GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 13 Dec 2018, 01:02

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

## Events & Promotions

###### Events & Promotions in December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
• ### The winning strategy for 700+ on the GMAT

December 13, 2018

December 13, 2018

08:00 AM PST

09:00 AM PST

What people who reach the high 700's do differently? We're going to share insights, tips and strategies from data we collected on over 50,000 students who used examPAL.
• ### GMATbuster's Weekly GMAT Quant Quiz, Tomorrow, Saturday at 9 AM PST

December 14, 2018

December 14, 2018

09:00 AM PST

10:00 AM PST

10 Questions will be posted on the forum and we will post a reply in this Topic with a link to each question. There are prizes for the winners.

# If n is an integer, is n even?

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 51162
If n is an integer, is n even?  [#permalink]

### Show Tags

26 Aug 2012, 02:12
3
5
00:00

Difficulty:

5% (low)

Question Stats:

85% (01:04) correct 15% (01:16) wrong based on 1688 sessions

### HideShow timer Statistics

If n is an integer, is n even?

(1) n^2 - 1 is an odd integer.
(2) 3n + 4 is an even integer.

Practice Questions
Question: 27
Page: 277
Difficulty: 600

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 51162
Re: If n is an integer, is n even?  [#permalink]

### Show Tags

26 Aug 2012, 02:13
5
5
SOLUTION:

If n is an integer, is n even?

(1) n^2 - 1 is an odd integer --> $$n^2-1=odd$$ --> $$n^2=odd+1=even$$. Now, since $$n$$ is an integer, then in order $$n^2$$ to be even $$n$$ must be even. Sufficient.
Notice that if we were not told that $$n$$ is an integer, then $$n$$ could be some irrational number (square root of an even number), for example $$\sqrt{2}$$, so not an even integer.

(2) 3n + 4 is an even integer --> $$3n + 4=even$$ --> $$3n=even-4=even$$. The same here, since $$n$$ is an integer, then in order $$3n$$ to be even $$n$$ must be even. Sufficient.
Notice that if we were not told that $$n$$ is an integer, then $$n$$ could be some fraction, for example $$\frac{2}{3}$$, so not an even integer.

_________________
##### General Discussion
Intern
Affiliations: CA, SAP FICO
Joined: 22 Nov 2012
Posts: 35
Location: India
Concentration: Finance, Sustainability
GMAT 1: 620 Q42 V33
GMAT 2: 720 Q47 V41
GPA: 3.2
WE: Corporate Finance (Energy and Utilities)
Re: If n is an integer, is n even?  [#permalink]

### Show Tags

16 Mar 2014, 17:55
Bunuel wrote:
SOLUTION:

If n is an integer, is n even?

(1) n^2 - 1 is an odd integer --> $$n^2-1=odd$$ --> $$n^2=odd+1=even$$. Now, since $$n$$ is an integer, then in order $$n^2$$ to be even $$n$$ must be even. Sufficient.
Notice that if we were not told that $$n$$ is an integer, then $$n$$ could be some irrational number (square root of an even number), for example $$\sqrt{2}$$, so not an even integer.

(2) 3n + 4 is an even integer --> $$3n + 4=even$$ --> $$3n=even-4=even$$. The same here, since $$n$$ is an integer, then in order $$3n$$ to be even $$n$$ must be even. Sufficient.
Notice that if we were not told that $$n$$ is an integer, then $$n$$ could be some fraction, for example $$\frac{2}{3}$$, so not an even integer.

Since n is a integer, can we not try with n as 0?
Math Expert
Joined: 02 Sep 2009
Posts: 51162
Re: If n is an integer, is n even?  [#permalink]

### Show Tags

16 Mar 2014, 22:45
X017in wrote:
Bunuel wrote:
SOLUTION:

If n is an integer, is n even?

(1) n^2 - 1 is an odd integer --> $$n^2-1=odd$$ --> $$n^2=odd+1=even$$. Now, since $$n$$ is an integer, then in order $$n^2$$ to be even $$n$$ must be even. Sufficient.
Notice that if we were not told that $$n$$ is an integer, then $$n$$ could be some irrational number (square root of an even number), for example $$\sqrt{2}$$, so not an even integer.

