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# If z is an integer, is z even?

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Intern
Joined: 28 Oct 2013
Posts: 4
If z is an integer, is z even?  [#permalink]

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Updated on: 28 Oct 2013, 23:07
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Difficulty:

5% (low)

Question Stats:

85% (00:43) correct 15% (00:33) wrong based on 149 sessions

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If z is an integer, is z even?

(1) z/2 is even.
(2) 3z is even.

Hi everyone,

This may be a very easy question but I need help logically breaking down. Any help would be very much appreciated. This is from a CAT from the MGMAT course.

The the question is phrased the only parameter is that Z is an integer, so no fractions/decimals. When you are testing (1) and (2) are you only testing with an even number because it states "is z even"?

thanks!

Originally posted by pchun008 on 28 Oct 2013, 17:11.
Last edited by Bunuel on 28 Oct 2013, 23:07, edited 1 time in total.
Edited the question.
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Joined: 02 Sep 2009
Posts: 64101
Re: If z is an integer, is z even?  [#permalink]

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28 Oct 2013, 23:10
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If z is an integer, is z even?

(1) z/2 is even --> $$\frac{z}{2}=even$$ --> $$z=2*even=even$$. Sufficient.

(2) 3z is even --> $$3z=odd*z=even$$, since given that z is an integer, then in order odd*z to be even z must an even integer. Sufficient.

Hope it's clear.
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Re: If z is an integer, is z even?  [#permalink]

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19 Apr 2020, 07:37
If z is an integer, is z even?

(1) z/2 is even.
so, z=2*even = even sufficient

(2) 3z is even.
3z= 4 , z=4/3 (rejected because z is an integer )
3z= 6, z=6/3 (accepted)
so, z= even sufficient

Re: If z is an integer, is z even?   [#permalink] 19 Apr 2020, 07:37