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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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08 Jun 2005, 18:48
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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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Director
Joined: 18 Apr 2005
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Location: Canuckland

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08 Jun 2005, 20:03
TS wrote:

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

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

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SVP
Joined: 05 Apr 2005
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08 Jun 2005, 20:03
B. using trial and error approach.

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08 Jun 2005, 20:05
sparky wrote:
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.

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Director
Joined: 03 Nov 2004
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08 Jun 2005, 20:17
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.

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Director
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08 Jun 2005, 20:19
HIMALAYA wrote:
from i, how do you know that the smaller numbers are 6 and 2? those numbers could be 4 and 3.

We are interested only in their product and not in their numbers

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SVP
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08 Jun 2005, 20:38
HIMALAYA wrote:
from i, how do you know that the smaller numbers are 6 and 2? those numbers could be 4 and 3.

We are interested only in their product and not in their numbers

absolutly correct. bumbed

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Senior Manager
Joined: 17 May 2005
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Location: Auckland, New Zealand

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09 Jun 2005, 03:22
TS wrote:

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

Ans = D

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Senior Manager
Joined: 17 Apr 2005
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09 Jun 2005, 08:27
cloudz9 wrote:
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

Ans = D

I think you are using statement (1) while evaluation DS for (2).

But is there any "smart" way to identify that there is only one solution to

x + y + xy = 20.

HMTG.

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Senior Manager
Joined: 15 Apr 2005
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10 Jun 2005, 06:39
TS wrote:

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

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.

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Senior Manager
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10 Jun 2005, 18:15
HowManyToGo wrote:
cloudz9 wrote:
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

Ans = D

I think you are using statement (1) while evaluation DS for (2).

But is there any "smart" way to identify that there is only one solution to

x + y + xy = 20.

HMTG.

dont think i used statement (1) to evaluate 2...
i only used what was in the initial question and what was in statement (2)

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Re: DS - revisited   [#permalink] 10 Jun 2005, 18:15
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