In the rectangular coordinate system above, if OB < BC then is the are

Hi TARGET730,

In DS questions, you have to be careful about any pictures that you're given - as a general rule, you CANNOT trust any pictures in DS questions. From the drawing, it "looks like" the base of the triangle is bigger than the height of the triangle, but we DO NOT KNOW that for sure. It might be that the base and the height are equal; it might also be that the height is bigger than the base. As such, we can only use the math "facts" that we're given to try to answer this question.

We're told that the length of OB is less than the length of BC. We're asked if the area of the triangle is less than 12. This is a YES/NO question.

Fact 1: Point A lies above the line Y = 5.

This tells us that the height of the triangle is > 5, but it dos not tell us anything about the base.

IF....
Height = 6
Base = 6
Area = (1/2)(6)(6) = 18 and the answer to the question is NO.

IF.....
Height = 6
Base = 1
Area = (1/2)(1)(6) = 3 and the answer to the question is YES.
Fact 1 is INSUFFICIENT

Fact 2: The mid-point of B and C is (6,0)

This Fact limits the possible base of the triangle, since OB < BC, the range for the base is....4 < base < 12, but tells us nothing about the height.
The examples that we used in Fact 1 (above) would fit here.
Fact 2 is INSUFFICIENT

Combined, we could have...
Base = 6
Height = 6
Area = (1/2)(6)(6) = 18 and the answer to the question is NO.

Base = 4.1
Height = 5.1
Area = (1/2)(4.1)(5.1) = just above 10 and the answer to the question is YES.
Combined, INSUFFICIENT

Final Answer:

GMAT assassins aren't born, they're made,
Rich