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The Wordsmiths 3

mathematics

If A:B = 1/4: 1/3 B:C = 1/4:1/3 then A:B:C?

A:B = 1/4:1/3 = 3:4 B:C = 1/4:1/3 = 3:4 -------------------- A:B:C = 9:12:16 ANSWER:C The answer is: C

C

mathematics

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

Speed = 60 * 5/18 = 50/3 m/sec Length of the train = speed * time = 50/3 * 9 = 150 m Answer: E The answer is: E

E

mathematics

A certain deck of cards contains 2 blue cards, 2 red cards, 2 yellow cards, and 2 green cards. If two cards are randomly drawn from the deck, what is the probability that they will both be not green?

The question asks they will both be not green. Considering that these are draws without replacement there are following possibilities : draw 1, draw 2 ===== ===== 1) Not green, green; 2) green, Not green; 3) green, green; 4) Not green, not green; The answer has to be either P(4) OR all exclusion of the 3 previous conditions i.e. 1- [P(1) + P(2) + P(3)] => neither of the draws are green P(4) = 6/8*5/7=15/28 1- [P(1) + P(2) + P(3)] = 1 - [ (6/8 * 2/7) + (2/8*6/7) + (2/8*1/7)] = 1 - [26/8*7] = 1 - [13/28] = 15/28 A The answer is: A

A

mathematics

Score Interval Number of Scores 50-59 2 60-69 10 70-79 15 80-89 27 90-99 18 The table shows a distribution of test scores. Which score interval contains the median of the 72 scores?

36th person 80-89 C The answer is: C

C

mathematics

If 15 ≤ x ≤ 25, and 0.2 ≤ y ≤ 0.6, what is the greatest possible value of 3/(x·y)?

or greatest possible value of 3/(x·y), x and y should be made minimum minimum value of x is 15 and minimum value of y is 0.2 so greatest possible value of 3/(15*0.2)= 1 ANSWER:D The answer is: D

D

mathematics

Find the average of the first 21 natural numbers?

Average of the first 'n' natural numbers = (n + 1)/2 We get (21+ 1)/2 = 11 ANSWER:D The answer is: D

D

mathematics

A team of four entered for a shooting competition. The best marks man scored 85 points. If he had scored 92 points, the average scores for. The team would have been 84. How many points altogether did the team score?

Explanation: 4 * 84 =336 - 7 = 329 Answer:B The answer is: B

B

mathematics

The average weight of 8 persons is increased by 2.5 kg when one of them who weighs 56 kg is replaced by a new man. The weight of the new man is

ANSWER: A The answer is: A

A

mathematics

Visitors to show were charged Rs.15 each on the first day. Rs.7.50 on the second day, Rs.2.50 on the third day and total attendance on the three days were in ratio 2:5:13 respectively. The average charge per person for the whole show is?

Answer: Option C 2: 5: 13 2x 5x 13x 15 7.5 2.5 30x + 37.5x + 32.5x = 100x/20x average = 5 The answer is: C

C

mathematics

If a, b, and c are consecutive odd positive integers and a < b < c, which of the following could be equal to c - b - a+1 ?

let we put values. a=1, b=3, c=5 5-3-1=1 1+1 =2 Answer :B The answer is: B

B

mathematics

Solve 2log53 X log9x + 1 = log53

Solution: We can rewrite the above equation in the below format => log532 X log9x = log53 - 1 => log59 X log9x = log53 - log55 => log59 X log9x = log5(3/5) By Using the change of base rule in Left side we get => log5x = log5(3/5) The value of X = 3/5 ANSWER IS A The answer is: A

A

mathematics

In a room of length 24mts, breadth 18mts, height 16 mts. what is the length of longest rod that can be placed in the room?

diagonal = 30m now hypo of (floor) diag and height will be =34 mtres. ANSWER:B The answer is: B

B

mathematics

Laxmi and Prasanna set on a journey. Laxmi moves northwards at a speed of 25kmph and Prasanna moves southward at a speed of 35 kmph. How far will be Prasanna from Laxmi after 60 minutes ?

Explanation: We know 60 min = 1 hr Total northward Laxmi's distance = 25kmph x 1hr = 25 km Total southward Prasanna's distance = 35kmph x 1hr = 35 km Total distance between Prasanna and Laxmi is = 25 + 35 = 60 km. Answer: C The answer is: C

C

mathematics

Rs.1300 is divided into three parts A, B and C. How much A is more than C if their ratio is 1/2:1/3:1/4?

1/2:1/3:1/4 = 6:4:3 3/13*1300 = 300 Answer:C The answer is: C

C

mathematics

Two pipes A and B can fill a tank in 12 and 24 minutes respectively. If both the pipes are used together, how long will it take to fill the tank?

Explanation: Tank can be filled by pipe A in 12 minutes and pipe B in 24minutes. => Part filled by A in 1 minute= 1/12 => Part filled by B in 1 minute= 1/24 => Part filled by both in 1 minute= 1/12 + 1/24 = 3/24=1/8 Time taken to fill the entire tank = 8 minutes ANSWER B The answer is: B

B

mathematics

An athlete runs 200 metres race in 20 seconds. What is his speed?

