Question

If x is an integer, is $9^x+9^{-x}=b$?
(1) $3^x+3^{-x}=\sqrt{b+2}$
(2) $x>0$

• 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 A Statement (1) alone is sufficient, but statement (2) alone is not sufficient.

• From statement 1, . Squaring both sides gives .
  

.

(property of exponents).

Now, ; subtract 2 from both sides; SUFFICIENT.

Statement 2 gives no information about the relationship between x and b; NOT sufficient.

• The correct answer is A; statement 1 alone is sufficient