Arithmetic & Algebraic Problems - DIVIDING THE LEGACY

Question: A man left $100.00 to be divided between his two sons Alfred and Benjamin. If one-third of Alfred's legacy be taken from one-fourth of Benjamin's, the remainder would be $11.00. What was the amount of each legacy?

Answer: The two legacies were $24.00 and $76.00, for if 8 (one-third of 24) be taken from 19 (one-fourth of 76) the remainder will be II.

Arithmetic & Algebraic Problems - PUZZLING LEGACIES

Question: A man bequeathed a sum of money, a little less than $1,500.00, to be divided as follows: The five children and the lawyer received such sums that the square root of the eldest son's share, the second son's share divided by two, the third son's share minus $2.00, the fourth son's share plus $2.00, the daughter'S share multiplied by two, and the square of the lawyer's fee all worked out at exactly the same sum of money. No dollars were divided, and no money was left over after the division. What was the total amount bequeathed?

Answer: The answer is $1,464.oo-a little less than $1,500.00. The legacies, in order, were $1,296.00, $72.00, $38.00, $34.00, and $18.00. The lawyer's fee would be $6.00.

CAT 2015 Preparation - How to Adopt New Test Format

With just 1 month left for CAT 2015, we bring you video of several format changes in CAT history in last 5-6 years and how one should see the latest change in normalization as a opportunity to score well in all the sections.

Driving force for this year CAT will be -

-> Time Management
-> Selection of Questions
-> Sectional Consistency

Read More at - http://www.endeavorcareers.com/gurus-speak/747-cat-2015-preparation-how-to-adopt-new-test-format

Arithmetic & Algebraic Problems - THE SEVEN APPLEWOMEN

Question: Here is an old puzzle that people are frequently writing to me about. Seven applewomen, possessing respectively 20, 40, 60, 80, 100, 120, and 140 apples, went to market and sold all the apples at the same price, and each received the same sum of money. What was the price?

Answer: Each woman sold her apples at seven for I¢, and 3¢ each for the odd ones over. Thus, each received the same amount, 20¢. Without questioning the ingenuity of the thing, I have always thought the solution unsatisfactory, because really indeterminate, even if we admit that such an eccentric way of selling may be fairly termed a "price." It would seem just as fair if they sold them at

different rates and afterwards divided the money; or sold at a single rate with different discounts allowed; or sold different kinds of apples at different values; or sold the same rate per basketful; or sold by weight, the apples being of different sizes; or sold by rates diminishing with the age of the apples; and so on. That is why I have never held a high opinion of this old puzzle.

In a general way, we can say that n women, possessing an + (n - 1), n(a + b) + (n - 2), n(a + 2b) + (n - 3), ... ,n[a + b(n - 1) 1 apples respectively, can sell at n for a penny and b pennies for each odd one over and each receive a + b(n - I) pennies. In the case of our puzzle a = 2, b = 3, and n = 7.

Arithmetic & Algebraic Problems - MARKET TRANSACTIONS

Question: A farmer goes to market and buys a hundred animals at a total cost of $1,000.00. The price of cows being $50.00 each, sheep $10.00 each, and rabbits 50¢ each, how many of each kind does he buy? Most people will solve this, if they succeed at all, by more or less laborious trial, but there are several direct ways of getting the solution.

Answer: The man bought 19 cows for $950.00, 1 sheep for $10.00, and 80 rabbits for $40.00, making together 100 animals at a cost of $1,000.00.

A purely arithmetical solution is not difficult by a method of averages, the average cost per animal being the same as the cost of a sheep.

By algebra we proceed as follows, working in dollars: Since x + y + z = 100 

by subtraction, or 99x + 19y = 1900. We have therefore to solve this indeterminate equation. The only answer is x = 19, Y = l. Then, to make up the 100 animals, z must equal 80.

Arithmetic & Algebraic Problems - NAME THEIR WIVES

Question: A man left a legacy of $1 ,000.00 to three relatives and their wives. The wives received together $396.00. Jane received $10.00 more than Catherine, and Mary received $10.00 more than Jane. John Smith was given just as much as his wife, Henry Snooks got half as much again as his wife, and Tom Crowe received twice as much as his wife. What was the Christian name of each man's wife?

