Two tracks are parallel. The first track has checkpoints and the second one has checkpoints. In how many ways can the checkpoints of first track be joined with the checkpoints of the second to form a triangle?

When 10 is added to a number, the resulting value is the same as the product of 5 with the difference of that number and 18. What is that number?

The terms in the series have the following relation with each other: where is a constant. What is the 5^th term of the series if the 4^th term is and the 7^th term is ?

For some directors, a successful film is marked not so much by box office revenues but instead by critical acclaim garnered through selections at prestigious film festivals.

A sporting goods store has a section that displays baseball caps, and each shelf in the section displays 10 caps. After 16 caps were sold, each shelf was left with 7 caps except for the final shelf, which held 9 caps. How many shelves are in the section displaying baseball caps?

If , then what is the value of ?

What is the value of x + y² ?

(1) x² − x − 2 = 0

(2) y² + y − 2 = 0

Nerve cells are often enclosed in a sheath of myelin, whose functions include containing nerve impulses within the cell and electric signals traveling more quickly.

Mining the ocean floor for gold may someday be worthwhile, but at present, doing so is prohibitively expensive.

A bag has 32 yellow, red, blue and green balls. If one ball is drawn from the bag at random, the probability that it will be green is 0.5, and the probability that it will be blue is 0.25. What is the probability that the ball will be either red or yellow?

A room has length , width , and height . What is the volume of the room?

(1)

(2) and

Is the mean of set greater than its median?

(1) All the elements in are consecutive multiples of .

(2) The sum of all the elements in is .

A set contains eight consecutive integers. What is the product of all the integers?

(1) The greatest integer in the set is 5

(2) The set contains both positive and negative integers

All four vertices of quadrilateral ABCD lie on a circle. What is the measure of ∠BAD?

(1) AC = CD

(2) $\angle \mathrm{ADC}$= $70°$

Is the integer x even?

(1) x³ + x² is even

(2) 3x is divisible by 6

A tank of gas is filled by two valves in 50 minutes. The first valve alone fills the tank in 2 hours, while the second valve can fill 20 cubic feet more gas than the first valve every minute. What is the capacity of the tank?

If is a positive integer, what is the value of ?

(1) is a perfect square

(2)

If x, y, and z are all integers, is xyz odd?

(1) x - 1 is even

(2) $(y-z)(x-z)$ is odd