Lines k and m are parallel to each other.

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jjjinapinch: Senior | Next Rank: 100 Posts; Posts: 83; Joined: Mon Jul 24, 2017 8:16 amFollowed by: 1 member

by jjjinapinch » Mon Jul 31, 2017 6:36 am

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Lines k and m are parallel to each other. Is the slope of line k positive?
(1) Line k passes through the point (3, 2).
(2) Line m passes through the point (-3, 2).

Official Guide question
Answer: E

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Source: Beat The GMAT — Data Sufficiency | Mon Jul 31, 2017 6:36 am

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by Brent@GMATPrepNow » Mon Jul 31, 2017 7:23 am

jjjinapinch wrote:Lines k and m are parallel to each other. Is the slope of line k positive?
(1) Line k passes through the point (3, 2).
(2) Line m passes through the point (-3, 2).

Official Guide question
Answer: E

Target question: Is the slope of line k positive?

Given: Lines k and m are parallel to each other.

Let's jump straight to....

Statements 1 and 2 combined
There are many cases that satisfy BOTH statements. Here are two:

Case a:

In this case, the slope of line k is POSITIVE

Case b:

In this case, the slope of line k is NEGATIVE

Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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by Jay@ManhattanReview » Mon Jul 31, 2017 11:28 pm

jjjinapinch wrote:Lines k and m are parallel to each other. Is the slope of line k positive?

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

Official Guide question
Answer: E

Nice solution by Brent.

Here's equation approach...

Say the equation of line k is y = mx + c and the equation of line m is y = mx + d;

where m = magnitude of the slope of the lines, and c and d are y-intercepts of lines K and m, respectively.

Since the lines are parallel to each other, their slope, thus magnitude would be equal.

We have to determine whether m is positive.

Statement 1: Line k passes through the point (3, 2).

We have: the equation of line k is y = mx + c;

Thus, 2 = 3m + c. We cannot get the value of m. Insufficient.

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

We have: the equation of line m is y = mx + d;

Thus, 2 = -3m + d. We cannot get the value of m. Insufficient.

Statement 1 & 2 combined:

We have 2 = 3m + c and 2 = -3m + d. There are three variables and only two linear equations, we cannot get the value of m. Insufficient.

The correct answer: E

Hope this helps!

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Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 amFollowed by: 22 members; Location: New York, NY; Thanked: 39 times

by Jeff@TargetTestPrep » Wed Aug 09, 2017 11:17 am

jjjinapinch wrote:Lines k and m are parallel to each other. Is the slope of line k positive?
(1) Line k passes through the point (3, 2).
(2) Line m passes through the point (-3, 2).

Official Guide question
Answer: E

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.

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.

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 know that line k passes through (3, 2) and line m passes through (-3, 2). However, we still do not have enough information to determine whether the slope of line k is positive or negative, since both lines can have positive slopes or both can have negative slopes.
Thus, statements one and two together are not sufficient to answer the question.

Answer: E

Jeffrey Miller
Head of GMAT Instruction
[email protected]

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by [email protected] » Wed Apr 04, 2018 4:49 pm

Hi All,

We're told that Line K and Line M are PARALLEL to each other (this means that they have the SAME SLOPE). We're asked if the slope of Line K is positive. This is a YES/NO question. You can approach it in a number of different ways, including by drawing a few pictures or as a 'concept question' (meaning that you don't have to actually do any math to solve it as long as you recognize the concepts involved).

1) Line K passes through the point (3, 2).

With just one co-ordinate, the Slope of Line K could be ANY value (positive, negative, 0 or undefined) so the answer could be YES or NO.
Fact 1 is INSUFFICIENT

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

With just one co-ordinate, the Slope of Line M could be ANY value (positive, negative, 0 or undefined) and since Line K is PARALLEL to Line M, the Slope of Line K could also be ANY value (positive, negative, 0 or undefined) and the answer could be YES or NO.
Fact 2 is INSUFFICIENT

Combined, we still only know one co-ordinate for each line, so there's still no way to determine the exact slope of either line.
Combined, INSUFFICIENT

Final Answer: E

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

Contact Rich at [email protected]

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