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If x, y, and z are positive integers and the expression xy(y - z) is a
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14 Dec 2021, 01:13
14 Dec 2021, 01:13
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If x, y, and z are positive integers and the expression xy(y - z) is an odd number, which of the following numbers can be even?
I. z
II. x + z
III. x + y
(A) None
(B) I only
(C) II only
(D) I and III
(E) II and III
I. z
II. x + z
III. x + y
(A) None
(B) I only
(C) II only
(D) I and III
(E) II and III
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: If x, y, and z are positive integers and the expression xy(y - z) is a
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14 Dec 2021, 06:43
14 Dec 2021, 06:43
1
Carcass wrote:
If x, y, and z are positive integers and the expression xy(y - z) is an odd number, which of the following numbers can be even?
I. z
II. x + z
III. x + y
(A) None
(B) I only
(C) II only
(D) I and III
(E) II and III
I. z
II. x + z
III. x + y
(A) None
(B) I only
(C) II only
(D) I and III
(E) II and III
Key property: If a, b and c are positive integers, and the product abc is odd, then a, b and c are each ODD
Since we're told xy(y - z) is ODD, we can conclude that x is odd, y is odd, and (y - z) is odd
If (y - z) is odd and y is odd, we can also conclude that z is even
I'll check the three statements...
I. z
z is definitely EVEN
II. x + z
If x is odd and z is even, then x + z is ODD
III. x + y
If x is odd and y is odd, then x + y is EVEN
Answer: D
gmatclubot
Re: If x, y, and z are positive integers and the expression xy(y - z) is a [#permalink]
14 Dec 2021, 06:43
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