How to motivate my sibling with her scheduled admission test?

The short answer is: you can't. Only your sister can motivate herself to take something seriously.

However, you can help her to motivate herself. The first step is to engage with her. You're not going to tell her things; you're not going to give advice. When I teach fatherhood classes, one thing we say is "don't give un-asked-for advice" which I think applies here. You want to listen to her and see what's important to her. This takes time because you're building up trust and establishing that you want to hear what she has to say and valuing both her and what she has to say.

After she grants you the right to help her, then you can talk about her plans. In the US, it's common to assume people want to go to college right after high school. However, that leaves a lot of people who aren't ready for college or have no idea why they're in college studying there, wasting both time and (Mom and Dad's) money. Maybe she wants to take a year off. Maybe she wants to study a skilled trade - of which there is a huge and growing shortage of practitioners. The point is: right now you only know she picked this program but you don't know why. Was it to please your parents? Was it because she wants to? Was it because "that's what she is supposed to do"?

In this stage, you stop "helicoptering". She's an adult now, and needs to make mistakes and learn from them. It's acceptable to talk with her and answer questions, but not acceptable to make decisions for her or tell her what to do. If she's used to just following advice and people telling her what to do, she won't learn to do things and decide for herself. You can tell her the mistakes you made, but you don't tell her how to avoid them. That's on her to decide that.

So, now we know why she selected this program and she trusts you. If we know that she picked this program because she's got a passion for it and that she needs to do better on this test, we can offer to help her study for it. Your pressure won't help here; she needs to come to that decision for herself. And you help that by showing true concern for her and having a trusting relationship with her, not by telling her what she needs to do and how to do it.

In the end, you can help her motivate herself. It's a long process built on showing her that you care about her and support her. It's nothing you'll accomplish in a couple weeks but in the end you'll have a stronger relationship with her and a better understanding of how she approaches life.