Question in the attachment

[eitijan]

Experts, please comment

[Knitgeek]

The question is asking you if there is enough information to determine if the slopes of each of the two lines.

Statement one doesn't allow you to calculate a second point for either line - Insufficient
Statement two doesn't allow you to calculate a second point for either line - Insufficient

Together the two statements allow you to find a second point for both lines and thus you can calculate the slope of each line and can answer the prompt - Sufficient

[eitijan]

Here,
slope of PQ = v/u
slope of AB = y/x
Combining 2 statements,
From statement1, y is negative and v is positive
From statement2, u=x and are positive
But sign of the slope tells the direction of the line.
As we are still not able to determine exact magnitude of the slopes to compare, we can't say slope of which line is greater .
Kindly resolve my gap.

[GMATGuruNY]

Here,
slope of PQ = v/u
slope of AB = y/x
Combining 2 statements,
From statement1, y is negative and v is positive
From statement2, u=x and are positive
But sign of the slope tells the direction of the line.
As we are still not able to determine exact magnitude of the slopes to compare, we can't say slope of which line is greater .
Kindly resolve my gap.

Statements combined:

Since PQ passes through (0, 0) and (u, v) -- and u and v are both POSITIVE -- the slope of PQ = (v-0)/(u-0) = (positive - 0)/(positive - 0) = positive/positive = POSITIVE.

Since AB passes through (0, 0) and (x, y) -- and x>0, while y<0 -- the slope of AB = (y-0)/(x-0) = (negative - 0)/(positive - 0) = negative/positive = NEGATIVE.

Since PQ>0 and AB<0, PQ>AB.
SUFFICIENT.

The correct answer is C.