頭(あたま)が切(き)れるto be sharp, to be keen, to be on the ball, to have a mind like a steel trap, to be clever

頭(あたま)が切(き)れる人(ひと)は頼(たよ)りになります。

People who are sharp-minded can be relied upon. {to be sharp, to be keen, to be on the ball, to have a mind like a steel trap, to be clever}

彼(かれ)は頭(あたま)が切(き)れるから問題(もんだい)を早(はや)く解決(かいけつ)するだろう。

He will likely solve the problem quickly because he is sharp. {to be sharp, to be keen, to be on the ball, to have a mind like a steel trap, to be clever}

頭(あたま)が切(き)れる人(ひと)に助言(じょげん)を頼(たの)んだら悩(なや)みが解決(かいけつ)しました。

When I sought advice from someone who is sharp-minded, my problems were resolved. {to be sharp, to be keen, to be on the ball, to have a mind like a steel trap, to be clever}

東京大学(とうきょうだいがく)に行(い)っていたとあれば頭(あたま)が切(き)れるのももっともだ。

If it's mentioned that they went to the University of Tokyo, it's only natural that they'd be sharp-minded. {to be sharp, to be keen, to be on the ball, to have a mind like a steel trap, to be clever}

どんなに勉強(べんきょう)をしたって頭(あたま)が切(き)れるようになるかどうかは分(わ)からない。

No matter how much you study, it's uncertain whether you'll become sharp-minded or not. {to be sharp, to be keen, to be on the ball, to have a mind like a steel trap, to be clever}