dpatwa wrote: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.