Is z an even integer? (1) z/2 is an even integer (2) 3z is an even

Similar question to practice: if-z-is-an-integer-is-z-even-162351.html

OA is wrong. It should be D. Please edit OA from A to D

OA is NOT wrong.

(2) 3z is even --> if z = 2, then it's even but if z = 2/3, then it's not.

1) statement 1 clearly states z to be a multiple of 4.. so suff
2) statement two does not prove z to be an even integer.. insuff
ans A

Is z an even integer?

(1) z/2 is an even integer.

For z/2 to be even, z must be a multiple of 4. Meaning z takes the following values {4,8,12,16,20 ...}
so z is even integer.

Sufficient
(2) 3z is an even integer.

{ Odd * Even = Even}
For 3z to be even integer. z must be an even integer, Since 3 is odd.
So z is even integer.

Sufficient
Ans:D

-Manoj Reddy
Please press +1 Kudos if this post is helpful

it has to be D.

1. Option z/2 = Even integer. => Z= 2 * even Integer => Z will be even. (Even * Even = Even)

2. 3Z is an even interger= Z must be even number for the end result to be even number.

So answer D.

Hi ManojReddy and shriramvelamuri,
Its very important that we check answer for every possiblity..
look at statement 2..
(2) 3z is an even integer.
z will be an even integer if z is an integer.
But is that mentioned anywhere.. NO..
what if z is a fraction say 2/3... 3z=2,an even integer.. but z is not an even integer, not even an integer..
B is not suff..
hope it is clear..

MANHATTAN GMAT OFFICIAL SOLUTION:

The wording of this question has a tendency to bias people towards integers. After all, the “opposite” of even is odd, and odd numbers are integers, too. However, the question does not state that z must be an integer in the first place, so do not assume that it is.

(1) SUFFICIENT: The fact that z/2 is an even integer implies that z = 2 × (an even integer), which much be an even integer. (In fact, according to statement (1), z must be divisible by 4).

(2) INSUFFICENT: The fact that 3z is an even integer implies that z = (an even integer)/3, which might not be an integer at all. For example, z could equal 2/3.

One way to avoid assuming is to invoke Principle #3: Work from Facts to Question. Statement (2) tells us that 3z = even integer = –2, 0, 2, 4, 6, 8, 10, etc. No even integers have been skipped over, nor have we allowed the question to suggest z values. That is how assumptions sneak in.

Next, we divide 3z by 3 to get z, so we divide the numbers on our list by 3: z = –2/3, 0, 2/3, 4/3, 2, 8/3, 10/3, etc. Only then do we check this list against our question and see that the answer is Maybe.

The correct answer is A.

!	If we had assumed that z must be an integer, we might have evaluated statement (2) with two cases: 3 × even = even, so z could be even. 3 × odd = odd, so z is definitely not odd. We would have incorrectly concluded that Statement (2) was sufficient and therefore incorrectly selected answer (D).

Another common assumption is that a variable must be positive. Do not assume that any unknown is positive unless it is stated as such in the information given (or if the unknown counts physical things or measures some other positive-only quantity).

Please tell me i'm getting more and more confused, i wan to know on the actual GMAT, on the test, if they say

z/2 is divisible by 2 => then automatically we assume z/2 as integer, then z is integer right?

For Statement 1 - What if we assume z is 2/3 or any other real number as such? Here the value for z/2 will now become 1/3
Then in this case the answer would have been Option E. Please explain this scenario as well.

If z = 2/3, then z/2 is NOT even as stated in the first statement, so z cannot be 2/3.

Target question: Is z an even integer?

Aside: Integer n is even if we can express n as n = 2k for some integer k

Statement 1: z/2 is an even integer.
This means z/2 =2k for some integer k
Multiply both sides by 2 to get: z = 4k
This tells us that z is a multiple of 4, which means z is definitely even
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: 3z is an even integer.
If we were told that z is an integer, then statement 2 would be sufficient. However, we aren't told that z is an integer.
With this in mind, consider these two possible cases:
Case a: z = 2. Works because 3z = 3(2) = 6, and 6 is even. In this case, the answer to the target question is YES, z is even
Case b: z = 2/3. Works because 3z = 3(2/3) = 2, and 2 is even. In this case, the answer to the target question is NO, z is not even
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer: A

Cheers,
Brent

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