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In the rectangular coordinate system shown above, which [#permalink]
 10 Feb 2010, 13:06
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In the rectangular coordinate system shown above, which quadrant, if any, contains no point ( x, y ) that satisfies the inequality 2x-3y≤−6? (the quadrants are the standard quadrants in a co-ordinate system, I can't really draw it out here) A. None B. Ι C. ΙI D. ΙII E. IV
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Re: GMAT Paper test - Test Code 14 [#permalink]
10 Feb 2010, 13:31
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loki wrote: 1. In the rectangular coordinate system shown above, which quadrant, if any, contains no point ( x, y ) that satisfies the inequality 2x-3y≤−6? (the quadrants are the standard quadrants in a co-ordinate system, I can't really draw it out here)
(A) None
(B) Ι
(C) ΙI
(D) ΙII
(E) IV
Please explain your answer. I will post the OA soon. {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: GMAT Paper test - Test Code 14 [#permalink]
10 Feb 2010, 13:52
Bunuel wrote: loki wrote: 1. In the rectangular coordinate system shown above, which quadrant, if any, contains no point ( x, y ) that satisfies the inequality 2x-3y≤−6? (the quadrants are the standard quadrants in a co-ordinate system, I can't really draw it out here)
(A) None
(B) Ι
(C) ΙI
(D) ΙII
(E) IV
Please explain your answer. I will post the OA soon. {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. Thats great! I understand it now. I always seem to have problems with co-ordinate geometry. The official answer is E.
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Re: GMAT Paper test - Test Code 14 [#permalink]
30 Apr 2010, 22:24
loki wrote: 1. In the rectangular coordinate system shown above, which quadrant, if any, contains no point ( x, y ) that satisfies the inequality 2x-3y≤−6? (the quadrants are the standard quadrants in a co-ordinate system, I can't really draw it out here)
(A) None
(B) Ι
(C) ΙI
(D) ΙII
(E) IV
Please explain your answer. I will post the OA soon. Let us represent the equation in the intercept form: x/a + y/b = 1 x/(-3) + y/(2) >= 1 Now plot these intercepts on the chart and you will find that the quadrant not being touched is IV.
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Re: GMAT Paper test - Test Code 14 [#permalink]
03 Nov 2011, 07:41
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Here's my approach, which i think is easiest. Draw the equation line by determining to points, the easiest points are (0,y) and (x,0). Those points are (-3,0) and (0,2). Draw the line through the 2 points. Now pick one point and see if the inequality should be shaded to the left or to the right. I picked (-3,0), the inequality states that x<=-3, so shade to the left. you'll clearly see that the only quadrant that has no shading is IV.
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Re: GMAT Paper test - Test Code 14 [#permalink]
20 Nov 2011, 16:38
loki wrote: 1. In the rectangular coordinate system shown above, which quadrant, if any, contains no point ( x, y ) that satisfies the inequality 2x-3y≤−6? (the quadrants are the standard quadrants in a co-ordinate system, I can't really draw it out here)
(A) None
(B) Ι
(C) ΙI
(D) ΙII
(E) IV
Please explain your answer. I will post the OA soon. Hello can someone please tell me whats wrong with this approach ? y >= -2/3 x + 6 Thus slope is negative lets find x-intercept ... substitute y=0 we get , x <= 9 . To find y-intercept substitute x=0, we get y >=6 Thus it should be 3rd quadrant... but this is wrong ...
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Rectangular Coordinate System [#permalink]
20 May 2012, 03:45
In a rectangular coordinat system which quadrant, if any, contains no point (x,y) that satifies the inequality 2x - 3y <= -6? A) None B) 1st C) 2nd D)3rd E) 4th How to solve this guys any idea?
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Re: Rectangular Coordinate System [#permalink]
20 May 2012, 04:02
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enigma123 wrote: In a rectangular coordinat system which quadrant, if any, contains no point (x,y) that satifies the inequality
2x - 3y <= -6?
A) None
B) 1st
C) 2nd
D)3rd
E) 4th
How to solve this guys any idea? 2x - 3y <= -6 => -2x + 3y >= 6 ---- (1) equate the both sides of the inequality: -2x + 3y = 6 =>x/(-3) + y/2 = 1 comparing with x/a + y/b = 1 x intercept is -3 and y intercept is 2 ie the line passes thru (-3,0) and (0,2) This line obviously passes through the 1st, 2nd and 3rd quadrant and going back to the original inequality (1) we understand the points that satisfy this inequality would be above this line which means there is no chance that any of these points would lie in quadrant 4. So the ans is E
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Re: Rectangular Coordinate System [#permalink]
20 May 2012, 12:14
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Re: In the rectangular coordinate system shown above, which [#permalink]
24 Sep 2012, 07:56
Any other way to solve this problem without plotting a graph considering that people get on average 2 mins per problem?
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Re: In the rectangular coordinate system shown above, which [#permalink]
05 Jan 2013, 02:14
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loki wrote: In the rectangular coordinate system shown above, which quadrant, if any, contains no point ( x, y ) that satisfies the inequality 2x-3y≤−6? (the quadrants are the standard quadrants in a co-ordinate system, I can't really draw it out here)
A. None
B. Ι
C. ΙI
D. ΙII
E. IV Try I: 2(1) - 3(10) = -28 Yes! Try II: 2(-10) - 3(1) = -17 Yes! Try III: 2(-10) - 3(-1) = -17 Yes! Try IV: Since y is negative and x is positive... 2x will always be positive and -3y will always be positive = No! Answer: E
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Re: In the rectangular coordinate system shown above, which
[#permalink]
05 Jan 2013, 02:14
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