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# If m and n are positive integers, is 3√m < √(m+n) ?

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Intern
Joined: 17 Dec 2012
Posts: 29
If m and n are positive integers, is 3√m < √(m+n) ? [#permalink]

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15 Aug 2013, 05:03
2
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Difficulty:

55% (hard)

Question Stats:

58% (01:16) correct 42% (01:44) wrong based on 106 sessions

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If m and n are positive integers, is 3√m < √(m+n) ?

(1) m + n > 8m
(2) n > 8m

Can someone explain how to solve this problem. The official explanation does not make complete sense to me.
[Reveal] Spoiler: OA

Last edited by Bunuel on 15 Aug 2013, 05:06, edited 1 time in total.
RENAMED THE TOPIC.
Math Expert
Joined: 02 Sep 2009
Posts: 44290
Re: Total GMAT Maths : If m and n are positive integers, is 3√m [#permalink]

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15 Aug 2013, 05:10
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Expert's post
If m and n are positive integers, is $$3\sqrt{m} < \sqrt{m+n}$$?

Since both sides of the inequality are non-negative we can safely square it. Thus the questions becomes: is $$9m<m+n$$? --> is $$8m<n$$?

(1) m + n > 8m --> $$n>7m$$. Not sufficient, consider n=8 and m=1 for a NO answer and n=9 and m=1 for an YES answer.

(2) n > 8m. Directly gives an YES answer to the question. Sufficient.

Hope it's clear.
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Re: If m and n are positive integers, is 3√m < √(m+n) ? [#permalink]

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11 Oct 2017, 13:59
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Re: If m and n are positive integers, is 3√m < √(m+n) ?   [#permalink] 11 Oct 2017, 13:59
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# If m and n are positive integers, is 3√m < √(m+n) ?

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