If 0.010

Question

If 0.010 < x - √5 < 0.011, approximation of 1/√5 - 1/x is which of the following options?

A. 0.01
B. 0.002
C. 0.02
D. 0.003
E. 0.03

stne · Answer

We know  \sqrt{5}  will be more then  2  but less than  3

Since approximate values are required let  \sqrt{5}\approx 2.1

0.010 < x - √5 < 0.011

0.010 < x - 2.1< 0.011

2.110 < x < 2.111

x \approx 2.11

Therefore  \frac{1}{\sqrt5 } - \frac{1}{2.1} \approx 0

So among the options, one that is closest to zero will be the answer.

Ans B

Jxmes · Answer

https://gmatclub.com/forum/download/file.php?id=83319 GMAT-Club-Forum-p7ycq3r9.png

hr1212 · Answer

0.010 + \sqrt{5} < x < 0.011 + \sqrt{5}

\sqrt{5}*(0.010 + \sqrt{5}) < \sqrt{5}*x < \sqrt{5}*(0.011 + \sqrt{5})

\sqrt{5}*x   ≈ 5 --- (1)

We need to calculate,

\frac{1}{\sqrt{5}} - \frac{1}{x}  =  \frac{x-\sqrt{5}}{\sqrt{5}*x}  =  \frac{x-\sqrt{5}}{5}

0.010 < x - \sqrt{5} < 0.011

\frac{0.010}{5} < \frac{x - \sqrt{5}}{5} < \frac{0.011}{5}

0.002 < \frac{x - \sqrt{5}}{5} < 0.0022

IMO: B

sujoykrdatta · Answer

0.01 < x - 5/√5 < 0.011 => 0.01 < (x√5 - 5)/5 < 0.011 => 0.05 < x√5 - 5 < 0.011 => 5.05 < x√5 < 5.011 Now: 1/√5 - 1/x = (x - √5)/x√5 The numerator is between 0.01 and 0.011 The denominator is between 5.05 and 5.011 Thus, approximately: (x - √5)/x√5 ~= 0.01/5.05 ~=1/500 = 0.002 Ans B

If 0.010 < x - 5 < 0.011, approximation of 1/5 - 1/x is which of the

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