| Updated The story has been updated to include the reaction of the United Federation of Teachers.

Testing company Pearson admitted Friday to egregious errors in the scoring of this year's Gifted and Talented tests. As a result, thousands of students who were told that they did not qualify for a G&T; district program now do, and others now qualify for the more competitive citywide programs.

All students were were deemed eligible still are. And the 400 tests that went missing have been found so those students will get scores.

"The fact that these errors occurred is simply unacceptable to Pearson as we fully understand the importance of accurate scoring," according to a statement from Scott Smith, the president of Learning Assessment at the testing company. "Pearson is truly sorry for our error and for the disruption and inconvenience caused to New York City families and children. We extend our deepest apologies to the New York City Department of Education.”

Schools Chancellor Dennis Walcott, in his own press release, agreed with the unacceptable part.

"While I appreciate his apology, it is unacceptable that these mistakes occurred in the first place. Pearson has an established record in this field and we depend on its professionalism and deep capacity to deliver for the public. But in this case they let our children and families down. I have told the company’s officials in no uncertain terms that I expect this will never happen again," Walcott said.

He also said he was grateful to the two parents who initially brought their concerns about the scoring to the attention of education officials who, in turn, immediately asked Pearson to investigate.

Specifically, 2,698 students, or 7.5 percent of test takers, who didn’t previously qualify for G&T; now qualify for a district program. And 2,037 students, or 5.7 percent of test takers, who previously qualified for district programs now also qualify for citywide programs.

The Department of Education will notify all affected families through email and automated phone calls. They will receive updated scores by April 29. Because of the gaffe, the department is extending its deadline to May 10 for families to submit their applications to gifted and talented programs.

Pearson outlined the three errors in its statement, embedded below.

“First, an error occurred in the assignment of students’ age. Specifically, the assignment accounted for years and months, but did not extend to days. When days are accounted for, some students are categorized in a different age band. Second, incorrect score conversion tables were applied in producing the scale scores for the NNAT2 and the OLSAT8. Finally, the mathematical formula used in combining the NNAT2 and OLSAT8scores to create the overall composite percentile contained an error."

NNAT2 and OLSAT8 refer to the two tests that comprise the exam. For more on the tests, read this SchoolBook article.

Just over 36,000 children took the G&T; exams this year compared to about 39,000 last year, a change from the steady rise of previous years. The exams are open to students entering Kindergarten through third grade.

Students needed to score at or above the 90th percentile to be eligible for a seat in a G&T; program. In early April, the D.O.E. said about a quarter of all tested students were eligible for seats, the same as last year. But fewer children were eligible for the more competitive, citywide programs that require a higher score, in the 97th percentile or higher.

But the new numbers change the outcome. Based on the updated results, more students are qualifying for G&T; compared to last year. According to the latest D.O.E. figures, 11,815 this year qualified for gifted programs compared to 9,644 students last year. For the citywide programs, 5,369 students qualified this year compared to 4,102 last year.

Last year, 2,144 students scored at the 99th percentile. This year, that number is up to 2,564. What hasn't changed is the lack of seats available for all the qualifying students.

Pearson said it is "conducting a complete, extensive investigation of every step in our processes to fully understand how these errors occurred. In addition, we will bring in external experts to further review our processes and provide recommendations for further actions Pearson can take to prevent this from ever happening again."

The president of the teacher's union, Michael Mulgrew, said the scoring error underscored the distrust many families have towards the Department of Education.

"Mayor Bloomberg may wonder why parents have so little faith in his management of the schools. Parents may wonder why the D.O.E. trusts the testing company - Pearson - to develop the curriculum for the new and more demanding state tests the kids are already sitting for this week," he said.

Here are the statement and the letter to parents from Pearson: