The trick here is recognizing that log_8 is 2^3 and log_{27}$ is 3^3. The moment you see that '3' in the denominator, you know it’s going to cancel the '3' in the power. Saves so much scratch paper

"Wait, if a had to be a non-integer, the answer would be {200} =  14.14$. But since CAT asked for an integer, 14 is the only logical choice. Don't over-calculate the decimals!

Always look at the constraints a > 10  b > c In TITA (questions, the 'greatest value' usually lies right at the boundary of your constraints. Testing 10 and 10 is the fastest way

I spent 3 minutes deriving the base change on this one during the mock. Seeing it as a^2 = b^2 + c^2 makes it look like a 10th-grade geometry question. Mind-blown