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# Is z an even integer?

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Math Expert
Joined: 02 Aug 2009
Posts: 6522
Is z an even integer?  [#permalink]

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Updated on: 30 Apr 2017, 03:37
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Difficulty:

75% (hard)

Question Stats:

34% (01:13) correct 66% (00:41) wrong based on 67 sessions

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Is z an even integer?

(1) $$z^2$$ is an even integer.

(2) y*z is an even integer, where z and y are integers.

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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Originally posted by chetan2u on 29 Apr 2017, 09:09.
Last edited by Bunuel on 30 Apr 2017, 03:37, edited 1 time in total.
Renamed the topic and edited the question.
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Re: Is z an even integer?  [#permalink]

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29 Apr 2017, 09:13
Statement 1 alone is sufficient and statement 2 is not sufficient.

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Posts: 6522
Re: Is z an even integer?  [#permalink]

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29 Apr 2017, 09:27
1
Munch wrote:
Statement 1 alone is sufficient and statement 2 is not sufficient.

Sent from my iPhone using GMAT Club Forum

Hi,
What if z is √2...
$$z^2=2$$ and thus an even integer but z is not an even integer.
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Re: Is z an even integer?  [#permalink]

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29 Apr 2017, 15:03
chetan2u wrote:
Is z an even integer?
1) $$z^2$$ is an even integer.
2) y*z is an even integer, where z and y are integers.

from 1

z could be a radical ... insuff

from 2

if y is even integer and no idea about z... insuff

both

z is an integer and z^2 is even thus z is even...C
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Re: Is z an even integer?  [#permalink]

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29 Apr 2017, 22:37
Statement 1: Z can be sqrt2 insufficient
Statement 2 : Not Unique answer.

Both we can derive unique answer that Z is an integer and even
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Re: Is z an even integer?  [#permalink]

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29 Apr 2017, 23:09
Even/Odd Questions are one of my favourite.
So much to learn.

Here is what i did on this one ->

Firstly => The most important step in any even/odd question before we move to the individual statements is check whether the involved numbers are integers or not.

We are not told that z is an integer.

Lets roll-->

Statement 1 =>
z^2 is even

If z is an integer => z would be even.
But what if z=$$√12$$ ?
z^2 is even
But $$√12$$ isnt even.

Not sufficient.

Statement 2 =>
So y and z are integers.

yz= even
So at-least one out of y or z must be even.
So if y is even => z can be even or odd.

Not sufficient.

Combing the two statements => As z is an integer and z^2 is even => z must be even.
Property in action =>Positive exponent does not affect the even/odd nature of any integer.

Hence C is sufficient.

SMASH THAT C.

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Re: Is z an even integer?  [#permalink]

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30 Apr 2017, 04:12
chetan2u wrote:
Is z an even integer?

(1) $$z^2$$ is an even integer.

(2) y*z is an even integer, where z and y are integers.

(1) $$z^2$$ is an even integer.

$$z^2=2 \implies z=\sqrt{2}$$ is not an even integer.
$$z^2=4 \implies z=2$$ is an even integer.

Hence (1) is insufficient.

(2) $$y$$ and $$z$$ are both integers.

Since $$y \times z$$ is even, $$y$$ or $$z$$ or both must be even.

If $$y$$ is odd, then $$z$$ must be even.
If $$y$$ is even, then $$z$$ could be odd.

Hence, insufficient.

Cobine (1) and (2), we have $$z$$ is an integer and $$z^2$$ is even. Hence $$z$$ must be even. Sufficient.

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Re: Is z an even integer?  [#permalink]

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10 Dec 2017, 15:17
1
Hi All,

We're asked if Z is an EVEN INTEGER. This is a YES/NO question. We can solve it by TESTing VALUES.

1) Z^2 is an EVEN integer.

IF...
Z^2 = 2, then Z = (root2) and the answer to the question is NO.
Z^2 = 4, then Z = 2 and the answer to the question is YES.
Fact 1 is INSUFFICIENT

2) (Y)(Z) is an EVEN integer and Z and Y are INTEGERS

IF...
Y = 1 and Z = 2, then the answer to the question is YES.
Y = 2 and Z = 1, then the answer to the question is NO.
Fact 2 is INSUFFICIENT

Combined, we know...
Y and Z are INTEGERS
Z^2 is an EVEN integer

The ONLY way to square an INTEGER and end up with an EVEN integer is if you started with an EVEN integer. Fact 2 tells us that Z MUST be an integer, so Z MUST be even and the answer to the question is ALWAYS YES.
Combined, SUFFICIENT

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Re: Is z an even integer? &nbs [#permalink] 10 Dec 2017, 15:17
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