Is n an Even Number GMAT Data Sufficiency

Question: Is n an even number?

1) n(n+1)is an even number
2) n(n+2)is an even number

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.

“Is n an even number” - is a topic of the GMAT Quantitative reasoning section of GMAT. GMAT Data Sufficiency questions come up with a problem statement that is heeded by two series of factual statements. The GMAT Quant section of the GMAT exam includes 31 MCQs that need to be finished in 62 minutes. This particular GMAT data sufficiency question checks the candidate’s level of skill and knowledge. A conceptual problem-solving question is presented and the tough portion mainly arises from the clever wording of the question that candidates generally miss. GMAT data sufficiency consists mainly of 15 questions which are two-fifths of the sum of 31 GMAT quant questions.

Solution and Explanation:

Approach Solution 1:

1. The statement states that n (n+1) is an even number.

Therefore, we can say that n (n+1) = even
Hence, n (n+1) is always even.
So the value of n can be either odd or even.
Therefore the statement alone is not sufficient since we cannot ensure the value of n is odd or even.

2. This statement suggests that n (n+ 2) is an even number.

It can be implied that n (n+2) = even only if the value of n is equal to even.
Since the product of an odd number and an odd number is always equal to odd (if the value of n is equal to odd)
Therefore, the value of n (n+2) is obviously even proved.
Hence statement (2) alone is sufficient to make sure the value of n is even.

Correct Answer: B

Approach Solution 2:

1. As per the given statement n (n+1) is an even number.

Case 1: if the value of n is equal to 1 that is an odd number, then we will get,
1(1+ 1) = 1∗2 = 2 which is an even number

Case 2: if the value of n is equal to 2 which is an even number, then we will get,
2(2+1) = 2∗3 = 6 which is an even number,

Therefore, the value of n may be either odd or even. The obvious answer of n cannot be derived from this given statement. Hence the statement alone is not sufficient.

2. According to the statement n (n+2) is an even number.

Case 1: if the value of n is equal to 1 which is an odd number, then we will get,
1(1+2) = 1∗3 = 3 is not an even number.
Therefore, this case is irrelevant as it does not satisfy the given statement.

Case 2: if the value of n is equal to 2 which is an even number, then we will get
2(2+2) = 2∗4 = 8 is an even number.
Therefore, case 2 is justified to prove the argument of statement 2.
Hence the value of n can only be an even number.

Thus statement two alone is sufficient to prove the value of n as an even number.

Correct Answer: B

Approach Solution 3:

1. The statement implies that n(n+1) is an even number

This implies that the value of n can either be odd or even.
Since the product of an odd number and the even number is equal to an even number.
Further, we can say, the product of an even number and an odd number is equal to an even number.
Therefore, the value of n cannot be derived from this given statement. It has been analysed from the statement that the value of n can either be odd or even. Hence statement one alone is not sufficient.

2. The statement cites that n(n+2) is an even number.

If the value of n is an odd number, then the value of n(n+2) will also be an odd number.
If the value of n is an even number, then the value of n(n+2) will also be an even number.

Therefore, the value of n should definitely be an even number.
Hence statement two alone is sufficient.

Correct Answer: B

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