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Is z even?

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Is z even? [#permalink]

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New post 04 May 2011, 23:27
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Is z even?

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

(2) 3z is even
[Reveal] Spoiler: OA
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Re: Is z even? [#permalink]

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New post 04 May 2011, 23:47
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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

Answer is A
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Re: Is z even? [#permalink]

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New post 05 May 2011, 00:03
for B, z has to be even, even though it has a fractional value.
hence D.
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Re: Is z even? [#permalink]

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New post 05 May 2011, 00:15
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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Re: Is z even? [#permalink]

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New post 05 May 2011, 03:42
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(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

Answer - A
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Re: Is z even? [#permalink]

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New post 05 May 2011, 06:41
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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Re: Is z even? [#permalink]

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New post 07 May 2011, 14:59
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

Answer is A.
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Re: Is z even? [#permalink]

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New post 30 Jun 2011, 03:56
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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Re: Is z even? [#permalink]

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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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Re: Is z even? [#permalink]

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New post 05 Jul 2011, 04:34
fluke wrote:
Is z even?

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

2. 3z is even

[Reveal] Spoiler:
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

hope it helps.:) ... :)
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Re: Is z even? [#permalink]

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Re: Is z even? [#permalink]

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Re: Is z even? [#permalink]

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New post 25 Nov 2014, 06:25
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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Re: Is z even? [#permalink]

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Re: Is z even? [#permalink]

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New post 25 Nov 2014, 06:37
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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Re: Is z even? [#permalink]

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New post 25 Aug 2015, 00:29
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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Re: Is z even? [#permalink]

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New post 26 Aug 2015, 00:39
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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Re: Is z even? [#permalink]

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New post 10 Dec 2015, 03:02
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
Answer A
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Re: Is z even? [#permalink]

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New post 22 Feb 2017, 12:02
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.
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Re: Is z even?   [#permalink] 22 Feb 2017, 12:02
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