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# GMAT Diagnostic Test Question 45

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Joined: 04 Dec 2002
Posts: 15153
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GMAT 1: 750 Q49 V42
GMAT Diagnostic Test Question 45 [#permalink]

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29 Sep 2013, 22:08
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GMAT Diagnostic Test Question 45

Field: Algebra
Difficulty: 600

If $$x=(\sqrt{5}-\sqrt{7})^2$$, then the best approximation of x is:

A. 0
B. 1
C. 2
D. 3
E. 4
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Last edited by Bunuel on 07 Oct 2013, 00:39, edited 1 time in total.
Updated
Founder
Joined: 04 Dec 2002
Posts: 15153
Location: United States (WA)
GMAT 1: 750 Q49 V42
Re: GMAT Diagnostic Test Question 45 [#permalink]

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29 Sep 2013, 22:10
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Explanation:

$$x=(\sqrt{5}-\sqrt{7})^2=5-2\sqrt{35}+7=12-2\sqrt{35}$$.

Since $$\sqrt{35}\approx{6}$$, then $$12-2\sqrt{35}\approx{12-2*6}=0$$.

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Intern
Joined: 05 Oct 2013
Posts: 21
Re: GMAT Diagnostic Test Question 45 [#permalink]

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21 Oct 2013, 10:56
bb wrote:

GMAT Diagnostic Test Question 45

Field: Algebra
Difficulty: 600

If $$x=(\sqrt{5}-\sqrt{7})^2$$, then the best approximation of x is:

A. 0
B. 1
C. 2
D. 3
E. 4

We have: $$0 < \sqrt{7} - \sqrt{5} = \frac{2}{\sqrt{7} + \sqrt{5}} < \frac{2}{4} = \frac{1}{2}$$. Therefore, $$0< (\sqrt{7} - \sqrt{5})^2 < \frac{1}{4}$$
Intern
Joined: 13 Dec 2013
Posts: 40
Schools: Fuqua (I), AGSM '16
GMAT 1: 620 Q42 V33
Re: GMAT Diagnostic Test Question 45 [#permalink]

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23 Feb 2014, 15:29
I'm not sure to understand the logic behind bb's analysis.
My approach was: SQRT(5) is close to 2.2 and SQRT(7) is close to 2.5.
The subtraction should be a decimal number, that becomes even smaller once raised to the 2nd power.
Therefore, the best estimate should be closer to 0 than to 1.
Math Expert
Joined: 02 Sep 2009
Posts: 39755
Re: GMAT Diagnostic Test Question 45 [#permalink]

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23 Feb 2014, 15:35
Enael wrote:
I'm not sure to understand the logic behind bb's analysis.
My approach was: SQRT(5) is close to 2.2 and SQRT(7) is close to 2.5.
The subtraction should be a decimal number, that becomes even smaller once raised to the 2nd power.
Therefore, the best estimate should be closer to 0 than to 1.

The OA is A, which is 0. The OE uses the square of the difference formula: $$(a-b)^2=a^2-2ab+b^2$$.
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Re: GMAT Diagnostic Test Question 45   [#permalink] 23 Feb 2014, 15:35
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# GMAT Diagnostic Test Question 45

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