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If n is a positive integer, is n odd?

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Bunuel
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If n is a positive integer, is n odd? [#permalink] If n is a positive integer, is n odd?   14 Jul 2014, 03:38
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If n is a positive integer, is n odd?

(1) 3n is odd.
(2) n + 3 is even.
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D
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BrentGMATPrepNow
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Re: If n is a positive integer, is n odd? [#permalink] If n is a positive integer, is n odd?   13 Dec 2019, 12:43
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Bunuel wrote:

GMAT weekly questions



If n is a positive integer, is n odd?

(1) 3n is odd.
(2) n + 3 is even.


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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Bunuel
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Re: If n is a positive integer, is n odd? [#permalink] If n is a positive integer, is n odd?   14 Jul 2014, 03:39
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Bunuel wrote:

GMAT weekly questions



If n is a positive integer, is n odd?

(1) 3n is odd.
(2) n + 3 is even.


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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Re: If n is a positive integer, is n odd? [#permalink] If n is a positive integer, is n odd?   12 Aug 2020, 22:38
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Bunuel wrote:

GMAT weekly questions



If n is a positive integer, is n odd?

(1) 3n is odd.
(2) n + 3 is even.



(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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Re: If n is a positive integer, is n odd? [#permalink] If n is a positive integer, is n odd?   13 Aug 2020, 11:31
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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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If n is a positive integer, is n odd? [#permalink] If n is a positive integer, is n odd?   Updated on: 04 Jan 2024, 23:43
If n is a positive integer, is n odd?

(1) 3n is odd.

(2) n + 3 is even.


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 more than any even number is an odd number. Either (1) or (2), taken separately, is sufficient to answer the question.

When I test (1) - I tried 3(4) = 12, which is even, therefore it is not odd / not sufficient.
When I test (2) - I tried 4 + 3 = 7, which is odd, therefore it is not odd / not sufficient.

This contradicts the solution and I am extremely confused.

Originally posted by danielpincente on 04 Jan 2024, 19:37.
Last edited by Bunuel on 04 Jan 2024, 23:43, edited 3 times in total.
Formatted the question
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Re: Help please - quant DS question [#permalink] If n is a positive integer, is n odd?   04 Jan 2024, 20:04
Statement 1 says 3n is ODD. 3(4) is even. 3(3) is odd. This statement one is sufficient

Statement 2 says 3+n is EVEN. 3+7= 10 (even. Statement 2 is sufficient.
I think you confused what the results of each statement said.

Posted from my mobile device
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Re: Help please - quant DS question [#permalink] If n is a positive integer, is n odd?   04 Jan 2024, 20:29
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danielpincente wrote:
Question:

If n is a positive integer, is n odd?

(1) 3n is odd.

(2) n + 3 is even.

When I test (1) - I tried 3(4) = 12, which is even, therefore it is not odd / not sufficient.
When I test (2) - I tried 4 + 3 = 7, which is odd, therefore it is not odd / not sufficient.

This contradicts the solution and I am extremely confused.


You are testing n as 4 or even, and it gives you the opposite answer. This means n is not even, and should be sufficient.

1) 3n is odd.
3*n = odd. For a product to be odd, both the integer should be odd. This n is odd.
Sufficient

2) n+3 is even.
Sum of two numbers is even when both are even or both are odd. Here one is given as 3, so n should also be odd.
Sufficient

D

What is the contradiction you are finding.
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Re: If n is a positive integer, is n odd? [#permalink] If n is a positive integer, is n odd?   05 Jan 2024, 07:37
danielpincente wrote:
If n is a positive integer, is n odd?

(1) 3n is odd.

(2) n + 3 is even.


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 more than any even number is an odd number. Either (1) or (2), taken separately, is sufficient to answer the question.

When I test (1) - I tried 3(4) = 12, which is even, therefore it is not odd / not sufficient.
When I test (2) - I tried 4 + 3 = 7, which is odd, therefore it is not odd / not sufficient.

This contradicts the solution and I am extremely confused.



We know that n is a positive integer

Stmt 1: 3n is odd.
Product of 2 odd numbers is odd, If the product is odd then both the numbers has to be odd.
Hence n is odd.

Statement 1 lone is sufficient.



Stmt 2: n + 3 is even.
o + o = e
e + e = e

Moreover we can consider n+3 = 2k,
So n = 2k - 3
=> n = 2(k-2) + 1
=> n = 2l+1 [If n has to be positive l >0]

Hence n is odd.

Statement 2 alone is also sufficient.

IMO D.
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Re: If n is a positive integer, is n odd? [#permalink]
05 Jan 2024, 07:37
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