Answer: As it is evident that Catherine, Jane, and Mary received respectively $122.00, $132.00, and $142.00, making together the $396.00 left to the three wives, if John Smith receives as much as his wife Catherine, $122.00; Henry Snooks half as much again as his wife Jane, $198.00; and Tom Crowe twice as much as his wife Mary, $284.00, we have correctly paired these married couples and exactly accounted for the $1,000.00.

Arithmetic & Algebraic Problems - DIGGING A DITCH

Question: Here is a curious question that is more perplexing than it looks at first sight. Abraham, an infirm old man, undertook to dig a ditch for two dollars. He engaged Benjamin, an able-bodied fellow, to assist him and share the money fairly according to their capacities. Abraham could dig as fast as Benjamin could shovel out the dirt, and Benjamin could dig four times as fast as Abraham could do the shoveling.

How should they divide the money? Of course, we must assume their relative abilities for work to be the same in digging or shoveling.

Answer: A. should receive one-third of two dollars, and B. two-thirds. Say B. can dig all in 2 hours and shovel all in 4 hours; then A. can dig all in 4 hours and shovel all in 8 hours. That is, their ratio of digging is as 2 to 4 and their ratio of shovelling as 4 to 8 (the same ratio), and A. can dig in the same time that B. can shovel (4 hours), while B. can dig in a quarter of the time that A. can shovel. Any other figures will do that fill these conditions and give two similar ratios for their working ability. Therefore, A. takes one-third and B. twice as much-two-thirds.

Arithmetic & Algebraic Problems - A WEIRD GAME

Question: Seven men engaged in play. Whenever a player won a game he doubled the money of each of the other players. That is, he gave each player just as much money as each had in his pocket. They played seven games and, strange to say, each won a game in turn in the order of their names, which

began with the letters A, B, C, D, E, F, and G.

When they had finished it was found that each man had exactly $1.28 in his pocket. How much had each man in his pocket before play?

Answer: The seven men, A, B, C, D, E, F, and G, had respectively in their pockets before play the following sums: $4.49, $2.25, $1.13, 57¢, 29¢, 15¢, and 8¢. The answer may be found by laboriously working backwards, but a simpler method is as follows: 7 + 1 = 8; 2 X 7 + 1 = 15; 4 X 7 + 1 = 29; and so on, where the multiplier increases in powers of 2, that is, 2, 4, 8, 16, 32, and 64.

Arithmetic & Algebraic Problems - THE PERPLEXED BANKER

Question: A man went into a bank with a thousand dollars, all in dollar bills, and ten bags. He said, "Place this money, please, in the bags in such a way that if I call and ask for a certain number of dollars you can hand me over one or more bags, giving me the exact amount called for without opening any of the bags." How was it to be done? We are, of course, only concerned with a single application, but he may ask for any exact number of dollars from one to one thousand.

Answer: The contents of the ten bags (in dollar bills) should be as follows: $1,2,4, 8, 16,32,64, 128,256, 4S9. The first nine numbers are in geometrical progression, and their sum, deducted from 1,000, gives the contents of the tenth bag.

Scoring Pattern and Parameters for GRE Exam

The GRE is a Section Adaptive Test such that, a good performance on the first section will lead to a second section with questions of higher difficulty level and therefore higher score per question, thereby significantly improving the chances of scoring very well on the test.

The total scaled score for the Quantitative Reasoning Section varies from 130 to 170. There is a similar scaled score range for Verbal Reasoning Section. The score is determined by a test taker’s performance over two sections each of Quantitative Reasoning and Verbal Reasoning, totalling to 40 questions each (2 sections of 20 questions each). 

But each test taker gets five sections instead of four, which means, either the Quantitative Reasoning or the Verbal Reasoning Section appears three times instead of two. The additional section resembles the other sections, but is an undisclosed, un-scored section, colloquially called a dummy section.

Read More at - http://www.endeavorcareers.com/gurus-speak/739-scoring-pattern-and-parameters-for-gre-exam

Arithmetic & Algebraic Problems - UNREWARDED LABOR

Question: A man persuaded Weary Willie, with some difficulty, to try to work on a job for thirty days at eight dollars a day, on the condition that he would forfeit ten dollars a day for every day that he idled. At the end of the month neither owed the other anything, which entirely convinced Willie of the folly of labor. Can you tell just how many days' work he put in and on how many

days he idled?

