That 25% chance is just because you're randomly choosing one of the 4 ninjas that will take part in the quiz. I do not think you can influence which ninja will have the most questions answered right.

Even if you don't choose the right ninja, you still have your own point system in answering the 20 questions to get it right so you'll get a gift pack at the end of the quiz. The extra 50 coupons and coins as shown in by the thread starter's image is just like lottery of picking the 1 in 4 ninjas.

What are the rewards for the other parts of the Cat Quiz?

I.e. the 3 different Gift Packs after earning those points.