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Math Expert
Joined: 02 Sep 2009
Posts: 59124

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16 Sep 2014, 00:13
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74% (00:59) correct 26% (01:06) wrong based on 153 sessions

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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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Math Expert
Joined: 02 Sep 2009
Posts: 59124

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16 Sep 2014, 00:14
1
Official Solution:

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

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

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

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

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Joined: 10 Sep 2014
Posts: 2
Schools: LBS '18

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06 Apr 2015, 20:38
1
Fractionalizing the result shows very clearly that the result is closer to 0 than to 1:
x=(√5−√7)^2 = [(5-7)/(√5+√7)]^2
=(-2)^2 / (√5+√7)]^2

= _4_
12+ √35

Now, √35 is close to 6, but undeniably between 5 and 6.
Even if you use both choices for the denominator's range:
12+2(5) = 22 --> x = 4/22 = 2/11
12+2(6) = 24 --> x = 4/24 = 1/6

1/6 < x < 2/11

With x(max) < 2/11, it is abundantly clear--with no room for error--that x is closer to 0.

Cheers!
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Joined: 03 Feb 2019
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16 Feb 2019, 04:43
1
ganeshj07 wrote:
If you approximate Root 5 and Root 7 you will get numbers between 2 - 3 and if you subtract one from another then you will definitely get less than 1 and any fraction if you Square then it will tend towards Zero hence its Zero

This is how I solved it more or less. Just wanted to point out that "if you square any fraction it will tend towards zero hence it's zero" is a bit misleading IMHO. While it is true that x^2 is less than x for all x whose absolute value between 0 and 1, and in that sense "tends" towards 0, this question specifically asked whether x^2 is closer to 0 or 1. There are plenty of examples, x = 0.75, x = 0.9, etc. where x^2 would be closer to 1 than to 0.
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Joined: 24 Dec 2013
Posts: 2
Location: United States
Concentration: General Management, Marketing

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16 Feb 2019, 06:48
1
mattlang1 wrote:
ganeshj07 wrote:
If you approximate Root 5 and Root 7 you will get numbers between 2 - 3 and if you subtract one from another then you will definitely get less than 1 and any fraction if you Square then it will tend towards Zero hence its Zero

This is how I solved it more or less. Just wanted to point out that "if you square any fraction it will tend towards zero hence it's zero" is a bit misleading IMHO. While it is true that x^2 is less than x for all x whose absolute value between 0 and 1, and in that sense "tends" towards 0, this question specifically asked whether x^2 is closer to 0 or 1. There are plenty of examples, x = 0.75, x = 0.9, etc. where x^2 would be closer to 1 than to 0.

Yes, You are right.... Square of anything more than 0.75 tend towards 1
Intern
Joined: 04 Sep 2018
Posts: 28
GPA: 3.33

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16 Jan 2019, 10:38
Hi, I didn't get this question at all or the solutions presented?

Can someone please explain this to me? Bought the gmat club tests, and I am working on building my concepts by solving the untimed quizzes.
Intern
Joined: 14 Jan 2018
Posts: 49
Location: India
Concentration: General Management, Entrepreneurship
GMAT 1: 660 Q50 V29
GPA: 3.8
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16 Jan 2019, 12:13
x=(5√−7√)2
So when we use (a-b)square formula which expands to a2 +b2 -2ab
we have 5+7-2*underrt(35)
We know under root (36) =6 so under rt (35) will be near to 6 or less than

So , X = 12-2*(Less than 6)
which gives us 0
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Joined: 24 Dec 2013
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16 Feb 2019, 03:12
If you approximate Root 5 and Root 7 you will get numbers between 2 - 3 and if you subtract one from another then you will definitely get less than 1 and any fraction if you Square then it will tend towards Zero hence its Zero
D01-45   [#permalink] 16 Feb 2019, 03:12
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