Problem Solving

Seed mixture X is 40 percent ryegrass and 60 percent bluegrass by weight; seed mixture Y is 25 percent ryegrass and 75 % fescue. If a mixture of X and Y contains 30% ryegrass, what percent of the weight of the mixture is X?

Xavier, Yvonne, and Zelda each try independently to solve a problem. If their individual probabilities for success are 1/4, 1/2 and 5/8, respectively, what is the probability that Xavier and Yvonne, but not Zelda, will solve the problem?

If x and y are positive integers such that y is a multiple of 5 and 3x + 4y = 200, then x must be a multiple of which of the following?

If (1/5) m * (1/4) 18 = 1 2 * (10) 35 , then m = ?

Each year for 4 years, a farmer increased the number of trees in a certain orchard by one fourth of the number of trees in the orchard the preceding year. If all the trees thrived and there were 6,250 trees in the orchard at the end of the 4-year period, how many trees were in the orchard at the beginning of the 4-year period?

A pharmaceutical company received $3millioninroyaltiesonthefirst$20 million in sales of the generic equivalent of one of its products and then $9millioninroyaltiesonthenext$108 million in sales. By approximately what percent did the ratio of royalties to sales decrease from the first $20millioninsalestothenext$108 million in sales?

In order to complete a reading assignment on time, Terry planned to read 90 pages per day. However, she read only 75 pages per day at first, leaving 690 pages to be read during the last 6 days before the assignment was to be completed. How many days in all did Terry have to complete the assignment on time?

If the speed of X meters per second is equivalent to the speed of Y kilometers per hour, what is Y in terms of X?

If X is the hundredths digit in the decimal 0.1X and if Y is the thousandths digit in the decimal 0.02Y, where X and Y are nonzero digits, which of the following is closest to the greatest possible value of 0.1 X 0.02 Y ?

Which of the following is equal to the average (arithmetic mean) of (x + 2)^2 and (x - 2)^2?

If the units digit of 5 , 610.37 10 k is 6, what is the value of k?

At his regular hourly rate, Don had estimated the labor cost of a repair job as $336andhewaspaidthatamount.However,thejobtook4hourslongerthanhehadestimatedand,consequently,heearned$2 per hour less than his regular hourly rate. What was the time Don had estimated for the job, in hours?

A positive integer is divisible by 3 if and only if the sum of its digits is divisible by 3. If the six-digit integer n is divisible by 3, and n is of the form 1k2,k24, where k represents a digit that occurs twice, how many values could k have?

In the table above, what is the number of green marbles in Jar R ?

List S consists of 10 consecutive odd integers, and list T consists of 5 consecutive even integers. If the least integer in S is 7 more than the least integer in T, how much greater is the average (arithmetic mean) of the integers in S than the average of the integers in T?

Two water pumps, working simultaneously at their respective constant rates, took exactly four hours to fill a certain swimming pool. If the constant rate of one pump was 1.5 times the constant rate of the other, how many hours would it have taken the faster pump to fill the pool if it had worked alone at it's constant rate?

On a recent trip, Cindy drove her car 290 miles, rounded to the nearest 10 miles, and used 12 gallons of gasoline, rounded to the nearest gallon. The actual number of miles per gallon that Cindy's car got on this trip must have been between

The ratio of the amount of Alex's fuel oil bill for the month of February to the amount of his fuel oil bill for the month of January was 3/2. If the fuel oil bill for February had been $40 more, the corresponding ratio would have been 5/3. How much was Alex's fuel oil bill for January?

What is the difference between the sixth and the fifth terms of the sequence 2, 4, 7, ... whose nth term is n + 2^(n - 1)?

In a certain sequence, the term x n is given by the formula x n = 2 * x n − 1 2 * x n − 2 for all n ≥ 2 . If x 0 = 3 and x 1 = 2 , what is the value of x 3 ?