The first time she sees him is not actually during the entrance exam, it's when she takes a glance from the 5th floor window and sees Tōtsuki's front yard packed with hopeful applicants.
She sees him-- an inferiorly dressed redhead running his mouth irritatedly on a typical rich, talentless deadbeat blonde whose father would probably sell his soul just to get his son into Tōtsuki, but she knows too well it's not how the elite school works. The Nakiri heiress isn't sure why the redhead seems furious-- perhaps too furious towards that piece of worthlessness.
To her, they're probably nothing but fruits that fall from the same tree, fighting over who's better when she knows both of them are equally garbage.
With a hair flip, she chuckles pompously and continue her steps, wondering why she stops at the first place.