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In the rectangular coordinate system above, the shaded regio

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05 Jan 2014, 12:01
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The Official Guide For GMAT® Quantitative Review, 2ND Edition

Attachment:

Untitled.png [ 11.71 KiB | Viewed 12411 times ]
In the rectangular coordinate system above, the shaded region is bounded by straight lines. Which of the following is NOT an equation of one of the boundary line s?

(A) x = 0
(B) y = 0
(C) x = 1
(D) x - y = 0
(E) x + 2y = 2

Problem Solving
Question: 21
Category: Geometry Simple coordinate geometry
Page: 64
Difficulty: 600

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05 Jan 2014, 19:46
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In the rectangular coordinate system above, the shaded region is bounded by straight lines. Which of the following is NOT an equation of one of the boundary line s?

(A) x = 0
(B) y = 0
(C) x = 1
(D) x - y = 0
(E) x + 2y = 2

Attachment:

untitled2.PNG [ 9.45 KiB | Viewed 12303 times ]

Sol:We need to find the which of the lines is not represented in the graph given.

It is easier to point out that ans is D because x=y is a line at 45 degree to X -axis and there is no line passing as can be seen in the graph. Let's see if we can confirm

X=0 (Y-Axis) and X=1 are vertical lines so Option A and C ruled out
Y=0 is the horizontal line (X-axis)

Equation of the line with points of intersection (0,1) and (2,0)

Slope of the line = (y2-y1)/(x2-x1)-----> (1-0)/(0-2) ie. -1/2
The Y intercept form of line is given by y=mx+c where m is the slope (we calculated) and c is the y intercept when x=0 and we know C is 1
Thus y=-1/2x+1-------> x+2y=2, Hence E is ruled out.

Ans is D
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06 Jan 2014, 07:45
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Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

Attachment:
Untitled.png
In the rectangular coordinate system above, the shaded region is bounded by straight lines. Which of the following is NOT an equation of one of the boundary line s?

(A) x = 0
(B) y = 0
(C) x = 1
(D) x - y = 0
(E) x + 2y = 2

x= 0 and y = 0 are both y and x axis respectively so definitely those lines are there.
x = 1 is the line is parallel to y axis.
Now if we see there is a line which satisfies y = 1 when x =0 (that is on y axis) and x = 2 when y = 0 (that is on x axis), so only equation which satisfies both is x + 2y = 2.
Hence Option D) is the equation which is not present.
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30 Jun 2015, 10:19
Definitely D.

x-y=0 ; x=y is a line with a positive slope going through the origin.

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10 Dec 2015, 10:38
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x = 0, x = 1 are two vertical lines so they are ruled out.
y = 0 is x-axis so ruled out
Left with these two choice
(D) x - y = 0
(E) x + 2y = 2

looking at the remaining line in the figure we know that the slope is negative. D is y=x has positive slope so thats the answer
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26 Apr 2016, 13:26
x - y = 0 will give a line as x = y which will be inclined to positive x - axis at a angle of 45 degrees.
Any sort of this line is not at all can be seen in the given diagram

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08 Oct 2016, 07:19
According to MGMAT, vertical lines have undefined slope, then how is C is possible answer? I infer it refers to the vertical line at point (1,0), but if the slope is undefined then how do we get the equation?

Would appreciate a response.

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18 Nov 2017, 13:46
Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

Attachment:
Untitled.png
In the rectangular coordinate system above, the shaded region is bounded by straight lines. Which of the following is NOT an equation of one of the boundary line s?

(A) x = 0
(B) y = 0
(C) x = 1
(D) x - y = 0
(E) x + 2y = 2

x-y=0➡y=x
equation y=x has a positive slope of 1 and runs through the origin at a 45° angle
not a boundary line
D

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22 Nov 2017, 12:27
Bunuel wrote:

Attachment:
Untitled.png
In the rectangular coordinate system above, the shaded region is bounded by straight lines. Which of the following is NOT an equation of one of the boundary line s?

(A) x = 0
(B) y = 0
(C) x = 1
(D) x - y = 0
(E) x + 2y = 2

The vertical line on the left (which is also the y-axis) has the equation of x = 0.

The vertical line on the right has the equation of x = 1.

The horizontal line at the bottom (which is also the x-axis) has the equation of y = 0.

The diagonal line at the top has the equation of y = (-½)x + 1. When simplifying answer choice E, we see that we have that same equation:

x + 2y = 2

2y = -x + 2

y = (-½)x + 1

Thus, the correct answer is D.

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Re: In the rectangular coordinate system above, the shaded regio   [#permalink] 22 Nov 2017, 12:27
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