Question

The range of the numbers in set S is x, and the range of the numbers in set T is y. If all of the numbers in set T are also in set S, is x greater than y?
(1) Set S consists of 7 numbers.
(2) Set T consists of 6 numbers.

• 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 E Statements (1) and (2) together are not sufficient.

Set S has a range of x, set T has a range of y, and T is a subset of S. Determine if x is greater than y.

1. It is given that S contains exactly 7 numbers, but nothing additional is known about T. Thus, if S = {1, 2, 3, 4, 5, 6, 7} and T = {1, 2, 3, 4, 5, 6}, then x = 7 − 1 = 6, y = 6 − 1 = 5, and x is greater than y. On the other hand, if S = {1, 2, 3, 4, 5, 6, 7} and T = {1, 3, 4, 5, 6, 7}, then x = 7 − 1 = 6, y = 7 − 1 = 6, and x is not greater than y; NOT sufficient.
2. It is given that T contains exactly 6 numbers, but nothing additional is known about T. Since the same examples given in (1) can also be used in (2), it cannot be determined if x is greater than y; NOT sufficient.

• Taking (1) and (2) together, the examples used in (1) can be used to show that it cannot be determined if x is greater than y. The correct answer is E; both statements together are still not sufficient.