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# M18-31

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Math Expert
Joined: 02 Sep 2009
Posts: 54371

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16 Sep 2014, 01:04
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Difficulty:

5% (low)

Question Stats:

88% (00:40) correct 12% (01:18) wrong based on 190 sessions

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$$\frac{1}{\sqrt{2}} + \frac{1}{2 +\sqrt{2}} = ?$$

A. $$\frac{1}{\sqrt{2}}$$
B. 1
C. $$\sqrt{2}$$
D. 2
E. $$2\sqrt{2}$$

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Math Expert
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Posts: 54371

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16 Sep 2014, 01:04
Official Solution:

$$\frac{1}{\sqrt{2}} + \frac{1}{2 +\sqrt{2}} = ?$$

A. $$\frac{1}{\sqrt{2}}$$
B. 1
C. $$\sqrt{2}$$
D. 2
E. $$2\sqrt{2}$$

Reduce the fractions to the common denominator: $$\frac{1}{\sqrt{2}} + \frac{1}{2 + \sqrt{2}} = \frac{(2 + \sqrt{2}) + \sqrt{2}}{2\sqrt{2} + 2} = 1$$.

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Joined: 23 Nov 2014
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20 Jun 2015, 01:05
how u take lcm and add plz elaborate?
Math Expert
Joined: 02 Sep 2009
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20 Jun 2015, 02:15
mzeeshang224 wrote:
how u take lcm and add plz elaborate?

$$\sqrt{2}(2 + \sqrt{2})=\sqrt{2}*2 + \sqrt{2}*\sqrt{2}=\sqrt{2}*2+2$$
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Joined: 01 Jun 2016
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GMAT 1: 600 Q42 V31
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07 Aug 2016, 12:14
How did you divide the MMC by the factors?
Intern
Joined: 04 Jan 2017
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22 Apr 2017, 06:31
Please can one disclose how the common denominator has been divided by the independent denominators
Manager
Joined: 12 Jun 2016
Posts: 214
Location: India
WE: Sales (Telecommunications)

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27 May 2017, 21:27
Hi wwambugu14,

Not sure if I understand you right. But Bunuel has simply added the two fractions.

The Common Denominator would be the LCM of $$\sqrt{2}$$ and $$(2 + \sqrt{2})$$. This would be the multiplication of the two. This turns out as - $$\sqrt{2}(2 + \sqrt{2})=\sqrt{2}*2 + \sqrt{2}*\sqrt{2}=\sqrt{2}*2+2$$

Once the Common denominator is set as the LCM its pretty much addition as we do with fractions. in the end, both Numerator and denominator end up to be $$\sqrt{2}*2+2$$ and we get one as the answer.

See the official solution for how its actually done.

Hope this helps.

wwambugu14 wrote:
Please can one disclose how the common denominator has been divided by the independent denominators

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13 Jul 2017, 06:33
I can´t crack the algebra, can someone please help or tell me where can I learn more? I tried to look for examples but I did not find any.
Thanks
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13 Jul 2017, 07:03
1
cocojiz wrote:
I can´t crack the algebra, can someone please help or tell me where can I learn more? I tried to look for examples but I did not find any.
Thanks

Multiple and divide first expression by $$\sqrt{2}$$ and second expression by $$2-\sqrt{2}$$ and use $$(a+b)(a-b)=a^2 - b^2$$ for second expression's denominator.
What we will get is :
$$\sqrt{2}/2$$ + (2- $$\sqrt{2}$$) / (4-2 )

that becomes:
($$\sqrt{2} + 2 - \sqrt{2}$$)/2
= 2/2
=1
=B

You can read more in GMATClub Maths book chapter Ratio and Proportions and "Algebraic Identities" from chapter Algebra.

Hope this helped
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14 Jul 2017, 03:52
When stuck with MCM, estimation work as well:

> 1/sqrt(2) ~ 1/1,41 ~ 1/1,5 ~ 2/3

> 1/(2+sqrt(2)) ~ 1/(3,41) ~ 1/3,3 ~ 1/3

> 2/3 + 1/3 = 1

Note that I rounded one up and one down.
Re: M18-31   [#permalink] 14 Jul 2017, 03:52
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# M18-31

Moderators: chetan2u, Bunuel

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