fskilnik wrote:
GMATH practice exercises (Quant Class 12)
Which of the following numbers is closest to \(\,100\left( {11 - \sqrt {119} } \right)\,\) ?
(A) 8.5
(B) 9.2
(C) 9.9
(D) 10.6
(E) 11.3
\(?\,\,\,:\,\,\,\,100\left( {11 - \sqrt {119} } \right)\,\,\,{\rm{approx}}{\rm{.}}\)
\(\left( {11 - \sqrt {119} } \right)\left( {11 + \sqrt {119} } \right) = {11^2} - 119 = 2\,\,\,\,\, \Rightarrow \,\,\,\,\,11 - \sqrt {119} = {2 \over {11 + \sqrt {119} }}\)
\(100 < 119 < 121\,\,\,\, \Rightarrow \,\,\,\,10 < \sqrt {119} < 11\,\,\,\,\mathop \Rightarrow \limits^{ + 11} \,\,\,\,21 < 11 + \sqrt {119} < 22\,\,\,\, \Rightarrow \,\,\,\,{1 \over {22}} < {1 \over {11 + \sqrt {119} }} < {1 \over {21}}\)
\({2 \over {22}} < {2 \over {11 + \sqrt {119} }} < {2 \over {21}}\,\,\,\,\, \Rightarrow \,\,\,\,100 \cdot {1 \over {11}} < \underbrace {100\left( {11 - \sqrt {119} } \right)}_{{\rm{focus}}\,{\rm{!}}} < 100 \cdot {2 \over {21}}\)
\(\left. \matrix{
{{100} \over {11}} = {{99 + 1} \over {11}} = 9{1 \over {11}}\,\, \cong \,\,9.1 \hfill \cr
{{200} \over {21}} = {{210 - 10} \over {21}} = 10 - {{10} \over {21}} = 9{{11} \over {21}}\,\, \cong \,\,9.5 \hfill \cr} \right\}\,\,\,\,\,\, \Rightarrow \,\,\,\,\left( {\rm{B}} \right)\)
The correct answer is (B).
We follow the notations and rationale taught in the
GMATH method.
Regards,
Fabio.
_________________
Fabio Skilnik ::
GMATH method creator (Math for the GMAT)
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