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In the rectangular coordinate system shown above, which [#permalink]
10 Feb 2010, 12:06

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E

Difficulty:

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Question Stats:

61% (02:10) correct
39% (01:04) wrong based on 287 sessions

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)

Re: GMAT Paper test - Test Code 14 [#permalink]
10 Feb 2010, 12:31

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Expert's post

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.

Re: GMAT Paper test - Test Code 14 [#permalink]
10 Feb 2010, 12:52

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.

Re: GMAT Paper test - Test Code 14 [#permalink]
30 Apr 2010, 21:24

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.

Re: GMAT Paper test - Test Code 14 [#permalink]
03 Nov 2011, 06:41

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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.

Re: GMAT Paper test - Test Code 14 [#permalink]
20 Nov 2011, 15:38

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 ...

Re: Rectangular Coordinate System [#permalink]
20 May 2012, 03:02

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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

_________________

Best Vaibhav

If you found my contribution helpful, please click the +1 Kudos button on the left, Thanks

Re: In the rectangular coordinate system shown above, which [#permalink]
05 Jan 2013, 01:14

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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!

Let convert this in to an equation 3y = 2x + 6 ------> y = \frac{2x}{3} + 2

We know that equation of any line is y = mx + c ------where m = slope and C = y intercept

So in our case slope = \frac{2}{3} and Y intercept = 2

With above values following line can be drawn

We can notice that in the original inequality 3y≥ 2x + 6 as the value of Y will go up, the corresponding value of X will also go up to satisfy the inequality and hence the line drawn above will also continue to incline in the same direction in 1st quadrant. We can deduce that this line will never pass thru IV quadrant. Hence Choice E is the answer.

Re: In the rectangular coordinate system shown above, which [#permalink]
08 Oct 2013, 08:34

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

I'm not sure if this is the right approach but the way i did it was:

2x-3y≤−6, so 2x-3y≤0 so it the subtraction of both HAS to be negative. Therefore, the only way for this to NOT happen is if 2x>0 and -3y<0 because then both will be positive and it is impossible to have a negative number as a result.

Hence (E)

gmatclubot

Re: In the rectangular coordinate system shown above, which
[#permalink]
08 Oct 2013, 08:34