Question

On the number line above, p, q, r, s, and t are five consecutive even integers in increasing order. What is the average (arithmetic mean) of these five integers?
(1) $q+5=24$
(2) The average (arithmetic mean) of q and r is 11.

• A. Statement (1) alone is sufficient, but statement (2) alone is not sufficient.
• B. Statement (2) alone is sufficient, but statement (1) alone is not sufficient.
• C. Both statements together are sufficient, but neither statement alone is sufficient.
• D. Each statement alone is sufficient.
• E. Statements (1) and (2) together are not sufficient.

Answer 1

Answer: (D)

Each statement alone is sufficient.

Since p, q, r, s, and t are consecutive even integers listed in numerical order, the 5 integers can also be given as p, p + 2, p + 4, p + 6, and p + 8. Determine the average of these 5 integers, which is the value of .

1. Given that q + s = 24, then (p + 2) + (p + 6) = 24. Therefore, 2p + 8 = 24, or p = 8, and hence p + 4 = 12; SUFFICIENT.
2. Given that , then q + r = 2 * 11 = 22, or (p + 2) + (p + 4) = 22. Therefore, 2p + 6 = 22, or p = 8, and hence p + 4 = 12; SUFFICIENT.

• The correct answer is D; each statement alone is sufficient.