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PS natural number

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PS natural number [#permalink]

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]

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: 1842

Location: New York

Followers: 20

Kudos [?]: 289 [0], given: 5

Re: PS natural number [#permalink]

12 Feb 2009, 15:01

walker wrote:

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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Your attitude determines your altitude
Smiling wins more friends than frowning

CEO

Joined: 17 Nov 2007

Posts: 3594

Concentration: Entrepreneurship, Other

Schools: Chicago (Booth) - Class of 2011

GMAT 1: 750 Q50 V40

Followers: 230

Kudos [?]: 1299 [0], given: 346

Re: PS natural number [#permalink]

12 Feb 2009, 15:30

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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