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If z is an integer greater than 1, is z even?

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Retired Moderator
Joined: 28 May 2014
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GMAT 1: 730 Q49 V41
If z is an integer greater than 1, is z even?  [#permalink]

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28 Nov 2017, 06:35
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75% (01:31) correct 25% (01:35) wrong based on 36 sessions

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If z is an integer greater than 1, is z even?

(1) 2z is not a factor of 8
(2) 3z/4 is a factor of 6

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Re: If z is an integer greater than 1, is z even?  [#permalink]

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28 Nov 2017, 06:47
If z is an integer greater than 1, is z even?
(1) 2z is not a factor of 8
z could be 2, 3,6,7
Insuff

(2) 3z/4 is a factor of 6
This means 3z/4 is an even integer.
Even if 3z/4 is an integer, z has to be a MULTIPLE of 4
So z is even
Sufficient
.B
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Re: If z is an integer greater than 1, is z even?  [#permalink]

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28 Nov 2017, 09:07
(1) 2z is NOT a factor of 8. Now 8 has only 4 factors: 1, 2, 4, 8. So 2z should be none of these four, hence z could be any integer apart from 1, 2, 4. But still z could take multiple values like 6, 8, 3, 7.. and thus could be either odd or even. So cant say. Insufficient.

(2) 3z/4 is a factor of 6. Now factors of 6 are also four: 1, 2, 3, 6.
If 3z/4 = 1, then z is NOT an integer, which contradicts given data. so rejected
If 3z/4 = 2, then again z is NOT an integer, so rejected
If 3z/4 = 3, then z=4, which is even
If 3z/4 = 6, then z=8, which is even

So basis this statement z can take 2 integer values - 4 and 8 - both of which are even. So z is even. Sufficient.

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This is not a quality discussion. It has been retired.

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Re: If z is an integer greater than 1, is z even? &nbs [#permalink] 28 Nov 2017, 09:07
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