Question

What is the tenths digit in the decimal representation of a certain number?
(1) The number is less than $\frac{1}{3}$.
(2) The number is greater than $\frac{1}{4}$

• 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.

1. Since the number is less than , the tenths digit can be $0,1,2,$ or $3$; Thus, statement 1 is insufficient.
2. Since the number is greater than , the tenths digit can be $2,3,4,...,9.$ Thus, statement 2 is insufficient.
3. From (1) and (2) taken together, the number, n, is greater than but less than . The tenths digit can be $2$ or $3$. Thus, statements (1) and (2) together are not sufficient.