I got exactly the same lesson in almost similar situation, but from a guy who was not even close to (someone who is close to) a Nobel's prize. He did a sum of a

I got exactly the same lesson in almost similar situation, but from a guy who was not even close to (someone who is close to) a Nobel's prize. He did a sum of a problem from the test using a small constants reference book and his head. Despite the numerous simplifications in the calculation, error of his result was less then 5%.