Speed=Distance/Time = 200/20 = 10 m/s = 10 * 18/5 = 36 km/hr Answer :D The answer is: D

D

mathematics

In February Wilson’s earnings were 40 percent of his family’s total income. In March Wilson earned 25 percent less than in February. If the rest of his family’s income was the same in both months, then, in March, Wilson’s earnings were approximately what percent W of his family’s total income?

Lets suppose the Total Family income in Feb = 100x Wilson's earning in Feb = 40% of 100x = 40x Earnings of remaining family in Feb = 100x - 40x = 60x Wilson's earning in March = 75% of Wilson's Feb earnings = 75% of 40x = 30x Earnings of remaining family in March = Earnings of remaining family in Feb = 60x Thus Wilson's earning as % of Total family income in March W= 30x/ (30+60)x = 30x/90x = 33.33% Thus Answer is E The answer is: E

E

mathematics

A reduction of 25% in the price of salt enables a lady to obtain 10kgs more for Rs.800, find the original price per kg?

Answer: 800*(25/100) = 200 --- 10 ? --- 1 => Rs.20 800 --- 600 ? --- 20 => Rs.26.67.Answer: B The answer is: B

B

mathematics

If a code word is defined to be a sequence of different letters chosen from the 10 letters A, B, C, D, E, F, G, H, I, and J, what is the ratio of the number of 6-letter code words to the number of 5-letter code words?

Number of ways to form 6-letter code: 10!/4! = 10*9*8*7*6*5 Number of ways to form 5-letter code: 10!/5! = 10*9*8*7*6 Ratio: 5 to 1 Answer : D The answer is: D

D

mathematics

If 8 workers can build 8 cars in 8 days, then how many days would it take 5 workers to build 5 cars?

8 workers can build 1 car per day on average. 1 worker can build 1/8 of a car per day. 5 workers can build 5/8 car per day. The time required to build 5 cars is 5 / (5/8) = 8 days The answer is C. The answer is: C

C

mathematics

A certain factory produces buttons and buckles at a uniform weight. If the total weight of 2 buttons and 2 buckles is one third of 11 buckles and 3 buttons, then the weight of 3 buttons and 7 buckles is how many times that of 5 buckles and 6 buttons?

Let x be the weight of a button and let y be the weight of a buckle. 2x + 2y = (1/3)(3x+11y) 3x = 5y x = 5y/3 3x + 7y = a(6x+5y) 12y = a(15y) a = 12/15 = 4/5 The answer is D. The answer is: D

D

mathematics

An gun can take a maximum of four shots at an enemy plane moving away from it. The probability of hitting the plane at the 1st, 2nd, third and 4th shots are 1.4, 1.3, 1.2 & 1.1 respectively. What is the probability that the plane is hit when all the four shots are fired?

Required probability: =(0.4×0.7×0.8×0.9)+(0.6×0.3×0.8×0.9)+(0.6×0.7×0.2×0.9)+(0.6×0.7×0.8×0.1)+(0.4×0.3×0.8×0.9)+(0.4×0.7×0.2×0.9)+(0.4×0.7×0.8×0.1)+(0.6×0.3×0.2×0.9)+(0.6×0.3×0.8×0.1)+(0.6×0.7×0.2×0.1)+(0.4×0.3×0.2×0.9)+(0.6×0.3×0.2×0.1)+(0.4×0.3×0.8×0.1)+(0.4×0.7×0.2×0.1)+(0.4×0.3×0.2×0.1)=(0.4×0.7×0.8×0.9)+(0.6×0.3×0.8×0.9)+(0.6×0.7×0.2×0.9)+(0.6×0.7×0.8×0.1)+(0.4×0.3×0.8×0.9)+(0.4×0.7×0.2×0.9)+(0.4×0.7×0.8×0.1)+(0.6×0.3×0.2×0.9)+(0.6×0.3×0.8×0.1)+(0.6×0.7×0.2×0.1)+(0.4×0.3×0.2×0.9)+(0.6×0.3×0.2×0.1)+(0.4×0.3×0.8×0.1)+(0.4×0.7×0.2×0.1)+(0.4×0.3×0.2×0.1) =0.2016+0.1296+0.756+0.336+0.864+0.504+0.224+0.324+0.144+0.0084+0.0216+0.0036+0.0096+0.0056+0.002=0.2016+0.1296+0.756+0.336+0.864+0.504+0.224+0.324+0.144+0.0084+0.0216+0.0036+0.0096+0.0056+0.002 =0.6976=0.6976 Edit: Thank you Vaibhav for providing an alternative method. Alternate Method: probability that the plane is hit when all the four shots are fired, P=1−probability of not hitting the targetP=1−probability of not hitting the target =1−(0.6×0.7×0.8×0.9)=1−(0.6×0.7×0.8×0.9) =1−0.3024=1−0.3024 =0.6976 B The answer is: B

B

mathematics

If 1535/1038 = a+1/[b+1/{c+(d+1/e)}]. Find a*b*c*d*e?

by expanding 1535/1038 make form like a+1/[b+1/{c+(d+1/e)} =1+(497/1038) now a=1 =1+{1/(1038/497)} =1+{1/(2+42/497)} =1+{1/(2+1/(497/42)} now b= 2 similarly expand c=11 d= 1 e=34/8 finally a*b*b*c*d*e 1*2*11*1*34/8 187/2 ANSWER:D The answer is: D

D

mathematics

Four milkmen rented a pasture. A grazed 24 cows for 3 months; B 10 for 5 months; C 35 cows for 4 months and D 21 cows for 3 months. If A's share of rent is Rs. 7200, find the total rent of the field.

