Unable to understand Data Sufficiency question.

[Uva@90]

Hi All,
I have basic problem in understanding the Data Sufficiency problem. I have given example below,

If n is a positive integer, is x+5 even?
1) x=n+1
2) n=13

In the above mentioned problem what should I infer whether x+5 is even from option 1 & 2 or whether option 1& 2 helps to find whether x+5 is even or odd ?

Please help me with this.

Thanks in advance.
Regards,
Uva.

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Hi Uva@90,

Data Sufficiency questions are a test of your ability to determine if information is enough to prove that a question can be answered (and that there's JUST ONE answer, as opposed to different answers).

In the case of this question, we're asked "Is X + 5 even?" This is what's called a YES/NO question, so you're looking to prove if the answer to the question is consistent (always YES or always NO) or if it changes (sometimes YES, sometimes NO). We also know from the prompt that N is a positive integer.

Fact 1 tells us that X = N + 1, so let's TEST IT.

If N = 1, then X = 2 and X + 5 = 7. Is that even? NO
If N = 2, then X = 3 and X + 5 = 8. Is that even? YES

Notice how the answers change? That means that Fact 1 is INSUFFICIENT to answer the question

Fact 2 tells us that N = 13, but doesn't tell us anything about X

If X = 1, then X + 5 IS even....YES
If X = 2, then X + 5 is NOT even...NO

The answers change, so Fact 2 is INSUFFICIENT to answer the question.

No you combine Facts...
Since N = 13, then X = 14 and X + 5 = 19. Is that even? NO.
Notice how there's JUST ONE ANSWER. It can only be NO. Thus, you have enough Data to answer the question.

Final answer: C (each Fact is insufficient on it's own, but together the Facts are sufficient)

GMAT assassins aren't born, they're made,
Rich

[Uva@90]

Thanks Rich for explaining so clearly.