swerve wrote:In the \(xy-\)plane, point \(O\) is located at the origin, point \(A\) has coordinates \((p, q)\), and point \(B\) has coordinates \((r, 0)\). If \(p, q\) and \(r\) are all positive values and \(AO > AB\), is the area of triangular region \(ABO\) less than 12?

1) \(r=7\)
2) \(p=4\) and \(q=3\)

The OA is B

Source: Princeton Review

Let's take each statement one by one.

1) \(r=7\)

No information about the height of the triangle. Insufficient.

2) \(p=4\) and \(q=3\)

Let's find out the maximum area of ∆ABO. See the image below.



Drop a perpendicular from vertex A on X-axis. The height of the ∆ABO = AA' = 3 and OA' = 4. Thus, OA = √(3^2 + 4^2) = √25 = 5. Since it is given that \(AO > AB\), AB < 5. Again, in the rightangles ∆AA'B, we would have A'B < 4.

Thus, the base of ∆ABO = 4 + <4 = <8

Area of ∆ABO < 1/2 * 3 * 8 => < 12.

Thus, the area of triangular region \(ABO\) less than 12. The answer is Yes. Sufficient.

The correct answer: B

Hope this helps!

-Jay
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This is just an inferior copy of an official question (inferior because it doesn't include a diagram, which the GMAT would include, and because it's needlessly wordy) :

https://gmatclub.com/forum/in-the-recta ... 29092.html