Problem Solving

For positive integers 'n', it is known that 1 + 3 + 5 + ... + (2*n - 1) = n 2 . Evaluate 1 + 3 + 5 + . . + 739 741 + 743 + . . + 1479 1 + 3 + 5 + . . + 739 741 + 743 + . . + 1479

In Company X, 30 percent of the employees live over ten miles from work and 60 percent of the employees who live over ten miles from work use car pools. If 40 percent of the employees of Company X use car pools, what percent of the employees of Company X live ten miles or less from work and use car pools?

The regular hourly wage for an employee of a certain factory is $5.60. If the employee worked 8 hours overtime and earned 1 1/2 times this regular hourly wage for overtime, how much overtime money was earned?

A ladder 25 feet long is leaning against a wall that is perpendicular to level ground. The bottom of the ladder is 7 feet from the base of the wall. If the top of the ladder slips down 4 feet, how many feet will the bottom of the ladder slip?

If 10 persons meet at a reunion and each person shakes hands exactly once with each of the others, what is the total number of handshakes?

Working alone, R can complete a certain kind of job in 9 hours. R and S, working together at their respective rates, can complete one of these jobs in 6 hours. In how many hours can S, working alone, complete one of these jobs?

What is the least possible product of 4 different integers, each of which has a value between –5 and 10, inclusive?

An investor purchased x shares of stock at a certain price. If the stock then increased in price $0.25pershareandthetotalincreaseforthexshareswas$12.50. how many shares of stock had been purchased?

After paying a 10 percent tax on all income over $3,000,apersonhadanetincomeof$12,000. What was the income before taxes?

One-fifth of the light switches produced by a certain factory are defective. Four-fifths of the defective switches are rejected and 1/20 of the non defective switches are rejected by mistake. If all the switches not rejected are sold, what percent of the switches sold by the factory are defective?

How many three-digit numerals begin With a digit that represents a prime number and end with a digit that represents a prime number?

If 2x + 5y =8 and 3x = 2y, what is the value of 2x + y?

(− 1) 2 − (− 1) 3 =

Which of the following integers does NOT have a divisor greater than 1 that is the square of an integer?

If r = 1 + 1 3 + 1 9 + 1 27 and s = 1 + 1 3 r , then s exceeds r by

The average (arithmetic mean) of 3 different positive integers is 100 and the largest of these 3 integers is 120. What is the least possible value of the smallest of these 3 integers?

If 0.497 mark has the value of one dollar, what is the value to the nearest dollar of 350 marks?

There are 4 card-processing machines in an office. The fastest of these machines processes x cards in 7 hours and the slowest processes x cards in 8 hours. Which of the following could NOT be the average time per machine for each of the 4 machines to process x cards?

A decorator bought a bolt of defective cloth that he judged to be 3/4 usable, in which case the cost would be $0.80 per usable yard. If it was later found that only 2/3 of the bolt could be used, what was the actual cost per usable yard?

If x ≠ 0, 2x = 5y, and 3z = 7x, what is the ratio of z to y?