Is x + 1 a Factor of 12? GMAT Data Sufficiency

Question: Is x + 1 a factor of 12?

1. x + 1 is even
2. x + 1 is a factor of 2 and 3

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.

Correct Answer: B
Approach Solution 1:
S1: x + 1 is even
Clearly this statement is insufficient, x + 1 could be 2 or 30
S2: x + 1 is a factor of 2 and 3
2 and 3 are consecutive integers, consecutive integers are co-prime, which means that they do not share any common factor but 1 (for example 5 and 6, two consecutive integers share only one common factor: 1)
So as x + 1 is a factor of both 2 and 3 then x + 1 = 1 and 1 is a factor of 12
Hence sufficient

Approach Solution 2:
S1: If x + 1 is even
x + 1 could be 2 in which case answer is yes
x + 1 could be 14 in which case answer is no
Hence this statement is not sufficient
S2: x + 1 could only be 1, 2, or 3 each of which is a factor of 12. So answer is yes
Hence this statement is sufficient

Approach Solution 3:
Statement I: If x + 1 is even
Hence, statement 1 is insufficient since x + 1 = 8, x + 1 = 4
Statement II x + 1 is a factor of 2 and 3.
Statement 2 is sufficient If x + 1 is a factor of 2 and 3 it has to be equal to 1. Hence x + 1 is a factor of 12.

“Is x + 1 a factor of 12?”- 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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