BOSTON—The man behind the scheme to help wealthy students get into elite colleges by cheating on tests and faking athletic credentials also advised some families to falsely claim students were racial minorities, exploiting the push to diversify campuses, according to two people familiar with the situation.

A son of Marjorie Klapper, a parent scheduled to plead guilty Friday for participating in the scheme, was incorrectly listed on his Common Application as being black and Hispanic, the people said. William “Rick” Singer, the college counselor who has agreed to plead guilty in the case and is awaiting sentencing, also arranged for a proctor to cheat on the ACT admissions test for the teen, according to a Federal Bureau of Investigation affidavit filed in the case.

Klapper, who lives in Menlo Park, Calif., was one of many parents charged whose child was misrepresented as a minority, according to one of the people, who is familiar with the investigation.

Singer frequently gave families the option of misrepresenting race and would say that not doing so could put their child at a “competitive disadvantage,” said one of the people, who is familiar with his business.

Read:SAT adds ‘adversity score’ amid concerns that wealthy students have an unfair advantage

Lawyers for Klapper didn’t respond to requests for comment, and efforts to reach Klapper were unsuccessful. The lawyer for Singer declined to comment.

In looking to present a teen as a minority, Singer was tapping into a hot-button aspect of college admissions that has led to numerous lawsuits: decisions that take into account, or even give preference to, students of certain races or ethnicities. Schools that pursue race-conscious admissions policies say they do so to provide a richer learning environment for all students and are following Supreme Court precedent that allows such an approach.

An expanded version of this report appears on WSJ.com.

Popular on WSJ.com:

SAT to give students ‘adversity score’ to capture social and economic background

The unfulfilled promise of DNA testing