Official Guide Explanation:
Data Sufficiency #75




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Solution and Metadata

Question: 75
Page: 279
Difficulty: 6 (Moderately Difficult)
Category 1: Geometry > Coordinate Geometry > Slope

Explanation: Since we're given slope, it's best to convert the equation ax + by + c = 0 into point - slope formula to look more like y = mx + b:

ax + by + c = 0

by= - ax - c

y = ((-ax - c)/(b))

y= - ((a)/(b))x - ((c)/(b))

The slope, in that equation, is given by -((a)/(b)), so we know that -((a)/(b)) = (2/3).

Statement (1) is sufficient. Given the value of a, we can solve for b:

-((a)/(b)) = (2/3)

-(4/(b)) = (2/3)

-12 = 2b

b= - 6

Statement (2) is insufficient. We can add this information to the equation as follows:

y= - ((a)/(b))x - ((-6)/(b))

y= - ((a)/(b))x + (6/(b))

But we can't solve for b. Choice (A) is correct.

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