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

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08 Jun 2005, 17:48

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Please explain the soln.....

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

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

The answer is D

it's a time consuming problem
1)sufficient, XYZ = Z*Z => XY=Z=12
2) sufficient, intellegent number picking, X + Y = 20 -Z = 20 -XY
X=2 or 6
Y=6 or 2

The answer is D. it's a time consuming problem 1)sufficient, XYZ = Z*Z => XY=Z=12 2) sufficient, intellegent number picking, X + Y = 20 -Z = 20 -XY X=2 or 6 Y=6 or 2

from i, how do you know that the smaller numbers are 6 and 2? those numbers could be 4 and 3.

I will go with D
From the stem we get n1*n2 = n3, where n1, n2 & n3 are the distinct numbers, so in order to n1*n2 we should either know n1 & n2 or n3.

From statement 1 we know n3, so n1*n2 has to be 12
From statement 2,
n1+n2+n3/3 = 20/3
n1+n2+(n1*n2) = 20, since we have eliminated n3 from the equation we can use some numbers to satisfy the equation.

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

From question:
sqrt(xyz) = x
xyz = x^2
yz=x

From statement(1):
x=12
thus, we know yz
-> sufficient

From statement(2)
xyz/3 = 20/3
xyz = 20
x = 20/yz
combining with above statement (yz=x):
yz=20/(yz)
(yz)^2 = 20
-> sufficient

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

My answer is A.

Let z be the largest number. Then from question we get Sqrt(xyz) = z
or xyz = z^2
or xy = z
since z = 12, xy = 12 hence statement 1 is sufficient.

Statement 2 tells that (x+y+z)/2 = 20/3
since z = xy
we get x+y+xy = 20
We may not be able compute the values for x and y. Hence statement 2 alone is not sufficient. Hence my answer is A. Let me know, if I am making a mistake somewhere.