If a coin has an equal probability of landing heads up or tails up each time it is flipped, what is the probability that the coin will land heads up exactly twice in 3 consecutive flips?

Is the positive integer n odd?

(1) n = 2k + 1, where k is a positive integer.

(2) 2n + 1 is an odd integer.

A certain bakery has 6 employees. It pays annual salaries of $14,000 to each of 2 employees, $16,000 to 1 employee, and $17,000 to each of the remaining 3 employees. The average (arithmetic mean) annual salary of these employees is closest to which of the following?

If x is equal to the sum of the even integers from 40 to 60, inclusive, and y is the number of even integers from 40 to 60, inclusive, what is the value of x + y ?

A certain movie depicted product A in 21 scenes, product B in 7 scenes, product C in 4 scenes, and product D in 3 scenes. The four product manufacturers paid amounts proportional to the number of scenes in which their product was depicted in the movie. If each manufacturer paid x dollars per scene, how much did the manufacturer of product D pay for this advertising?

(1) The manufacturers of products A and B together paid a total of $560,000 for this advertising.

(2) The manufacturer of product B paid $60,000 more for this advertising than the manufacturer of product C paid.

Is xy + xz = 0 ?

(1) x = 0

(2) y + z = 0

What is the value of the positive integer m ?

(1) When m is divided by 6, the remainder is 3.

(2) When 15 is divided by m, the remainder is 6.

Which of the following is equal to the average (arithmetic mean) of \({(x + 2)}^2\) and \({(x – 2)}^2\)?

The 15 homes in a new development are each to be sold for one of three different prices so that the developer receives an average (arithmetic mean) of $200,000 per home. If 4 of the homes are to be sold for $170,000 each and 5 are to be sold for $200,000 each, what will be the selling price of each of the remaining 6 homes?

Amount Charged | Percent Bonus

$.01 to $1000 .5

$1000.01 to $3000 1.0

$3000.01 to $6000 1.5

$6000.01 to $10000 2.0

At the end of each year, a certain credit card company pays a bonus to each of its credit card holders based on the amount, up to \$10,000, that the cardholder charged throughout the year. A 0.5 percent bonus is paid on the first $1,000 charged, a 1.0 percent bonus is paid on the next $2,000 charged and so on, as indicated in the table above. What is the maximum annual bonus, in dollars?

Is p > r/(\(r^2\)+2)

(1) p = r

(2) r > 0

Of the people who attended a workshop, 60 percent were teachers and some of the teachers were teachers of language arts. What percent of the people who attended the workshop were teachers of language arts?

(1) 200 people attended the workshop.

(2) 72 of the teachers who attended the workshop were not teachers of language arts.

Store S sold a total of 90 copies of a certain book during the seven days of last week, and it sold different numbers of copies on any two of the days. If for the seven days Store S sold the greatest number of copies on Saturday and the second greatest number of copies on Friday, did Store S sell more than 11 copies on Friday?

(1) Last week Store S sold 8 copies of the book on Thursday.

(2) Last week Store S sold 38 copies of the book on Saturday.

The contents of a certain box consist of 14 apples and 23 oranges.  How many oranges must be removed from the box so that 70 percent of the pieces of fruit in the box will be apples?

If \((2^x)(3^y)\) = 288, where x and y are positive integers, then \([2^{(x – 1)}][3^{(y – 2)}] =\)

The mass of 1 cubic meter of a substance is 800 kilograms under certain conditions.  What is the volume, in cubic centimeters, of 1 gram of this substance under these conditions?  (1 kilogram = 1,000 grams and 1 cubic meter = 1,000,000 cubic centimeters)

For any positive integer n, the length of n is defined as the number of prime factors whose product is n.  For example, the length of 75 is 3, since 75 = 3 x 5 x 5.  How many two-digit positive integers have length 6?

Set S consists of five consecutive integers, and set T consists of seven consecutive integers. Is the median of the numbers in set S equal to the median of the numbers in set T ?

(1) The median of the numbers in set S is 0.

(2) The sum of the numbers in set S is equal to the sum of the numbers in set T.

Lisa bought a house for $70,000 and paid closing costs equal to 2 percent of the purchase price. Later Lisa sold the house for $82,000 and paid a broker’s commission equal to 10 percent of the selling price. What was Lisa’s profit from the two transactions?

Sets A, B, and C have some elements in common. If 16 elements are in both A and B, 17 elements are in both A and C, and 18 elements are in both B and C, how many elements do all three of the sets A, B, and C have in common?

(1) Of the 16 elements that are in both A and B, 9 elements are also in C.

(2) A has 25 elements, B has 30 elements, and C has 35 elements.