If the line L passes through the point (3,n) and (n,3)

Question

If the line L passes through the point (3,n) and (n,3), where n is not equal to 3, which of the following must be true?

1. Line L does pass the origin.
2. The slope of L is negative
3. 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

Bunuel · Answer

Please post PS questions in PS forum and provide the OA along with a question.

Divyadisha · Answer

Slope of the given line= 3-n/n-3

Given information is that n is not equal to 3, that means n <3 or n>3. In both these conditions the slope will be negative.

1) n<3 (n=2)
3-2/2-3= -1
2) n<3 (n= 0)
3-0/0-3= -1
3) n<3 (n=-3)
3+3/ -3-3= -2/3
4) n>3
3-4/4-3= -1

We have proved that II is true.

A line with -ve slope may or may not pass through origin and may or may not pass through 1st quadrant.

MarceloY · Answer

How you could know that the line mustn t pass through the first quadrant?

Krunaal · Answer

We need to find which of the statements must be true, which means for all cases the statement should stand valid.

For statement 3, in a case where n = -3, the line having slope -1 will pass through the origin, and won't pass through the first quadrant. Hence, statement 3 may not be true in all cases.

If the line L passes through the point (3,n) and (n,3)

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GMAT Problem Solving (PS) Questions

If the line L passes through the point (3,n) and (n,3)

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