If the square root of the product of three distinct positive : DS Archive
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# If the square root of the product of three distinct positive

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If the square root of the product of three distinct positive [#permalink]

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26 May 2005, 18:20
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Please provide expl.... Thnx.

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
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26 May 2005, 19:02
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
26 May 2005, 19:02
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# If the square root of the product of three distinct positive

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