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If 0.0030<x−√30<0.0031, which of the following...

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Answer

by EconomistGMATTutor » Wed Nov 01, 2017 9:31 am
This is an interesting question.

First thing you have to notice is 0.0030<x-√30<0.0031 implies that $$x\approx\sqrt{30}.$$

By the other hand, $$\frac{1}{\sqrt{30}}-\frac{1}{x}=\frac{x-\sqrt{30}}{\sqrt{30}\cdot x}.$$

Now, as $$x\approx\sqrt{30},\ then\ \sqrt{30}\cdot x\approx\sqrt{30}\cdot\sqrt{30}=30.$$

Finally, if we divide 0.0030<x-√30<0.0031 by √30*x we will get $$\frac{0.0030}{\sqrt{30}\cdot x}<\frac{x-\sqrt{3}0}{\sqrt{30}\cdot x}<\frac{0.0031}{\sqrt{30}\cdot x}\ <=>\ \frac{0.003}{30}<\frac{x-\sqrt{30}}{\sqrt{30}\cdot x}<\frac{0.0031}{30}$$

After simplifiying we get $$0.0001<\frac{x-\sqrt{30}}{\sqrt{30}\cdot x}<0.000103.$$

So, the correct option is C.

I really hope this can help you.

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