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Which of the following numbers is closest to 100*(11-sqrt(

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by fskilnik@GMATH » Thu Feb 14, 2019 12:50 pm

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GMATH practice exercise (Quant Class 12)

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Answer: [spoiler]____(B)__[/spoiler]
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by GMATGuruNY » Thu Feb 14, 2019 2:42 pm
fskilnik@GMATH wrote:GMATH practice exercise (Quant Class 12)

Image

Answer: [spoiler]____(B)__[/spoiler]
100(11 - √119)(11 + √119) = 100(11² - √119²) = 100(121-119) = 100*2 = 200.

When the correct answer is multiplied by 11+√119, the result must be as close as possible to 200.
11+√119 = 11 + (a bit less than 11) = a bit less than 22.
Since 9*22 = 198, multiplying 9.2 by a bit less than 22 will yield a product close to 200.

The correct answer is B.
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by fskilnik@GMATH » Thu Feb 14, 2019 5:01 pm
fskilnik@GMATH wrote:GMATH practice exercise (Quant Class 12)

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$$?\,\,\,:\,\,\,\,100\left( {11 - \sqrt {119} } \right)\,\,\,{\rm{approx}}{\rm{.}}$$

$$\left( {11 - \sqrt {119} } \right)\left( {11 + \sqrt {119} } \right) = {11^2} - 119 = 2\,\,\,\,\, \Rightarrow \,\,\,\,\,11 - \sqrt {119} = {2 \over {11 + \sqrt {119} }}$$
$$100 < 119 < 121\,\,\,\, \Rightarrow \,\,\,\,10 < \sqrt {119} < 11\,\,\,\,\mathop \Rightarrow \limits^{ + 11} \,\,\,\,21 < 11 + \sqrt {119} < 22\,\,\,\, \Rightarrow \,\,\,\,{1 \over {22}} < {1 \over {11 + \sqrt {119} }} < {1 \over {21}}$$

$${2 \over {22}} < {2 \over {11 + \sqrt {119} }} < {2 \over {21}}\,\,\,\,\, \Rightarrow \,\,\,\,100 \cdot {1 \over {11}} < \underbrace {100\left( {11 - \sqrt {119} } \right)}_{{\rm{focus}}\,{\rm{!}}} < 100 \cdot {2 \over {21}}$$

$$\left. \matrix{
{{100} \over {11}} = {{99 + 1} \over {11}} = 9{1 \over {11}}\,\, \cong \,\,9.1 \hfill \cr
{{200} \over {21}} = {{210 - 10} \over {21}} = 10 - {{10} \over {21}} = 9{{11} \over {21}}\,\, \cong \,\,9.5 \hfill \cr} \right\}\,\,\,\,\,\, \Rightarrow \,\,\,\,\left( {\rm{B}} \right)$$


The correct answer is (B).


We follow the notations and rationale taught in the GMATH method.

Regards,
Fabio.
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