Ratio of shares of A, B, C, D = (24 x 3) : (10 x 5) : (35 x 4) : (21 x 3) = 72 : 50 : 140 : 63. Let total rent be Rs. x. Then, A’s share = Rs. (72x)/325 (72x)/325=7200 = x=(7200 x 325)/72 = 32500 Hence, total rent of the field is Rs. 32500. Answer is E. The answer is: E

E

mathematics

Two identical machines have the ability to produce both nuts and bolts. However, it takes 1 second to produce a bolt but 2 seconds to produce a nut. What is the fastest the two machines, working together, can produce 1,400 nuts and 1,400 bolts?

I used the Rate formula (R=\frac{1}{T}) Rate of 1st machine = Rate of making 1 bolt + Rate of making 1 nut = 1 + \frac{1}{2} Rate of 1st machine = Rate of 2nd machine After this I got lost. Please can you help how to approach using algebra? I wouldn't complicate: 1 machine needs 1,400*1 seconds to produce 1,400 bolts, so 2 need half of that, so 1,400/2 seconds.=700 1 machine needs 1,400*2 seconds to produce 1,400 nuts, so 2 need half of that, so 1,400*2/2 seconds.=1400 total = 2100 sec D The answer is: D

D

mathematics

In how many different ways can 2 identical blue balls and 2 identical red balls be shared among 4 children such that each child receives a ball?

GGG RRR Therefore total number of ways is 4! but there are two groups of 2 identical things. Therefore total number of "different" ways is 4!/ (2!) (2!) = 24 ANS:B The answer is: B

B

mathematics

If 200!/10^n is an integer, what is the largest possible value of n?

We have to basically count the number of 5s withing 200 200/5 =40 200/5^2=8 200/5^3=1 We know for sure that there will be at least 49 even numbers(multiples of 2)within 200 So there are 49 10s in 200! ANSWER:E The answer is: E

E

mathematics

If 1.5 cm of a pencil is purple, 0.5 cm of the remaining is black and the remaining 2 cm is blue, what is the total length of the pencil?

Purple is 1.5 cm Black is 0.5 cm Blue is 2 cm 1.5+0.5+2=4 cm Answer is D) 4 cm The answer is: D

D

mathematics

A and B are playing mathematical puzzles. A asks B "which whole numbers, greater than one, can divide all the nine three digit numbers 111,222,333,444,555,666, 777,888 and 999?" B immediately gave the desired answer. It was :-

Explanation : Each of the number can be written as a multiple of 111. And, The factors of 111 are 3 and 37. Thus, the desired answer is 3, 37 and 111. Answer : B The answer is: B

B

mathematics

Solve for x and check: - 12x = 72

Solution : Dividing each side by -12, we obtain (-12x/-12)=(72/-12) Therefore : x=-6 Check : -12x=72 (-12*-6)=72 72=72 ANSWER : C The answer is: C

C

mathematics

The average age of an adult class is 40years. 10 new students with an avg age of 32years join the class. Therefore decreasing the average by 4year. Find what was the original strength of class?

Let original strength = y Then , 40y + 10 x 32 = ( y + 10) x 36 ⇒ 40y + 320 = 36y + 360 ⇒ 4y = 40 ∴ y = 10 A The answer is: A

A

mathematics

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

Face value of each share = Rs.10 Total dividend received by John = 100×10×12/100 = Rs.120 Let market value of 100 shares = Rs.x x×10/100=120 x = 1200 ie, Market value of 100 shares = Rs.1200 Hence, Market value of each share = Rs.12 Answer is A The answer is: A

A

mathematics

If p/q =4/5, then the value of 18/7 + {(2q - p) / (2q + p)} is ?

Answer Given Exp. = 18 / 7 + {(2q - p) / (2q + p)} Dividing numerator as well as denominator by q, Exp = 18/7 + {2-p/q) / (2 + p/q)} = 18/7 + {(2 - 4/5) / (2 + 4/5)} = 18/7 + 6/14 = 18/7 + 3/7 =21/7 =3 Correct Option: E The answer is: E

E

mathematics

A call center has two teams. Each member of Team A was able to process 1/5 calls as compared to each member of Team B. If Team A has 5/8 as many number of call center agents as Team B, what fraction of the total calls was processed by Team B?

Let team B has 8 agents, so team A has 5 agents Let each agent of team B picked up 5 calls, so total calls by team B = 40 So, each agent in Team A picked up 1 calls, so total calls for team A = 5 Fraction for team B = 40/(40+5) = 8/9 = Answer = C The answer is: C

C

mathematics

A train 280 m long, running with a speed of 63 km/hr will pass a tree in?

