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Source: Official Guide Revised GRE 1st Ed. Part 8; Section 6; #11


In the xy-plane, line k is a

In the xy-plane, line k is a line that does not pass through the origin. Which of the following statements individually provide(s) sufficient additional information to determine whether the slope of line k is negative? Indicate all such statements. The x-intercept of line k is twice the y-intercept of line k., The product of the x-intercept and the y-intercept of line k is positive., Line k passes through the points (a, b) and (r, s), where (a ? r)(b ? s) 0. 12

6 Explanations


Pronob Kumar Barman

Thank you, Chris.

Aug 26, 2019 • Comment


Zainab Iftikhar

I'm confused about A as well because wouldn't the point (0,0) technically satisfy the conditions but could therefore have any slope?

0*2 = 0 so theoretically that should work and it seemed like one of those GRE tricks at first glance.

Mar 24, 2019 • Comment

Sam Kinsman

Hi Kelly, keep in mind that the question says that "line k is a line that does not pass through the origin." So it cannot go through the point (0,0).

Mar 27, 2019 • Reply


Abigail Stricker

I couldn't get why A is correct. Did he put numbers to that would obey this kind of line to test out if A applied?

Aug 20, 2018 • Comment

David Recine

A states that the x-intercept of the line is twice the y-intercept of the line. But more importantly, a states that the x intercept and the y intercept will always be the same sign. After all, a negative number cannot be twice the value of a positive number, or vice versa.

And if the two intercepts of a line are both the same sign, the line will have to be negative, sloping down and to the right. Any positive line would slope up and to the right, meaning that it would have to start at a negative point on one axis and then go to a positive point on the other.

(If this sounds confusing, draw the two axes, and plot any line where x and y are either both negative or both positive. You'll find it's impossible to draw a line that slopes down and to the right. You'll only get positive up-right sloping lines!)

Aug 21, 2018 • Reply


Ahmed Shehata

Hello David, i mean the explanation state that why not x intercept is double y intercept ---> I agree but that is not sufficient info to state that slope is -ve like what question ask. I think the explanation can go this way if x intercept is double the y intercept then they have to be same sign uhhh (similar to b ) so its enough to proof that the slope is -ve why ? because b *2 = 2b , -b*2 = -2b so they will be same sign for sure which is proof that slope is -ve !!

Feb 17, 2018 • Comment

David Recine


I'm still not quite clear on what you're saying. It sounds like you're saying that you understand that negative slopes will have the same sign for both intercepts, and that (A) indicates the intercepts for the line will both have the same sign. But you're still saying you have doubts that (A) is sufficient? If so, why do you feel (A) is not sufficient? (And if I got that wrong, let me know as well!)

Feb 20, 2018 • Reply


sourov datta

Thanks Chris . Nice explanation .

Jul 1, 2016 • Comment

Cydney Seigerman, Magoosh Tutor

On behalf of Chris, you're very welcome :D Happy studying!

Jul 4, 2016 • Reply


Chris Lele

Oct 11, 2012 • Comment

Damien Sighaka

Hello, thanks for your explanations nevertheless i dont understand why the x intercept is twice the y intercept: If the line was crossing the y axis at 4, and the x axis at one, it would still have a negative slope but a different ratio between x and y...

Jun 28, 2017 • Reply

Sam Kinsman

Hi Damien,

You're right that if a line crosses the y axis at 4 and the x axis at 1, it has a negative slope - but the x intercept is NOT twice the y intercept. That's correct!

However, the question is not asking us whether ALL lines with a negative slope will have an x intercept that is twice the y intercept.

You could think of the question as saying this: "consider all the lines that have an x intercept that is twice the y intercept. Do all of these lines have the same kind of slope (positive or negative)?"

In the video, Mike shows that all of the lines that have an x intercept that is twice the y intercept must be lines with a negative slope. Therefore, if we know that a line has an x intercept that is twice the y intercept, we have enough information to determine that it has a negative slope.

I hope that clarifies!


Jul 6, 2017 • Reply

Ahmed Shehata

No, I am sorry i am still confused. That is individually sufficient information that determine whether the slope is positive or negative as you mentioned it can be positive. if that is the case then i will likely chose all because it neither augment the argument nor deny it! basically this not sufficient information to say that the slope is negative .. if i can consider the word additional then maybe yes additional information that by saying it i do not decide yet so i take the question which of answers does not individually proof that the slope is positive ! Thank you. sorry i know sometimes we dont need to think too much but i got confused

Feb 11, 2018 • Reply

Ahmed Shehata

Sorry if the English is not great. Please let me know if i need to clarify it :D

Feb 11, 2018 • Reply

David Recine

I think what you're saying is that it looks like (A) and (B) only prove that the line COULD be positive, while still leaving a possibility for negative as well. Did I get that right? If so, let me know. And if I got it wrong, try explaining it again. Once I hear back from you either way, we can keep working on this. :)

Feb 15, 2018 • Reply

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