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Coordinate Geometry .. If line L passes through point (3, n)

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Coordinate Geometry .. If line L passes through point (3, n)

by Yaj » Wed Aug 21, 2013 3:34 am
If line L passes through point (3, n) and (n, 3), where n is not equal to 3, which of the following must be true?
I. Line L does pass the origin.
II. The slope of L is negative.
III. Line L must passes through the first quadrant

(A) I only
(B) II only
(C) III only
(D) I and II
(E) II and III

[spoiler]OA:B[/spoiler]

How can we solve this? is picking numbers the only way?

Thanks so much!
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by ganeshrkamath » Wed Aug 21, 2013 7:36 am
Yaj wrote:If line L passes through point (3, n) and (n, 3), where n is not equal to 3, which of the following must be true?
I. Line L does pass the origin.
II. The slope of L is negative.
III. Line L must passes through the first quadrant

(A) I only
(B) II only
(C) III only
(D) I and II
(E) II and III

[spoiler]OA:B[/spoiler]

How can we solve this? is picking numbers the only way?

Thanks so much!
Statement 1:
Put n = -3: the line doesn't pass through the origin.
Not always true.

Statement 2:
Slope = (n-3)/(3-n) = -1
Always true.

Statement 3:
Put n = -4: the line doesn't pass through the first quadrant.
Not always true.

Choose B

The trick in this type of questions is to find a value that makes the statement false.

Cheers
Last edited by ganeshrkamath on Wed Aug 21, 2013 8:01 am, edited 1 time in total.
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by Brent@GMATPrepNow » Wed Aug 21, 2013 7:58 am
Yaj wrote:If line L passes through point (3, n) and (n, 3), where n is not equal to 3, which of the following must be true?
I. Line L does pass the origin.
II. The slope of L is negative.
III. Line L must passes through the first quadrant

(A) I only
(B) II only
(C) III only
(D) I and II
(E) II and III
The point (3, n) is somewhere on the line x = 3 (the red line below)
Image

The point (n, 3) is somewhere on the line y = 3 (the blue line below)
Image

Pick a few points.
If n = 1, we get the points (3,1) and (1,3)
If n = -7, we get the points (3, -7) and (-7,3)
See the 2 resulting green lines below below.
Image

At this point, we should get an idea of all of the possibilities for line L. Now check the statements.

I. Line L does pass the origin (this needs not be true)
II. The slope of L is negative.(TRUE)
III. Line L must passes through the first quadrant (this needs not be true)

Answer: B

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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