Speed = 63 * 5/18 = 35/2 m/sec Time taken = 280 * 2/35 = 16 sec Answer: B The answer is: B

B

mathematics

Solve x2 – 7x = 0

This quadratic factors easily: Copyright © Elizabeth Stapel 2002-2011 All Rights Reserved x2 – 7x = 0 x(x – 7) = 0 x = 0 or x – 7 = 0 x = 0 or x = 7 The solution is x = 0, 7 ANSWER A The answer is: A

A

mathematics

If x*y = xy + 2(x + y) for all integers x and y, then 2* (–3) =

2*(-3) = 2*(-3) + 2 (2 + (-3) ) = -6 -2 = -8 Option (C) The answer is: C

C

mathematics

If s and t are positive integers such that s/t = 36.42, which of the following could be the remainder when s is divided by t ?

s/t= 36.42 s = 36.42t s = (36 + 0.42)t s = 36t + (42/100)t s = 36t + (21/50)t So remainder will be multiple of 21. The only multiple of 21 is 42. Ans. A The answer is: A

A

mathematics

The difference between two numbers is 2395. When the larger number is divided by the smaller one, the quotient is 6 and the remainder is 15. The smaller number is

Let the smaller number be x. Then, larger number = (2395 + x) Therefore 2395 + x = (6x + 15) ‹=› 5x = 2380 ‹=› x = 476. ANSWER:C The answer is: C

C

mathematics

Rs. 700 is divided among A, B, C so that A receives half as much as B and B half as much as C. Then C's share is

C=x B=x/2 A=x/4 A:B:C=1:2:4 C's Share Rs(4/7)*700 = 400 ANSWER B The answer is: B

B

mathematics

Walking across campus, a student interviewed a group of students. 20% of the students took a finance class last semester, 45% took a marketing class last semester, and 40% took neither a finance nor a marketing class last semester. What percent of the students in the group took both a finance and a marketing class?

{Total} = {finance} + {marketing} - {both} + {neither} 100 = 20 + 45 - {both} + 40 {both} = 5%. The answer is E. The answer is: E

E

mathematics

A circular path of 16 m radius has marginal walk 3 m wide all round it. Find the cost of leveling the walk at Rs.2 per m2?

Explanation: π (19^2 - 16^2) = 22/7 * (361-256) = 330 330 * 2 = Rs.660 Answer: Option A The answer is: A

A

mathematics

Jennifer had $180 to spend on herself. She spent 1/5 of the money on a sandwich, 1/6 for a ticket to a museum, and 1/2 of it on a book. How much money does Jennifer have left over?

1/5 x $180 = $36 for sandwich 1/6 x $180 = $30 for museum 1/2 x $180 = $90 for book $36 + $30 + $90 = $156 spent $180 - $156 = $24 left over correct answer E The answer is: E

E

mathematics

Of the 400 employees in a certain company, 25 percent will be relocated to City X and the remaining 75 percent will be relocated to City Y. However, 40 percent of the employees prefer City Y and 60 percent prefer City X. What is the highest possible number of employees who will be relocated to the city they prefer?

240 prefer X (Group 1); 160 prefer Y (Group 2). City Y needs 300 people: letall 160 who prefer Y (entire Group 2) be relocated there, the rest 140 will be those who prefer X from Group 1; City X needs 100 people: 240-140=100 from Group 1 will be relocated to X, which they prefer. So, the highest possible number of employees who will be relocated to the city they prefer is 160+100=260. Answer: E. The answer is: E

E

mathematics

The game of blackjack is played with a deck consisting of 13 cards (one of each of the numbers 2-10, one jack, one queen, one king, and one of ace) in each of four suits: clubs, diamonds, hearts, and spades. In a game of blackjack, if your first card is a spade, what are the W odds that it is an ace?

The question should ask about the probability not the odds. There are 13 spades, the probability W that the spade we already have is an ace is therefore 1/13. Answer: C. The answer is: C

C

mathematics

A cyclist covers a distance of 750 m in 2 min 30 sec. What is the speed in km/hr of the cyclist?

Speed = { 750 } m/sec =5 m/sec = { 5 * 18 } km/hr =18km/hr Ans: E The answer is: E

E

mathematics

The price of a car and AC are in the ratio 3:2. If the scooter costs $500 more than the AC. then the price of the AC?

Let the price of the Car and AC is 3x and 2x 3x-2x = 500 x = 500 Price of AC = 3*500 = $1500 Answer is A The answer is: A

A

mathematics

If y = 30p, and p is prime, what is the greatest common factor of y and 5p, in terms of p?

Y=30p other number is 5p then GCF(30p,5P)=5P; C is the correct answer The answer is: C

C

mathematics

A money lender lends Rs.2000 for six months at 20% p.a. rate. It the interest is reckoned quarterly than find the amount given after time limit?

A = 2000(21/20)2 = 2205 Answer: A The answer is: A

A

mathematics

-84x19+100=?

Given exp.=-84x(20-1)+100 =-(84x20)+84+100 =-1680+184 =-1496 Answer is C The answer is: C

C

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 $1,000 higher than the average rental price for all one-bedroom apartments, and if the average rental price for all two-bedroom apartments is $9,000 higher that M, then what percentage of apartments in the building are two-bedroom apartments?

