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# In the rectangular coordinate system, what is the area of the region d

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GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 935
In the rectangular coordinate system, what is the area of the region d  [#permalink]

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26 Feb 2019, 16:30
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Difficulty:

75% (hard)

Question Stats:

45% (02:38) correct 55% (02:33) wrong based on 33 sessions

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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

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Re: In the rectangular coordinate system, what is the area of the region d  [#permalink]

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26 Feb 2019, 22:06
1
fskilnik wrote:
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

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

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Re: In the rectangular coordinate system, what is the area of the region d  [#permalink]

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27 Feb 2019, 08:25
1
1
fskilnik wrote:
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

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

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

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

Regards,
Fabio.
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Fabio Skilnik :: GMATH method creator (Math for the GMAT)
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Re: In the rectangular coordinate system, what is the area of the region d   [#permalink] 27 Feb 2019, 08:25
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