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Math Expert V
Joined: 02 Sep 2009
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If n is an integer, is n + 1 odd?  [#permalink]

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Difficulty:   5% (low)

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The Official Guide for GMAT® Review, 13th Edition - Quantitative Questions Project

If n is an integer, is n + 1 odd?

(1) n + 2 is an even integer.
(2) n -1 is an odd integer.

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Question: 7
Page: 275
Difficulty: 550

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Math Expert V
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Re: If n is an integer, is n + 1 odd?  [#permalink]

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5
2
SOLUTION

If n is an integer, is n + 1 odd?

In order $$n+1$$ to be odd, $$n$$ must be even. So, the question basically asks whether $$n$$ is an even number.

(1) n + 2 is an even integer --> $$n+2=even$$ --> $$n=even-2=even$$. Sufficient.
(2) n -1 is an odd integer --> $$n-1=odd$$ --> $$n=odd+1=even$$. Sufficient.

Answer: D.
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Re: If n is an integer, is n + 1 odd?  [#permalink]

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1
A. N, N+1, N+2. If N+2 is even, then N+1 is odd
Sufficient

B. N-1, N, N+1. If N-1 is odd, then N+1 is odd.
Sufficient

Intern  Joined: 26 Jun 2012
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Re: If n is an integer, is n + 1 odd?  [#permalink]

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1
The following Rules will be handy in order to solve this question:

Even Number (+/-) Odd Number = Odd Number------->(a)
Even Number (+/-) Even Number = Even Number------>(b)
Odd Number (+/-) Odd Number = Even Number.------->(c)

Now coming to the question stem: is N + 1 = Odd. From the question stem itself we know that 1 is an odd number and that the result is odd. From equation (a) above we know that this is only possible when n is even. So, the question is actually asking as if n is even?

Statement (1): n + 2`= Even. "2" as we know is even so this result is only possible if n is even (b). SUFFICIENT

Statement (2): n- 1 = Odd. "1" is an Odd Number. This result is only possible if n is even (b). SUFFICIENT

Ans (D)
Math Expert V
Joined: 02 Sep 2009
Posts: 55150
Re: If n is an integer, is n + 1 odd?  [#permalink]

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1
SOLUTION

If n is an integer, is n + 1 odd?

In order $$n+1$$ to be odd, $$n$$ must be even. So, the question basically asks whether $$n$$ is an even number.

(1) n + 2 is an even integer --> $$n+2=even$$ --> $$n=even-2=even$$. Sufficient.
(2) n -1 is an odd integer --> $$n-1=odd$$ --> $$n=odd+1=even$$. Sufficient.

Answer: D.
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Re: If n is an integer, is n + 1 odd?  [#permalink]

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statement 1 :n+2=even, n=even, n+1 == odd, sufficient
Statement 2; n-1=odd,n=even, n+1 == odd, sufficient

hence D
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Re: If n is an integer, is n + 1 odd?  [#permalink]

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Bunuel wrote:
The Official Guide for GMAT® Review, 13th Edition - Quantitative Questions Project

If n is an integer, is n + 1 odd?

(1) n + 2 is an even integer.
(2) n -1 is an odd integer.

We need to determine whether n + 1 is odd. Remember, if n is even, then n + 1 will be odd, and if n is odd, n + 1 will be even.

Statement One Alone:

n + 2 is an even integer.

Statement one tells us that n is an even integer (since 2 more than an even integer is also an even integer). Because n is an even integer, we know that n + 1 is odd. Statement one is sufficient to answer the question. We can eliminate answer choices B, C, and E.

Statement Two Alone:

n – 1 is an odd integer.

Since subtraction rules for even and odd integers are the same as addition rules for even and odd integers, we know that if n – 1 is odd, then n itself must be even, and hence n + 1 must also be odd. Statement two is sufficient to answer the question.

Answer: D
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GRE 1: Q169 V154 Re: If n is an integer, is n + 1 odd?  [#permalink]

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Here is my solution->
Some Basic Rules before we attempt this Even/odd Question

Even+Even=Even
Even+Odd=Odd
Odd+Even=Odd
Odd+Odd=Even

Similarly

Even-Even=Even
Even-Odd=Odd
Odd-Even=Odd
Odd-Odd=Even

The Question is asking us whether n+1 is odd or not
n+1 will be odd only when n is even.
Hence question can be rephrased into "is n even"
Statement 1
n+2 is even => n=even -2 => even
Hence sufficient
Statement 2
n-1=odd
Hence n=odd+1=> even

hence sufficient
Hence D

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Re: If n is an integer, is n + 1 odd?  [#permalink]

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Top Contributor
Bunuel wrote:
The Official Guide for GMAT® Review, 13th Edition - Quantitative Questions Project

If n is an integer, is n + 1 odd?

(1) n + 2 is an even integer.
(2) n -1 is an odd integer.

Target question: Is n + 1 odd?

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

Statement 1: n + 2 is an even integer.
In other words: n + EVEN = EVEN
In other words: n = EVEN - EVEN
By Rule #3, n must be even, which means n+1 is ODD
The answer to the target question is YES, n+1 IS odd
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: n -1 is an odd integer.
In other words: n - ODD = ODD
In other words: n = ODD + ODD
By Rule #1, n must be even, which means n+1 is ODD
The answer to the target question is YES, n+1 IS odd
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: D

Cheers,
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Re: If n is an integer, is n + 1 odd?  [#permalink]

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#1
n+2 even ; n has to be even so n+1 is odd sufficient
#2
n-1 is odd integer ; n = even integer so
n+1 is odd; sufficient
IMO D

Bunuel wrote:
The Official Guide for GMAT® Review, 13th Edition - Quantitative Questions Project

If n is an integer, is n + 1 odd?

(1) n + 2 is an even integer.
(2) n -1 is an odd integer.

Practice Questions
Question: 7
Page: 275
Difficulty: 550

GMAT Club is introducing a new project: The Official Guide for GMAT® Review, 13th Edition - Quantitative Questions Project

Each week we'll be posting several questions from The Official Guide for GMAT® Review, 13th Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project:
1. Please provide your solutions to the questions;
2. Please vote for the best solutions by pressing Kudos button;
3. Please vote for the questions themselves by pressing Kudos button;
4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

Thank you!

_________________
If you liked my solution then please give Kudos. Kudos encourage active discussions. Re: If n is an integer, is n + 1 odd?   [#permalink] 25 Mar 2019, 08:44
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