Q13:

An integer greater than 1 that is not prime is called composite.  If the two-digit integer n is greater than 20, is n composite?

(1)       The tens digit of n is a factor of the units digit of n.

(2)       The tens digit of n is 2.

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.

Choose A.

(1) is sufficient. Because n is greater than 20, the tens digit of n cannot be 1, but can only be 2, 3, ... If the tens digit of n is a factor of the units digit of n, then n can be divided by the tens digit. Because 1 is excluded, n can be divided by 2, 3, ..., which is the tens digit number.

(2) is not sufficient. Think about 21 and 23.