PersonA bought a Camera at an electronics show with the intention of reselling it at a 30% profit. However, he misjudged the value of the Camera and could only sell it at a 35% loss. If PersonA decided to sell the Camera for $728, how much did he actually sell it for?
I found this problem from a GRE Question pattern, I do find the answer. I am trying to find easiest and quickest method to solve these kind of problems. We are restricted to time duration on solving critical reasoning problems.
The intended selling price was $728$. This is $1.3$ times the buying price. So the buying price was $\dfrac{728}{1.3}$. The selling price was buying price times $0.65$, that is, $\dfrac{728}{1.3}\times 0.65$. But $0.65$ is half of $1.3$, so we just divide $728$ by $2$, getting $364$.
Remark: One should not start to multiply, divide too early, since problem-setters often arrange for convenient cancellations. Even when there are not, premature calculation is not a good idea, for it turns something that has structure into a jumble of digits.