Question

What is the value of n in the list above?
(1) k < n
(2) The median of the numbers in the list is 10.

• 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

The correct option is C Both statements together are sufficient, but neither statement alone is sufficient.

Given the list k, n, 12, 6, 17, determine the value of n.

1. Although k < n, no information is given about the value of k or n; NOT sufficient.
2. Since the median of the numbers in the list is 10 and there are 5 numbers in the list, 10 is one of those 5 numbers. Therefore, n = 10 or k = 10. If n = 10, then the value of n has been determined. However, if k = 10, then n can be any number that is 10 or less, so the value of n cannot be determined; NOT sufficient.

• Taking (1) and (2) together, if k < n and the median of the list is 10, then 12 and 17 are to the right of the median and the list in ascending order is either 6, k, n, 12, 17 or k, 6, n, 12, 17. In either case, n is the middle number, and since the median is 10, n = 10.
• The correct answer is C; both statements together are sufficient.