Is z an even integer?

Question

(1)  z^2  is an even integer.

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

Munch · Answer

Statement 1 alone is sufficient and statement 2 is not sufficient.

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chetan2u · Answer

Hi,
What if z is √2...
 z^2=2  and thus an even integer but z is not an even integer.

yezz · Answer

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

vivek2k70 · Answer

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

stonecold · Answer

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.

broall · Answer

(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.

The answer is C.

EMPOWERgmatRichC · Answer

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

Final Answer:  C

GMAT assassins aren't born, they're made, 
Rich

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Is z an even integer?

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GMAT Data Sufficiency (DS) Questions

Is z an even integer?

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