Retake exam blunder after 11-Plus leak
Pupils who had to re-sit an 11-Plus exam after claims some students had seen the exam before found a question which had appeared in a mock paper.
The mistake was spotted by girls retaking the English exam in Plymouth.
Exam board GL Assessment said it was "down to human error" and said a further retest would not be necessary.
An investigation was launched last month amid allegations some children had already seen an 11-plus paper before sitting the exam.
GL Assessment said at the time that "extensive security measures" were in place to prevent exam papers being leaked.
But students retaking the English resit on Saturday said they found a passage which had previously appeared in the mock exam held last summer.
One mother whose daughter retook the papers said: "The whole thing has been terrible from start to finish.
"We are fuming - it shows great unprofessionalism and as parents we feel that they don't give a damn."
Greg Watson, chief executive of GL Assessment, said the firm was "acutely aware" the re-test had to be taken "as soon as possible after the suspected fraud".
"It wasn't fair on children or their parents to delay," he said.
"All previous standard 11-plus exams were checked for duplication but unfortunately all ancillary practice papers were not. The passage had appeared on one of those.
"We take full responsibility for the passage duplication on the re-test paper, and we can only apologise to all parents and children affected."
He said that a further retest would not be necessary because "we have enough statistically robust data to be able to assess the children accurately and fairly".