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

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

29 Dec 2012, 15:11

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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.

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Re: The ratio of [m]2 + [square_root]6[/square_root][/m] to [m] [#permalink]

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

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}.

Answer: B.
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Re: The ratio of 2 + 6^(1/2) to 3 is approximately equal to whic [#permalink] 30 Dec 2012, 07:13

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

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

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