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
_________________
Manhattan Review GMAT Prep
Locations:
GMAT Classes Glasgow |
GMAT Prep Courses Hyderabad |
LSAT Prep Courses San Diego |
Manhattan Prep Classes SAT | and many more...
Schedule your free consultation with an experienced GMAT Prep Advisor!
Click here.
