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If z is an integer, is z even?

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If z is an integer, is z even?

by VJesus12 » Thu Mar 01, 2018 6:00 am
If z is an integer, is z even?

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

(2) z + 5 is an odd integer.

The OA is the option B.

The statement (1) implies that z is even. Isn't it? I am confused here. Experts, can you help me?<i class="em em-confused"></i>
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by Vincen » Sat Mar 03, 2018 2:37 am
Hi.

I think that the correct option is D.

Let's start with the second statement.

If z+5 is an odd integer, then z+5=2k+1. Hence $$z=2k-4=2\left(k-2\right)\ \leftrightarrow\ z\ is\ even.$$ Therefofe (2) is sufficient.

Now, if $$\frac{z}{2}\ is\ NOT\ an\ odd\ integer\ \Rightarrow\ \ \frac{z}{2}\ is\ an\ EVEN\ integer\ \Rightarrow\ \ z\ is\ EVEN.$$ Hence, (1) is sufficient.

This is why I think that D is the correct option.
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by Jay@ManhattanReview » Wed Mar 07, 2018 9:22 pm
VJesus12 wrote:If z is an integer, is z even?

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

(2) z + 5 is an odd integer.

The OA is the option B.

The statement (1) implies that z is even. Isn't it? I am confused here. Experts, can you help me?<i class="em em-confused"></i>
Given: z is an integer

We have to determine whether z is even.

Let's take each statement one by one.

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

First thing first: "z/2 is not an odd integer" does not mean that z/2 is even. It can be any real number except even.

Case 1: Say z/2 = 3, then z = 6, an even integer. The answer is Yes.
Case 2: Say z/2 = 3.5, then z = 7, an odd integer. The answer is No.

(2) z + 5 is an odd integer.

=> z + Odd = Odd
z = Odd - Odd = Even. Sufficient.

The correct answer: B

Hope this helps!

-Jay
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