by Sage Pearce-Higgins Sat Dec 28, 2019 3:47 am
I think that you're referring to DS 48 from the Diagnostic test of the OG 2020. Here's the kind of thinking I'd encourage you to have:
-There are two equations and two unknowns here, so that it's likely you could solve these, unless there's some sort of special situation.
-There's a number squared, suggesting that there could be a positive and negative solution. However, since we're dealing with the side lengths of a rectangle, we don't need to worry about negative solutions.
-Putting the two equations together would give a quadratic that might have two positive solutions. However, that makes sense as the two possible solutions will represent two rectangles that simply have their length and width reversed. So, sure, you'll get two possible values for the length, but only one possible value for the perimeter.
-Even though there's no integer constraint in this problem, know that GMAT does favour integer solutions to problems.
Try solving these equations (a good study task, but not something to do in a test situation) and you'll hopefully get a better idea of how things work.