The sum of the integers in list S is the same as the sum of the integers in list T. Does S contain more integers than T ?

(1) The average (arithmetic mean) of the integers in S is less than the average of the integers in T.

(2) The median of the integers in S is greater than the median of the integers in T.

Three boxes of supplies have an average (arithmetic mean) weight of 7 kilograms and a median weight of 9 kilograms.  What is the maximum possible weight, in kilograms, of the lightest box?

If x is a positive integer, what is the least common multiple of x, 6, and 9 ?

(1) The least common multiple of x and 6 is 30.

(2) The least common multiple of x and 9 is 45.

In a class of 30 students, 2 students did not borrow any books from the library, 12 students each borrowed 1 book, 10 students each borrowed 2 books, and the rest of the students each borrowed at least 3 books.  If the average (arithmetic mean) number of books borrowed per student was 2, what is the maximum number of books that any single student could have borrowed?

If $1,000 is deposited in a certain bank account and remains in the account along with any accumulated interest, the dollar
amount of interest, I, earned by the deposit in the first n years is given by the formula \(I = 1000((1 + (r/100))^{n-1})\), where r
percent is the annual interest rate paid by the bank. Is the annual interest rate paid by the bank greater than 8 percent?

(1) The deposit earns a total of $210 in interest in the first two years.

(2) \((1+(r/100))^2 > 1.15\)

Each of the 25 balls in a certain box is either red, blue, or white and has a number from 1 to 10 painted on it. If one ball is to be selected at random from the box, what is the probability that the ball selected will either be white or have an even number painted on it?

(1) The probability that the ball will both be white and have an even number painted on it is 0.

(2) The probability that the ball will be white minus the probability that the ball will have an even number painted on it is 0.2.

A basket contains 5 apples, of which 1 is spoiled and the rest are good.  If Henry is to select 2 apples from the basket simultaneously and at random, what is the probability that the 2 apples selected will include the spoiled apple?

For which of the following functions f is \(f(x) = f(1 – x)\) for all x?

In the xy-plane, what is the y-intercept of line l?

(1) The slope of line l is 3 times its y-intercept.

(2) The x-intercept of line l is -1/3

Did it take Pei more than 2 hours to walk a distance of 10 miles along a certain trail? (1 mile = 1.6 kilometers, rounded to the nearest tenth.)

(1) Pei walked this distance at an average rate of less than 6.4 kilometers per hour.

(2) On average, it took Pei more than 9 minutes per kilometer to walk this distance.

The perimeter of a certain isosceles right triangle is16+16√2. What is the length of the hypotenuse of the triangle?

To furnish a room in a model home, an interior decorator is to select 2 chairs and 2 tables from a collection of chairs and tables in a warehouse that are all different from each other.  If there are 5 chairs in the warehouse and if 150 different combinations are possible, how many tables are in the warehouse?

If a, b, k, and m are positive integers, is \(a^k\) a factor of \(b^m\)?

(1) a is a factor of b.

(2) k ≤ m

If m, r, x, and y are positive, is the ratio of m to r equal to the ratio of x to y ?

(1) The ratio of m to y is equal to the ratio of x to r.

(2) The ratio of m + x to r + y is equal to the ratio of x to y.

In a certain board game, a stack of 48 cards, 8 of which represent shares of stock, are shuffled and then placed face down.  If the first 2 cards selected do not represent shares of stock, what is the probability that the third card selected will represent a share of stock?

7.51 8.22 7.86 8.36
8.09 7.83 8.30 8.01
7.73 8.25 7.96 8.53

A vending machine is designed to dispense 8 ounces of coffee into a cup.  After a test that recorded the number of ounces of coffee in each of 1,000 cups dispensed by the vending machine, the 12 listed amounts, in ounces, were selected from the data.  If the 1,000 recorded amounts have a mean of 8.1 ounces and a standard deviation of 0.3 ounce, how many of the 12 listed amounts are within 1.5 standard deviations of the mean?

If the probability that event S will not occur is 1 – y, then the probability that event S will occur is

Each employee on a certain task force is either a manager or a director. What percent of the employees on the task force are directors?

(1) The average (arithmetic mean) salary of the managers on the task force is $5,000 less than the average salary of all employees on the task force.

(2) The average (arithmetic mean) salary of the directors on the task force is $15,000 greater than the average salary of all employees on the task force.

Committee X has 4 members, committee Y has 5 members, and these committees have no members in common.  If a task force is to be formed consisting of one member of X and one member of Y, how many different task forces are possible?

In the xy-plane, line k has positive slope and x-intercept 4.  If the area of the triangle formed by line k and the two axes is 12, what is the y-intercept of line k ?