Ratio of 2 Bedroom Apartment: 1 Bedroom Apartment = 1000 : 9000 -----> 1 : 9 Let total number of Apartments be X No. of 2 Bedroom Apartment = (1 / 10) * X percentage of apartments in the building are two-bedroom apartments ----> (1/10) * 100 ---> 10% Answer : E The answer is: E

E

mathematics

The tax on a commodity is diminished by 22% but its consumption is increased by 9%. Find the decrease percent in the revenue derived from it?

100 * 100 = 10000 78 * 109 = 8502 10000------- 1200 100 ------- ? = 15% ANSWER:C The answer is: C

C

mathematics

If the compound interest on a certain sum of money for 4 years at 10% per annum be Rs. 993, what would be the simple interest?

Let P = Principal A - Amount We have a = P(1 + R/100)3 and CI = A - P ATQ 993 = P(1 + R/100)3 - P ? P = 3000/- Now SI @ 10% on 3000/- for 4 yrs = (3000 x 10 x 4)/100 = 1200/- Answer: C. The answer is: C

C

mathematics

Anna left for city A from city B at 5.20 a.m. She traveled at the speed of 80 km/hr for 2 hrs 15 min. After that the speed was reduced to 60 km/hr. If the distance between two cities is 350 kms, at what time did Anna reach city A?Anna left for city A from city B at 5.20 a.m. She traveled at the speed of 80 km/hr for 2 hrs 15 min. After that the speed was reduced to 60 km/hr. If the distance between two cities is 350 kms, at what time did Anna reach city A?

Distance covered in 2 hrs 15 min i.e., 2 1/4 hrs = 80 * 9/4 = 180 hrs. Time taken to cover remaining distance = (350 - 180)/60 = 17/6 hrs = 2 5/6 = 2 hrs 50 min Total time taken = (2 hrs 15 min + 2 hrs 50 min) = 5 hrs 5 min. So, Anna reached city A at 10.25 a.m. Answer: E The answer is: E

E

mathematics

There is a right angle triangle inside a circle of diameter 18cm. Inside this triangle ,there is another circle of diameter 6 cm. Find the perimeter of the triangle.

1)The radius of the incircle of a right triangle with legs a and b and hypotenuse c is r=(a+b-c)/2 2)The radius of the circumcircle is half the length of the hypotenuse R=c/2 3)Thus the sum of the circumradius and the inradius is half the sum of the legs R+r=(a+b)/2 From 2nd Rule c=18cm From 3rd Rule a+b= 2*(9+3) =24cm Hence Perimeter a+b+c= 24+18= 42 cm ANSWER:E The answer is: E

E

mathematics

Compound interest of Rs.6000 at 10% per annum for 1 1/2years will be (interest compounded half yearly).

10% interest per annum will be 5% interest half yearly for 3 terms( 1 1/2 years) So compound interest=6000[1+(5/100)]^3 - 6000=6000[(21/20)^3 -1] =6000(9261-8000)/8000 =6*1261/8 =945 ANSWER:D The answer is: D

D

mathematics

-54x29+100=?

Given exp.=-54x(30-1)+100 =-(54x30)+54+100 =-1620+154 =-1466 Answer is A The answer is: A

A

mathematics

If 8 men or 12 women can do a piece of work in 20 days, in how many days can the same work be done by 6 men and 11 women?

8men = 12women (i.e 2men = 3women) 12women 1 day work= 1/20 soln: 6men(9women)+ 11women=20women=? 1 women 1 day work =12*20= 1/240 so, 20 women work= 20/240=1/12 ans: 12days ANSWER:C The answer is: C

C

mathematics

A, B and C can do a work in 6, 8 and 12 days respectively doing the work together and get a payment of Rs.1800. What is B’s share?

WC = 1/6:1/8:1/12 => 4:3:2 3/9 * 1800 = 600 Answer:A The answer is: A

A

mathematics

There are between 110 and 120 cards in a collection of cards. If they are counted out 3 at a time, there are 2 left over, but if they are counted out 4 at a time, there is 1 left over. How many cards are in the collection?

The numbers with the form 4n+1 are 113 and 117. Only 113 has the form 3k+2. The answer is B. The answer is: B

B

mathematics

An object thrown directly upward is at a height of h feet after t seconds, where h = -14 (t-3)^2 + 140. At what height, in feet, is the object 2 seconds after it reaches its maximum height?

We see that h will be a maximum h=140 when t-3=0, that is when t=3. At t=5, h = -14(5-3)^2 + 140 = -14(4) + 140 = 84 The answer is D. The answer is: D

D

mathematics

An article is bought for Rs.600 and sold for Rs.500, find the loss percent?

600 ---- 100 100 ---- ? => 16 2/3% Answer: D The answer is: D

D

mathematics

what is the value of (4)^-6 ?

4^-6= 1/(4)^6= 1/4096 ANSWER:E The answer is: E

E

mathematics

If 3^z is a factor of 30!, which of the following could be the value of z?

