Yes, you can use the Survey Flow to add branch logic where the logic is equal to these conditions.
It might be easiest for you to create two blocks with a descriptive text question:
Block 1 = "Eligible"
Block 2 = "Not eligible"
In survey flow, you would embed block 1 under the branching logic for what you have described. Then the next element, not embedded under the branching logic is Block 2.
So once the person goes through the screening block they will see Block 1 if the qualify, and if they don't qualify, they will skip over block 1 and go to block 2. If you are comfortable with Qualtrics, you can change this from a block to embedded data field that pipes into a custom end of survey message as either "eligible" or not "eligible". It will save your interviews one extra click per survey.

I am trying to use your 1st method. I add two blocks. But the problem is that if the participant is eligible, then I can see block 1. Then I can keep clicking, so I can see block 2 also. How to avoid this?
(If the participant is not eligible, then it's fine. I directly skip to block 2. No problem in this case.)

I think I can add skip logic in Block 1 "Eligible". To let this descriptive text question skip to the end of survey.