Steven Mercer, a private college consultant based in Santa Monica, Calif., called $10 million “an entry-level gift that might not even get the attention of the admission office.”

He added, “You have to sometimes go quite a bit higher.”

Mr. Taylor of Ivy Coach agreed that even after a $10 million gift, a student’s application would not be greeted with “no questions asked.”

“It’s not guaranteed,” he said.

Certainty appears to be what parents were seeking when they hired William Singer, the consultant who pleaded guilty on Tuesday to charges of racketeering, money laundering and obstruction of justice. “I created a guarantee,” Mr. Singer said in a Boston courtroom.

In conversations with parents recorded by federal authorities, Mr. Singer styled his services as a first-class cabin for tech titans, rich investors and other luminaries trying to lock down a scarce spot at a prized school, such as Yale, Georgetown and the University of Southern California. Court papers said he promised to slot them in as athletes — with fabricated or embellished records — and on schools’ “V.I.P. lists.”

[Read more about how the authorities say the scheme worked, from bribes to doctored photos.]

According to court papers, Mr. Singer also promised parents that their children would get an ACT score in the 30s, or a 1400 or better SAT score.

Consultants who abide by the law can never offer a promise of admission to a specific school, said Mr. Taylor of Ivy Coach, no matter how much they charge or how much a parent is willing to donate. “If they tip you off that they have connections with admissions officers, that’s a red flag,” he said.

Ivy Coach students sign and submit their own applications, according to Mr. Taylor. He said the fact that Mr. Singer was submitting applications on behalf of his clients was “a mark of unscrupulousness in and of itself.”