Douglas Belkin, Jennifer Levitz and Melissa Korn:

At Scarsdale High School north of New York City, one in five students is eligible for extra time or another accommodation such as a separate room for taking the SAT or ACT college entrance exam.

At Weston High School in Connecticut, it is one in four. At Newton North High School outside Boston, it’s one in three.

“Do I think that more than 30% of our students have a disability?” said Newton Superintendent David Fleishman. “No. We have a history of over-identification [as learning-challenged] that is certainly an issue in the district.”

Across the country, the number of public high-school students getting special allowances for test-taking, such as extra time, has surged in recent years, federal data show.

And students in affluent areas such as Scarsdale, Weston and Newton are more likely than students elsewhere to get the fastest-growing type of these special allowances, known as “504” designations, a Wall Street Journal analysis of data from 9,000 public schools found.

The special allowances don’t apply specifically to college entrance exams. They apply to all tests the students take while in school.

The effect, however, is to make these students much more likely to receive extra time or another special accommodation when they take an exam to get into college.

The 504 designation is meant to give students who have difficulties such as anxiety or ADHD a chance to handle the stress of schoolwork at their own pace and level the playing field. It often lets them have a separate room for test-taking and more time to do it.

The Journal analysis shows that at public schools in wealthier areas, where no more than 10% of students are eligible for free or reduced-cost school lunches, an average of 4.2% of students have 504 designations giving them special test-taking allowances such as extra time.

The Madison School District’s Section 504 page.