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# If w, y, and z are positive integers, and w = y z, is w a

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Manager
Joined: 01 Nov 2007
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If w, y, and z are positive integers, and w = y z, is w a [#permalink]  28 Jan 2008, 14:56
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If w, y, and z are positive integers, and w = y – z, is w a perfect square?

(1) y + z is a perfect square.

(2) z is even
VP
Joined: 09 Jul 2007
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Location: London
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Re: DS - perfect squares [#permalink]  28 Jan 2008, 17:44
JCLEONES wrote:
If w, y, and z are positive integers, and w = y – z, is w a perfect square?

(1) y + z is a perfect square.

(2) z is even

first of all. perfect squares: 0, 1, 4, 9, 16....
0 is a positive even integer
1.
assume y=4 and z=0 then yes w=4 perf. sq.
assume y=12 and z=4 then no w=8 is not a perf. sq.
not suff.

2.
z is even. there is no info about y and it can be anything
refer to the 1st statement again not suff.

combined. not suff.

E
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Re: DS - perfect squares [#permalink]  29 Jan 2008, 11:51
JCLEONES wrote:
If w, y, and z are positive integers, and w = y – z, is w a perfect square?

(1) y + z is a perfect square.

(2) z is even

1: can be 12+4 thus 12-4 is not a perfect square. Or can be 10+6=16 and 10-6=4 Insuff.

2: no help.

z is even in the cases we worked with in S1. Thus Insuff for both.

E
Re: DS - perfect squares   [#permalink] 29 Jan 2008, 11:51
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