@ anurag
Anurag@Gurome wrote:You might want to check the part highlighted in red.
What you've wrote is only possible if O, P and Q are collinear points. But that may not be the case.
yep
in fact, you should say "can't", not just "may not". those 3 points form a triangle, so they can't be collinear.
--
@ original poster
that's ... a
lot of theory.
to realize that statement 2 is insufficient, just consider the fact that you have a triangle whose base goes from (0, 0) to (13, 0), and then a top vertex P that can be
literally anywhere above that base.
i.e., P could be at, say, (5, 0.00001), in which case the area of the triangle is way less than 48. or P could be at, say, (5, 1,000,000), in which case the area of the triangle is much, much greater than 48.
--
finally, on this problem, if you know the conventions by which gmac creates data sufficiency problems, you can actually figure out that the second statement CAN'T mean what you think it means.
here's how:
on an official DS problem, the two numbered statements will NEVER contradict each other.
if you think that the two numbered statements are mutually contradictory, your interpretation of at least one of them is definitely wrong.
in this problem, the first statement guarantees that the area of the triangle is
greater than 48; you probably understand this, since you've posted as if it's no problem.
therefore, if your interpretation of the second statement leads you to conclude that the area must be
less than 48, then that interpretation must be wrong: you can't have one statement that guarantees that the area is less than 48, but another one that guarantees that the area is more than 48.
