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Source: — Problem Solving |
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by GmatKiss » Tue Nov 01, 2011 3:40 am
GmatKiss wrote:Please help to solve this question
Can we substitute numbers to solve this one?
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by shankar.ashwin » Tue Nov 01, 2011 3:46 am
I guess you could, Sub n=1.

You get,

1/(Sqrt2 - 1) = Sqrt2 +1. Only E is of this form.
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by GmatKiss » Tue Nov 01, 2011 3:51 am
shankar.ashwin wrote:I guess you could, Sub n=1.

You get,

1/(Sqrt2 - 1) = Sqrt2 +1. Only E is of this form.
Sorry, i think am missing a basic thing here,

How is,
1/(Sqrt2 - 1) = Sqrt2 +1 ??
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by shankar.ashwin » Tue Nov 01, 2011 4:03 am
Whenever you have a square root in the denominator, try to simplify it. In this problem; multiply and divide the expression by Sqrt2 +1.
We do this to make the denominator of the form (a+b)*(a-b) = a^2-b^2

(Sqrt2 +1)
(Sqrt2 +1) * (Sqrt2 - 1)

Here, (Sqrt2 +1) * (Sqrt2 -1) = 2-1 = 1 (so the denominator becomes 1) and the numerator we multiplied (Sqrt2 +1) stays on.
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by neelgandham » Tue Nov 01, 2011 4:29 am
GmatKiss wrote:Please help to solve this question
Easiest way as mentioned by Shankar,is to rationalise the denominator but multiplying the numerator and denominator by the conjugate of the denominator like shown in the attachment to convert the irrational denominator to a rational one.
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by GMATGuruNY » Tue Nov 01, 2011 5:29 am
GmatKiss wrote:Please help to solve this question
Plug in a value for n and ballpark.
No need to worry about rationalizing the denominator.

Let n = 2.
1/(√n+1 - √n) = 1/(√3-√2) ≈ 1/(1.7 - 1.4) = 1/.3 = 10/3.

Now we plug n=2 into the answers to see which comes closest to our target of 10/3.

Only E works:
√(n+1) + √n = √3+√2 ≈ 1.7 + 1.4 = 3.1.

The correct answer is E.
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by GmatKiss » Tue Nov 01, 2011 6:01 am
Thanks all :) Each solution is simple and impressive :)
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by nsamkari » Thu Nov 03, 2011 8:52 pm
ANSWER IS [/spoiler]E
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