Data Sufficiency

If K and L are lines in the XY-plane, is the product of the slopes of K and L equal to -1?

(1) Line L passes through the origin and the point (1,2)
(2) Line K is x-intercept 4 and y-intercept 2.

A, B, C, D or E ?


Thanks you for you help!!

zozo123 wrote:If K and L are lines in the XY-plane, is the product of the slopes of K and L equal to -1?

(1) Line L passes through the origin and the point (1,2)
(2) Line K is x-intercept 4 and y-intercept 2.

A, B, C, D or E ?


Thanks you for you help!!

Clearly neither (1) nor (2) is insufficient as you need the slope of both
lines to determine the product. So, answer cannot be A, B or D.

1 tells us that slope of line L = (2-0) / (1-0) = 2

For 2, we need to find slope m in y = mx+c for line K

x-intercept is when y = 0, so 0 = mx + c or m = -c/x = -c/4
y-intercept is when x = 0, so 2 = c.

Using c=2 in m=-c/4, we get m = -1/2

Product = -1

Is it C?

If K and L are lines in the XY-plane, is the product of the slopes of K and L equal to -1?

(1) Line L passes through the origin and the point (1,2)
(2) Line K is x-intercept 4 and y-intercept 2

Statement 1 : Slope of line = y2-y1 / x2-x1 = 2-0/1-0 = 2. However we still do not know the slope of line K...Hence insufficient

Statement 2: Co-ordinates of line K = (4,0) and (0,2)...Hence slope = 2-0/0-4 = -1/2. Still insufficient, since we do not know anything about line L

Statement I and II : Slope of K * Slope of L = -1/2 * 2 = -1. Hence sufficient

Hi,

the answer is C, you're right!! thanks.