Data Sufficiency

Hi abhasjha,

This DS question is a great "concept" question.

We're told that we have 2 lines: L and K. We're asked if the product of their slopes = -1. This is a YES/NO question.

*The ONLY way for the product of 2 slopes to equal -1 is when the the lines are PERPENDICULAR (there is one exception though - if one of the lines is horizontal, then it has a slope of 0, so the product would = 0).

Fact 1: Line L passes through (0,0) and (1,2)

This gives us the slope of Line L (2), but does not tell us anything about line K.
Fact 1 is INSUFFICIENT

Fact 2: Line K has X-intercept 4 and Y-intercept 2.

This gives us two points on Line K: (4,0) and (0,2), which we can use to figure out the slope of Line K (-1/2). We don't know anything about Line L though.
Fact 2 is INSUFFICIENT

Combined, we know enough about both lines to figure out their slopes (even if you didn't do the work initially). With these slopes, we know that the lines ARE perpendicular, but we don't really have to do that work either.
Combined, SUFFICIENT.

Final Answer: C

GMAT assassins aren't born, they're made,
Rich

abhasjha wrote: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.

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 our free video: https://www.gmatprepnow.com/module/gmat- ... cy?id=1103

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?

Aside: We have a free video with tips on rephrasing the target question: https://www.gmatprepnow.com/module/gmat- ... cy?id=1100

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

Cheers,
Brent