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# The product of integers x, y, and z is even, is z even?

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The product of integers x, y, and z is even, is z even?  [#permalink]

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Updated on: 03 Apr 2012, 02:03
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Difficulty:

45% (medium)

Question Stats:

65% (01:38) correct 35% (01:57) wrong based on 189 sessions

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The product of integers x, y, and z is even, is z even?

(1) x/y = z

(2) z = xy

Originally posted by dzodzo85 on 03 Apr 2012, 01:54.
Last edited by Bunuel on 03 Apr 2012, 02:03, edited 1 time in total.
Edited the question
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Re: The product of integers x,y, and z is even, is z even?  [#permalink]

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03 Apr 2012, 02:00
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The product of integers x,y, and z is even, is z even?

1. X/Y = Z

2. Z=XY

x*y*z = 2k, where k is an integer

At least one of them is even

1. X/Y = Z

if x = 6, y = 2, then z = 3, not even

if x = 6, y = 3, then z = 2, even

2. Z=XY

so (z)^2 = 2*k (because x*y*z = 2k, where k is an integer)

Sufficient, as if square of an integer is even ,then the integer is even

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Re: The product of integers x,y, and z is even, is z even?  [#permalink]

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03 Apr 2012, 02:04
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dzodzo85 wrote:
The product of integers x,y, and z is even, is z even?

1. X/Y = Z

2. Z=XY

The product of integers x, y, and z is even, is z even?

Notice that since x, y, and z are integers and xyz=even then at least one of the unknowns must be even.

(1) x/y = z --> x=yz --> if y=even then z can be even as well as odd. Not sufficient.

(2) z = xy --> from xyz=even: z^2=even --> z=even. Sufficient.

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Re: The product of integers x,y, and z is even, is z even?   [#permalink] 03 Apr 2012, 02:04
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# The product of integers x, y, and z is even, is z even?

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