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In the rectangular coordinate system, what is the area of th

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by fskilnik@GMATH » Tue Feb 26, 2019 3:13 pm

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GMATH practice exercise (Quant Class 20)

Image

Answer: [spoiler]____(C)__[/spoiler]
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
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by jpcameron17 » Wed Feb 27, 2019 6:18 am
Could you please upload the image of the system described? It's impossible to answer the question otherwise.
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by fskilnik@GMATH » Wed Feb 27, 2019 7:09 am
jpcameron17 wrote:Could you please upload the image of the system described? It's impossible to answer the question otherwise.
The "image of the system" is part of the solution! As you will see below, it is almost the whole solution itself!

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Fabio.
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by fskilnik@GMATH » Wed Feb 27, 2019 7:11 am
fskilnik@GMATH wrote:GMATH practice exercise (Quant Class 20)

Image
Image

$$? = {S_{{\rm{shaded}}}}\,\,\,:\,\,\,\,\left\{ \matrix{
\,xy > 0\, \hfill \cr
\,0 < y < 2\,\,\,\, \hfill \cr
\,x < y + 1 \hfill \cr} \right.\,\,\,\,\,\, \cong \,\,\,\,\,\,\,\,\,\left\{ \matrix{
\,x > 0\, \hfill \cr
\,0 < y < 2\,\,\,\, \hfill \cr
\,y > x - 1 \hfill \cr} \right.\,$$

$$? = {S_{\rm{I}}} + {S_{{\rm{II}}}} = 1 \cdot 2 + {{\left( {3 - 1} \right) \cdot 2} \over 2} = 4\,\,\,\,\, \Rightarrow \,\,\,\,\left( {\rm{C}} \right)$$

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

Regards,
Fabio.
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