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In the rectangular coordinate system shown above, which quad

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In the rectangular coordinate system shown above, which quad [#permalink] New post 03 Mar 2014, 00:21
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A
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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
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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Re: In the rectangular coordinate system shown above, which quad [#permalink] New post 03 Mar 2014, 00:21
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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.

Answer: E.
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Re: In the rectangular coordinate system shown above, which quad [#permalink] New post 04 Mar 2014, 02:07
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My answer is Option E i.e. 4th Quadrant

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)


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Q.png [ 21.53 KiB | Viewed 1113 times ]

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Re: In the rectangular coordinate system shown above, which quad [#permalink] New post 08 Mar 2014, 10:41
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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.

Answer: E.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: In the rectangular coordinate system shown above, which quad [#permalink] New post 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
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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