This is a badly-worded question.
bb wrote:
GMAT Diagnostic Test Question 45
5 boxes are placed in a stack by weight from lightest to heaviest. The heaviest box weighs \(x\) kg and then next heaviest weighs \(x%\) less than the heaviest box and the next heaviest box weighs \(x-x%\) less than the next heaviest, and so on. If the heaviest box weighs 10kg, approximately what percent less weight is the lightest box than the heaviest one?
A. 30
B. 40
C. 50
D. 60
E. 70
"The heaviest box weighs \(x\) kg and then next heaviest weighs \(x%\) less than the heaviest box"
Except for the "then" typo, so far so good.
"the next heaviest box weighs \(x-x%\) less than the next heaviest"
If I follow the OE, this is not written correctly.
First, it shouldn't say "than the next heaviest"; it should say "than the previous heaviest box".
Second, \(x-x%\) makes no sense. The OE says "The weight of the second heaviest box = x – x% of x = 10 kg – 10% of 10 kg = 9 kg". In other words, the second-heaviest box should weigh \(x - x * x%\). So the third-heaviest box should weigh \((x - x * x%)%\) less than \(x - x * x%\).
Not only is this wrong, but it's way too complicated and the wording forces you to give part of the answer away.
I would simply write:
If the heaviest box weighs \(x\) kg, then the next heaviest weighs \(x%\) less than the heaviest box. If this second-heaviest box weighs \(y\) kg, then the next heaviest weighs \(y%\) less than this second-heaviest box. And so on, for all 5 boxes.