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02 Mar 2020, 06:26
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
66% (01:00) correct
34%
(01:35)
wrong
based on 393
sessions
History
Date
Time
Result
Not Attempted Yet
If \(x\) is a positive number and \(\sqrt{x+{\sqrt{x+\sqrt{x+\sqrt{x+...}}}}}=10\), where the given expression extends to an infinite number of roots, then what is the value of \(x\)?
A. 80
B. 90
C. 100
D. 110
E. 120
Are You Up For the Challenge: 700 Level Questions
A. 80
B. 90
C. 100
D. 110
E. 120
Are You Up For the Challenge: 700 Level Questions
02 Mar 2020, 06:30
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Bunuel
Similar questions to practice:
https://gmatclub.com/forum/tough-and-tri ... l#p1029228
https://gmatclub.com/forum/find-the-valu ... 38049.html
https://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.
General Discussion
02 Mar 2020, 06:35
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Bunuel
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
