Preliminary enrollment figures from the D.C. public school system and city charter schools pose a troubling question that could be used to test students' reasoning skills: If a city school system loses about 1,100 students in one year, and charter schools grow by nearly 3,300 students the same year, where are all the new charter students coming from?

The answer, for now, is unknown.

The regular school system is reporting enrollment this school year of 70,762, which is 1,127 students fewer than last school year. The city's fast-growing public charter schools, meanwhile, say they have 6,912 students, including 480 in adult education classes, an increase of 3,253 over last school year.

Since the overwhelming majority of students in the three-year-old charter movement have come from regular public schools, the numbers released this week raise questions about whether one or both of the figures are inflated--as has been the case with school enrollment reports in the past.

The enrollment figures have been submitted to the D.C. financial control board and are being audited, as required by law, with results expected by the end of the month. Last year was the first time auditors confirmed the accuracy of the school system's count--and even then, demographers were skeptical of the numbers.

Control board Chief of Staff Russell Smith said the panel has "significant questions" about the preliminary figures but will wait for the audit before drawing any conclusions.

At stake is the credibility of both the school system and the fledgling charter movement--as well as their budgets. Charter schools are funded each year based on how many pupils are currently enrolled, while D.C. schools are funded based on their enrollment the previous year.

"We know our number is accurate," D.C. School Superintendent Arlene Ackerman said. "We took very careful measures to check and recheck and make sure we did it the right way."

The total count, Ackerman said, excludes several hundred students who had not submitted proof of D.C. residency until after last month's deadline--and thus were not counted in the official Oct. 7 tally.

In contrast, charter schools had such trouble documenting their students' residency that they requested and were given an extra month to complete the count. Ackerman said this raises the possibility that large numbers of charter students are illegally coming from suburban schools--a theory strongly disputed by charter officials.

Nelson Smith, executive director of the D.C. Public Charter School Board, said that auditors initially identified problems with the residency documentation for nearly one in four charter students, but that individual charter schools are clarifying that information.

"I think you'll find very few kids who are not D.C. residents," Smith said. "And if they aren't, they'll pay tuition or they'll leave."

Smith said some students may have transferred from private or parochial schools to charters--which, like regular public schools, are taxpayer funded and free of charge to city residents. And he said charter advocates know of a few families who have moved from the suburbs into the city specifically to enroll their youngsters in charter schools.

But neither of these groups, he acknowledged, seems likely to account for the sharp increase in charter pupils.

"We don't know yet," Smith said. "We haven't had time to do a rundown of where they [charter students] come from."

School system officials use the enrollment numbers to reassign teachers from school to school, according to need. A schools spokeswoman said yesterday that information on those reassignments is not yet available.

Schools that lost more than 100 students included Leckie and Shadd elementaries, Hart Middle School and Deal and Shaw junior high schools. Hendley Elementary grew by 80 students, while Anacostia, Ballou and Eastern high schools each added more than 100 students to their rolls.