DS, some one please help urgently

[AmunaGmat]

I got this from MGMAT CAT?

Does line S intersect line segment QR? The segment has Q(1,3) and R(2,2)
(1) The equation of line S is y = -x + 4.
(2) The slope of line S is -1.

Number 1, when I plug the values I got the same points in the x-axis, and I answered yes.
Number 2, lines with the equal slope are parallel, then I answered no,

I chosed D, answers are different but the data is sufficient to answer both questions
But I got it wrong, the QA is A.

am I missing some rules?

[RonPurewal]

Number 2, lines with the equal slope are parallel, then I answered no,

statement 1: i'll take it as given that you understand how to do this part, since you correctly deduced that statement 1 is sufficient.
however, there's a much shorter path to that particular conclusion:
just realize that this is ONE LINE, and so, by necessity, the answer to the question must be "definite yes" or "definite no".
in other words, since statement 1 narrows you down to exactly one line, that line either does or doesn't intersect the given segment; there is no possible "maybe" about it.
therefore, sufficient; no need to calculate or deduce anything. that's always nice.

--

statement 2:
yes, as you've correctly deduced, this line has the same slope as the segment in question.
however, there are still two possibilities:
* the line is parallel to the segment (which you took to be the only possibility);
* the line includes (i.e., lies on top of) the segment.
in the latter case, the answer to "do they intersect?" is yes, since "intersect", after all, just means "share at least one point". an intersection doesn't have to mean what it does in normal spoken language (i.e., crossing at some sort of angle and sharing only one point).
so, this is a maybe.
insufficient.

--

this problem is a bit on the "ha! gotcha" side, but it's not so tricky that it would be unreasonable for the real gmat.

[malikrulzz]

Number 2, lines with the equal slope are parallel, then I answered no,

statement 1: since statement 1 narrows you down to exactly one line, that line either does or doesn't intersect the given segment; there is no possible "maybe" about it.
therefore, sufficient; no need to calculate or deduce anything. that's always nice.

--

statement 2:
yes, as you've correctly deduced, this line has the same slope as the segment in question.
however, there are still two possibilities:
* the line is parallel to the segment (which you took to be the only possibility);
* the line includes (i.e., lies on top of) the segment.
in the latter case, the answer to "do they intersect?" is yes, since "intersect", after all, just means "share at least one point". an intersection doesn't have to mean what it does in normal spoken language (i.e., crossing at some sort of angle and sharing only one point).
so, this is a maybe.
insufficient.
quote]

Overlapping can also happen in case 1 as slope is -1 and equaltion is exactly the same

[RonPurewal]

Overlapping can also happen in case 1 as slope is -1 and equaltion is exactly the same

well, yes. if you take (waste) the time to do the algebra, then you'll find out that, in fact, they do overlap: the segment is contained within the line.

again, though, it is a complete waste of time to figure this out. given statement (1), you have a specified line and a specified segment.
therefore, the answer to the question is either "definite yes" or "definite no"; it can't possibly be "maybe". so we know this is sufficient, and there's no reason to waste the substantial amount of time needed to figure out whether it's "yes" or "no".

[malikrulzz]

Thanks Ron

[JonathanSchneider]

:)