Question

For any integers x and y, min (x, y) and max (x, y) denote the minimum and the maximum of x and y, respectively. For example, min (5, 2) = 2 and max (5, 2)= 5. For the integer w,what is the value of min (10, w)?
(1) W = max (20, z) for some integer z.
(2) W = max(10, w)

• 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.

If , then min(10,w) = 10, and if w < 10, then min(10,w) = w. Therefore, the value of min(10, w) can be determined if the value of w can be determined.

1. Given that w = max(20,z), then . Hence, , and so min(10,w) = 10; SUFFICIENT.
2. Given that w = max(10,w), then , and so min(10,w) = 10; SUFFICIENT.
   

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