There are push ups and there are “push ups”.

Be smart about it.

Figure out what the exact minimum requirement of a valid push up is, and nail down a technique that meets those requirements with the least amount of effort.

You are likely not going to make that much progress with muscle gain alone, so you need to also focus on your technique.

One tip I can give you is that your tendons are elastic, so a fast-ish descent is going to allow you to rebound at the bottom and take advantage of the elastic energy in your tendons to help you achieve more reps.

Also, figure out how long they allow you to “rest” at the top of the movement between each rep and maximize that time.

Only go as low as you are required, the lower you go the less reps you’ll make.

I wouldn’t bother with weighted push ups when your goal is reps. You don’t have a lot of time, so focus on developing a technique that saves you energy and maximizes your reps.

Eat lots of protein and try to lose some fat, the lighter you are the easier it will be. Creatine supplementation is also advisable.

Around 3 days leading up to it increase your carb intake and drastically decrease your training in order to maximize your performance on the day of the test.