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

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CEO
Joined: 15 Aug 2003
Posts: 3454

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

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14 Sep 2003, 06:26
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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

Kudos [?]: 918 [0], given: 781

Intern
Joined: 12 Sep 2003
Posts: 31

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Location: Peru
Re: PS : Square Root [#permalink]

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14 Sep 2003, 20:24

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

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Re: PS : Square Root   [#permalink] 14 Sep 2003, 20:24
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