Hi honchos,
manpreetsingh86's explanation is right on, but I do want to point out one error in it:
A 3/4/5 right triangle is NOT a 30/60/90 right triangle - those are 2 different triangles.
Here's another way to look at this question:
We're asked if all 3 angles in triangle ABC are less than 90 degrees. This is a YES/NO question.
Fact 1: AB < BC < AC
This tells us the relationship among the lengths of the 3 sides. We know that none of the sides are equal to one another, so none of the corresponding angles are equal to one another.
We could have....
...a 30/60/90 and the answer to the question would be NO.
...a 50/60/70 and the answer to the question would be YES.
Fact 1 is INSUFFICIENT
Fact 2: Angle ABC = 80
This tells us one of the angles, but we don't know if it's the biggest angle or not.
We could have...
a...10/80/90 and the answer to the question would be NO.
a...30/70/80 and the answer to the question would be YES.
Fact 2 is INSUFFICIENT
Combined, we know...
Angle ABC = 80
Angle ABC is across from AC
AB < BC < AC
The biggest angle is always across from the biggest side
Thus the biggest angle is 80, so the other 2 angles are BOTH less than 80.
The answer to the question is ALWAYS YES.
Combined, SUFFICIENT.
Final Answer:
GMAT assassins aren't born, they're made,
Rich
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