Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Line \(\ell\) lies in the xy-plane and does not pass through the origin. What is the slope of line \(\ell\) ?

(1) The x-intercept of line \(\ell\) is twice the y-intercept of line \(\ell\) (2) The x-and y-intercepts of line \(\ell\) are both positive

Target question:What is the slope of line l?

Statement 1: The x-intercept of line \(\ell\) is twice the y-intercept of line l Let k = the y-intercept of line l This means 2k = the x-intercept of line l If the y-intercept is k, then line l passes through the y-axis at the point (0, k) If the x-intercept is 2k, then line l passes through the x-axis at the point (2k, 0) Since (0, k) and (2k, 0) are both points on line l, we can apply the slope formula to these points to find the slope of line l. We get: slope = (k - 0)/(0 - 2k) = k/(-2k) = -1/2 So, the slope of line l = -1/2 Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: The x-and y-intercepts of line l are both positive If we're able to imagine different lines (with DIFFERENT SLOPES) that satisfy this condition, we'll quickly see that statement 2 is not sufficient. However, if we don't automatically see this, we can take the following approach... There are many different cases that satisfy statement 2 yet yield different answers to the target question. Here are two: Case a: the x-intercept is 1 and the y-intercept is 1, which means line l passes through (1, 0) and (0, 1). Applying the slope formula, we get: slope = (0 - 1)/(1 - 0) = -1 Case b: the x-intercept is 2 and the y-intercept is 1, which means line l passes through (2, 0) and (0, 1). Applying the slope formula, we get: slope = (0 - 1)/(2 - 0) = -1/2 Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Line \(\ell\) lies in the xy-plane and does not pass through the origin. What is the slope of line \(\ell\) ?

(1) The x-intercept of line \(\ell\) is twice the y-intercept of line \(\ell\) (2) The x-and y-intercepts of line \(\ell\) are both positive

When I see something like this, I just start drawing. For me, it's easier to look at the slopes and compare them, versus trying to understand the slopes based on numbers and equations.

For statement 1, draw a couple of lines that have an x-intercept twice the y-intercept. Don't forget negatives (for instance, x-intercept of -2 and y-intercept of -1). You should notice that all of the slopes of these lines are equal.

Note that this is an example of a DS problem with a 'nice but not necessary' statement. Be very careful to analyze the statements each on their own before putting them together. It's nice to know that the slopes are both positive (statement 2), because it gives you a clearer picture of what's going on. But critically, it's not necessary to know that. You can answer the question even without it.
_________________

Chelsey Cooley | Manhattan Prep Instructor | Seattle and Online

I have a question. You both consider the slop is negative., while it could be positive too. For example, the line could intersect the 'y' in point (0,1) and 'x' in point (-2,0). This line satisfies the condition too. What did not you take it into consideration?

I have a question. You both consider the slop is negative., while it could be positive too. For example, the line could intersect the 'y' in point (0,1) and 'x' in point (-2,0). This line satisfies the condition too. What did not you take it into consideration?

Thanks

In your example, the x-intercept is -2 and the y-intercept is 1

However, statement 1 says that the x-intercept twice the y-intercept. -2 is not twice 1

I have a question. You both consider the slop is negative., while it could be positive too. For example, the line could intersect the 'y' in point (0,1) and 'x' in point (-2,0). This line satisfies the condition too. What did not you take it into consideration?

Thanks

In your example, the x-intercept is -2 and the y-intercept is 1

However, statement 1 says that the x-intercept twice the y-intercept. -2 is not twice 1

Cheers, Brent

Thanks Brent. What I understand from Fact 1 is the that 'twice' means x-intercept 'double' the y-intercept regardless of any sign. It treated the intercept as distance from zero to the intercept regardless the sign. Where is the problem in my understanding?

Line l lies in the xy-plane and does not pass through the origin. What [#permalink]

Show Tags

21 Jun 2017, 04:35

AbdurRakib wrote:

Line \(\ell\) lies in the xy-plane and does not pass through the origin. What is the slope of line \(\ell\) ?

(1) The x-intercept of line \(\ell\) is twice the y-intercept of line \(\ell\) (2) The x-and y-intercepts of line \(\ell\) are both positive

This question requires no pen to paper. From 1 we know that slope is .5 regardless of the signs of the x and y-intercepts (2). 2 is basically irrelevant and insufficient without knowing the values. Hence A, 1 alone is sufficient.

Last edited by rulingbear on 22 Jun 2017, 19:34, edited 1 time in total.

Thanks Brent. What I understand from Fact 1 is the that 'twice' means x-intercept 'double' the y-intercept regardless of any sign. It treated the intercept as distance from zero to the intercept regardless the sign. Where is the problem in my understanding?

Thanks in advance

I think you might be confusing the x- and y-intercepts with the DISTANCE from the origin. An x-intercept of -2 is 2 units away from the origin (0,0) and a y-intercept of 1 is 1 units away from the origin.

Re: Line l lies in the xy-plane and does not pass through the origin. What [#permalink]

Show Tags

22 Jun 2017, 15:39

GMATPrepNow wrote:

Mo2men wrote:

Thanks Brent. What I understand from Fact 1 is the that 'twice' means x-intercept 'double' the y-intercept regardless of any sign. It treated the intercept as distance from zero to the intercept regardless the sign. Where is the problem in my understanding?

Thanks in advance

I think you might be confusing the x- and y-intercepts with the DISTANCE from the origin. An x-intercept of -2 is 2 units away from the origin (0,0) and a y-intercept of 1 is 1 units away from the origin.

We’ve given one of our favorite features a boost! You can now manage your profile photo, or avatar , right on WordPress.com. This avatar, powered by a service...

Sometimes it’s the extra touches that make all the difference; on your website, that’s the photos and video that give your content life. You asked for streamlined access...

A lot has been written recently about the big five technology giants (Microsoft, Google, Amazon, Apple, and Facebook) that dominate the technology sector. There are fears about the...

Post today is short and sweet for my MBA batchmates! We survived Foundations term, and tomorrow's the start of our Term 1! I'm sharing my pre-MBA notes...