Similar questions to practice:
http://gmatclub.com/forum/tough-and-tri ... l#p1029228
http://gmatclub.com/forum/find-the-valu ... 38049.html
http://gmatclub.com/forum/find-the-valu ... 75403.html
https://gmatclub.com/forum/if-the-expre ... 32547.html
https://gmatclub.com/forum/if-the-expre ... 98647.html
https://gmatclub.com/forum/if-z2-2-2-2- ... 41717.html


Hope it helps.
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What we have is \(\sqrt{x+{\sqrt{x+\sqrt{x+\sqrt{x+...}}}}}=10\)

Squaring both sides

\(x+\)\({\sqrt{x+\sqrt{x+\sqrt{x+...}}}}=100\)

But \(\sqrt{x+{\sqrt{x+\sqrt{x+\sqrt{x+...}}}}}\) on left side after the first x+ is same as given in question which has given va;ue i.e. 10 therefore

\(x+\)10\(=100\)

\({x}=90\)

Answer: Option B
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CAT Question

\(\sqrt{x+{\sqrt{x+\sqrt{x+\sqrt{x+...}}}}}=10\)

squaring both sides...
x + \(\sqrt{x+{\sqrt{x+\sqrt{x+\sqrt{x+...}}}}}=100\)
Which is basically-
x + 10 = 100
x=90

I've mentioned this in other threads with similar types of questions -- there are no official GMAT questions like this. These are all prep company questions. The GMAT cannot test infinite sums (of fractions or of roots) because the first thing you need to do to answer these types of questions is prove the sum "converges" (it doesn't grow to infinity, and it gets closer and closer to a single value), and that requires calculus, which isn't tested on the GMAT.

So while the 'trick' that can be used to solve these questions is interesting, it's not something anyone will need on the test.
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