Practice GMAT Data Sufficiency Question

What is the value of xn – ny – nz?

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)	Statement (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.

Correct Answer: C

Factor the original equation:
xn – ny – nz = n(x - y - z)
If we know the value of both n and x - y - z, we can determine the value of xn – ny – nz.
Evaluate Statement (1) alone.
1. Since x – y – z = 10, based upon the above factoring:
  xn – ny – nz = n(10)
  However, we do not know the value of n so we cannot solve for the value of xn – ny – nz.
2. Statement (1) is NOT SUFFICIENT.
Evaluate Statement (2) alone.
1. Since n = 5, based upon the above factoring:
  xn – ny – nz = 5(x - y - z)
  However, we do not know the value of x - y - z so we cannot solve for the value of xn – ny – nz.
2. Statement (2) is NOT SUFFICIENT.
Evaluate Statements (1) and (2) together.
1. Since n = 5 and x - y - z = 10, based upon the above factoring:
  xn – ny – nz = n(x - y - z)=5(10)=50
2. Statements (1) and (2), when taken together, are SUFFICIENT.
Since Statement (1) alone is NOT SUFFICIENT and Statement (2) alone is NOT SUFFICIENT, but Statements (1) and (2), when taken together, are SUFFICIENT, answer C is correct.