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Retired Moderator Joined: 20 Dec 2010
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15 00:00

Difficulty:   65% (hard)

Question Stats: 45% (01:08) correct 55% (00:54) wrong based on 407 sessions

### HideShow timer Statistics Is z even?

(1) $$\frac{z}{2}$$ is even

(2) 3z is even
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3
2
(1)
Z = 2 * even

=> z is even

Sufficient

(2) 3z = even

3 is odd

So z is even if z is an integer

But if z = 8/3

Not Sufficient

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2
2
The trap for this problem is that there is no integer constraints. Let us look at each statement

1) z/2 is even so z = 4k and k is integer so z is definitely even integer. Suff. Cross BCE

2) 3z is even, so 3z = 2k, k integer. Z could be equal to 2/3 and 3z is even but answer NO, and z could be equal to 2 and answer is A. Insuff. Cross off D

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for B, z has to be even, even though it has a fractional value.
hence D.
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amit2k9 wrote:
for B, z has to be even, even though it has a fractional value.
hence D.

I didn't get this. Care to explain a bit more?
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fluke wrote:
amit2k9 wrote:
for B, z has to be even, even though it has a fractional value.
hence D.

I didn't get this. Care to explain a bit more?

z = 2/3, 8/3 will always give decimal values .66 repeating. As no where in the question it has been mentioned that z is an integer.

Thus z is even.
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1. Sufficient

z/2 is even => z/2 = 2k where k is an integer

=> z = 4k => even

2. Not sufficient

3Z is even

3(2) is even = > z =2 even

3(2/3) is even => z = 2/3 not even

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I thought we associate even and odd numbers only with integers ... hence fumbled on this ..
please explain!! A bit ...(i think i am getting confused)
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1
assiduo wrote:
I thought we associate even and odd numbers only with integers ... hence fumbled on this ..
please explain!! A bit ...(i think i am getting confused)

Yes, you are right.

If the statement says:
x is even; x must be an even integer
y is odd; y must be an odd integer

If the statement says;

3x is even; "3x" MUST be an EVEN integer, however x alone may OR may not be an integer in this case.
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fluke wrote:
Is z even?

1. $$\frac{z}{2}$$ is even

2. 3z is even

OA:A But i think the answer shd be D.

Original post by AnkitK

Hey Fluke
i think the only trap here is to consider Z as a real no
not integer
if we consider z to be integer than definitely D is the answer

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fluke wrote:
Is z even?

(1) $$\frac{z}{2}$$ is even

(2) 3z is even

Similar question to practice: if-z-is-an-integer-is-z-even-162351.html
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fluke wrote:
Is z even?

(1) $$\frac{z}{2}$$ is even

(2) 3z is even

OA is wrong. It should be D. Please edit OA from A to D
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ammuseeru wrote:
fluke wrote:
Is z even?

(1) $$\frac{z}{2}$$ is even

(2) 3z is even

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.
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Bunuel wrote:
ammuseeru wrote:
fluke wrote:
Is z even?

(1) $$\frac{z}{2}$$ is even

(2) 3z is even

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.

Yeah, you are right. Thanks for correction.

R/
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Bunuel wrote:
ammuseeru wrote:
fluke wrote:
Is z even?

(1) $$\frac{z}{2}$$ is even

(2) 3z is even

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.

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?
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jimwild wrote:
Bunuel wrote:
OA is NOT wrong.

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

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?

z/2 is divisible by 2 means that z/2 must be an integer. z/2 = integer --> z = 2*integer = integer.

On the GMAT when we are told that $$a$$ is divisible by $$b$$ (or which is the same: "$$a$$ is multiple of $$b$$", or "$$b$$ is a factor of $$a$$"), we can say that:
1. $$a$$ is an integer;
2. $$b$$ is an integer;
3. $$\frac{a}{b}=integer$$.
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fluke wrote:
Is z even?

(1) $$\frac{z}{2}$$ is even

(2) 3z is even

Trickyyyy...)

(1) $$\frac{z}{2}$$ = even --> z=2*even and thus is always even, SUFFICIENT
(2) Nowhere are we told that Z is an integer, hence let's say $$3*\frac{10}{3}=10$$which is even BUT z is not even. 3*2 is even and z is also even, there are different answers possible. NOT SUFFICIENT
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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.
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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.
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dipanjan93 wrote:
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.
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