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# (2+2 * sqrt (6) )/2

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Math Expert
Joined: 02 Sep 2009
Posts: 51185
(2+2 * sqrt (6) )/2  [#permalink]

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19 Jan 2014, 22:55
1
6
00:00

Difficulty:

5% (low)

Question Stats:

89% (00:17) correct 11% (00:24) wrong based on 992 sessions

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The Official Guide For GMAT® Quantitative Review, 2ND Edition

$$\frac{2+2\sqrt{6}}{2}=$$

(A) $$\sqrt{6}$$
(B) $$2\sqrt{6}$$
(C) $$1+\sqrt{6}$$
(D) $$1+2\sqrt{6}$$
(E) $$2+\sqrt{6}$$

Problem Solving
Question: 50
Category: Arithmetic Operations on radical expressions
Page: 68
Difficulty: 600

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Re: (2+2 * sqrt (6) )/2  [#permalink]

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19 Jan 2014, 22:56
SOLUTION

$$\frac{2+2\sqrt{6}}{2}=$$

(A) $$\sqrt{6}$$
(B) $$2\sqrt{6}$$
(C) $$1+\sqrt{6}$$
(D) $$1+2\sqrt{6}$$
(E) $$2+\sqrt{6}$$

$$\frac{2+2\sqrt{6}}{2}=1+\sqrt{6}$$.

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Re: (2+2 * sqrt (6) )/2  [#permalink]

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19 Jan 2014, 23:32
1
(2 + 2(root)6)/2 = (2/2) + (2(root6)/2 = 1 + root 6 which is answer option C.
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Joined: 17 Oct 2013
Posts: 41
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GMAT Date: 02-04-2014
Re: (2+2 * sqrt (6) )/2  [#permalink]

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20 Jan 2014, 00:53
1
Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

$$\frac{2+2\sqrt{6}}{2}=$$

(A) $$\sqrt{6}$$
(B) $$2\sqrt{6}$$
(C) $$1+\sqrt{6}$$
(D) $$1+2\sqrt{6}$$
(E) $$2+\sqrt{6}$$

Problem Solving
Question: 50
Category: Arithmetic Operations on radical expressions
Page: 68
Difficulty: 600

GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition - Quantitative Questions Project

Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project:
2. Please vote for the best solutions by pressing Kudos button;
3. Please vote for the questions themselves by pressing Kudos button;
4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

Thank you!

$$\frac{2*(1+\sqrt{6})}{2}=1+\sqrt{6}$$
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Re: (2+2 * sqrt (6) )/2  [#permalink]

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20 Jan 2014, 19:10
1
Since 2 is a common factor in numerator and denominator , so taking 2 from each component of numerator and cancelling it with denominator.
(2+2*6^1/2)/2
=[2(1+6^1/2)]/2
=(2/2)(1+6^1/2)
=1+6^1/2

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Re: (2+2 * sqrt (6) )/2  [#permalink]

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20 Jan 2014, 20:23
1
Taking the common number 2 from numerator gives us the result 1+\sqrt{6}; {2 gets canceled out}

Ans is (C)
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Joined: 27 May 2012
Posts: 631
Re: (2+2 * sqrt (6) )/2  [#permalink]

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23 Jan 2014, 05:41
3
Bunuel wrote:
$$\frac{2+2\sqrt{6}}{2}=$$

(A) $$\sqrt{6}$$
(B) $$2\sqrt{6}$$
(C) $$1+\sqrt{6}$$
(D) $$1+2\sqrt{6}$$
(E) $$2+\sqrt{6}$$

Take 2 common from Numerator , then cancel the 2 from Numerator and Denominator

$$\frac{2+2\sqrt{6}}{2}= \frac{2(1+\sqrt{6})}{2}=1+\sqrt{6}$$

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Re: (2+2 * sqrt (6) )/2  [#permalink]

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18 Oct 2017, 11:43
Can anyone explain to me why this is incorrect?

1) multiple both sides of expression by 2
2) subtracting 2 from both sides
3) leaves you with 2squareroot6

Thanks
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Joined: 22 May 2016
Posts: 2204
Re: (2+2 * sqrt (6) )/2  [#permalink]

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18 Oct 2017, 14:29
1
Bunuel wrote:

$$\frac{2+2\sqrt{6}}{2}=$$

(A) $$\sqrt{6}$$
(B) $$2\sqrt{6}$$
(C) $$1+\sqrt{6}$$
(D) $$1+2\sqrt{6}$$
(E) $$2+\sqrt{6}$$
Quote:

modernx wrote:
Can anyone explain to me why this is incorrect?

1) multiple both sides of expression by 2
2) subtracting 2 from both sides
3) leaves you with 2squareroot6

Thanks

modernx , I think you must have assumed that RHS of equation = 1. It doesn't say that. So the best we can do is to simplify the fraction.

$$\frac{2+2\sqrt{6}}{2}=$$

$$\frac{2+2\sqrt{6}}{2} = 1$$ (NO) -
Multiply by 2 to clear the fraction

$$2+2\sqrt{6} = 2$$
Subtract 2 from both

$$2\sqrt{6} = 0$$ (NO)

Look at your statement #1. . . "both sides of the equation." There is not a right hand side value. . . It's easy to do when you are in a hurry or tired.

You cannot assume that the right hand side equals one. Hope that helps.
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Joined: 08 Aug 2017
Posts: 6
Re: (2+2 * sqrt (6) )/2  [#permalink]

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18 Oct 2017, 14:39
modernx wrote:
Can anyone explain to me why this is incorrect?

1) multiple both sides of expression by 2
2) subtracting 2 from both sides
3) leaves you with 2squareroot6

Thanks
[/quote][/quote]
, I think you must have assumed that RHS of equation = 1. It doesn't say that. So the best we can do is to simplify the fraction.

$$\frac{2+2\sqrt{6}}{2}=$$

$$\frac{2+2\sqrt{6}}{2} = 1$$ (NO) -
Multiply by 2 to clear the fraction

$$2+2\sqrt{6} = 2$$
Subtract 2 from both

$$2\sqrt{6} = 0$$ (NO)

Look at your statement #1. . . "both sides of the equation." There is not a right hand side value. . . It's easy to do when you are in a hurry or tired.

You cannot assume that the right hand side equals one. Hope that helps. [/quote]

Thanks for the clear explanation
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Re: (2+2 * sqrt (6) )/2  [#permalink]

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24 Oct 2017, 05:11
Quote:

$$\frac{2+2\sqrt{6}}{2}=$$

(A) $$\sqrt{6}$$
(B) $$2\sqrt{6}$$
(C) $$1+\sqrt{6}$$
(D) $$1+2\sqrt{6}$$
(E) $$2+\sqrt{6}$$

Distributing the 2 in the denominator, we have:

2/2 + (2√6)/2 = 1 + √6

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Re: (2+2 * sqrt (6) )/2 &nbs [#permalink] 24 Oct 2017, 05:11
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