Can we substitute numbers to solve this one?GmatKiss wrote:Please help to solve this question
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Source: Beat The GMAT — Problem Solving |
Sorry, i think am missing a basic thing here,shankar.ashwin wrote:I guess you could, Sub n=1.
You get,
1/(Sqrt2 - 1) = Sqrt2 +1. Only E is of this form.
How is,
1/(Sqrt2 - 1) = Sqrt2 +1 ??
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.
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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neelgandham
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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.GmatKiss wrote:Please help to solve this question
- Attachments
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Anil Gandham
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GMATGuruNY
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Plug in a value for n and ballpark.GmatKiss wrote:Please help to solve this question
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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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
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