even is carried over and added to 3rd prime) O + O = E (Carry over and 4th prime) E + O = O (5th prime) O + O = E (6th prime) Through Cyclicity, we can find out that the sum of any Even No of ODDS will always be EVEN. Since 98th no is Even, the answer will also be EVEN. Now, include the first two prime nos. i.e. 2 & 3. E + 2(E) + 3(O) = O Hence, the statement is TRUE. III. The sum of first five non-negative even numbers is divisible by both 4 and 5 First five non negative even nos. = 0, 2, 4, 6 and 8 Sum = 20. Divisible by both 4 AND 5 Answer : E The answer is: E

E

mathematics

The ratio of the earnings of P and Q is 9:10. If the earnings of P increases by one-fourth and the earnings of Q decreases by one-fourth, then find the new ratio of their earnings?

Let the earnings of P and Q be 9x and 10x respectively. New ratio = [9x + 1/4 (9x)]/[10x - 1/4 (10x)] => 9*(1 + 1/4)/10*(1 - 1/4) => 9/10 * (5/4)/(3/4) = 3/2 Answer: B The answer is: B

B

mathematics

There are an average of 117 jellybeans in each of 34 bags of various sizes. After adding another bag, the average number of jellybeans per bag increases by 7. How many jellybeans are in the new bag?

Total jellybeans in 34 bags = 34*117 = 3978 Total jellybeans in 35 bags = 35*124 = 4340 Number of jellybeans in new bag = 3978-4340 = 362 jellybeans Answer is E The answer is: E

E

mathematics

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

Total fruits = 9 Since there must be at least two apples, = 25/42. Answer: A The answer is: A

A

mathematics

Working alone at its constant rate, pump P pumped out ¼ of the water in a tank in 2 hours. Then pumps Q and R started working and the three pumps, working simultaneously at their respective constant rates, pumped out the rest of the water in 3 hours. If pump Q, working alone at its constant rate, would have taken 18 hours to pump out the rest of the water, how many hours would it have taken pump R, working alone at its constant rate, to pump out all of the water that was pumped out of the tank?

Rate of pump P = 1/8 3 hours are required to pump out the remaining (3/4)ths of tank --> 1 hr to pump out 1/4 Rate of P + Rate of Q + Rate of R = 1/4 Rate of Q + Rate of R = 1/4 - 1/8 = 1/8 Q takes 18 hours to pump out the remaining (3/4)ths of tank --> 6 hrs per (1/4)ths --> 24 hrs to pump out fully. Rate of Q = 1/24 1/24 + Rate of R = 1/8 Rate of R = 1/8 - 1/24 = 1/12 Time required to pump out all the water by R = 12 hrs Answer: B The answer is: B

B

mathematics

To celebrate a colleague's retirement, the T coworkers in an office agreed to share equally the cost of a catered lunch. If the lunch costs a total of R dollars and S of the coworkers fail to pay their share, which of the following represents the additional amount, in dollars, that each of the remaining coworkers would have to contribute so that the cost of the lunch is completely paid?

Since no absolute values are given in the question we can replace the given parameters with assumed numbers, Let Total colleagues be 100 (T) Let total contribution be 500 (R) (point to note is that its total cost not per person) Those who dont pay are S (30) Per person cost = R/T = 800/100 = 8 So cost for those who failed to pay = (R/T) * S = SR/T = 30*8=240 The equation for people who would bear the total cost after S people fail = (T-S)=70 There fore the solution is (SR/T)/ (T-S) = SR/T(T-S) = 240/70 Answer D Hope this helps !!! The answer is: D

D

mathematics

A lady gives a dinner party to 5 guests to be selected from nine friends. The number of ways of forming the party of 5, given that two of the friends will not attend the party together is

Number of ways of selecting 5 guests from nine friends = 9C5 Out of these, 7C3 ways are those in which two of the friends occur together [3 more persons to be selected out of remaining 7] ∴ Number of ways, in which two of the friends will not attend the party together = 9C5 – 7C3 = 91. Answer C The answer is: C

C

mathematics

Which of the following describes all values of x for which 1–x^2 >0?

Which of the following describes all values of x for which 1–x^2 >= 0? (A) x >= 1 Plugged in 2. 1–(2)^2 >= 0 -3>=0? NO. Wrong (B) x <= –1 Plugged in -2. 1–(-2)^2 >= 0 -3>=0? NO. Wrong (C) 0 <= x <= 1 Plugged in 0, 1, and 1/2. All of them work. But E is better because it describes all the values of x (D) x <= –1 or x >= 1 A and B answer this. Wrong. (E) –1 < x < 1 X is a positive or negative fraction. x = -1/2 x = 1/2 x = 0 Plug all of them. They work. Answer is E. The answer is: E

E

mathematics

What is 2 2/3 - 1 1/4 divided by 1/2 - 1/5 ?

