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by pradeepss » Mon Sep 22, 2008 3:21 pm
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?

1. (51/2 − 1)

2. (51/2 + 1) / 2

3. (51/2 + 1) / 4

4. (51/2 + 1) / (51/2 − 1)

5. (51/2 + 3) / (51/2 − 1)
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Re: Quant

by Morgoth » Mon Sep 22, 2008 3:58 pm
pradeepss 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?

1. (51/2 − 1)

2. (51/2 + 1) / 2

3. (51/2 + 1) / 4

4. (51/2 + 1) / (51/2 − 1)

5. (51/2 + 3) / (51/2 − 1)

IMO (51/2 + 3) / (51/2 − 1)

x smaller number
y larger number

(x+y)/y = y/x

(51/2 + 3) / (51/2 − 1) = 57/49 ~ 106/57

Whats the OA?
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by Ian Stewart » Mon Sep 22, 2008 4:34 pm
Let x be the number, and let's divide x up so that:

x = y + z

and y > z. Because the question tells us that the ratio of x to y is equal to the ratio of y to z, we have the following:

(y+z)/y = y/z

so

1 + z/y = y/z

If we let r = y/z (notice that r is what the question is asking for), this becomes:

1 + 1/r = r
0 = r^2 - r- 1

You can use the quadratic formula (ruling out the negative solution, since r must be positive) to find that r = (1 + sqrt(5))/2.

That's just the famous 'golden ratio', incidentally. I'm not sure where the answer choices in the original post came from...
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by lunarpower » Tue Sep 23, 2008 2:20 am
incidentally. I'm not sure where the answer choices in the original post came from...
applying my awesome psychic cold reading powers, which even work across broadband connections, i deduce that "51/2" is supposed to be 5^(1/2), or, √5.
likewise for the rest.
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by Morgoth » Tue Sep 23, 2008 3:42 am
I have a question about finding roots of quadratic equation.

r^2-r-1 = 0

Are you using the b^2-4ac formula for finding the roots, if not what is the other way of finding the precise root when one cannot simplify the equation. [trial & error]

If yes, then i presume this cannot be a part of GMAT since GMAT does not expects us to remember the b^2-4ac formula as discussed previously on this forum itself.

It'd be nice if you could point me in the right direction.

Thanks.
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Hmm that was a bit ambigous

by sumidi » Tue Sep 23, 2008 10:56 am
I dont know why you all thought the same(maybe it shows I haven't done enought questions like these). But when I read the first line "A natural number is divided into two positive unequal parts " I instantly assumed

x= y*z
NOT

x = y + z

Silly Silly me.
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by stop@800 » Tue Sep 23, 2008 12:46 pm
Morgoth wrote:I have a question about finding roots of quadratic equation.

r^2-r-1 = 0

Are you using the b^2-4ac formula for finding the roots, if not what is the other way of finding the precise root when one cannot simplify the equation. [trial & error]
If you can't simplify the equation [in terms of sum and products] then there is very good probability that the roots are not integers.

so you will have to use below mention formula

roots = (-b + sqrt(b^2 - 4ac)) / (2a) and (-b - sqrt(b^2 - 4ac)) / (2a)

If yes, then i presume this cannot be a part of GMAT since GMAT does not expects us to remember the b^2-4ac formula as discussed previously on this forum itself.

It'd be nice if you could point me in the right direction.

Thanks.
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Re: Hmm that was a bit ambigous

by Ian Stewart » Tue Sep 23, 2008 2:47 pm
sumidi wrote:I dont know why you all thought the same(maybe it shows I haven't done enought questions like these). But when I read the first line "A natural number is divided into two positive unequal parts " I instantly assumed

x= y*z
NOT

x = y + z

Silly Silly me.
Not silly at all - I think that's a perfectly natural way to interpret the question, and I considered that interpretation as well before realizing that you wouldn't be able to get a unique answer that way. If this were a real GMAT question (it clearly is not!), the wording would not be so open to interpretation- it would be clear what was meant on the real test.

Morgoth- yes, I've used the quadratic formula in my solution. I have never seen a real GMAT question that requires the quadratic formula, and for that reason, I don't think this question is much like anything you'll see on the real test.

Ron- you do indeed have awesome powers. :)
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Re: Quant

by pradeepss » Tue Sep 23, 2008 6:28 pm
Morgoth wrote:
pradeepss 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?

1. (51/2 − 1)

2. (51/2 + 1) / 2

3. (51/2 + 1) / 4

4. (51/2 + 1) / (51/2 − 1)

5. (51/2 + 3) / (51/2 − 1)

IMO (51/2 + 3) / (51/2 − 1)

x smaller number
y larger number

(x+y)/y = y/x

(51/2 + 3) / (51/2 − 1) = 57/49 ~ 106/57

Whats the OA?

Let N be the natural number and L be the larger of the two individual parts.
Then, the given relation is N / L = L / (N − L).
∴ N 2 − LN = L2.
Let the required ratio be R = N / L. Dividing the above equation by L2 gives
R2 − R − 1 = 0.
The solution to the above quadratic equation isR = (1 + 51/2) / 2.
Since N is a natural number, only the positive root is considered for R.
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