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# The ratio of 2 + 6^(1/2) to 3 is approximately equal to whic

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Manager
Joined: 11 Aug 2012
Posts: 127
Schools: HBS '16, Stanford '16
The ratio of 2 + 6^(1/2) to 3 is approximately equal to whic [#permalink]

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29 Dec 2012, 15:11
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Difficulty:

55% (hard)

Question Stats:

49% (02:10) correct 51% (01:00) wrong based on 182 sessions

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The ratio of $$2 + \sqrt{6}$$ to 3 is approximately equal to which of the following ratios?

A. 2 to 1
B. 3 to 2
C. 4 to 3
D. 7 to 6
E. 13 to 12

A fast method to solve it? Thanks!
[Reveal] Spoiler: OA

Last edited by Bunuel on 30 Dec 2012, 07:06, edited 1 time in total.
Renamed the topic and edited the question.
Intern
Joined: 21 Mar 2009
Posts: 20
Re: The ratio of [m]2 + [square_root]6[/square_root][/m] to [m] [#permalink]

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30 Dec 2012, 04:38
danzig wrote:
The ratio of $$2 + \sqrt{6}$$ to $$3$$ is approximately equal to which of the following ratios?

A. 2 to 1
B. 3 to 2
C. 4 to 3
D. 7 to 6
E. 13 to 12

A fast method to solve it? Thanks!

fast method revolves around estimation : 2*2 = 4 and 3*3 = 9 so sq root of 6 will fall between 2 and 3. To further gauze the same : 2.4*2.4=5.76 while 2.5*2.5 = 6.25 so we know we are looking for ratio slightly greater than 2+2.4/3 i.e. 4.4/3<x<4.5/3 fortunately 4.5 is a multiple of 3 so we can write 4.4/3<x<1.5 i.e. very close to 1.5

Now A is too big, B is close we know our ratio is near1.5 i.e 3 to 2 so wait until we find a better fit, C is definitely far away than is 1.5 so c is out.

D: its basically 3.5 to 3 and so this too is far wide than B.

E: denomitar is a multiplied by 4 will be numerator, it means we are talking about 13/4 i.e. 3.something so E is out.

SO B stands out
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Joined: 02 Sep 2009
Posts: 39588
Re: The ratio of 2 + 6^(1/2) to 3 is approximately equal to whic [#permalink]

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30 Dec 2012, 07:13
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danzig wrote:
The ratio of $$2 + \sqrt{6}$$ to 3 is approximately equal to which of the following ratios?

A. 2 to 1
B. 3 to 2
C. 4 to 3
D. 7 to 6
E. 13 to 12

A fast method to solve it? Thanks!

$$2.5^2=6.25$$, thus $$\sqrt{6}$$ is a bit less than 2.5.

Hence, $$2 + \sqrt{6}\approx{2+2.5}=4.5$$.

So, $$\frac{2 + \sqrt{6}}{3}\approx{\frac{4.5}{3}}=1.5=\frac{3}{2}$$.

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Re: The ratio of 2 + 6^(1/2) to 3 is approximately equal to whic [#permalink]

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02 Nov 2014, 07:42
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Re: The ratio of 2 + 6^(1/2) to 3 is approximately equal to whic [#permalink]

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06 Jan 2016, 19:34
1
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solved it other way:
sqrt(6) > sqrt(4)
but sqrt(6)<sqrt(9). thus
the answer should be between 4/3 and 5/3.
we can eliminate A, D, and E right away.
between B and C, we need a number greater than 4/3, since 4/3 is when sqrt(4), thus C is incorrect and B is the answer.
Director
Joined: 23 Jan 2013
Posts: 585
Schools: Cambridge'16
Re: The ratio of 2 + 6^(1/2) to 3 is approximately equal to whic [#permalink]

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12 Jan 2016, 22:10
2+sqrt6=2+2.4=4.4

4.4/3=44/30=22/15 means that 22 is 15 and its half, so 1.5 or 3/2

B
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Joined: 12 Aug 2015
Posts: 2185
Re: The ratio of 2 + 6^(1/2) to 3 is approximately equal to whic [#permalink]

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29 Nov 2016, 14:00
Here is what i did =>
√6+2 => 2.4+2=> 4.4
hence m/n=> 4.4/3 => 1.5 (approx)
m/n=1.5=3/2

Hence B
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Re: The ratio of 2 + 6^(1/2) to 3 is approximately equal to whic   [#permalink] 29 Nov 2016, 14:00
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