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Math Expert V
Joined: 02 Sep 2009
Posts: 58402
The integer x is even and the integer y is odd. Is the integer z odd?  [#permalink]

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Difficulty:   15% (low)

Question Stats: 80% (01:25) correct 20% (01:41) wrong based on 59 sessions

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The integer x is even and the integer y is odd. Is the integer z odd?

(1) xyz+ 1 is odd.

(2) xy + xz + yz is even.

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Manager  S
Joined: 24 Nov 2018
Posts: 107
Location: India
GPA: 3.27
WE: General Management (Retail Banking)
Re: The integer x is even and the integer y is odd. Is the integer z odd?  [#permalink]

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Bunuel wrote:
The integer x is even and the integer y is odd. Is the integer z odd?

(1) xyz+ 1 is odd.

(2) xy + xz + yz is even.

x is even & y is odd.

1) xyz+1=odd. xy is even, z can be either even or odd. Insufficient.

2) xy=even, xz=even, as x is even. hence, yz is even. As Even + Even + x is even, So, x is even.
Since y is odd, so z is even. Z isn't odd. Sufficient.

IMO, Option B.
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Joined: 31 Oct 2013
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Re: The integer x is even and the integer y is odd. Is the integer z odd?  [#permalink]

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Bunuel wrote:
The integer x is even and the integer y is odd. Is the integer z odd?

(1) xyz+ 1 is odd.

(2) xy + xz + yz is even.

Note : x = even. y=odd.

Statement 1; xyz + 1 = odd. xyz=even as x is even. it's not possible to identify specifically whether z is odd or even. NOT sufficient.

Statement 2. xy =even. xz =even. y =odd. So, z has to be an even integer in order to make the statement true. Sufficient. z =even.

The correct answer is B.
Manager  B
Joined: 15 Jan 2019
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GMAT 1: 650 Q42 V38 GPA: 4
Re: The integer x is even and the integer y is odd. Is the integer z odd?  [#permalink]

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Bunuel wrote:
The integer x is even and the integer y is odd. Is the integer z odd?

(1) xyz+ 1 is odd.

(2) xy + xz + yz is even.

even = e, odd = o

e.e = e e+e=e
e.o=e e+o=o
o.o =o o+o=e

use this and its easy Re: The integer x is even and the integer y is odd. Is the integer z odd?   [#permalink] 08 Oct 2019, 00:55
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