Practice GMAT Data Sufficiency Question
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Q is less than 10. Is Q a prime number?
- Q2 - 2 = P; P is prime and P < 10.
- Q + 2 is NOT prime, but Q is a positive integer.
Correct Answer: C
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Evaluate Statement (1) alone.
- First solve the equation from Statement (1) for P.
Q2 - 2 = P
Q2 = P + 2
Q = Sqrt(P + 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 |
- 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.
- Statement (1) is NOT SUFFICIENT.
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Evaluate Statement (2) alone.
- 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.
- Let L = 4. This implies that Q = 2, which is a prime number.
- Let L = 8. This implies that Q = 6, which is not a prime number.
- Whether Q is prime or not depends on L, so the question cannot be answered.
- Statement (2) is NOT SUFFICIENT.
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Evaluate Statement (1) and (2) together.
- 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.
- 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.
- The only possibility that remains after applying Statements (1) and (2) is Q = 2. Thus, Q is a prime number.
- Statement (1) and (2) together are SUFFICIENT.
- 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.
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