Prime Numbers

Is X, a prime number, equal to 41?

1. X = A^2 + 5, where A is an integer
2. X^2 > 1,000

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

Without further information, we cannot definitively answer the question. Statement 1 alone is not sufficient to answer the question. Statement 2 tells us that X^2 > 1,000. This means that X > 32 or X < -32.

For example, if X = -33, then X^2 = 1,089, which is greater than 1,000. This gives us a range for r but not a single value of X. Both statements together provide us with no additional information.

Correct Answer - Choice E