WASHINGTON, Oct 31 (Reuters) - The U.S. Supreme Court is set to hear arguments on Monday in two major cases involving Harvard University and the University of North Carolina that could imperil decades-old affirmative action policies that factor race into student admissions to boost Black and Hispanic enrollment on American campuses.Blum's group told the justices in court papers that the Constitution requires colorblind admissions, quoting a famous line by conservative Chief Justice John Roberts from a 2007 ruling: "The way to stop discrimination on the basis of race is to stop discriminating on the basis of race."The two schools and President Joe Biden's administration, backing them, said categorically banning any consideration of an individual's race would be inconsistent with equal protection.The challengers' arguments to equate the two "trivialize the grievous legal and moral wrongs of segregation," the U.S. Justice Department said in a brief.Affirmative action has withstood Supreme Court scrutiny for decades, including in a 2016 ruling involving a white student, backed by Blum, who challenged the University of Texas after being rejected for admission, though the justices have narrowed its application."