Statement (1) implies that n is odd, for if n were even, any multiple of n would be even. Therefore, the answer must be A or D.
Statement (2) also implies that n is odd, since 3 less than any even number is an odd number.

Since either (1) or (2), taken separately, is sufficient to answer the question, the best answer is D.
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Given: n is a positive integer

Target question: Is n odd?

Some important rules:
#1. ODD +/- ODD = EVEN
#2. ODD +/- EVEN = ODD
#3. EVEN +/- EVEN = EVEN

#4. (ODD)(ODD) = ODD
#5. (ODD)(EVEN) = EVEN
#6. (EVEN)(EVEN) = EVEN


Statement 1: 3n is odd
Since 3 is ODD, we are told that (ODD)(n) = ODD
From Rule #4 above, we can conclude that n is ODD
The answer to the target question is YES, n IS odd
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: n + 3 is even
in other words, n + ODD = EVEN
From Rule #1 above, we can conclude that n is ODD
The answer to the target question is YES, n IS odd
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: D

Cheers,
Brent
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(1) If 3n is odd- We know that if we multiply any odd number by an odd number the resultant is a odd number.
Therefore n is odd.

(2) n+3 is even- When we add odd number with an odd number the resultant is an odd number.

Therefore D
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Hi all,

if we didn't know the rules mentioned by BrentGMATPrepNow, we could us the trial and error method:

If n is a positive integer, is n odd?

(1) 3n is odd.

n=2 -> 3n = 6 (EVEN)
n=3 -> 3n = 9 (ODD)
n=4 -> 3n = 12 (EVEN)
n=5 -> 3n = 15 (ODD)

It seems when n is ODD, 3n is odd, so if we are given that 3n is odd, we can say that n is odd for sure

SUFFICIENT

(2) n + 3 is even

n=2 -> n + 3 (ODD)
n=3 -> n + 3 (EVEN)
n=4 -> n + 3 (ODD)
n=5 -> n + 3 (EVEN)

It seems when n is ODD, n + 3 is even, so if we are given that n + 3 is even, we can say that n is odd for sure

SUFFICIENT

ANSWER D

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