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is 0 an even integer?

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by CITI29 » Sun Jul 13, 2008 4:18 pm

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Answers

A

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Difficulty—

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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Source: — Data Sufficiency |

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by Ian Stewart » Mon Jul 14, 2008 1:19 am
Yes, 0 is always an even integer.
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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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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
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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 −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.
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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.
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by [email protected] » Tue Oct 02, 2012 6:32 pm
Is zero positive?
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by anuprajan5 » Tue Oct 02, 2012 8:25 pm
Claudia,

0 is a non negative even integer.

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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.
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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 −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

Answer = D

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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
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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 −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

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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 −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
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