Problem Solving

An operation @ is defined by the equation a@b = (a - b) / (a + b), for all numbers a and b such that a ≠ -b. If a ≠ -c and a@c = 0, then c =

If the operation @ is defined by x @ y = √ x y x @ y = x y − √ for all positive numbers x and y, then (5@45)@60 =

(x + 1 x − 1) 2 If x ≠ 0 and x ≠ 1, and if x is replaced by 1/x everywhere in the expression above, then the resulting expression is equivalent to

If T = 5/9 * (K - 32), and if T = 290, then K =

If y (3 x − 5 2) = y and y ≠ 0 , then x =

Mary's income is 60 percent more than Tim's income, and Tim's income is 40 percent less than Juan's income. What percent of Juan's income is Mary's income?

When 1/10 percent of 5,000 is subtracted from 1/10 of 5,000, the difference is

Which of the following is the value of √ 3 √ 0.000064 − − − − √ 3 − − − − − √

If a = − 0.3 , which of the following is true?

On Saturday morning, Malachi will begin a camping vacation and he will return home at the end of the first day on which it rains. If on the first three days of the vacation the probability of rain on each day is 0.2, what is the probability that Malachi will return home at the end of the day on the following Monday?

The price of lunch for 15 people was $207 including a 15% gratuity for service. What was the average price per person, EXCLUDING the gratuity?

A bar over a sequence of digits in a decimal indicates that the sequence repeats indefinitely. What is the value of (10 4 − 10 2) (0.00 12 ¯ ¯) (10 4 − 10 2) (0.00 12 ¯) ?

In a certain game, a large container is filled with red, yellow, green, and blue beads worth, respectively, 7, 5, 3, and 2 points each. A number of beads are then removed from the container. If the product of the point values of the removed beads is 147,000, how many red beads were removed?

150 is what percent of 30 ?

The average (arithmetic mean) score on a test taken by 10 students was x. If the average score for 5 of the students was 8, what was the average score, in terms of x, for the remaining 5 students who took the test?

The diagram above shows the various paths along which a mouse can travel from point X, where it is released, to point Y, where it is rewarded with a food pellet. How many different paths from X to Y can the mouse take if it goes directly from X to Y without retracing any point along a path?

On the graph above, when x = 1/2, y = 2; and when x = 1, y = 1. The graph is symmetric with respect to the vertical line at x = 2. According to the graph, when x = 3, y =

Circle.png [ 3.73 KiB | Viewed 74313 times ] The circle with center C shown above is tangent to both axes. If the distance from O to C is equal to k, what is the radius of the circle, in terms of k ?

Each • in the mileage table above represents an entry indicating the distance between a pair of the five cities. If the table were extended to represent the distances between all pairs of 30 cities and each distance were to be represented by only one entry, how many entries would the table then have?

Angles.png [ 9.95 KiB | Viewed 50676 times ] In the figure above, if z = 50, then x + y =