PR DS #9

[dpatwa]

If points (a, b) and (c, b) (not shown) lie in the coordinate system above, which quadrants contain the line that passes through (a, b) and (c, b)?

(1) a is a positive integer and c is a negative integer.
(2) b is a positive integer.


[spoiler]The OA is B, but I think it's C.[/spoiler] What do people think?

[pahwa]

It is asking about Quadrants.

A. Insuff as b is unknown
B. Insuff as a and c is unknown.

Together give us 2 quadrants first and second. Hence both statements together.

[baf2010]

I agree with both of you, so I don't understand why the answer isn't that. The solution says that the knowledge of B is enough to help us figure it out, but I don't get why. Anyone understand?

[Anurag@Gurome]

If points (a, b) and (c, b) (not shown) lie in the coordinate system above, which quadrants contain the line that passes through (a, b) and (c, b)?

(1) a is a positive integer and c is a negative integer.
(2) b is a positive integer.

It's intuitive that the points (a, b) and (c, b) will lie on the straight line y = b. If you don't understand why, then find the equation of the line that contain these two points.

Say the equation is y = mx + k, where m is the slope of the line and k is the y-intercept. Slope of the line will be = (b - b)/(c - a) = 0 => m = 0
Thus, y = k.
Put any of the points on these equation to find the value of k => k = b
Thus equation of the line is y = b

Therefore if b is positive, then quadrant I and II contains the line and if b is negative, then quadrant III and IV contain the line.

Statement 1: a is a positive integer and c is a negative integer.
Nothing about b.

Not sufficient

Statement 2: b is a positive integer.
Quadrant I and II contains the line.

Sufficient

The correct answer is B.

[baf2010]

Thanks, this actually points to something I guess is good to just ask-- so when they say line, it absolutely HAS to be a continuing line unless otherwise specified? I.e. it wasnt'a line segment that was just in quadrant 1 or 2? Is the line only cut off if a boundary is explicitly given?


Thanks again!