Question

What is the sum of a certain pair of consecutive odd integers?
(1) At least one of the integers is negative.
(2) At least one of the integers is positive.

• 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.

• It is given that at least one of the integers is negative. So, the sum could be −4 supposing the integers were −3 and −1 and the sum could be 0 if the integers were −1 and 1. Thus, statement 1 is not sufficient.
• From statement 2, it is given that at least one of the integers is positive. So, the sum could be 0 (if the integers were −1 and 1) and the sum could be 4 (if the integers were 1 and 3); Thus, statement 2 is not sufficient.
• Considering both the statements together, the smaller of the two numbers cannot be less than −1 and the larger of the two numbers cannot be greater than 1. Therefore, the integers must be −1 and 1, and the sum must be 0. Thus, both are statements are together sufficient.