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Is x+y+z a square of an integer? 1). Xyz (or x, y, and z) is

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Manager
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Is x+y+z a square of an integer? 1). Xyz (or x, y, and z) is [#permalink]

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New post 31 May 2009, 06:10
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Is x+y+z a square of an integer?
1). Xyz (or x, y, and z) is odd, and x is the least one.
2). X, y, and z are three different integers.

Kudos [?]: 59 [0], given: 0

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Re: square of an integer [#permalink]

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New post 31 May 2009, 09:58
E....not enough info.
Pluggin numbers can easily show different outcomes.

Stmt. 1 --- tell all 3 are odd. Not suff.
Stmt 2 --- does not tells much.
Combining both - does not helps.
what is OA?

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Re: square of an integer [#permalink]

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New post 31 May 2009, 10:00
Even after Combining both the statements, we only that there are three odd integers.

x = 1, y = 5, z = 3 \(\Rightarrow\) the SUM is Square of an integer.
x = 3, y = 5, z = 7 \(\Rightarrow\) the SUM is NOT Square of an integer.

Thus, both statements are INSUFFICIENT.

Answer E.

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Concentration: Technology, Marketing
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Re: square of an integer [#permalink]

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New post 01 Jun 2009, 15:55
vcbabu wrote:
Is x+y+z a square of an integer?
1). Xyz (or x, y, and z) is odd, and x is the least one.
2). X, y, and z are three different integers.


Stmt 1: x, y, and z is odd, and x is the least one.

for x=3 y=3 z=3 x+y+z is a square of an integer
for x=1 y=3 z=7 x+y+z is not a square of an integer.

Stmt 1 INSUFFICIENT.

Stmt 2: X, y, and z are three different integers.

for x=1 y=3 z=5 x+y+z is a square of an integer.
for x=1 y=3 z=7 x+y+z is not a square of an integer.

Stmt 2 INSUFFICIENT.

Together , using diffenet , odd integers for x, y, and z is odd, and x is the least one.

for x=1 y=3 z=5 x+y+z is a square of an integer.
for x=1 y=3 z=7 x+y+z is not a square of an integer.

IMO E
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Re: square of an integer [#permalink]

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New post 01 Jun 2009, 21:07
vcbabu wrote:
Is x+y+z a square of an integer?
1). Xyz (or x, y, and z) is odd, and x is the least one.
2). X, y, and z are three different integers.


Question:\((X+Y+Z=M^{2}\) where M is any integer?\()\)

Question:\((sqrt{X+Y+Z}=M\) where M is any integer?\()\)

\(X=1\), \(Y=3\), \(Z=5\)

\(X+Y+Z=9=3^2\)

==>YES

\(X=1\), \(Y=3\), \(Z=7\)

\(X+Y+Z=11\)

==> NO

YES & NO==>INSUFFICIENT


Final Answer, \(E\).
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Hades

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Re: square of an integer   [#permalink] 01 Jun 2009, 21:07
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Is x+y+z a square of an integer? 1). Xyz (or x, y, and z) is

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