3^z is a factor of 30!, what values can z take. Powers of 3 in 30! = [30/3] + [30/9] +[30/27] , where [x] is the integral part of x Powers of 3 in 30! = 10 + 3 + 1 = 14 Hence the maximum value of 3^z in 30! = 3^14 Correct Option: D The answer is: D

D

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

Pick a team of 3 people from a group of 10 people.

10c3 = 120 Answer is D. The answer is: D

D

mathematics

A box contains 10 tablets of medicine A and 13 tablets of medicine B. What is the least number of tablets that should be taken from the box to ensure that at least two tablets of each kind are among the extracted.

The worst case scenario will be if we remove all 13 tablets of medicine B first. The next 2 tablets we remove have to be of medicine A, so to guarantee that at least two tablets of each kind will be taken we should remove minimum of 13+2=15 tablets. Answer: B. The answer is: B

B

mathematics

The ratio of the number of boys and girls in a college is 7:8. If the percentage increase in the number of boys and girls be 20% and 10% respectively. What will be the new ratio?

Originally, let the number of boys and girls in the college be 7x and 8x respectively. Their increased number is (120% of 7x) and (110% of 8x). i.e., (120/100 * 7x) and (110/100 * 8x) i.e., 42x/5 and 44x/5 Required ratio = 42x/5 : 44x/5 = 21:22 Answer: C The answer is: C

C

mathematics

Three pipes A,B and C are attached to a tank.A and B can fill it in 20 and 30 minutes respectively while C can empty it in 15 minutes.If A,B and C are kept open successively for 1 minute each, how soon will the tank be filled?

the term successively and NOT SIMULTANEOUSLY.AT THE END OF 3 mts, i/60 part of the tank is filled.we have to consider a three-minute block starting from 3 mts, 6 mts,9 mts....etc upto 177 mts. at the end of 165 mts,55/60 part of the tank was filled. at the end of the next suceessive minutes,i.e, 166,167th minute, the part filled is 5/60.so 55/60+5/60. this means the whole tank is filled at the end of 167 th minute. ANSWER:C The answer is: C

C

mathematics

In what ratio must water be mixed with milk to gain 16 2/3% on selling the mixture at cost price ?

Required ratio is cheaper quantity : dearer quantity = (d-m) : (m-c) Answer with Explanation: Step i) Let C.P of 1 litre of mild be Rs.1 And S.P of1 litre of mild be Rs.1 Gain = 50/3 per cent  C.P of 1 litre of mixture =              1 3 50 100 100 x = Re. 100 x 3/350 x 1 = 6/7 (Mean price) Step (ii) By the rule of allegation I. C.P of 1 liter of water = 0 II. C.P of 1 liter of milk = 1 III. Mean price (p) = 6/7 IV. d – m = 1 – 6/7 = 1/7 V. m – c = 6/7 - 0 = 6/7  ratio of water and milk = 1/7 : 6/7 = 1 : 6 Answer:D The answer is: D

D

mathematics

A hollow spherical metallic ball has an external diameter 6 cm and is 1/2 cm thick. The volume of metal used in the metal is:

Explanation: Please note we are talking about "Hollow" ball. Do not ignore this word in this type of question in a hurry to solve this question. If we are given with external radius and thickness, we can get the internal radius by subtracting them. Then the volume of metal can be obtained by its formula as, External radius = 3 cm, Internal radius = (3-0.5) cm = 2.5 cm Volume of sphere =4/3πr3 =4/3∗22/7∗[3(2)−2.52]cm3 =4/3∗22/7∗91/8cm3 =143/3cm3=47 2/3cm3 Option B The answer is: B

B

mathematics

Last year’s receipts from the sale of greeting cards during the week before Mother’s Day totaled $240 million, which represented 12 percent of total greeting card sales for the year. Total greeting card sales for the year totaled how many million dollars?

12% ---- 240 millions for 100% => ( 240 * 100% )/12% = 2000. Option B. The answer is: B

B

mathematics

Anthony and Cindy were each given x dollars in advance to perform at a community festival. Anthony eventually performed on all 14 days of the festival, while Cindy performed on 7 fewer days than Anthony performed. If Cindy gives Anthony y dollars of her advance payment so that they would have each received the same daily rate, what was Anthony paid in advance, in terms of y?

Anthony performed for 14 days meansw Cindy performed for(14-7)=7 days. If Cindy gives y dollars to Anthony their Daily rate will be equal.It means (x+y)/14=(x-y)/7 Solving we get, x=3y Now Anthony's Advance is x=3y .So answer should be B. The answer is: B

B

mathematics

3 women and a few men participated in a chess tournament. Each player played two matches with each of the other players. If the number of matches that men played among themselves is 78 more than those they played with the women, how many more men than women participated in the tournament?

let the number of men=m.. so 3 women and m men will play= 2*3m=6m games m will play each other in mC2 way so number of games = 2*mC2= m(m-1) Difference in two = m(m-1)-6m=78 m^2-7m-78=0 m^2-13m+6m-78=0 (m-13)(m+6)=0 so m = 13 or -6 cannot be -ive so m=13 difference in number of women and men= 13-3=10.. Imp that we do not choose 13 as the answer ANS D The answer is: D

D

mathematics

P and Q are both positive integers. When P is divided by Q, the remainder is some positive integer D, and when P is divided by (Q + 6), the remainder is also D. If P/Q = 1020.75 and P/(Q + 6) = 816.6, then which of the following gives the correct set of {D, Q}?

p/q= d=p/q+6 d= .75 q d= .6(q+6) we get d = 18 and q = 24. Answer = E. The answer is: E

E

mathematics

7 teams compete in a track competition. If there are 12 events in the competition, no event ends in a tie, and no team wins more than 3 events, what is the minimum possible number of teams that won at least one event?

