Hi All,
We're asked if the area of the triangular region above is LESS than 20. This is a YES/NO question and can be solved by TESTing VALUES and using some specific Geometry rules. When dealing with Geometry questions, it's important to remember that we CANNOT trust the picture. We know that we have a triangle with sides X, Y and Z, but we know NOTHING about the side lengths nor the angles.
1) X^2 + Y^2 ≠Z^2
Fact 1 tells us that this triangle is NOT a right triangle (if it WAS a right triangle, the X^2 + Y^2 would equal Z^2). However, we don't know anything about the 3 sides, so there's no way to determine whether the area is less than 20, exactly 20 or greater than 20.
Fact 1 is INSUFFICIENT.
2) X + Y < 13
Fact 2 is fairly easy to deal with if the triangle was a right triangle (note: that restriction only applied in Fact 1 - it does not apply here)...
IF we have a right triangle, Y is the base and X is the height and...
Y=10 and X=1, then the area = (1/2)(10)(1) = 5 and the answer to the question is YES
Y= almost 6.5 and X= almost 6.5, then the area = (1/2)(almost 6.5)(almost 6.5) = about 21 and the answer to the question is NO.
Fact 2 is INSUFFICIENT.
Combined, we know:
The triangle is NOT a right triangle
X + Y < 13
Using the work that we did in Fact 2, we have enough proof to answer the question. We know that we don't actually have a right triangle, but we can still make a triangle that is 'really, really close' to being a right triangle, such that the areas would actually be just a tiny bit less than the ones we already calculated:
IF... the triangle is really close to being a right triangle and....
Y=10 and X=1, then the area = (1/2)(10)(1) = a little less than 5 and the answer to the question is YES
Y= almost 6.5 and X= almost 6.5, then the area = (1/2)(almost 6.5)(almost 6.5) = a little less than "about 21" and the answer to the question is NO.
Combined, INSUFFICIENT
Final Answer: E
GMAT assassins aren't born, they're made,
Rich
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