Lines k and m are parallel to each other. Is the slope of

Question

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).

DS12533

Bunuel · Accepted Answer

It's straight E.

The best way to solve this problem is to visualize it. We have line k, which passes through the point (3, 2) and its parallel line m, which passes through the point (-3,2). If you draw one such pair and fix, then you can rotate them 360 degrees to get infinite number of lines with negative as well positive slopes.

Answer: E.

For more on this issue please check Coordinate Geometry chapter of Math Book (link in my signature).

Hope it helps.

agnok · Answer

To find a slope we need at least 2 points on a line. Here only one point is given for each line.

MathRevolution · Answer

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

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).

In the original condition, there are 4 variables(x1, x2, y1, y2) from the slope=(y2-y1)/(x2-x1). (There are 2 lines, which makes 8 variables. However, since the lines are parallel, which makes 4 variables) In order to match with the number of equations, you need 4 equations, which is likely to make E the answer.
When 1) & 2), you cannot figure out the slope of either line k or line m in a unique way, which is not sufficient. 
Therefore, the answer is E.

 For cases where we need 3 more equations, such as original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 80% chance that E is the answer (especially about 90% of 2 by 2 questions where there are more than 3 variables), while C has 15% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since E is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, C or D.

kunalsinghNS · Answer

If i go by the defination of parallel lines : Parallel lines are two lines that are always the same distance apart and never touch.

if i take into consideration both option then both lines have a common intercept on Y-axis that is 2 so how come the two lines are parallel to each other ?

Bunuel · Answer

One of the infinitely many possible cases is given below: https://gmatclub.com/forum/download/file.php?id=36315 If you rotate both lines simultaneously you'll get other cases. Untitled.png

BrentGMATPrepNow · Answer

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 : 
 https://i.imgur.com/I3MiMwa.png 
In this case,  the slope of line k is POSITIVE

Case b : 
 https://i.imgur.com/Hv2yBFs.png 
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

ScottTargetTestPrep · Answer

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

GMATinsight · Answer

Answer: Option E

Video solution by  GMATinsight

https://www.youtube.com/watch?v=hfNI5HBMcIE

avigutman · Answer

Video solution from Quant Reasoning: Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1 https://www.youtube.com/watch?v=_L4xx1NZ388

bumpbot · Answer

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.

Lines k and m are parallel to each other. Is the slope of

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

Lines k and m are parallel to each other. Is the slope of

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards