There are 9 keys on a keychain, of which 5 are for exterior locks and 4 are for interior locks. How many possible selections of 5 keys from the keychain contain at least one key for an exterior lock and at least one key for an interior lock?

The ratio of coupons Troy has to coupons Padma has is 9:4. After Troy gives Padma 6 of his coupons, the ratio of coupons Troy has to coupons Padma has will be 8:5. How many more coupons will Troy have than Padma after the 6 coupons are given?

Ms. Li must choose a passcode for her bank account. The passcode is to consist of 4 different digits from 0 to 9 inclusive except the first digit must be odd. How many different combinations for the passcode are there?

What is the median duration of a client engagement, billed in weeks, to the nearest week, at a particular company?

1. Exactly 30 percent of the client engagements last 4 or more weeks.
2. Exactly 40 percent of the client engagements last 2 or fewer weeks.

If by agreement a service department must reply to any customer inquiry within 84 hours, does the last moment by which it must respond to a particular inquiry occur on a Friday?

1. The inquiry was placed on a Tuesday.
2. The inquiry was made between 2:00 p.m. and 4:00 pm.

During a particular trip, how much time had elapsed once 90% of the total distance of the trip had been traveled?

1. The total distance of the trip was 40 miles and the total time elapsed was exactly 4 hours.
2. The average speed of the trip was exactly 10 miles per hour.

The numbers of marbles of each of four different colors in a box are in the ratio 3 to 4 to 6 to 8. If there are 24 marbles of one of the colors, which of the following CANNOT be the total number of marbles in the box?

Producers of jazz albums tend to back artists that they expect will gain popularity in the key European market, or who are popular already.

Carbon dioxide comprises, on average, about 397 parts per million of the Earth's atmosphere, on a molecular basis. In an even sample of the Earth's atmosphere consisting of 4 billion molecules, approximately how many of those molecules would be expected to be carbon dioxide? (1 billion = 1,000,000,000)

If two 2-digit positive integers have their respective tens digits exchanged, the difference between the pair of integers changes by 4. What is the greatest possible difference between the original pair of integers?

There are four cards in a box, each with a different number written on it -- either 1, 3, 4 or 5. What is the probability that the difference between the numbers on two randomly selected cards is not greater than 3?

Is ${10}^x+16$ divisible by 4?

(1) x is a positive prime number

(2) x is an odd number

If xyz ≠ 0, is x⁹y⁴z⁵ > 0?

(1) yz < 0

(2) xz > 0