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On the final day of its current session, the Supreme Court agreed to reconsider an affirmative action case involving the University of Texas at Austin. CreditJacquelyn Martin/Associated Press 
WASHINGTON — The Supreme Court agreed on Monday to take a second look at the use of race in admissions decisions by the University of Texas at Austin, reviving a potent challenge to affirmative action in higher education.
The move, which supporters of race-conscious admissions programs called baffling and ominous, signaled that the court may limit or even end such affirmative action. The advocates speculated that the court’s most conservative members had cast the four votes needed to grant review of the case in the hope that Justice Anthony M. Kennedy would supply the fifth vote to strike down the Texas admissions plan.
Justice Kennedy has never voted to uphold an affirmative action program.
The consequences would be striking if the court sided with the plaintiff in the case, a white woman named Abigail Fisher, and did away with racial preferences in higher education. It would, all sides agree, reduce the number of black and Latino students at nearly every selective college and graduate school, with more Asian-American and white students gaining entrance instead.
“Over the last few days, liberals have been celebrating a string of important victories involving health care and same-sex marriage,” said Justin Driver, a law professor at the University of Chicago. “But liberals have also been bracing themselves for the other shoe to drop. This decision to grant review means, at a minimum, that the other shoe will remain suspended in midair for the next several months.”
A decision barring the use of race in admissions would undo a 2003 ruling that the majority said it expected to last for 25 years. In that 5-to-4 decision, in Grutter v. Bollinger, the Supreme Court said that public colleges and universities could not use a point system to increase minority enrollment but could take race into account in vaguer ways to ensure academic diversity.
The case that the court agreed on Monday to hear, Fisher v. University of Texas, No. 14-981, arose from a lawsuit filed by Ms. Fisher, who said the university had denied her admission based on her race. She has since graduated from Louisiana State University.
In a statement, Ms. Fisher said, “I hope the justices will rule that U.T. is not allowed to treat undergraduate applicants differently because of their race or ethnicity.”
Gregory L. Fenves, the president of the University of Texas at Austin, said his school’s admissions program was lawful.
“Under the Supreme Court’s existing precedent, the university’s commitment to using race as one factor in an individualized, holistic admissions policy allows us to assemble a student body that brings with it the educational benefits of diversity for all students,” he said in a statement. “Our admissions policy is narrowly tailored, constitutional and has been upheld by the courts multiple times.”
When the court last considered Ms. Fisher’s case in 2013, supporters of affirmative action were nervous. But the court deferred conclusive action in what appeared to be a compromise decision.
In 2013, Justice Kennedy, writing for the majority, said the federal appeals court in New Orleans had been insufficiently skeptical of the Texas program, which has unusual features. The appeals court then endorsed the program for a second time.
In returning to the case, at least some justices seemed ready to issue a major decision on the role race may play in government decision making.
Most applicants from Texas are admitted under a part of the program that guarantees admission to top students in every high school in the state. (This is often called the Top 10 program, though the percentage cutoff can vary by year.)
The Top 10 program has produced significant racial and ethnic diversity. In 2011, for instance, 26 percent of freshmen who enrolled under the program were Hispanic, and 6 percent were black. Texas is about 38 percent Hispanic and 12 percent black.
The remaining Texas students and those from elsewhere are considered under standards that take account of academic achievement and other factors, including race and ethnicity. Many colleges and universities base all of their admissions decisions on such “holistic” grounds.
In 2003, the Supreme Court endorsed such holistic admissions programs in Grutter v. Bollinger, saying it was permissible to consider race as one factor among many to achieve educational diversity. Writing for the majority in that case, Justice Sandra Day O’Connor said she expected that “25 years from now,” the “use of racial preferences will no longer be necessary.”
The question in the Texas case was whether the flagship state university was entitled to supplement its race-neutral Top 10 program with a race-conscious holistic one.
The Supreme Court’s 2013 decision in Fisher v. University of Texas reaffirmed that educational diversity is an interest sufficient to overcome the general ban on racial classifications by the government. But it added that public institutions must have good reasons for the methods they use to achieve that goal.
Colleges and universities, Justice Kennedy wrote, must demonstrate that “available, workable race-neutral alternatives do not suffice” before using race in admissions decisions.
Courts reviewing government programs that make distinctions based on race subject them to a form of judicial review known as “strict scrutiny,” which requires the government to identify a compelling goal and a close fit between means and ends.
Last year, in its second encounter with the case, a divided three-judge panel of the United States Court of Appeals for the Fifth Circuit, in New Orleans, ruled that the Texas admissions plan satisfied strict scrutiny.
“We are persuaded that to deny U.T. Austin its limited use of race in its search for holistic diversity would hobble the richness of the educational experience,” Judge Patrick E. Higginbotham wrote for the majority.
The Top 10 program is inadequate, he said, because it is a blunt instrument and a product of widespread segregation in Texas high schools.
In dissent, Judge Emilio M. Garza said the university’s justifications for using race were “subjective, circular or tautological.”
As in the earlier appeal, Justice Elena Kagan has recused herself from the case because she worked on it as United States solicitor general.