is 0 an even integer?

Question

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.

Ian Stewart · Answer

Yes, 0 is always an even integer.

aniruddhkashyap · Answer

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?

ajith · Answer

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

eaakbari · Answer

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

sanju09 · Answer

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.

claudia.minoiu@gmail.com · Answer

Is zero positive?

anuprajan5 · Answer

Claudia, 0 is a non negative even integer. Regards Anup

sanju09 · Answer

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.

Brent@GMATPrepNow · Answer

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

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

Brent@GMATPrepNow · Answer

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

GMAT Kolaveri · Answer

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
[email protected]

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

Rich.C@EMPOWERgmat.com · Answer

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]

Jeff@TargetTestPrep · Answer

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
[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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