(2) 3n + 4 is an even integer --> $$3n + 4=even$$ --> $$3n=even-4=even$$. The same here, since $$n$$ is an integer, then in order $$3n$$ to be even $$n$$ must be even. Sufficient.
Notice that if we were not told that $$n$$ is an integer, then $$n$$ could be some fraction, for example $$\frac{2}{3}$$, so not an even integer.

Since n is a integer, can we not try with n as 0?

Yes, n can be 0 but 0 is even too.
_________________
Senior Manager
Joined: 20 Aug 2015
Posts: 390
Location: India
GMAT 1: 760 Q50 V44
Re: If n is an integer, is n even?  [#permalink]

### Show Tags

08 Dec 2015, 23:06
Bunuel wrote:
If n is an integer, is n even?

(1) n^2 - 1 is an odd integer.
(2) 3n + 4 is an even integer.

Given: n is an integer
Required: is n even?

Statement 1: $$n^2$$ - 1 is an odd integer
$$n^2$$ - 1 = (n-1)(n+1) = odd.
This means both n-1 and n+1 are odd
Odd*Odd = Odd
Odd*Even = Even
Even*Even = Even

n-1, n, n+1 are three consecutive integers.
Since we know that both n-1 and n+1 are odd
Hence n has to be even.

SUFFICIENT

Statement 2: 3n + 4 is an even integer
Even + Even = Even
Even + Odd = Odd
Odd + Odd + Odd

Since 3n+4 = even and 4 is an even integer.
Hence 3n = even. Therefore n = even
SUFFICIENT

Option D
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 4294
Location: United States (CA)
Re: If n is an integer, is n even?  [#permalink]

### Show Tags

09 Aug 2016, 12:33
1
Quote:
If n is an integer, is n even?

(1) n^2 - 1 is an odd integer.
(2) 3n + 4 is an even integer.

We need to determine whether integer n is even. Let's review four facts about even and odd integers: 1) An integer and its square are either both even or both odd. 2) The sum (or difference) between an even integer and an odd integer is always odd. 3) The sum of two even integers (or two odd integers) is always even. 4) If the product of two integers is even, at least one of them must be even.

Statement One Alone:

(n^2) - 1 is an odd integer.

Since (n^2) - 1 is an odd integer, we know that n^2 must be even and thus n must be even. Statement one is sufficient to answer the question. We can eliminate answer choices B, C, and E.

Statement Two Alone:

3n + 4 is an even integer.

Since 3n + even = even integer, we know that 3n must be even, and since 3 is odd, n must be even. Statement two is sufficient to answer the question.

_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

CEO
Joined: 11 Sep 2015
Posts: 3235
Re: If n is an integer, is n even?  [#permalink]

### Show Tags

09 Dec 2017, 06:33
1
Top Contributor
Bunuel wrote:
If n is an integer, is n even?

(1) n^2 - 1 is an odd integer.
(2) 3n + 4 is an even integer.

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

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

Target question: Is integer n EVEN?

Statement 1: n² - 1 is an odd integer
n² - 1 = (n + 1)(n - 1)
So, statement 1 is telling us that (n + 1)(n - 1) = ODD
From rule #4 (above), we can conclude that BOTH (n + 1) and (n - 1) are ODD
If (n + 1) is ODD, then n must be EVEN (since 1 is ODD, we can apply rule #2 to conclude that n is EVEN)
If (n - 1) is ODD, then n must be EVEN (by rule #2 )
So, the answer to the target question is YES, n is even
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: 3n + 4 is an even integer
In other words, (3n + EVEN) is EVEN
From rule #3, we can conclude that 3n is EVEN

Since 3 is odd, we can write: (ODD)(n) = EVEN
From rule #5, we can conclude that n is EVEN
So, the answer to the target question is YES, n is even
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Cheers,
Brent
_________________

Test confidently with gmatprepnow.com

Re: If n is an integer, is n even? &nbs [#permalink] 09 Dec 2017, 06:33
Display posts from previous: Sort by