Question: If x is a positive integer, then is x prime?

1. 3x + 1 is prime
2. 5x + 1 is prime

1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
4. EACH statement ALONE is sufficient.
5. Statements (1) and (2) TOGETHER are NOT sufficient.

Answer:

Solution with Explanation:
Approach Solution (1):

We are given that x is a positive integer and must determine whether x is prime.

Statement 1 Alone:

3x + 1 is prime

Using the information in statement one, x does not necessarily have to be prime. For instance, if x = 2, then 3x + 1 = 7 is prime or if x = 4, then 3x + 1 = 13 is prime. In the former case, x = 2 is prime; however, in the latter case, x = 4 is not prime. Statement one alone is not sufficient to answer the question. We can eliminate answer choices A and D.

Statement 2 Alone:

5x + 1 is prime

Using the information in statement one, x does not necessarily have to be prime. For instance, if x = 2, then 5x + 1 = 11 is prime or if x = 6, then 5x + 1 = 31 is prime. In the former case, x = 2 is prime; however, in the latter case, x = 6 is not prime. Statement two alone is not sufficient to answer the question. We can eliminate answer choices B.

Statement 1 and 2 together:

Using the information from statements 1 and 2, we still cannot determine whether x is prime. For instance, if x = 2, then both 3x + 1 = 7 and 5x + 1 = 11 are prime, or if x = 12, then both 3x + 1 = 37 and 5x + 1 = 61 are prime. In the former case, x = 2 is prime; however, in the latter case, x = 12 is not prime.

Correct Option: E

Approach Solution (2):

There is one variable (x) in the original condition. So we need 1 equation. Since condition 1 and condition 2 each have 1 equation, there is a high chance that D is the correct answer.
The condition 1 has x = 2 yes, x = 6 no not sufficient
The condition 2 has x = 2 yes, x = 6 no not sufficient

Since the condition 1 and the condition 2 have x = 2 yes, x = 6 no not sufficient

Correct Option: E

Approach Solution (3):

x = positive integer

1) 3x + 1 is prime
If 3x + 1 = 7 = prime
x = 2, which is prime
If 3x + 1 = 19 = prime
x = 6, which is not a prime

Not sufficient

2) 5x + 1 is prime
If 5x + 1 = 11 = prime
x = 2, which is prime
If 5x + 1 = 31 = prime
x = 6, which is not a prime

Not sufficient

Combining 1 and 2, we will get:
Still not sufficient

Correct Option: E

“If x is a positive integer, then is x prime?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Quantitative Review". GMAT Quant section consists of a total of 31 questions. GMAT Data Sufficiency questions consist of a problem statement followed by two factual statements. GMAT data sufficiency comprises 15 questions which are two-fifths of the total 31 GMAT quant questions.

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