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# x/y condition

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VP
Joined: 18 May 2008
Posts: 1206

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26 Feb 2009, 10:31
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

I have read in some question that $$x/y <=1$$ MUST be true for all positive values if $$x$$ is a prime factor of $$y^2$$
Is this a standard formula?
SVP
Joined: 07 Nov 2007
Posts: 1765
Location: New York

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26 Feb 2009, 10:56
ritula wrote:
I have read in some question that $$x/y <=1$$ MUST be true for all positive values if $$x$$ is a prime factor of $$y^2$$
Is this a standard formula?

y^2 = k*x = l^2*x*x { here k= l^2*x to make RHS perfect square.}

y = (lx)

x/y =1/l (clearly L is >=1)

so
$$x/y <=1$$
must be true.
_________________

Smiling wins more friends than frowning

Manager
Joined: 26 Dec 2008
Posts: 57
Schools: Booth (Admit R1), Sloan (Ding R1), Tuck (R1)

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26 Feb 2009, 16:03
x2suresh wrote:
ritula wrote:
I have read in some question that $$x/y <=1$$ MUST be true for all positive values if $$x$$ is a prime factor of $$y^2$$
Is this a standard formula?

y^2 = k*x = l^2*x*x { here k= l^2*x to make RHS perfect square.}

y = (lx)

x/y =1/l (clearly L is >=1)

so
$$x/y <=1$$
must be true.

Was thinking along the same lines, but how can we justify that y = whole number? What if y = sqrt(5), and x = 5? or y = sqrt(10) and x = 5?

Thx
SVP
Joined: 07 Nov 2007
Posts: 1765
Location: New York

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26 Feb 2009, 18:58
xyz21 wrote:
x2suresh wrote:
ritula wrote:
I have read in some question that $$x/y <=1$$ MUST be true for all positive values if $$x$$ is a prime factor of $$y^2$$
Is this a standard formula?

y^2 = k*x = l^2*x*x { here k= l^2*x to make RHS perfect square.}

y = (lx)

x/y =1/l (clearly L is >=1)

so
$$x/y <=1$$
must be true.

Was thinking along the same lines, but how can we justify that y = whole number? What if y = sqrt(5), and x = 5? or y = sqrt(10) and x = 5?

Thx

above rule is valid only if Y is integer..
_________________

Smiling wins more friends than frowning

SVP
Joined: 07 Nov 2007
Posts: 1765
Location: New York

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26 Feb 2009, 18:58
xyz21 wrote:
x2suresh wrote:
ritula wrote:
I have read in some question that $$x/y <=1$$ MUST be true for all positive values if $$x$$ is a prime factor of $$y^2$$
Is this a standard formula?

y^2 = k*x = l^2*x*x { here k= l^2*x to make RHS perfect square.}

y = (lx)

x/y =1/l (clearly L is >=1)

so
$$x/y <=1$$
must be true.

Was thinking along the same lines, but how can we justify that y = whole number? What if y = sqrt(5), and x = 5? or y = sqrt(10) and x = 5?

Thx

above rule is valid only if Y is integer..
_________________

Smiling wins more friends than frowning

SVP
Joined: 17 Jun 2008
Posts: 1507

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28 Feb 2009, 17:01
I agree with xyz1. It is not mentioned whether y is an integer. Hence, the given inequality may or may not be true.

In geenral, if x is a prime factor of y, then x/y <= 1 will always be true as x <= y.

For example, x = 2, y = 2
or, x = 3, y = 6
and so on.
SVP
Joined: 29 Aug 2007
Posts: 2457

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01 Mar 2009, 07:15
ritula wrote:
I have read in some question that $$x/y <= 1$$ MUST be true for all positive values if $$x$$ is a prime factor of $$y^2$$
Is this a standard formula?

Agree that the relationship doesnot hold true.

Since x and y^2 are but y could be +ve or -ve number, (x/y) <= 1 or y.

Did you get the question correctly, ritula?

Either "$$x/y <= 1$$ should be x/y^2 <= 1" or "y^2 is y".
_________________

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VP
Joined: 18 May 2008
Posts: 1206

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01 Mar 2009, 09:10
The statement is correct
GMAT TIGER wrote:
ritula wrote:
I have read in some question that $$x/y <= 1$$ MUST be true for all positive values if $$x$$ is a prime factor of $$y^2$$
Is this a standard formula?

Agree that the relationship doesnot hold true.

Since x and y^2 are but y could be +ve or -ve number, (x/y) <= 1 or y.

Did you get the question correctly, ritula?

Either "$$x/y <= 1$$ should be x/y^2 <= 1" or "y^2 is y".
Re: x/y condition   [#permalink] 01 Mar 2009, 09:10
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# x/y condition

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