The United States Supreme Court listened to 75 minutes of oral arguments Wednesday morning in the case brought by New Haven firefighters accusing the city of reverse discrimination.

The case, Ricci v. DeStefano, could have a major impact on the use of race in hiring decisions. And judging from their questions and statements, the nine justices appeared to be highly divided on the case, with the four most conservative on the court supporting the firefighters and the four most liberal supporting the city. Justice Anthony Kennedy — who is widely viewed as the swing vote in what will likely be a 5-4 decision — asked pointed questions to both sides.

The case centers on the New Haven Civil Service Board’s decision not to certify a 2003 promotion exam for the position of lieutenant and captain. Because no black firefighter received a score on the exam high enough to likely get a promotion, the city said it feared it would be sued for discrimination if the exam was certified. One Hispanic and 19 white firefighters sued the city, saying they were denied promotion based on their race alone.

Chief Justice John Roberts, a conservative, objected to the city’s decision to throw out the exams after sorting the results by race. Roberts said he did not understand how the city’s actions did not constitute intentional racial discrimination. He asked the city’s attorney, Christopher Meade, how many times the city would be permitted to administer the test until accepting the outcome.

“They get do-overs until it comes out right?” he asked. “Throw out this test; they do another test; oh, it’s just as bad, throw that one out; get another one that’s a little better.”

Meade responded by saying it depends on the city’s intent. He argued that the test was unintentionally flawed, justifying the city’s decision to throw out the results. Because the city acted to comply with Title VII, which is designed to prohibit employers from discriminating, its actions were legal, he argued.

“There’s no entitlement to be promoted on the basis of a flawed or discriminatory test,” Meade told the court.

Attorney Gregory Coleman, who argued for the plaintiffs, told the justices that because the city never proved that the test itself is discriminatory, its actions were illegal.

Justice David Souter disagreed with Coleman’s reasoning, saying his argument “leaves a municipality or a governmental body like New Haven in a ‘damned if you do, damned if you don’t’ situation.” If the city did certify the results and go ahead with the promotions, it would likely be sued by the minority firefighters under a disparate impact claim — a claim that different races of firefighters were affected disproportionately regardless of the city’s intentions, he said.

Justice Kennedy said he had difficulty justifying the city’s actions. He questioned Attorney Edwin Kneedler — who argued on behalf of the United States government to support New Haven’s main claims — about Kneedler’s claim that even though the city classified the successful and unsuccessful applicants by race, the city’s actions were not race-based.

“You want us to say this isn’t race? I have trouble with this argument,” Kennedy stated.

Kennedy said the city must prove the test to be significantly deficient before it can be set aside. No test is perfect, he said.

“I’ve given law school examinations … and bar examinations for years,” he said. “There’s never been one, when I don’t look at it after the fact and say, you know, this could be better … this was not quite right.”

The plaintiffs arrived at the court gallery in their formal firefighter uniforms. Two black New Haven firefighters were also present, but were dressed in civilian clothes. The courtroom was packed for the morning arguments.

On the steps of the court after the conclusion of the arguments, Frank Ricci, the lead plaintiff in the case, spoke to reporters while surrounded by the other firefighters.

“We’re all happy to have our day in court,” he said.

The Supreme Court is expected to issue a ruling on the case in June.

The Associated Press contributed reporting.