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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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11 Nov 2005, 00:53
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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
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11 Nov 2005, 01:10
A... i think this has been discussed before
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11 Nov 2005, 03:04
D)...sqrt(xyz)=z !...1) sqrt(xy12)=12...suff...2)...x+y+z=20...only the set 12 6 2 satifies 2) and sqrt(xyz)=z...suff
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11 Nov 2005, 07:42
it should be A.

if the larges one is 12, then the smaller one can be 3,4 or 6,2 eitherway the product of the two smaller number is 12 so 1 is suff...

now average of 3 integer is 20/3 , that means sum is 20

now it can be 12, 6 and 2

at the same time it can be 3, 5 and 15 as well

so statement is not suff...

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11 Nov 2005, 08:41
christoph wrote:
nakib77 wrote:
it should be A.

if the larges one is 12, then the smaller one can be 3,4 or 6,2 eitherway the product of the two smaller number is 12 so 1 is suff...

now average of 3 integer is 20/3 , that means sum is 20

now it can be 12, 6 and 2

at the same time it can be 3, 5 and 15 as well

so statement is not suff...

you are right.... i change my answer to D.
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11 Nov 2005, 09:22
late on this...I get D also...

(1) is fairly simple...

(20) a+b+c=20

we are told that sqrt(abc)=c

so lets 12.6.2 works just fine...(2) is suff...
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11 Nov 2005, 09:41
yes.. i change my answer to D

Thanks
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11 Nov 2005, 09:49
one more vote for A.
a is staright farward i.e x=yz

can not solve this with B
cause 2 equations 3 variables
x=yz (from question stem)
x+y+z=20 ( from B)
can not solve for 3 variables using 2 equations.

hence A

what is OA..?
11 Nov 2005, 09:49
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# If the square root of the product of three distinct positive

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