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If the square root of the product of three distinct positive

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Senior Manager
Joined: 19 May 2004
Posts: 291

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

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15 Nov 2004, 13:24
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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 of the three distinct numbers is 12.
(2) The average (arithmetic mean) of the three numbers is 20/3

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Director
Joined: 07 Nov 2004
Posts: 683

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15 Nov 2004, 13:35
I think its A.

Translating the question stem: x<y<z and sqrt(xyz) = z ie: xyz = z^2 or xy = z

S(1): z = 12 => xy = 12 sufficient
S(2): x+y+z = 20 insufficient

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Senior Manager
Joined: 19 Oct 2004
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Location: Missouri, USA

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15 Nov 2004, 14:09
I'll go with D.

agree with whatever gayathri said except statement 2---

x+y+z=20

we know xy=z.

hence, x+y+xy=20
lets try n find two values for x and y such that the above eq. is satisfied.
its possible only when x=6, y=2 or x=2 and y=6. eitherways, xy=12.
hence, statement 2 is SUFFICIENT.

Hence, D.
_________________

Let's get it right!!!!

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Director
Joined: 31 Aug 2004
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15 Nov 2004, 14:24
Will go with D too.

1st statement is enough ok

2nd statement means that, assuming a, b, c are the 3 positive integers, ab=c and (a+b+c)/3=20/3 id est a+b+ab=20 : this is true only if a=2 and b=6 or a =6 and b=2 (ab=12)

So statement 2 is enough

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Senior Manager
Joined: 19 May 2004
Posts: 291

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15 Nov 2004, 14:32
I thought this was a trick one
Well done!

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Director
Joined: 07 Nov 2004
Posts: 683

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15 Nov 2004, 19:15

I seem to have this problem with DS where I rush to the answer too soon

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15 Nov 2004, 19:15
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