Any applicant who fails to pass one or more sections of an examination given or approved by the board upon the first trial shall have a right to retake the examination. Any applicant who fails to pass the examination upon the first trial may be given credit for such sections of the examination as the board determines have been successfully completed by the applicant, but such credits shall be extended only to the succeeding examination. If the applicant shall fail to pass the examination on the second trial the applicant shall complete such additional or remedial instruction and training as the board shall, by rules and regulations, require prior to a third trial. After the third trial the board, within its discretion, may deny the applicant another examination.