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# Is z an integer?

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Is z an integer? [#permalink]  24 Jan 2014, 01:27
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62% (01:46) correct 38% (00:47) wrong based on 65 sessions
Is z an integer?

(1) 2z is an even number.

(2) 4z is an even number.
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Re: Is z an integer? [#permalink]  24 Jan 2014, 02:02
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Is z an integer?

(1) 2z is an even number --> $$2z=even$$ --> $$z=\frac{even}{2}=integer$$. Sufficient.

(2) 4z is an even number --> $$4z=even$$ --> $$z=\frac{even}{4}$$: if that even number is a multiple of 4 (for example 4), then z will be an integer but if that even number is even but not a multiple of 4 (for example 2), then z will not be an integer. Not sufficient.

Hope it's clear.
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Re: Is z an integer? [#permalink]  24 Jan 2014, 04:20
Bunuel wrote:
Is z an integer?

(1) 2z is an even number --> $$2z=even$$ --> $$z=\frac{even}{2}=integer$$. Sufficient.

(2) 4z is an even number --> $$4z=even$$ --> $$z=\frac{even}{4}$$: if that even number is a multiple of 4 (for example 4), then z will be an integer but if that even number is even but not a multiple of 4 (for example 2), then z will not be an integer. Not sufficient.

Hope it's clear.

But what is z=4.3?? 2z=8.6 which is an even number but z is not an integer here
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Re: Is z an integer? [#permalink]  24 Jan 2014, 05:28
Expert's post
nfr007 wrote:
Bunuel wrote:
Is z an integer?

(1) 2z is an even number --> $$2z=even$$ --> $$z=\frac{even}{2}=integer$$. Sufficient.

(2) 4z is an even number --> $$4z=even$$ --> $$z=\frac{even}{4}$$: if that even number is a multiple of 4 (for example 4), then z will be an integer but if that even number is even but not a multiple of 4 (for example 2), then z will not be an integer. Not sufficient.

Hope it's clear.

But what is z=4.3?? 2z=8.6 which is an even number but z is not an integer here

4.3 is not even. Only integers can be even or odd:

An even number is an integer that is "evenly divisible" by 2, i.e., divisible by 2 without a remainder.

An odd number is an integer that is not evenly divisible by 2.

Theory on Number Properties: math-number-theory-88376.html

All DS Number Properties Problems to practice: search.php?search_id=tag&tag_id=38
All PS Number Properties Problems to practice: search.php?search_id=tag&tag_id=59

Hope this helps.
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Re: Is z an integer? [#permalink]  24 Jan 2014, 07:30
Statement 1 is sufficient.
S1 says 2z is even.Thus,if z is fractional,it could be .5,1.5,2.5... to make 2z an integer.But even then 2z will be odd only,not even.
Therefore,only when z is an integer,2z will be even integer.
In statement 2,4z could be even if z=.5,1.5... Or z=1,2,3...On this basis we cannot conclude that z is an integer.Not sufficient.
Ans.A

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Re: Is z an integer? [#permalink]  01 Feb 2014, 04:57
Stmt1: For 2z to be even z has to be integer. For a non-integer 2z cannot be even. SUFF
Stmt2: 4z is even. Now if z=1.5(a non-integer) 4z=6 (even number). if z=2, 4z=8(even number). INSUFF.
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Re: Is z an integer?   [#permalink] 01 Feb 2014, 04:57
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