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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]  14 Sep 2003, 05:26
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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

Thanks
Praetorian
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Re: PS : Square Root [#permalink]  14 Sep 2003, 19:24

1- Sufficient
If we use A,B,C in increasing order, from the stem we've got the form
Sqr (ABC) = C, so; ABC=C^2; AB=C; C=12; AB=12

2- Sufficient
A+B+C=20
AB=C
A+B+AB=20;
As we need a product we better remain with the form:
A(1+(B/A)+B)=20
So, we just pick numbers where A could only be 1,2,4, and 5 (remember C is the biggest number). Then A=2, B=6

Re: PS : Square Root   [#permalink] 14 Sep 2003, 19:24
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