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# In the rectangular coordinate system shown above, which quad

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Kudos [?]: 28803 [1] , given: 2849

In the rectangular coordinate system shown above, which quad [#permalink]  03 Mar 2014, 00:21
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Difficulty:

45% (medium)

Question Stats:

55% (02:30) correct 45% (01:32) wrong based on 159 sessions
The Official Guide For GMAT® Quantitative Review, 2ND Edition

Attachment:

Untitled.png [ 7.91 KiB | Viewed 1204 times ]
In the rectangular coordinate system shown above, which quadrant, if any, contains no point (x,y) that satisfies the inequality 2x - 3y\leq{- 6} ?

(A) None
(B) I
(C) II
(D) III
(E) IV

Problem Solving
Question: 123
Category: Geometry Simple coordinate geometry
Page: 77
Difficulty: 600

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Math Expert
Joined: 02 Sep 2009
Posts: 23381
Followers: 3607

Kudos [?]: 28803 [0], given: 2849

Re: In the rectangular coordinate system shown above, which quad [#permalink]  03 Mar 2014, 00:21
Expert's post
SOLUTION

In the rectangular coordinate system shown above, which quadrant, if any, contains no point (x,y) that satisfies the inequality 2x - 3y\leq{- 6} ?

(A) None
(B) I
(C) II
(D) III
(E) IV

{2x-3y}\leq{-6} --> y\geq{\frac{2}{3}x+2. Thi inequality represents ALL points, the area, above the line y={\frac{2}{3}x+2. If you draw this line you'll see that the mentioned area is "above" IV quadrant, does not contains any point of this quadrant.

Else you can notice that if x is positive, y can not be negative to satisfy the inequality y\geq{\frac{2}{3}x+2, so you can not have positive x, negative y. But IV quadrant consists of such (x,y) points for which x is positive and y negative. Thus answer must be E.

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Kudos [?]: 20 [7] , given: 131

Re: In the rectangular coordinate system shown above, which quad [#permalink]  04 Mar 2014, 02:07
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KUDOS

To draw the line on the Coordinate system consider the Inequality : 2x - 3y\leq{- 6} as 2x - 3y={- 6}

We get points (0,2) & (-3,0 )
So the line looks some what as in the attachment.

To find out which area is covered by the graph put the Cordinate (0,0) in the original question 2x - 3y\leq{- 6}

We get: 0 \leq {-6}. Which is False.

So (0,0) does not lie in the area covered by the graph, Therefore the equation covers the area above the line.

Thus 4th Quadrant does not contain any point that satisfies the inequality. ( Rest 3 Quadrants will have a few points that would satisfy the inequality)

Not experienced enough to comment on the difficulty level.
Attachments

Q.png [ 21.53 KiB | Viewed 1113 times ]

Math Expert
Joined: 02 Sep 2009
Posts: 23381
Followers: 3607

Kudos [?]: 28803 [1] , given: 2849

Re: In the rectangular coordinate system shown above, which quad [#permalink]  08 Mar 2014, 10:41
1
KUDOS
Expert's post
SOLUTION

In the rectangular coordinate system shown above, which quadrant, if any, contains no point (x,y) that satisfies the inequality 2x - 3y\leq{- 6} ?

(A) None
(B) I
(C) II
(D) III
(E) IV

{2x-3y}\leq{-6} --> y\geq{\frac{2}{3}x+2. Thi inequality represents ALL points, the area, above the line y={\frac{2}{3}x+2. If you draw this line you'll see that the mentioned area is "above" IV quadrant, does not contains any point of this quadrant.

Else you can notice that if x is positive, y can not be negative to satisfy the inequality y\geq{\frac{2}{3}x+2, so you can not have positive x, negative y. But IV quadrant consists of such (x,y) points for which x is positive and y negative. Thus answer must be E.

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Kudos [?]: 321 [0], given: 678

Re: In the rectangular coordinate system shown above, which quad [#permalink]  09 Mar 2014, 02:28
Attachment:
The attachment Untitled.png is no longer available
In the rectangular coordinate system shown above, which quadrant, if any, contains no point (x,y) that satisfies the inequality 2x - 3y\leq{- 6} ?

(A) None
(B) I
(C) II
(D) III
(E) IV

Sol: The inequality can be 2x=3y=-6 can be re-written in Y intercept form as y=2x/3 +2
Attachment:

Untitled1.png [ 11.93 KiB | Viewed 1016 times ]

Notice that the slop of the line is positive and hence it will definitely pass through Quad 1 and 3.
If the slope was negative then the line will definitely pass through Quad 2 and 4.

Now for x=0, y= 2 that means line will have to pass through Quad 2 as well.
Hence No point in Quad 4 will satisfy the given equation.
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Re: In the rectangular coordinate system shown above, which quad   [#permalink] 09 Mar 2014, 02:28
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