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# If the square root of the product of three distinct positive

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Intern
Joined: 11 Dec 2003
Posts: 49
Location: IN
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If the square root of the product of three distinct positive [#permalink]  26 May 2005, 18:20
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If the square root of the product of three distinct positive
integers is equal to the largest of the three numbers, what is the
product of the two smaller numbers?

(1) The largest number is 12.
(2) The average (arithmetic mean) of the three numbers is 20/3
Director
Joined: 18 Apr 2005
Posts: 548
Location: Canuckland
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D.

X<Y<Z, sqrt(XYZ) = Z => XY = Z

1) Z=12 so XY=12 sufficient
2) X+Y+Z=20 sufficient because say Z is the largest number, so Z=20 - Y -X
therefore it must be that XY=20 - Y - X, it works for X and Y being equal to 2 or 6
so XY=12 and no others
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