Answer: Weary Willie must have worked 1673 days and idled l3Y.! days. Thus the former time, at $8.00 a day, amounts to exactly the same as the latter at $10.00 a day.

Arithmetic & Algebraic Problems - BUYING BUNS

Question: Buns were being sold at three prices: one for a penny, two for a penny, and three for a penny. Some children (there were as many boys as girls) were given seven pennies to spend on these buns, each child to receive exactly the same value in buns. Assuming that all buns remained whole, how many buns, and of what types, did each child receive?

Answer: There must have been three boys and three girls, each of whom received two buns at three for a penny and one bun at two for a penny, the cost of which would be exactly 7¢.

Arithmetic & Algebraic Problems - GENEROUS GIFTS

Question: A generous man set aside a certain sum of money for equal distribution weekly to the needy of his acquaintance. One day he remarked, "If there are five fewer applicants next week, you will each receive two dollars more." Unfortunately, instead of there being fewer there were actually four more persons applying for the gift. "This means," he pointed out, "that you will each receive one dollar less." How much did each person receive at that last distribution?

Answer: At first there were twenty persons, and each received $6.00. Then fifteen persons (five fewer) would have received $8.00 each. But twenty-four (four more) appeared and only received $5.00 each. The amount distributed weekly was thus $120.00.

Arithmetic & Algebraic Problems - LOOSE CASH

Question: What is the largest sum of money-all in current coins and no silver dollars-that I could have in my pocket without being able to give change for a dollar, half dollar, quarter, dime, or nickel?

Answer: The largest sum is $1.19, composed of a half dollar, quarter, four dimes, and four pennies.

Best Tips for Preparing Quantitative Ability Section

With the pattern changes that CAT 2015 has come up with, the quantitative ability section would have 34 questions with a section time limit of 60 minutes.

The section would have questions from Geometry, arithmetic, algebra and modern mathematics. The reliance on mental calculation will decrease substantially owing to the on-screen calculator.

Any QA selection in CAT will be a mix of easy, moderate and difficult questions.

Even the difficult questions are no match for the difficulty level of the paper based CATs of 2006 or 2007. An easy question typically takes 1.5 to 2 minutes to solve whereas a tough question would take 6-8 minute for a normal test taker.

Read More at - http://www.endeavorcareers.com/gurus-speak/738-tips-for-preparing-quantitative-ability-section

Arithmetic & Algebraic Problems - DOLLARS AND CENTS

Question: A man entered a store and spent one-half ofthe money that was in his pocket. When he came out he found that he had just as many cents as he had dollars when he went in and half as many dollars as he had cents when he went in. How much money did he have on him when he entered?

Answer: The man must have entered the store with $99.98 in his pocket.

Arithmetic & Algebraic Problems - CONCERNING A CHECK

Question: A man went into a bank to cash a check. In handing over the money the cashier, by mistake, gave him dollars for cents and cents for dollars. He pocketed the money without examining it, and spent a nickel on his way home. He then found that he possessed exactly twice the amount of the check. He had no money in his pocket before going to the bank. What was the exact amount of that check?

Answer: The amount must have been $31.63. He received $63.31. After he had spent a nickel there would remain the sum of $63.26, which is twice the amount of the check.

What is GRE Exam? – Format and Test Structure

The GRE (Graduate Record Examination) is a standardized aptitude test conducted online (paper based only in some countries) on a daily basis across the world. The test is conducted in two variants:

1.    The GRE General Test: An approximately 4 hour test conducted online round the year that tests quantitative reasoning, verbal reasoning and analytical writing skills of the test taker.

2.    The GRE Subject Test: Required in some instances, GRE Subject Tests evaluate subject-specific knowledge of a test taker. GRE Subject Tests are paper based tests conducted on fixed dates in a year, in most countries of the world. Currently, GRE offers Subject Tests in seven subjects viz. Physics, Biology, Mathematics, Cell and Molecular Biology, Chemistry, Literature in English and Psychology.

Read in Detail at - http://endeavorcareers.com/gurus-speak/734-what-is-gre-exam-format-and-test-structure