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>
If z is an integer, is z even?
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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.
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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- Jay@ManhattanReview
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Given: z is an integerVJesus12 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>
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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