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# If 0.0030<x-√30<0.0031, which of the following options is the approxim

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Senior SC Moderator
Joined: 14 Nov 2016
Posts: 1315
Location: Malaysia
If 0.0030<x-√30<0.0031, which of the following options is the approxim  [#permalink]

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23 Feb 2017, 19:38
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65% (02:44) correct 35% (01:07) wrong based on 55 sessions

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If $$0.0030<x-\sqrt{30}<0.0031$$, which of the following options is the approximation of  $$\frac{1}{\sqrt{30}}-\frac{1}{x}$$?

A. 0.001
B. 0.002
C. 0.0001
D. 0.0002
E. 0.0003

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Joined: 13 Oct 2016
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Re: If 0.0030<x-√30<0.0031, which of the following options is the approxim  [#permalink]

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24 Feb 2017, 01:46
3
AustinKL wrote:
If $$0.0030<x-\sqrt{30}<0.0031$$, which of the following options is the approximation of  $$\frac{1}{\sqrt{30}}-\frac{1}{x}$$?

A. 0.001
B. 0.002
C. 0.0001
D. 0.0002
E. 0.0003

Hi

$$0.0030<x-\sqrt{30}<0.0031$$

$$\sqrt{30} + 0.0030 < x < \sqrt{30} + 0.0031$$

$$\frac{1}{\sqrt{30}}-\frac{1}{x}$$ = $$(x - \sqrt{30}) / x * \sqrt{30}$$

$$min = \frac{0.003}{(\sqrt{30} + 0.003)*\sqrt{30}} = \frac{0.003}{30 + 0.003*\sqrt{30}} ≈ \frac{0.003}{30} = \frac{3*0.001}{3*10} = 0.0001$$

$$max = \frac{0.0031}{(\sqrt{30} + 0.0031)*\sqrt{30}} = \frac{0.0031}{30 + 0.0031*\sqrt{30}} ≈ \frac{0.0031}{30} = \frac{0.003}{30} + \frac{0.0001}{30} ≈ \frac{0.003}{30} = 0.0001$$
.

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Joined: 09 Mar 2016
Posts: 940
If 0.0030<x-√30<0.0031, which of the following options is the approxim  [#permalink]

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30 Sep 2018, 12:09
1
hazelnut wrote:
If $$0.0030<x-\sqrt{30}<0.0031$$, which of the following options is the approximation of  $$\frac{1}{\sqrt{30}}-\frac{1}{x}$$?

A. 0.001
B. 0.002
C. 0.0001
D. 0.0002
E. 0.0003

here is my approach

The $$\sqrt{30}$$ is about 5.4

Hence x is between $$0.0030<x-5.4<0.0031$$ add 5.4 to both sides so difference between maximum and minimum value is 0.0001

so I clicked on C
If 0.0030<x-√30<0.0031, which of the following options is the approxim &nbs [#permalink] 30 Sep 2018, 12:09
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