2 2/3 - 1 1/4 = 8/3 - 5/4 = (32 - 15 )/12 = 17/12 1/2 - 1/5 = (5-2)/10 = 3/10 So 17/12/3/10 = 17/12 *10/ 3 = 85/18 Answer - E The answer is: E

E

mathematics

5/9 of the part of the population in a villagae are males.if 30 % of the males are married.the percentage of unmarried females in the total population is..

Let total population = p no. of males =5p/9 no. of females =(p-5p/9)=4p/9 married males = 30% of 5p/9=30*5p/100*9 =p/6 married females = p/6 unmarried females =(4p/9-p/6)=5p/18 %age of unmarried females in the total population = {(5p/18)/p}*100= 250/9% ANSWER:A The answer is: A

A

mathematics

A man walks at a speed of 5 km/hr and runs at a speed of 10 km/hr. How much time will the man require to cover a distance of 10 km, if he completes half of the distance, i.e., (5 1/4) km on foot and the other half by running?

Required time = (5)/5 + (5)/10 = 1.5 hours. Answer:E The answer is: E

E

mathematics

A man can row upstream at 37 kmph and downstream at 53 kmph, and then find the speed of the man in still water?

US = 37 DS = 53 M = (53 + 37)/2 = 45 Answer:E The answer is: E

E

mathematics

If 30% of a number is equal to one-fourth of another number, what is the ratio of first number to the second number?

Let 30% of A = 1/4 B. Then, 30A/100 = 1B/4 => 3A/10 = 1B/4 A/B = (1/4 * 10/3) = 5/6 A:B = 5:6. Answer: E The answer is: E

E

mathematics

A, B and C started a business with a total investment of Rs. 90000. A invests Rs. 6000 more than B and B invests Rs. 3000 less than C. If the total profit at the end of a year is Rs. 8640, Find B's share.

Explanation: Let C's investment = Rs. x B's investment = Rs. (x - 3000) A's investment = Rs. (x - 3000 + 6000) = Rs. (x + 3000) Now, (A + B + C)'s investment = Rs. 90000 => x + (x - 3000) + (x + 3000) = 90000 => 3x = 90000 => x = 30000 Hence, A's investment = Rs. 33000 B's investment = Rs. 27000 C's investment = Rs. 30000 Ratio of the capitals of A, B and C = 33000 : 27000 : 30000 = 11 : 9 : 10 A's share = Rs. [(9/30) × 8640] = Rs. 2592 Answer: Option A The answer is: A

A

mathematics

In a group of 6 boys and 4 girls, four children are to be selected. In how many different ways can they be selected such that at least one boy should be there

Explanation: In a group of 6 boys and 4 girls, four children are to be selected such that at least one boy should be there. So we can have (four boys) or (three boys and one girl) or (two boys and two girls) or (one boy and three gils) This combination question can be solved as (6C4)+(6C3∗4C1)++(6C2∗4C2)+(6C1∗4C3) =[6×5/2×1]+[(6×5×4/3×2×1)×4]+[(6×5/2×1)(4×3/2×1)]+[6×4] =15+80+90+24=209 Option D The answer is: D

D

mathematics

Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is?

Let the speeds of the two trains be x m/sec and y m/sec respectively. Then, length of the first train = 27 x meters, and length of the second train = 17 y meters. (27 x + 17 y) / (x + y) = 23 ==> 27 x + 17 y = 23 x + 23 y ==> 4 x = 6 y ==> x/y = 3/2. Answer:B The answer is: B

B

mathematics

If x is an integer, which of the following is a possible value of H=(x^2 +2x – 7)/9?

x is an integer, which of the following is a possible value of H=(x^2 +2x – 7)/9? Used process of elimination A. -2.4 when this is multiplied by 9, x is not an integer B. 0.268 when this is multiplied by 9, x is not an integer C. 1.166 repeating when this is multiplied by 9, x is not an integer D. 4.555 repeating E. 8.125 when this is multiplied by 9, x is not an integer Answer choice D seems to fit The answer is: D

D

mathematics

Vishal invested 10% more than Trishul. Trishul invested 10% less than Raghu. If the total sum of their investments is Rs. 6069, how much amount did Raghu invest ?

Let money invested by Raghu = Rs. x Money invested by Trishul = 9/10 x = 0.9x Money invested by Vishal = 9/10x * 110/100 = 0.99x Also, x+0.9x+0.99x = 6069 = x= 6069/2.89 = 2100 Therefore, amount invested by Raghu is Rs. 2100. Answer: C The answer is: C

C

mathematics

A bag contains 4 white, 5 red and 6 blue balls. Three balls are drawn at random from the bag. The probability that all of them are red, is:

Let S be the sample space. Then, n(S) = number of ways of drawing 3 balls out of 15 = 15C3 = (15*14*13)/(3*2*1) = 455 Let E = event of getting all the 3 red balls n(E) = 5C3 = 5C2 =(5*4)/(2*1) = 10 P(E) =n(E)/n(S) = 10/455 = 2/91 Answer should be B The answer is: B

B

mathematics

The average of 20 numbers is zero. Of them, How many of them may be greater than zero, at the most?

