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# In the rectangular coordinate system above, the shaded region is bound

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In the rectangular coordinate system above, the shaded region is bound  [#permalink]

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04 Dec 2014, 07:46
1
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Difficulty:

25% (medium)

Question Stats:

75% (01:29) correct 25% (01:27) wrong based on 225 sessions

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Tough and Tricky questions: Coordinate Geometry.

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

A) x = 0
B) y = 0
C) x = 1
D) x − 3y = 0
E) y + 1/3*x = 1

Kudos for a correct solution.

Source: Chili Hot GMAT

Attachment:

2014-12-04_1846.png [ 7.38 KiB | Viewed 4709 times ]

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Re: In the rectangular coordinate system above, the shaded region is bound  [#permalink]

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04 Dec 2014, 10:46
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Note here that the straight lines with no slope are the easiest to identify. This includes x = 0, x = 1 and y = 0. The last thing to determine the is slanted line that forms the upper boundary of the shape.

We have two points (3,0) and (0,1)--from this we can determine that the y-intercept is 1 (from the second point) and the slope = (1-0)/(0-3) = -1/3. The equation of the line is y = -1/3*x + 1

Rearrange to get E, which means Choice D is NOT one of the bounding equations.
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Re: In the rectangular coordinate system above, the shaded region is bound  [#permalink]

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04 Dec 2014, 11:08
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A) x = 0 - stands for Y axis.
B) y = 0 - stands for X axis
C) x = 1 - stands for vertical line passing through point (1,0)
D) x − 3y = 0 ..... y=x/3... compare to y=mx+c form.... we get positive slope.... line in graph has negative slope.... answer
E) y + 1/3*x = 1 ..... y=-x/3+1..... compare to y=mx+c..... we get negative slope.... could be the equation of slanting line

Ans = D
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Re: In the rectangular coordinate system above, the shaded region is bound  [#permalink]

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04 Dec 2014, 22:20
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Answer = D) x − 3y = 0

Range of Y: 0 <= y <= 1

Range of X: 0 <= x <= 3

Option A, B, C, E is in the range as shown in pink dots (Refer diagram below)

Attachment:

2014-12-04_1846.png [ 8.49 KiB | Viewed 4561 times ]

Only for option D, for x = 1, y = 3 (Out of range shown by red dot)
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Re: In the rectangular coordinate system above, the shaded region is bound  [#permalink]

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18 Jul 2015, 05:54
A,B and C are staight lines and are shown in the grafik, so we are left with DE --> If the equation is one of the lines than any of the given points gives us a solution

D) x − 3y = 0 --> X=3Y, let test numbers (0,1) 0=3 is not true... our answer is (D)
E) y + 1/3*x = 1 --Y using same logix as above 1+1/3*0=1 it's TRUE
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Re: In the rectangular coordinate system above, the shaded region is bound  [#permalink]

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14 Jul 2016, 10:50
Bunuel wrote:

Tough and Tricky questions: Coordinate Geometry.

Attachment:
2014-12-04_1846.png
In the rectangular coordinate system above, the shaded region is bounded by a straight line. Which of the following is NOT an equation of one of the boundary lines?

A) x = 0
B) y = 0
C) x = 1
D) x − 3y = 0
E) y + 1/3*x = 1

Kudos for a correct solution.

Source: Chili Hot GMAT

Solving D in the form of y=mx+b gives us
y=x/3
This certainly means a positive slope .. but there is no line in the diagram that have a positive slope.
All the lines either have zero slopes (horizontal lines), Infinite slope (vertical lines) or negative slope (The inclined line )
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Re: In the rectangular coordinate system above, the shaded region is bound  [#permalink]

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25 Jun 2018, 22:12

First 3 choices are vertical and horizontal line constituting the 3 sides of shaded region.

Substitute the 3 coordinates of the shaded region on the remaining 2 choices and option D does not satisy one of the coordinates

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Re: In the rectangular coordinate system above, the shaded region is bound  [#permalink]

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25 Jun 2018, 23:26
You can also eliminate choice D since the line mentioned has a positive slope, it would go THROUGH the shaded region.
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Re: In the rectangular coordinate system above, the shaded region is bound  [#permalink]

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25 Aug 2019, 22:36
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Re: In the rectangular coordinate system above, the shaded region is bound   [#permalink] 25 Aug 2019, 22:36
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