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

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Math Expert
Joined: 02 Sep 2009
Posts: 55683
(2+2 * sqrt (6) )/2  [#permalink]

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19 Jan 2014, 23:55
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Difficulty:

5% (low)

Question Stats:

91% (00:23) correct 9% (00:46) wrong based on 812 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, 23:56
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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20 Jan 2014, 00:32
2
(2 + 2(root)6)/2 = (2/2) + (2(root6)/2 = 1 + root 6 which is answer option C.
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Re: (2+2 * sqrt (6) )/2  [#permalink]

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20 Jan 2014, 01:53
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, 20:10
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, 21:23
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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Re: (2+2 * sqrt (6) )/2  [#permalink]

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23 Jan 2014, 06:41
4
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, 12:43
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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Re: (2+2 * sqrt (6) )/2  [#permalink]

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18 Oct 2017, 15:29
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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Re: (2+2 * sqrt (6) )/2  [#permalink]

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18 Oct 2017, 15:39
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, 06:11
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  [#permalink]

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29 Jan 2019, 15:38
Who cannot solve this question should stay at home... lol
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Re: (2+2 * sqrt (6) )/2  [#permalink]

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17 Jun 2019, 13:06
Top Contributor
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) $$2+\sqrt{6}$$

Here's the long solution so that students can see exactly what's happening algebraically.

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

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

$$=1 \times \frac{1+\sqrt{6}}{1}$$

$$=1+\sqrt{6}$$

Cheers,
Brent
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Re: (2+2 * sqrt (6) )/2   [#permalink] 17 Jun 2019, 13:06
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