Explanation: Average of 20 numbers = 0 =>Sum of 20 numbers/20=0 Hence at the most, there can be 19 positive numbers. (Such that if the sum of these 19 positive numbers is x, 20th number will be -x) ANSWER IS D The answer is: D

D

mathematics

If f(x) = 6x^4 - 4x^3 - 3x^2 + 6x , then f(-1) =

f(-1) = 6(-1)^4 - 4(-1)^3 - 3(-1)^2 + 6(-1) = 6+4-3-6 = 1 The answer is D. The answer is: D

D

mathematics

A cricket bat is sold for $850, making a profit of $255. The profit percentage would be

255/(850 - 255) = 255/595 = 51/119=43% . Answer: E. The answer is: E

E

mathematics

If s and t are positive integers such that s/t = 64.12, which of the following could be the remainder when s is divided by t ?

s/t = 64.12 = 64+12/100 = 64+3/25 i got 3, and in the options the multiple of is 45 Answer - E The answer is: E

E

mathematics

The average salary of all the workers in a workshop is Rs. 8000. The average salary of 10 technicians is Rs. 12000 and the average salary of the rest is Rs. 6000. The total number of workers in the workshop is :

Explanation: Lot the total number of workers be v Then, 8OOOv = (12000 * 10) + 6000 (v - 10) <=> 2000v = 60000 <=> v = 30 Answer: D) 30 The answer is: D

D

mathematics

At noon, ship A is 100km west of ship B. Ship A is sailing east at 35 km/hr and ship B is sailing north at 25km/hr. How fast is the distance between the ships changing at 4.00pm.

Let the position of ship B at noon be at the origin =>ship A has x-coordinate = -100km and B has x-coordinate =0km At 4.00 p.m., ship A is at x = -100+4*35=40km and B is at x = 0 and y = 4 * 25 = 100 km Distance between them at 4.00 p.m. = √[(100)^2 + (40)^2] = 20√(29) km Distance between the ships, s^2 = x^2 + y^2 => 2s ds/dt = 2x dx/dt + 2y dy/dt => rate of change of distance between the ships, ds/dt = (x dx/dt + y dy/dt) / s = [40 * 35 + 100 * 25] / [20√(29)] km/hr = (1400 + 2500) / [20√(29)] km/hr = 195/√(29) km/hr ≈ 36.21 km/hr. ANSWER:B The answer is: B

B

mathematics

How long does a train 110 m long running at the speed of 54 km/hr takes to cross a bridge 132 m length?

Speed = 54 * 5/18 = 15 m/sec Total distance covered = 110 + 132 = 242 m. Required time = 242/15 = 16.13 sec. Answer: D The answer is: D

D

mathematics

How long will it take a sum of money invested at 5% p.a. S.I. to increase its value by 50%?

Sol. Let the sum be x. Then, S.I. = 50% of x = x/2; Rate =5%. ∴ Time = [100 * x/2 * 1/x*5] = 10 years. Answer A The answer is: A

A

mathematics

In Arun's opinion, his weight is greater than 65 kg but leas than 72 kg. His brother does not agree with Arun and he thinks that Arun's weight is greater than 60 kg but less than 70 kg. His mother's view is that his weight cannot be greater than 68 kg. If all of them are correct in their estimation, what is the average of diferent probable weights of Arun ?

Let Arun's weight be X kg. According to Arun, 65 < X < 72. According to Arun's brother, 60 < X < 70. According to Arun's mother, X < 68. The values satisfying all the above conditions are 66 and 67. Required average = (66 + 67) / 2 = 66.5 kg Answer:B The answer is: B

B

mathematics

From a pack of 52 cards, one card is drawn. What is the probability that the card drawn is a face card (Jack, Queen and King only)?

Answer: Solution Let S be the sample space. Then, n(S) = 52C1 = 52. Let E = event of getting 1 face card. n(E) = number of ways of choosing 1 face card out of 12 =12C1 = 12 P(E) = n(E) / n(S) = 12 / 52 = 3/13. Answer B The answer is: B

B

mathematics

Find the distance covered by a man walking for 30min at a speed of 5km/hr?

Distance = 5*30/60 =2.5 km Answer is D The answer is: D

D

mathematics

If a man lost 4% by selling oranges at the rate of 12 a rupee at how many a rupee must he sell them to gain 44%?

96% ---- 12 144% ---- ? 96/144 * 12 = 8 Answer: B The answer is: B

B

mathematics

Each week, Harry is paid x dollars per hour for the first 30 hours and 1.5x dollars for each additional hour worked that week. Each week, James is paid x dollars per per hour for the first 40 hours and 2x dollars for each additional hour worked that week. Last week James worked a total of 42 hours If Harry and James were paid the same amount last week, how many hours did Harry work last week ?

James worked for 41 hours hence he earned 40*x+2*2x=44x dollars; We know that Harry also earned the same 44x dollars, out of which he earned 30x dollars for thefirst 30 hoursplus 14x additional dollars. Since for each additional hour he gets 1.5x dollars then he worked for 14x/1.5x=9 additional hours, so Harry worked for total of 30+9=39 hours. Answer: E. The answer is: E

E