I haven’t yet failed a take-home design test. Might be luck, but I’ve always made it to the next round. This is my top advice:

Test-readers are exhausted, so get to the point in the first sentence. Explain your deeper reasoning as a follow-up. End before the reader gets bored.

^ Like that.

Every word must tell. You need to answer in useful depth, but as efficiently as possible. A short, accurate answer is better than an essay.

Here’s an excerpt from a design test I wrote for [REDACTED] many years ago. I had to design a new keyword-mechanic and explain why it would be good for the game.

I could have spent 3 pages on this answer. Instead, I spent 3 sentences.

Other questions demand multiple paragraphs. However, you should still follow this principle: Make the point immediately, and end before the reader gets bored.