Which of the following numbers is closest to 100*(11-sqrt(119)) ?

Question

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

GMATGuruNY · Accepted Answer

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.

B

fskilnik · Answer

?\,\,\,:\,\,\,\,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.

kylebecker9 · Answer

I'm sure there is a smarter way to do this, but it's clear that  \sqrt{119}  is something slightly less than  11

However, the answer choices are not spread far enough apart to be done at this point.

So then I thought about solving  (10+x)^2 = 119  where I know  x<1  
Trying  x=0.9  gives us  10^2+2*10*0.9+0.9^2 
Bingo, this is  100+18+0.81  which is very close to  119  but a little less, so our x was a little too low

Now to solve  100*(11-10.9) = 100* 0.1 = 10

Well shoot we know it's a little less but is it  9.9  or  9.2 ?

To have gotten  9.9 , we would have needed  x = .901 . That would not have been enough to get all the way to  119  in  10^2+2*10*0.901+0.901^2

Therefore, best guess is that  B  is the right answer

nick1816 · Answer

200/(11+root119)
=200/(11+10.9)
=9.13

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Which of the following numbers is closest to 100*(11-sqrt(119)) ?

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Which of the following numbers is closest to 100*(11-sqrt(119)) ?

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