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tough question

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by kvcpk » Tue Jul 06, 2010 11:53 pm
5x+2y >= 10

5x+2y =10 is a line that intersects x axis at 2 and y axis at 5.

Now 5x+2y>=10 will always beupwards to the line since (0,0) does not satisfy the equation.

So Quadrant 3 or C should not have any value fo rthis inequality

pick 3
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by gmatmachoman » Wed Jul 07, 2010 12:45 am
kvcpk wrote:5x+2y >= 10

5x+2y =10 is a line that intersects x axis at 2 and y axis at 5.

Now 5x+2y>=10 will always beupwards to the line since (0,0) does not satisfy the equation.

So Quadrant 3 or C should not have any value fo rthis inequality

pick 3
My way of solving it :

When both x& y values are negative, the inequality does NOT hold true.

Ex: x= -1 y= -2

5x+2y >= 10
5*-1+2*-2

-5-4 is NOT >= 10.

So values in 3rd quadrant will fail for the inequality.

Pick C
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by sanju09 » Wed Jul 07, 2010 3:51 am
gmatmachoman wrote:
kvcpk wrote:5x+2y >= 10

5x+2y =10 is a line that intersects x axis at 2 and y axis at 5.

Now 5x+2y>=10 will always beupwards to the line since (0,0) does not satisfy the equation.

So Quadrant 3 or C should not have any value fo rthis inequality

pick 3
My way of solving it :

When both x& y values are negative, the inequality does NOT hold true.

Ex: x= -1 y= -2

5x+2y >= 10
5*-1+2*-2

-5-2 is NOT >= 10.

So values in 3rd quadrant will fail for the inequality.

Pick C
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by GMATGuruNY » Wed Jul 07, 2010 6:12 am
bupbebeo wrote:Which quadrant of the rectangular coordinate system to the left does not contain any point (x, y) expressed by the inequality -5x - 2y ≤ -10 ?


Image



1. A
2. B
3. C
4. D
5. None
Let's rewrite the equation so that it's in the form y = mx + b and we can see the slope and the y-intercept:

-5x - 2y ≤ -10
- 2y ≤ 5x -10
y>=(-5/2)x + 5

The line y = (-5/2)x + 5 represents the lower border of the region expressed by the inequality. The border has a negative slope and crosses the y axis at (0,5). So it never passes through quadrant C. Since the inequality represents the region that includes the border and every y value greater than -- meaning above -- the border, no points in quadrant C are included.

The correct answer is C.

Whenever you are given the equation for a line that is not in the form y = mx + b, rewrite the equation in this form so that you can see the slope and the y-intercept and understand how the line looks.
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