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26 Feb 2019, 16:30
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
45% (02:23) correct
55%
(02:29)
wrong
based on 174
sessions
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Date
Time
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Not Attempted Yet
GMATH practice exercise (Quant Class 20)
\(\left\{ \matrix{\\
\,xy > 0\, \hfill \cr \\
\,0 < y < 2\,\,\,\, \hfill \cr \\
\,x < y + 1 \hfill \cr} \right.\)
In the rectangular coordinate system, what is the area of the region defined by the points (x,y) that satisfy the system of inequalities above?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 5.5
\(\left\{ \matrix{\\
\,xy > 0\, \hfill \cr \\
\,0 < y < 2\,\,\,\, \hfill \cr \\
\,x < y + 1 \hfill \cr} \right.\)
In the rectangular coordinate system, what is the area of the region defined by the points (x,y) that satisfy the system of inequalities above?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 5.5
26 Feb 2019, 22:06
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fskilnik
Suggestion : Draw the figure
As we can see that the figure drawn is a trapezium with parallel sides of length 1 and 3 unit lengths and distance between the parallel sides is 2 units
hence area of the shaded region = (1/2)(sum of parallel sides*Distance between them = (1/2)*(1+3)*2 = 4 units
Answer: Option C
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27 Feb 2019, 08:25
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fskilnik
\(? = {S_{{\rm{shaded}}}}\,\,\,:\,\,\,\,\left\{ \matrix{\\
\,xy > 0\, \hfill \cr \\
\,0 < y < 2\,\,\,\, \hfill \cr \\
\,x < y + 1 \hfill \cr} \right.\,\,\,\,\,\, \cong \,\,\,\,\,\,\,\,\,\left\{ \matrix{\\
\,x > 0\, \hfill \cr \\
\,0 < y < 2\,\,\,\, \hfill \cr \\
\,y > x - 1 \hfill \cr} \right.\,\)
\(? = {S_{\rm{I}}} + {S_{{\rm{II}}}} = 1 \cdot 2 + {{\left( {3 - 1} \right) \cdot 2} \over 2} = 4\,\,\,\,\, \Rightarrow \,\,\,\,\left( {\rm{C}} \right)\)
We follow the notations and rationale taught in the GMATH method.
Regards,
Fabio.