3(max wins) x 4 = 12 (4 teams win three events) The answer is B. The answer is: B

B

mathematics

A fruit seller had some oranges. He sells 40% oranges and still has 420 oranges. How many oranges he had originally?

Explanation : He sells 40% of oranges and still there are 420 oranges remaining => 60% of oranges = 420 ⇒ (60 × Total Oranges)/100 = 420 ⇒ Total Oranges/100 = 7 ⇒ Total Oranges = 7 × 100 = 700 Answer : Option B The answer is: B

B

mathematics

If a: b = 7: 5, b: c = 9: 11, find a: b: c?

a: b = 7: 5 b: c = 9: 11 a: b: c = 63: 45: 55 Answer: B The answer is: B

B

mathematics

A family with 1 mother, 1 father, and 2 children sit in a car with 2 front seats and 3 back seats. If the mother drives with a child in the front, and the father sits in the back center seat with the other two children on either side of him, how many seating arrangements are possible?

Mother has a fixed place and father, so there are 2! ways to arrange the children, hence A The answer is: A

A

mathematics

Amar takes as much time in running 12 meters as a car takes in covering 48 meters. What will be the distance covered by Amar during the time the car covers 1.6 km?

D 400 m Distance covered by Amar = 12/4.8 (1.6km) = 2.5(1600) = 400 m Answer is D The answer is: D

D

mathematics

John has taken four (8) tests that have an average of 82. In order to bring his course grade up to a ‘B’, he will need to have a final average of 87. What will he need to average on his final two tests to achieve this grade?

87-82=5*8=40 points 2*87=174 174+40=214 points to be scored in the 2 tests. Avg of 2 tests = 214/2=107 Answer: D Traditional Method: Total scored till now 82*8=656 Total score to avg 87 in 10 tests = 87*10=870 Total to be scored on 2 tests = 870-656=214 Avg on 2 tests = 214/2 = 107 Answer D The answer is: D

D

mathematics

In a garden, there are 10 rows and 12 columns of mango trees. The distance between the two trees is 2 metres and a distance of one metre is left from all sides of the boundary of the garden. The length of the garden is

Explanation: Each row contains 12 plants. There are 11 gapes between the two corner trees (11 x 2) metres and 1 metre on each side is left. Therefore Length = (22 + 2) m = 24 m. Answer: C The answer is: C

C

mathematics

Thomas's age and Matt's age are in the ratio 2:3. Two years ago the ratio of their ages was 1:2. Find the ratio of their ages four years hence?

Let ages of Thomas and Matt be x and y respectively. x/y = 2/3 => x = 2/3 y (x- 2)/(y - 2) = 1/2 => 2x - 4 = y - 2 => 2x = y + 2 But x = 2/3 y 2 * 2/3 y = y + 2 4y = 3y + 6 => y = 6years => x = 4 years Ratio of their ages five years hence, (4 +4)/(6 + 4) = 8/10. => 4:5 Answer:D The answer is: D

D

mathematics

If the range W of the six numbers 4,3,14,7,10 and x is 12, what is the difference between the greatest possible value of x and least possible value of x?

The range W of a set is the difference between the largest and smallest elements of a set. Without x, the difference between the largest and smallest elements of a set is 14-3=11<12, which means that in order 12 to be the range of the set x must be either the smallest element so that 14-x=12 ---> x=2 OR x must the largest element so that x-3=12 --> x=15. The the difference between the greatest possible value of x and least possible value of x is 15-2=13. Answer: D. The answer is: D

D

mathematics

What least number must be added to 1096, so that the sum is completely divisible by 23 ?

1096/23 = 47.6-- that is 23 * 47 = 1081 Now, 1096- 1081 = 15 To get completely divided by 23 add 8 to 1096 Ans -E The answer is: E

E

mathematics

In how many ways can a committee consisting of 4 men and 5 women be formed from a group of 7 men and 7 women?

Group consisting of 7 men and 7 women 4 men can be selected from 7 men in 7C4 ways 5 women can be selected from 7 women in 7C5 ways Therefore, Total number of ways= 7C4 7C5 ANSWER:A The answer is: A

A

mathematics

In a certain sequence, the first term is 5, and each successive term is 1 more than the reciprocal of the term that immediately precedes it. What is the fifth term in this sequence?

let five terms in the sequence be a,b,c,d,e a=5 b= 1+1/5=6/5 c=1+5/6= 11/6 d= 1+6/11 = 17/11 e= 1+11/17 = 28/17 hence answer should be E. The answer is: E

E

mathematics

In an animal behavior experiment, 25 tagged white pigeons and 250 tagged gray pigeons were released from a laboratory. Within one week, 88 percent of the white pigeons and 80.5 percent of the gray pigeons had returned to the laboratory. What percent of the total number of pigeons returned to the laboratory?

