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PS natural number

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SVP
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PS natural number [#permalink]

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New post 12 Feb 2009, 14:05
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A natural number is divided into two positive unequal parts such that the ratio of the original number to the larger (divided) part is equal to the ratio of the larger part to the smaller part. What is the value of this ratio?

A (5^1/2 − 1)

B (5^1/2 + 1) / 2

C (5^1/2 + 1) / 4

D (5^1/2 + 1) / (5^1/2 − 1)

E (5^1/2 + 3) / (5^1/2 − 1)

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Re: PS natural number [#permalink]

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New post 12 Feb 2009, 14:17
B

n - a natural number
x - larger part
y - smaller part

n/x=x/y=a --> (x+y)/x=x/y=a --> 1+y/x=x/y=a ---> 1+1/a=a

a^2-a-1=0

\(a=\frac{1\pm\sqrt{5}}{2}\)

We have two positive parts, so a is positive: \(a=\frac{1+\sqrt{5}}{2}\)
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Location: New York
Re: PS natural number [#permalink]

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New post 12 Feb 2009, 15:01
walker wrote:
B

n - a natural number
x - larger part
y - smaller part

n/x=x/y=a --> (x+y)/x=x/y=a --> 1+y/x=x/y=a ---> 1+1/a=a

a^2-a-1=0

\(a=\frac{1\pm\sqrt{5}}{2}\)

We have two positive parts, so a is positive: \(a=\frac{1+\sqrt{5}}{2}\)


I arrived till a^2-a-1=0

I forgot how to solve the this quadratic equation... Do you need to remember the formula..
or easy way to find "a" from the equation ?
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Schools: Chicago (Booth) - Class of 2011
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Re: PS natural number [#permalink]

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New post 12 Feb 2009, 15:30
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Expert's post
I think we need to remember it.

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This is not a quality discussion. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.

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Re: PS natural number   [#permalink] 12 Feb 2009, 15:30
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