Given that n is an integer, is n – 1 divisible by 3? GMAT Data Sufficiency

Question: Given that n is an integer, is n – 1 divisible by 3?

1. is not divisible by 3
2. , where k is positive multiple of 3

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. Statements (1) and (2) TOGETHER are NOT sufficient.

Answer: A

Approach Solution (1):
1. is not divisible by 3 --- n(n + 1) is not divisible by 3 --- neither n nor n + 1 is divisible by 3. Now, n – 1, n, and n + 1 are three consecutive integers, thus one of them must be divisible by 3, so if n and n + 1 are not, then n – 1 must be.
Sufficient
2. , where k is a positive multiple of 3.
Not sufficient
Correct option: A

Approach Solution (2):
1. Neither n nor n + 1 are divisible by 3. Thus, n – 1 must be divisible by 3, since every 3^rd integer is divisible by 3.
Sufficient
2. 

Because we know k is divisible by 3, but not 9 (3*3), n – 1 could or could not be divisible by 3.
Not sufficient
Correct option: A

Approach Solution (3):
(1) states thatis not divisible by 3
Or, n (n + 1) is not divisible by 3
Thus, neither “n” nor “n + 1” is a multiple of 3
Since every 3^rd integer on the number line is a multiple of 3, this means that “n + 2” is a multiple of 3. And, again since every 3^rd number is a multiple of 3, (n + 2) – 3 or “n – 1” is a multiple of 3
Sufficient
(2) is an inequality. Even if it said:
n – 1 > a multiple of 3
It would still be insufficient because you can be greater than a multiple of 3 (or a non-multiple of 3) with or without being a multiple of 3 yourself.
Insufficient
Correct option: A

“Given that n is an integer, is n – 1 divisible by 3?”- 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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