If the universities admit their applicants without testing their academic abilities, it will become such a mess later on.
ご質問ありがとうございます。
"If the universities admit their applicants"＝「もし大学が志願者を入学させたら」
（☆"applicants"の代わりに"candidates"も使えます）
"without testing their academic abilities,"＝「彼等の学力を試験しないで」
"it will become such a mess later on."＝「後で大変なことになります。」
ご参考に。
If we don’t screen students before admitting them, it will cause problems later.
"選抜しないで学生を入学させると、後で大変なことになる"
- If we don’t screen students before admitting them, it will cause problems later.
選抜試験 - screening, entrance exam, selection exam
今、日本では、選抜試験が機能していない大学がたくさんあります。試験で学力の選抜をしないで学生を入学させると、分数がわからない学生も入ってきてしまいます。後で大変なことになるんです！
- There are many universities in Japan today that do not have entrance exams. If students are admitted without using an examination to evaluate their academic abilities, students who don’t even know fractions will be admitted. This will be a big problem later on!
アメリカ合衆国 
