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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]  10 Aug 2009, 09:59
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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
Senior Manager
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Re: square root of a product [#permalink]  10 Aug 2009, 10:19
B for me.

1. The product of the other two numbers must be 12, but are they 4x3 or 6x2? So Insuff.

2. Avg is 20/3, therefore the sume of the other two is 8. Only 6 & 2 fits both the criteria. Suff.
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Re: square root of a product [#permalink]  10 Aug 2009, 11:08
D for me.

If x,y, z are the integers in increasing order, from the stem xy = z (largest integer)

1) Z = 12 i.e. xy [product of two smaller numebers] = 12. Suff

2) x+y+z = 20 and xy = z (from question stem) ; only values which hold true are 2, 6, 12. Suff.
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Re: square root of a product [#permalink]  10 Aug 2009, 11:18
D seems right, for some reason I was adding 4x3 & 6x2.
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Re: square root of a product [#permalink]  10 Aug 2009, 22:57
sqrt xyz = z therfore xyz = z^2 from st one if z^2 = 144 therfore xy = 12

st two

sum of three numbers = x+y+z = 20 but from question stem z = xy

therfore x+y+xy = 20 ie x(1+y)+y = 20 therfore x = 20-y/1+y

WE KNOW THAT ODD/EVEN CAN NEVER GIVE AN INTIGER THUS Y CAN NEVER BE ODD ie : if y is odd 20-y is odd and Y+1 IS EVEN AND THUS

x = 20-y/1+y WOULD BE A FRACTION ( BUT X IS A POSITIVE INTIGER)

THUS Y COULD BE {2,4,8,} ANY VALUE FOR Y > 8 WILL YIELD 20-Y/1+Y<1 ,THUS BLUGGING IN VALUES FOR Y WE SEE THAT ONLY 2 CAN YIELD A POSITIVE INTIGER X = 6

AND THUS Y = 2 AND Z = 12 .... SUFF

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Re: square root of a product [#permalink]  11 Aug 2009, 03:53
But if you look at the question itself it is asking the product of other two numbers.
(xyz)^1/2=Z

Z= 12 then (xy.12)^1/2 = 12 .. solving it xy = 12 _ Sufficient enough as you are able to determine the product of the rest of two numbers

I think statement 1 alone should be sufficient to answer the questions (which is to determine the product of other two numbers)
_________________

Re: square root of a product   [#permalink] 11 Aug 2009, 03:53
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