Number properties some times give me a fit, because they derail my timing as I dilly dally between plugging in numbers and using concepts. Plugging in numbers might sound easy but I some times double check my math. Kills my time. The moment I see number properties I would like to be able to make a decision whether I should plug in numbers and solve the problem or use concept to solve it.

How are people on BTG arriving at this? What are you doing with DS number property questions that involve inequalities and we need to consider fractions, positives, negatives, zeros etc. Are you guys following plug in numbers for every problem ? Do the problems have any thing in them that helps us identify which approach is good for them?

That said, I don't know how to solve this problem by plugging numbers.

Y/N Q.

(1) pqp=p

which means pqp-p=0 means p(qp-1)=0 which means either p=0 or qp=1

How can qp be 1 if p=0? Insufficient

(2) qpq=q

How can qp be 1 if q=0? Insufficient

Taking both together as well, qp cant be 1 if p=0 and q=0 Hence E

Everyone has a different approach. Some sacrifice time for accuracy and vice versa. It is the few that can do both. THis is a particular problem that should be approached with a conceptual and macro approach. It is very true to try to decide and recognize the best approach for each question. I just like to prove my answer with answers.