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PS natural number

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SVP
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PS natural number [#permalink] New post 12 Feb 2009, 13:05
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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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CEO
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Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
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Re: PS natural number [#permalink] New post 12 Feb 2009, 13:17
Expert's post
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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SVP
SVP
User avatar
Joined: 07 Nov 2007
Posts: 1824
Location: New York
Followers: 29

Kudos [?]: 572 [0], given: 5

Re: PS natural number [#permalink] New post 12 Feb 2009, 14:01
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 ?
_________________

Your attitude determines your altitude
Smiling wins more friends than frowning

Expert Post
CEO
CEO
User avatar
Joined: 17 Nov 2007
Posts: 3574
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Followers: 421

Kudos [?]: 2287 [0], given: 359

GMAT ToolKit User Premium Member
Re: PS natural number [#permalink] New post 12 Feb 2009, 14:30
Expert's post
I think we need to remember it.
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Re: PS natural number   [#permalink] 12 Feb 2009, 14:30
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