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Bunuel
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If z is an integer, is z even? (1) z/2 is not an odd integer. (2) z 29 Sep 2021, 01:01
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

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35% (medium)

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63% (01:07) correct 37% (01:00) wrong based on 163 sessions

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If z is an integer, is z even?

(1) z/2 is not an odd integer.

(2) z + 5 is an odd integer.
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B
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If z is an integer, is z even? (1) z/2 is not an odd integer. (2) z Updated on: 30 Sep 2021, 07:59
Originally posted by Showmeyaa on 29 Sep 2021, 13:28.
Last edited by Showmeyaa on 30 Sep 2021, 07:59, edited 2 times in total.
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Bunuel
If z is an integer, is z even?

(1) z/2 is not an odd integer.

(2) z + 5 is an odd integer.
Show more

Is z even?

1)z/2 is not odd:
Case1:
z/2 = even
z = 2*even = even
Case2:
z/2 is not an integer.
1/2 = not an integer, z = odd - Insufficient!
2)z + 5 = odd:
z = odd - 5 = even! - Sufficient!
Answer - (B)!
Edit: Updated the answer choice (A)!
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If z is an integer, is z even? (1) z/2 is not an odd integer. (2) z 30 Sep 2021, 01:08
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Showmeyaa
Bunuel
If z is an integer, is z even?

(1) z/2 is not an odd integer.

(2) z + 5 is an odd integer.

Is z even?

1)z/2 is not odd:
So, z/2 = even
z = 2*even = even - Sufficient!

2)z + 5 = odd:
z = odd - 5 = even! - Sufficient!

IMO, (D)!
Show more

Bunuel, Showmeyaa

\(\frac{z}{2}\) is not an odd integer could also mean that \(\frac{z}{2}\) is not an integer at all, right?

E.g. \(z = 3\) satisfies that \(z\) is an integer and \(\frac{z}{2}\) \(= \frac{3}{2} = 1.5\) satisfies that it is not an odd integer

Should the answer not be B or am I missing something?
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If z is an integer, is z even? (1) z/2 is not an odd integer. (2) z 30 Sep 2021, 01:18
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Bunuel
If z is an integer, is z even?

(1) z/2 is not an odd integer.

(2) z + 5 is an odd integer.

Is z even?

1)z/2 is not odd:
So, z/2 = even
z = 2*even = even - Sufficient!

2)z + 5 = odd:
z = odd - 5 = even! - Sufficient!

IMO, (D)!

Bunuel, Showmeyaa

\(\frac{z}{2}\) is not an odd integer could also mean that \(\frac{z}{2}\) is not an integer at all, right?

E.g. \(z = 3\) satisfies that \(z\) is an integer and \(\frac{z}{2}\) \(= \frac{3}{2} = 1.5\) satisfies that it is not an odd integer

Should the answer not be B or am I missing something?
Show more

Yes, the OA is B. For (1) we could have that z = 1. In this case z/2 is not an odd integer and z is not even.
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If z is an integer, is z even? (1) z/2 is not an odd integer. (2) z 30 Sep 2021, 01:30
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If z is an integer, is z even?

Let's analyse each statement one by one.

(1) z/2 is not an odd integer.

z/2 is not an odd integer doesn't mean that z/2 is an even integer. z/2 could be any real number other than odd integer.

Example:
z/2 = 4 then z = 8 => is z even? YES

z/2 = 1.5 then z =3 => is z even? No

Since both Yes or No are possible for the Question , Statement 1 alone is insufficient.

(2) z + 5 is an odd integer.

z + ODD = ODD
From the above statement, we can conclude that Z is even.
is z even? YES

Note: EVEN + ODD = ODD
ODD + ODD = EVEN

Option B is the correct answer.

Hope it helps,
Clifin J Francis,
GMAT SME
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If z is an integer, is z even? (1) z/2 is not an odd integer. (2) z 30 Sep 2021, 07:56
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Bunuel
If z is an integer, is z even?

(1) z/2 is not an odd integer.

(2) z + 5 is an odd integer.

Is z even?

1)z/2 is not odd:
So, z/2 = even
z = 2*even = even - Sufficient!

2)z + 5 = odd:
z = odd - 5 = even! - Sufficient!

IMO, (D)!

Bunuel, Showmeyaa

\(\frac{z}{2}\) is not an odd integer could also mean that \(\frac{z}{2}\) is not an integer at all, right?

E.g. \(z = 3\) satisfies that \(z\) is an integer and \(\frac{z}{2}\) \(= \frac{3}{2} = 1.5\) satisfies that it is not an odd integer

Should the answer not be B or am I missing something?
Show more

Yes, you are correct. z/2 is not an odd integer could also mean that it is not even an integer. Thanks, kudos to you!
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