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# Ratio equals

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Manager
Joined: 25 May 2009
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21 Jun 2009, 10:28
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Solve, what ratio with two integers is equal to the ratio $$1 + \sqrt{5}$$ to $$2$$?

[Reveal] Spoiler:
I am getting 4:3 using conjugates, the actual question says 'nearly equal' and estimates that 8:5 is correct, but I believe that 4:3 is more accurate.

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GMAT Tutor
Joined: 24 Jun 2008
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21 Jun 2009, 11:17
I3igDmsu wrote:
Solve, what ratio with two integers is equal to the ratio $$1 + \sqrt{5}$$ to $$2$$?

I am getting 4:3 using conjugates, the actual question says 'nearly equal' and estimates that 8:5 is correct, but I believe that 4:3 is more accurate.

The ratio is not exactly equal to any ratio involving integers, which is why the question asks for an approximation. Since root(5) is greater than root(4), or 2, then 1 + root(5) must be greater than 3, and the ratio in question should be slightly greater than 3 to 2. Since 4 to 3 is less than 3 to 2, it should not be the right answer.
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Manager
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Concentration: Finance
GMAT Date: 12-16-2011

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21 Jun 2009, 15:30
What answer are you getting if you use conjugates?

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GMAT Tutor
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21 Jun 2009, 15:46
I3igDmsu wrote:
What answer are you getting if you use conjugates?

There's no reason to use conjugates here, but if you did, you'd find:

root(5) + 1 to 2
= [root(5) + 1] * [root(5) - 1] to 2*[root(5) - 1]
= 5 - 1 to 2*root(5) - 2
= 2 to root(5) - 1

It's harder to get an estimate now than it was in the original question, which is why it doesn't make much sense to use conjugates here. Still, even with a rough estimate of root(5) here, you can see that the answer should be somewhere between 3 to 2 and 2 to 1.
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Manager
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22 Jun 2009, 14:59

root 5 aproximately equals 2.24, so 3.25 to 2 equals 13 to 8.......

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Senior Manager
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25 Jun 2009, 21:16
\sqrt{5} is almost equal to 2.2,
so 3.2 : 2 (multiply by 5 to get integers on both sides)
you get 16 : 10
or 8 : 5

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Senior Manager
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26 Jun 2009, 01:29
As integers increase, one can find a so near ratio. root 5 is something near 2,23. So equation comes near 1,62. One can say this 81/50. That is to say, something missing in question.

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Intern
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26 Jun 2009, 13:15
I got 13/8 as well. took underroot of 5 and added 1 and then divided by 2 =325/200 = 13/8

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Re: Ratio equals   [#permalink] 26 Jun 2009, 13:15
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