Problem Solving

If 25 percent of p is equal to 10 percent of q, and pq ≠ 0, then p is what percent of q ?

How many positive integers less than 20 are either a multiple of 2, an odd multiple of 9, or the sum of a positive multiple of 2 and a positive multiple of 9 ?

If 8 2 x + 3 = 2 3 x + 6 , then x =

In a recent election, James received 0.5 percent of the 2,000 votes cast. To win the election, a candidate needed to receive more than 50 percent of the vote. How many additional votes would James have needed to win the election?

One night a certain hotel rented 3/4 of its rooms, including 2/3 of their air conditioned rooms. If 3/5 of its rooms were air conditioned, what percent of the rooms that were not rented were air conditioned?

If a number between 0 and 1/2 is selected at random, which of the following will the number most likely be between?

On a certain road 10% of the motorists exceed the posted speed limit and receive speeding tickets, but 20% of the motorists who exceed the posted speed limit do not receive speeding tickets. What percent of the motorists on the road exceed the posted speed limit?

Increasing the original price of an article by 15 percent and then increasing the new price by 15 percent is equivalent to increasing the original price by

If x^4 + y^4 = 100, then the greatest possible value of x is between

For any positive integer n, n>1, the "length" of n is the number of positive primes (not necessary distinct) whose product is n. For ex, the length of 50 is 3, since 50=2x5x5. What is the greatest possible length of a positive integer less than 1000.

Machines A and B always operate independently and at their respective constant rates. When working alone, Machine A can fill a production lot in 5 hours, and Machine B can fill the same lot in x hours. When the two machines operate simultaneously to fill the production lot, it takes them 2 hours to complete the job. What is the value of x ?

Which of the following must be equal to zero for all real numbers x ? I. − 1 x II. x + (-x) III. x^0

A soccer team played 25% more matches year-on-year in the second year of its formation. It won 84% of the matches it played in the second year, which was an improvement of 5% over the percentage of matches won in the first year. In the third year, the team played 4% fewer matches year-on-year but lost only 12.5% of the matches it played, which was one less than the number of matches lost by the team in the second year. Which of the following statements must be correct? I. The team lost the same number of matches in the first yea and the second year II. The team won the same number of matches in the second year and the third year III. The team played five more matches in the third year than the first year

The table above gives the gasoline costs and consumption rates for a certain car driven at 50 miles per hour, using each of two brands of gasoline. How many miles farther can the car be driven at this speed on $12worthofbrandXgasolinethanon$12 worth of brand Y gasoline?

Which of the following CANNOT yield an integer when divided by 10 ?

If s, u, and v are positive integers and 2s = 2u + 2v, which of the following must be true? I. s = u II. u ≠ v III. s > v

The value of − 89 − − √ 3 − 89 3 is:

In a certain class consisting of 36 students, some boys and some girls, exactly 1/3 of the boys and exactly 1/4 of the girls walk to school. What is the greatest possible number of students in this class who walk to school?

Four hours from now, the population of a colony of bacteria will reach 1.28 * 10 6 10 6 . If the population of the colony doubles every 4 hours, what was the population 12 hours ago?

38 69 22 73 31 47 13 82 Which of the following numbers is greater than three fourths of the numbers but less than one fourth of the numbers in the list above?