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## is 0 an even integer?

tagged by: Brent@GMATPrepNow

This topic has 5 expert replies and 6 member replies
CITI29 Senior | Next Rank: 100 Posts
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#### is 0 an even integer?

Sun Jul 13, 2008 4:18 pm
was wondering if 0 is an even interger for a question like this:

If n is an integer, is n even?
(1) n2 −1 is an odd integer.
(2) 3n + 4 is an even integer.

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sanju09 GMAT Instructor
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Wed Oct 03, 2012 1:32 am
claudia.minoiu@gmail.com wrote:
Is zero positive?
(A) 0 is an even integer.

(B) 0 is a neutral integer too, hence 0 is neither positive nor negative.

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anuprajan5 Master | Next Rank: 500 Posts
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Tue Oct 02, 2012 8:25 pm
Claudia,

0 is a non negative even integer.

Regards
Anup

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sanju09 GMAT Instructor
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Wed Oct 03, 2012 1:32 am
claudia.minoiu@gmail.com wrote:
Is zero positive?
(A) 0 is an even integer.

(B) 0 is a neutral integer too, hence 0 is neither positive nor negative.

_________________
The mind is everything. What you think you become. â€“Lord Buddha

Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
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anuprajan5 Master | Next Rank: 500 Posts
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Tue Oct 02, 2012 8:25 pm
Claudia,

0 is a non negative even integer.

Regards
Anup

GMAT Kolaveri Master | Next Rank: 500 Posts
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Wed Oct 03, 2012 7:49 am
CITI29 wrote:
was wondering if 0 is an even interger for a question like this:

If n is an integer, is n even?
(1) n2 -1 is an odd integer.
(2) 3n + 4 is an even integer.
Type of Question: Yes or No
We need to find out whether n is even.

ST 1: n^2 - 1 is odd. Therefore n^2 and 1 should have opposite parity. 1 is odd. hence n^2 should be even. n is even. Is n even? We have a definite YES! SUFFICIENT.

ST 2: 3n + 4 is even. In this case too both the numbers should have the same parity. 4 is even. 3n should be even. 3 is odd. Hence n should be even. Is n even? We have a definite YES! SUFFICIENT.

OA: D

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Brent@GMATPrepNow GMAT Instructor
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Wed Oct 03, 2012 6:06 am

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Brent@GMATPrepNow GMAT Instructor
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Wed Oct 03, 2012 6:04 am
CITI29 wrote:
If n is an integer, is n even?
(1) n^2 -1 is an odd integer.
(2) 3n + 4 is an even integer.
Target question: Is n even?

Statement 1: n^2 -1 is an odd integer.
If n^2 -1 is an odd integer, then n^2 must be an even integer.
If n^2 is an even integer, then n must be even.
Rationale: (odd)^2 - odd, but (even)^2 = even
As such, statement 1 is SUFFICIENT

Statement 2: 3n + 4 is an even integer.
If 3n + 4 is an even integer, then 3n must be an even integer (since Even + Even = Even).
If 3n must be an even integer, then n must be even.
Rationale: (odd)(even) = even and
As such, statement 2 is SUFFICIENT

Cheers,
Brent

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claudia.minoiu@gmail.com Newbie | Next Rank: 10 Posts
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Tue Oct 02, 2012 6:32 pm
Is zero positive?

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sanju09 GMAT Instructor
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Mon Apr 19, 2010 1:18 am
aniruddhkashyap wrote:
Ian Stewart wrote:
Yes, 0 is always an even integer.
This is one of the problem from the "tough math problems set" floating around on this site......

51. How many integers from 0 to 50, inclusive, have a remainder of 1 when divided by 3?

A.14 B.15. C.16 D.17 E.18

Soln: if we arrange this in AP, we get
4+7+10+.......+49

so 4+(n-1)3=49: n=16
C is my pick

They have not considered 1 as one of the options......is this incorrect?
A positive integer divisor n has exactly n number of possible remainders to succumb. In case the dividend is smaller than the divisor, the remainder happens to be same in value as the dividend. In the presented example, 1 is a member of list so the account is erroneous.

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eaakbari Master | Next Rank: 500 Posts
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Mon Apr 19, 2010 12:43 am
CITI29 wrote:
was wondering if 0 is an even interger for a question like this:

If n is an integer, is n even?
(1) n2 -1 is an odd integer.
(2) 3n + 4 is an even integer.
(1)
Implies n^2 is even which means n is even
Hence Suff.

(2)
Since 3n+4 is even
and even + even = even
Hence 3n must be even, that means n is even
Hence Suff

And to reiterate what Ian said, 0 zero is a non-positive, non -negative even integer.

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ajith Legendary Member
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Sun Apr 18, 2010 11:20 pm
aniruddhkashyap wrote:
Ian Stewart wrote:
Yes, 0 is always an even integer.
This is one of the problem from the "tough math problems set" floating around on this site......

51. How many integers from 0 to 50, inclusive, have a remainder of 1 when divided by 3?

A.14 B.15. C.16 D.17 E.18

Soln: if we arrange this in AP, we get
4+7+10+.......+49

so 4+(n-1)3=49: n=16
C is my pick

They have not considered 1 as one of the options......is this incorrect?
1 has to be a part of it since it leaves a remainder of 1 when divided by 3

so the solution quoted is incorrect, in my opinion

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