is 0 an even integer?

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CITI29: Senior | Next Rank: 100 Posts; Posts: 93; Joined: Tue Mar 18, 2008 9:28 am; Thanked: 2 times

by CITI29 » Sun Jul 13, 2008 4:18 pm

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was wondering if 0 is an even interger for a question like this:

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

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Source: Beat The GMAT — Data Sufficiency | Sun Jul 13, 2008 4:18 pm

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Ian Stewart: GMAT Instructor; Posts: 2623; Joined: Mon Jun 02, 2008 3:17 amFollowed by: 355 members; Location: Montreal; Thanked: 1090 times; GMAT Score:780

by Ian Stewart » Mon Jul 14, 2008 1:19 am

Yes, 0 is always an even integer.

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aniruddhkashyap: Newbie | Next Rank: 10 Posts; Posts: 5; Joined: Sun Apr 11, 2010 11:25 pm

by aniruddhkashyap » Sun Apr 18, 2010 11:13 pm

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?

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ajith: Legendary Member; Posts: 1275; Joined: Thu Sep 21, 2006 11:13 pmFollowed by: 2 members; Location: Arabian Sea; Thanked: 125 times

by ajith » 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

n=17 is the correct answer

Always borrow money from a pessimist, he doesn't expect to be paid back.

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eaakbari: Master | Next Rank: 500 Posts; Posts: 435; Joined: Mon Mar 15, 2010 6:15 amFollowed by: 1 member; Thanked: 32 times

by eaakbari » 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 âˆ’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

Answer D

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

Whether you think you can or can't, you're right.
- Henry Ford

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » 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.

The mind is everything. What you think you become. -Lord Buddha

Sanjeev K Saxena
Quantitative Instructor
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[email protected]: Newbie | Next Rank: 10 Posts; Posts: 7; Joined: Sun Sep 16, 2012 7:29 pm

by [email protected] » Tue Oct 02, 2012 6:32 pm

Is zero positive?

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anuprajan5: Master | Next Rank: 500 Posts; Posts: 279; Joined: Mon Jun 25, 2012 10:56 pmFollowed by: 10 members; Thanked: 60 times

by anuprajan5 » Tue Oct 02, 2012 8:25 pm

Claudia,

0 is a non negative even integer.

Regards
Anup

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Wed Oct 03, 2012 1:32 am

[email protected] 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. -Lord Buddha

Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com

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by Brent@GMATPrepNow » Wed Oct 03, 2012 6:04 am

CITI29 wrote: If n is an integer, is n even?
(1) n^2 âˆ’1 is an odd integer.
(2) 3n + 4 is an even integer.

Target question: Is n even?

Statement 1: n^2 âˆ’1 is an odd integer.
If n^2 âˆ’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

Answer = D

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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is 0 an even integer?

by Brent@GMATPrepNow » Wed Oct 03, 2012 6:06 am

If anyone wants to practice more Data Sufficiency questions involving odd and even integers, here are a few more:

https://www.beatthegmat.com/what-about- ... 17014.html
https://www.beatthegmat.com/is-the-inte ... 19182.html
https://www.beatthegmat.com/og-13th-ds- ... 22138.html
https://www.beatthegmat.com/even-or-not ... nt=Chicago

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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GMAT Kolaveri: Master | Next Rank: 500 Posts; Posts: 287; Joined: Fri Mar 23, 2012 12:33 amFollowed by: 6 members; Location: Pune,India; Thanked: 60 times

is 0 an even integer?

by GMAT Kolaveri » 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 âˆ’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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by [email protected] » Tue Mar 27, 2018 2:49 pm

Hi All,

We're told that N is an INTEGER. We're asked if N is EVEN. This is a YES/NO question (and to answer the initial question posted - YES, zero is an EVEN integer). This question can be answered by TESTing VALUES or with Number Property rules.

1) N^2 -1 is an ODD integer.

Since N^2 - 1 = Odd
N^2 = Odd + 1
N^2 = Even

We're told that N is an INTEGER, and the only types of integers that end up EVEN when SQUARED are EVEN integers. Thus, N MUST be Even and the answer to the question is ALWAYS YES.
Fact 1 is SUFFICIENT

2) 3N + 4 is an EVEN integer.

Since 3N + 4 = Even
3N = Even - 4
3N = Even
(Odd)(N) = Even

Since the product of the two integers is EVEN, at least one of the two integers MUST be even. Since 3 is Odd, N must be Even - and the answer to the question is ALWAYS YES.
Fact 2 is SUFFICIENT

Final Answer: D

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 amFollowed by: 22 members; Location: New York, NY; Thanked: 39 times

by Jeff@TargetTestPrep » Mon Jul 30, 2018 10:50 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 âˆ’1 is an odd integer.
(2) 3n + 4 is an even integer.

We need to determine whether integer n is 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.

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.

Answer: D

Jeffrey Miller
Head of GMAT Instruction
[email protected]

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

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