Question

If $n$ is a positive integer and $k=5.1\times {10}^n$, what is the value of $k$?
(1) $6,000<k<500,000$
(2) $k^2=2.601\times {10}^9$

• 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 D Each statement alone is sufficient.

Given that , where n is a positive integer, then the value of k must follow the pattern shown in the table.

1. Given that 6000 < k < 500000, then k must have the value 51,000, and so n = 4; SUFFICIENT.
2. Given that , then = 51000, and so n = 4; SUFFICIENT.

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