Weighted mix method is best here.... Ratio is 1:10 for 88:80.5... So the answer required = 80.5+ (88-80.5)*1/10=80.5+7.5*1/10 80.5+0.75=81.25 E The answer is: E

E

mathematics

The simple interest on a sum of money will be Rs.1000 after 10 years. If the principal is trebled after 5 years what will be the total interest at the end of the tenth year?

P --- 10 ---- 1000 P --- 5 ----- 500 3P --- 5 ----- 1500 ------ => 2000 Answer: E The answer is: E

E

mathematics

A train is running at a speed of 40 km/hr and it crosses a post in 18 seconds. What is the length of the train?

Explanation: Speed of the train, v = 40 km/hr = 40000/3600 m/s = 400/36 m/s Time taken to cross, t = 18 s Distance Covered, d = vt = (400/36)× 18 = 200 m Distance covered is equal to the length of the train = 200 m Answer: Option C The answer is: C

C

mathematics

The simple interest and the true discount on a certain sum for a given time and at a given rate are Rs. 85 and Rs. 80 respectively.The Sum is :

Solution Sum = S.I xT.D/ ( S.I) - ( T.D)= 85 x80/85 - 80=Rs.1360. Answer C The answer is: C

C

mathematics

(0.96)(power 3) - (0.1)(power 3)/ (0.96)(power 2) + 0.096 + (0.1)(power 2) is:

Given expression = (0.96) (power 3) - (0.1)(power 3) / (0.96)(power 2) + (0.96 x 0.1) + (0.1)(power 2) = a (power 3) - b(power 3) / a(power 2) + ab + b(power 2) = (a - b) = (0.96 - 0.1) = 0.86 Answer is A. The answer is: A

A

mathematics

A bowl contains pecans, cashews, and almonds in a ratio of 5 : 8 : 12, respectively. If some of the nuts of one of the three types are removed, which of the following could be the ratio of pecans to cashews to almonds remaining in the bowl? i. 1 : 2 : 3 ii. 2 : 3 : 4 iii. 4 : 7 : 10

i. The ratio 2 : 3 is the same as the given ratio 8 : 12. If one pecan were removed, the new ratio would be 4 : 8 : 12, or 1 : 2 : 3. ii. None of the nuts currently have a ratio of 3 : 4. The cashews and almonds do have a ratio of 2 : 3, but there are not enough pecans in the bowl to complete the ratio. iii. The ratio 4 : 10 is the same as the given ratio 6 : 15. To see this, multiply the ratio by 3/2 . The new ratio is 6 : 10.5 : 15. Unfortunately, this means that there are fewer cashews that this ratio would require. Removing cashews won’t create the desired ratio. Answer : B The answer is: B

B

mathematics

How many figures are required to number the pages the pages of a book containing 1210 pages?

1 to 9 = 9 * 1 = 9 10 to 99 = 90 * 2 = 180 100 to 999 = 900 * 3 = 2700 1000 to 1210 = 211 * 4 =844 ----------- 3733 ANSWER:E The answer is: E

E

mathematics

On the first of the year, James invested x dollars at Proudstar bank in an account that yields 2.4% in interest every quarter year. At the end of the year, during which he made no additional deposits or withdrawals, he had y dollars in the account. If James had invested the same amount in an account which pays interest on a yearly basis, what must the interest rate be for James to have y dollars at the end of the year?

If the interest were compounded annually instead of quarterly then in one year the interest would be 2.4*4=9.6%. Now, since the interest is compounded quarterly then there would be interest earned on interest (very small amount) thus the actual interest would be a little bit more than 9.6%, Answer: E The answer is: E

E

mathematics

In an examination 40% failed in Hindi, 45% failed in English. If 25% students failed in both the subjects. Then the percentage of failed students is?

15+25+20 = 60 ANSWER A The answer is: A

A

mathematics

If a tire rotates at 400 revolutions per minute when the car is traveling 144km/h, what is the circumference of the tire?

400 rev / minute = 400 * 60 rev / 60 minutes = 24,000 rev / hour 24,000 * C = 144,000 m : C is the circumference C = 6 meters correct answer B The answer is: B

B

mathematics

A person buys an article at Rs.500. At what price should he sell the article so as to make a profit of 35%?

Cost price = Rs.500 profit = 35% of 500 = Rs.175 Selling price = Cost price + Profit = 500 + 175 = 675 Answer: E The answer is: E

E

mathematics

Two pipes A and B can fill a cistern in 9 and 18 minutes respectively, and a third pipe C can empty it in 24 minutes. How long will it take to fill the cistern if all the three are opened at the same time?

1/9 + 1/18 - 1/24 = 1/8 8/1= 8 Answer:C The answer is: C

C

mathematics

Find the remainder when 6^23 is divided by 5 ?

6^23 = 6^(4*5+3) = 6^(20) * 6^3 last 3 digits = 216 216/5 remainder = 1 ANSWER:C The answer is: C

C