Jeff Miller

GMAT OFFICIAL GUIDE DS – Lines k and m are parallel to each other…

Lines k and m are parallel to each other…

Solution:

We are given that lines k and m are parallel to each other, and when two lines are parallel they have the same slope. We must determine whether the slope of line k is positive.

Solution:

Statement One Alone: 

Line k passes through the point (3, 2).

Using the information in statement one, the slope of line k can be positive or negative. An infinite number of lines can pass through the point (3, 2), some of which have positive slopes and some of which have negative slopes. Statement one alone is not sufficient to answer the question. We can eliminate answer choices A and D.

Statement Two Alone: 

Line m passes through the point (-3, 2).

Using the information in statement two, we know that the slope of line m can be positive or negative. An infinite number of lines can pass through the point (-3, 2), some of which have positive slopes and some of which have negative slopes. Statement two alone is not sufficient to answer the question. We can eliminate answer choice B.

Statements One and Two Together: 

Using the information in statements one and two we still do not have enough information to determine whether the slope of line k is positive or negative. Let’s further illustrate below.

Option 1: The slope of line k is negative.

Notice that line k slopes downward from left to right; thus, line k has a negative slope.

Option 2: The slope of line k is positive.

Notice that line k slopes upward from left to right; thus line k has a positive slope.

We see that we have a scenario in which line k has a positive slope and a scenario in which line k has a negative slope. Thus, statements one and two together are not sufficient to answer the question.

Answer: E 

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