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Is z even? [#permalink]
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04 May 2011, 23:27
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Is z even? (1) \(\frac{z}{2}\) is even (2) 3z is even
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Re: Is z even? [#permalink]
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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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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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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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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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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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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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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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30 Jun 2011, 04:30
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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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05 Jul 2011, 04:34
fluke wrote: Is z even?1. \(\frac{z}{2}\) is even2. 3z is evenOA: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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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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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/ Ammu



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Re: Is z even? [#permalink]
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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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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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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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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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