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Line l lies in the xy-plane and does not pass through the origin. What
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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
(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
Originally posted by AbdurRakib on 19 Jun 2017, 05:42.
Last edited by Bunuel on 02 Jul 2021, 02:09, edited 1 time in total.
Last edited by Bunuel on 02 Jul 2021, 02:09, edited 1 time in total.
Edited the question.
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Re: Line l lies in the xy-plane and does not pass through the origin. What
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Updated on: 03 Jul 2020, 08:07
Updated on: 03 Jul 2020, 08:07
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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
(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
Answer: A
Originally posted by BrentGMATPrepNow on 19 Jun 2017, 06:17.
Last edited by BrentGMATPrepNow on 03 Jul 2020, 08:07, edited 1 time in total.
Last edited by BrentGMATPrepNow on 03 Jul 2020, 08:07, edited 1 time in total.
Re: Line l lies in the xy-plane and does not pass through the origin. What
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19 Jun 2017, 13:17
19 Jun 2017, 13:17
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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
(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.
