BTGModeratorVI wrote: ↑

Wed Feb 03, 2021 10:33 am

If l and k are lines in the xy-plane, is the product of the slopes of l and k equal to -1 ?

(1) Line l passes through the origin and the point (1,2).
(2) Line k has x-intercept 4 and y-intercept 2.

Answer: C
Source: official guide

IMPORTANT: For geometry and coordinate plane Data Sufficiency questions, we are often checking to see whether the statements "LOCK" a particular line, angle, length, or shape into having just one possible position or measurement. This concept is discussed in much greater detail in the video below.

Target question: Is the product of the slopes of l and k equal to -1?

IMPORTANT: The product of the slopes will equal -1 if the lines are perpendicular to each other (unless the two lines are horizontal and vertical, in which case the product will equal zero). This allows us to REPHRASE the target question as...

REPHRASED target question: Are the two lines perpendicular to each other?

Statement 1: Line l passes through the origin and the point (1, 2)
NOTICE that statement 1 LOCKS line l into ONE AND ONLY ONE line.
That said, we have no information about line k, so we cannot determine whether the two lines are perpendicular to each other.
Since we cannot answer the REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: Line k has x-intercept 4 and y-intercept 2.
NOTICE that statement 1 LOCKS line k into ONE AND ONLY ONE line.
That said, we have no information about line l, so we cannot determine whether the two lines are perpendicular to each other.
Since we cannot answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 LOCKS in the shape of line l
Statement 2 LOCKS in the shape of line k
So, we COULD very well determine whether or not the two lines are perpendicular to each other
Since we can answer the REPHRASED target question with certainty, the combined statements are SUFFICIENT

Answer: C