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root{463} is between

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Intern
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Joined: 10 Aug 2012
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root{463} is between [#permalink] New post 12 Aug 2012, 08:31
00:00
A
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Difficulty:

  15% (low)

Question Stats:

89% (01:20) correct 11% (00:55) wrong based on 80 sessions
\sqrt{463} is between

(A) 21 and 22
(B) 22 and 23
(C) 23 and 24
(D) 24 and 25
(E) 25 and 26

What is the fastest way to solve this problem?
[Reveal] Spoiler: OA
Intern
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Re: [square_root]463[/square_root] is between [#permalink] New post 12 Aug 2012, 08:35
The way I solved it was by realizing

20^2= 400

so 21^2 = 20^2 +20 + 1*21 = 441

and

22^2 = 20^2 +20*2 + 2*21 = 440 + 40 + 42 > 500

so \sqrt{463} is >21 but <22

still wasn't that fast, but it made me think there might be some formula or something.
Director
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Re: [square_root]463[/square_root] is between [#permalink] New post 12 Aug 2012, 08:58
JustinDragna wrote:
The way I solved it was by realizing

20^2= 400

so 21^2 = 20^2 +20 + 1*21 = 441

and

22^2 = 20^2 +20*2 + 2*21 = 440 + 40 + 42 > 500

so \sqrt{463} is >21 but <22

still wasn't that fast, but it made me think there might be some formula or something.


Your reasoning is perfect. And there is no magic formula to help here.
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Love GMAT Quant questions and running.

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Joined: 05 Jul 2012
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Re: [square_root]463[/square_root] is between [#permalink] New post 12 Aug 2012, 18:27
JustinDragna wrote:
The way I solved it was by realizing

20^2= 400

so 21^2 = 20^2 +20 + 1*21 = 441

and

22^2 = 20^2 +20*2 + 2*21 = 440 + 40 + 42 > 500

so \sqrt{463} is >21 but <22

still wasn't that fast, but it made me think there might be some formula or something.



The other way is to find the square root of 463 first and then compare it, but even this method will require atleast 3-4 iterations and is pretty long.
Re: [square_root]463[/square_root] is between   [#permalink] 12 Aug 2012, 18:27
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