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can some1 post the ans with solution.

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by mayur c » Mon Apr 12, 2010 7:26 am
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?
Note: Read 51/2 as "5 raised to 1/2"

(51/2 − 1)

(51/2 + 1) / 2

(51/2 + 1) / 4

(51/2 + 1) / (51/2 − 1)

(51/2 + 3) / (51/2 − 1)

Correct Ans is B
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by thephoenix » Mon Apr 12, 2010 7:35 am
mayur c wrote: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?
Note: Read 51/2 as "5 raised to 1/2"

(51/2 − 1)

(51/2 + 1) / 2

(51/2 + 1) / 4

(51/2 + 1) / (51/2 − 1)

(51/2 + 3) / (51/2 − 1)

Correct Ans is B
is the no. missing
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by rockeyb » Mon Apr 12, 2010 10:41 am
Yup I agree some thing is definitely missing.

Let x be the larger part y be the smaller part .


from the question we know x + y = N (The natural number )

Now N/ x = x / y as per the question .

But I cant see how the ration comes out to be (5^1/2) / 2 ?
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by kevincanspain » Mon Apr 12, 2010 1:54 pm
mayur c wrote: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?
Note: Read 51/2 as "5 raised to 1/2"

(51/2 − 1)

(51/2 + 1) / 2

(51/2 + 1) / 4

(51/2 + 1) / (51/2 − 1)

(51/2 + 3) / (51/2 − 1)

Correct Ans is B
Suppose n= x + y where y>x

(x+y)/y = y/x

x^2 +xy - y^2 = 0

x= (-y + sqrt(y^2 -4(1)(-y^2))/2 since x > 0 (using quadratic form. a=1 b=y c=-y^2

x = (-y + ysqrt(5))/2

x= y(sqrt(5) - 1)/2


y/x = 2/(sqrt(5) - 1) = 2(sqrt(5) + 1)/4 = (sqrt(5) + 1)/2
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by Brent@GMATPrepNow » Mon Apr 12, 2010 2:46 pm
mayur c wrote: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?
Note: Read 51/2 as "5 raised to 1/2"

(51/2 − 1)

(51/2 + 1) / 2

(51/2 + 1) / 4

(51/2 + 1) / (51/2 − 1)

(51/2 + 3) / (51/2 − 1)

Correct Ans is B
This ratio is known as the Golden Ratio (aka Golden Mean, Golden Section, etc) and it appears in many unlikely places.
For more info, see https://en.wikipedia.org/wiki/Golden_ratio
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