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by divya23 » Wed Jun 01, 2011 9:58 pm
In the xy-coordinate plane,the slope of line l is 3/4.Does line l pass through the point(-2/3,1/2)?
1.Line l passes through the point (4,4).
2.Line l passes through the point (-4,-2).

[spoiler]OA = D[/spoiler]
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Source: — Data Sufficiency |
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by cans » Wed Jun 01, 2011 10:28 pm
slope = 3/4
thus line: y=(3/4)x + c where c is y-intercept
a) passes through (4,4) thus (4,4) satisfies line and thus 4=3+c or c=1
now check for (-2/3,1/2)
(-2/3)*(3/4)+1 = 1/2 which is y, thus line passes. Sufficient
b) (-4,-2) solving this we get c=1
thus line passes
Sufficient
IMO D
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by Anurag@Gurome » Wed Jun 01, 2011 10:29 pm
divya23 wrote:In the xy-coordinate plane,the slope of line l is 3/4.Does line l pass through the point(-2/3,1/2)?
1.Line l passes through the point (4,4).
2.Line l passes through the point (-4,-2).

[spoiler]OA = D[/spoiler]

Solution:
Let the equation of line be y = (3/4)x+c.
Consider (1) alone.
It means that 4 = 3 + c.
Or c = 1.
So, if (-2/3, ½) has to pass through this line, ½ should be equal to (-2/3)*(3/4) + 1 which is true.
Or (1) alone is sufficient.
Next, consider (2) alone.
It means that -2 = (3/4)*(-4) + c.
Or, c = 1.
So, if (-2/3, ½) has to pass through this line, ½ should be equal to (-2/3)*(3/4) + 1 which is true.
Or (2) alone is also sufficient.

The correct answer is (D).
Anurag Mairal, Ph.D., MBA
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by aftableo2006 » Mon Jun 06, 2011 9:00 pm
condition a alone is not sufficient but condition b alone is sufficient so the correct answer is D
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