NEW HAVEN  Frank Ricci has been a firefighter here for 11 years, and he would do just about anything to advance to lieutenant.

The last time the city offered a promotional exam, he said in a sworn statement, he gave up a second job and studied up to 13 hours a day. Mr. Ricci, who is dyslexic, paid an acquaintance more than $1,000 to read textbooks onto audiotapes. He made flashcards, took practice tests, worked with a study group and participated in mock interviews.

Mr. Ricci did well, he said, coming in sixth among the 77 candidates who took the exam. But the city threw out the test, because none of the 19 African-American firefighters who took it qualified for promotion. That decision prompted Mr. Ricci and 17 other white firefighters, including one Hispanic, to sue the city, alleging racial discrimination.

Their case, which will be argued before the Supreme Court on April 22, is the Roberts court’s first major confrontation with claims of racial discrimination in employment and will require the justices to choose between conflicting conceptions of the government’s role in ensuring fair treatment regardless of race.