# Practice GMAT Data Sufficiency Question

Q is less than 10. Is Q a prime number?
1. Q2 - 2 = P; P is prime and P < 10.
2. Q + 2 is NOT prime, but Q is a positive integer.
 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.
1. Evaluate Statement (1) alone.
1. First solve the equation from Statement (1) for P.
Q2 - 2 = P
Q2 = P + 2
Q = Sqrt(P + 2)
2. Since P is a prime less than 10, try the possible values for P.
 P Sqrt(P + 2) 2 2 3 Sqrt(5) 5 Sqrt(7) 7 3
3. As seen in the table, when P = 2 or P = 7, then Q is prime. Otherwise, Q is not a prime number, nor even an integer. Whether Q is prime or not depends on P, so the question cannot be answered.
4. Statement (1) is NOT SUFFICIENT.
2. Evaluate Statement (2) alone.
1. Since Q + 2 is not prime, let L be a number that is not prime, and L = Q + 2. Examine two different examples for L.
2. Let L = 4. This implies that Q = 2, which is a prime number.
3. Let L = 8. This implies that Q = 6, which is not a prime number.
4. Whether Q is prime or not depends on L, so the question cannot be answered.
5. Statement (2) is NOT SUFFICIENT.
3. Evaluate Statement (1) and (2) together.
1. From the table above, only two values of P allow for Q to be an integer--which is demanded in Statement (2). In particular, when P = 2, Q = 2 and when P = 7, Q = 3.
2. So far, there are only two possibilities for values of Q. Now apply Statement (2). Q + 2 may not be a prime number. Thus, the case where Q = 3 is no longer a possibility because Q + 2 = 5, which is a prime number.
3. The only possibility that remains after applying Statements (1) and (2) is Q = 2. Thus, Q is a prime number.
4. Statement (1) and (2) together are SUFFICIENT.
4. Since Statement (1) alone is NOT SUFFICIENT and Statement (2) alone is NOT SUFFICIENT yet Statements (1) and (2), when taken together, are SUFFICIENT, answer C is correct.