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# PS natural number

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SVP
Joined: 07 Nov 2007
Posts: 1741
Location: New York

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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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CEO
Joined: 17 Nov 2007
Posts: 3486
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40

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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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SVP
Joined: 07 Nov 2007
Posts: 1741
Location: New York

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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 ?
_________________

Smiling wins more friends than frowning

CEO
Joined: 17 Nov 2007
Posts: 3486
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40

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12 Feb 2009, 15:30
1
KUDOS
Expert's post
I think we need to remember it.

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