This is an article 78 proceeding to review and annul the adoption of a mathematical formula by the civil service commission for grading a promotion examination for captain in the police department. The rules of the examination specifically stated that if a candidate failed to pass any part of the examination he would be deemed to have failed *437the entire examination and no further part would he graded. After the examination was held, the commission determined that it was too difficult and that not enough candidates would pass, and applied the formula which had the effect of reducing the passing grade for part I of the two-part written examination.
The use of the formula by the commission is challenged by 9 candidates in behalf of themselves and 70 others similarly situated (hereinafter referred to as the petitioners) who allege that they passed part I without the aid of the formula. The petitioners contend that they are the only candidates entitled to be graded on the entire examination and that they are prejudiced by the adoption of the formula since it allows candidates, who would otherwise be eliminated, to attain a higher grade on the entire examination than some or all of the petitioners. They are opposed not only by the respondents, the civil service commission of this city and the police commissioner, but by 55 of the 250 other candidates who allegedly will receive passing grades for part I if the formula adopted by the commission is upheld. Those 55 candidates have been permitted to intervene in this proceeding by a prior order of the court.
Notice of the examination in question was given on January 12, 1956. The notice referred to record and seniority tests, as well as the written examination. It was this notice which warned that failure to pass any part of the examination meant failure of the entire examination. On April 24,1956, paragraph 1 of section V of rule V of the Rules and Regulations of the Civil Service Commission of the City of New York was amended to provide, among other things, that: ‘ ‘ Where there is an insufficient number of candidates in open competition or promotion examinations to provide an adequate eligible fist to meet the needs of the service, the Director of Examinations may, with the approval of the Personnel Director, provide a mathematical formula of penalties for incorrect answers on the basis of test difficulty and other relative factors in the rating of written tests of the objective type ”. On June 2, 1956 the written examination was taken by 656 police lieutenants. According to the instructions distributed with the written examination, a passing grade of 70% was required for each of the two parts; part I consisted of 100 multiple choice questions and part II consisted of six essay questions. Two of the multiple choice questions have been deleted by the commission, and no issue is raised here with respect to those questions. The commission then, without ascertaining the identity of the candidates, sampled the answers to part I and found that only 79 candidates *438would receive a passing grade. Aware that the last list for promotion to police captain contained 202 eligibles and that the list was exhausted within the four-year period authorized by subdivision 7 of section 14 of the Civil Service Law, the commission decided that the difficulty of the examination and the needs of the service required an adjustment of the passing grade. The commission proceeded to rate all candidates on part I by the application of a formula which deducted .77 % for each incorrect answer. Without the formula each incorrect answer for the approved 98 questions would result in the loss of 1.020%. By the use of the formula, 329 candidates will pass part I, of whom 208 candidates will also pass part II. It is conceded that unless the formula is adopted, only 70 candidates of the 79 who passed part I, would also pass part II.
The chief challenge made by the petitioners is that the adoption of the formula violates the New York State Constitution and the statutes and rules regulating the civil service commission. In Matter of Abramson v. Commissioner of Educ. (1 A D 2d 366), the Appellate Division of the Third Department reviewed the Commissioner of Education’s determination which held that it was unconstitutional to allow a 5% credit to all candidates for the position of assistant to the principal in the elementary schools. That case, closely analogous to the present proceeding, involved a multiple phase examination in which the passing of the first part of the examination was a condition precedent to a candidate’s participation in the other parts of the examination. There, the commissioner said (p. 373) that the action of the board of examiners improperly “ enabled candidates who would otherwise have failed the first phase of the examination to continue in the remaining phases with the possibility of their attaining higher final average grades than those attained by candidates who had passed the first phase without the aid of the credit.” The appellate court found, however, that the existence of this possibility did not justify the commissioner’s contention that the board of examiners had no constitutional power to rectify the error of having given an examination which it later learned was too difficult. Annuling the commissioner’s determination and remanding the matter to him for further proceedings, the court unanimously held that the action of the board of examiners was not unconstitutional. It said (p. 372-373): “ We do not believe that the New York State Constitution prohibited the board of examiners from adopting the examination procedure which it used here. *439There is nothing in the Constitution which prohibits an examining board from lowering the pass mark for the whole class if it determines in good faith, after an examination has been given, that it was too difficult and that the previously announced pass mark should not be adhered to. * * * The procedure adopted by the board did not, in our opinion, violate the constitutional principle of competitiveness. * * * The action of the board was wholly consistent with the letter and spirit of the constitutional provision that appointments in the civil service ‘ shall be made according to merit and fitness to be ascertained, as far as practicable, by examination which, as far as practicable, shall be competitive ’ (N. Y. Const., art. V, § 6).”
The rationale and doctrine of the Abramson case, when applied to the present proceeding, fully support the proposition that there is nothing unconstitutional in the use of a mathematical formula to adjust the grades of all candidates who took a multiple phase examination which required that all its parts must be passed, where the examination is found to be too difficult and where, without the aid of the formula, there would be too few successful candidates to provide an adequate promotion list. Moreover, the adoption of the formula by the commission herein is, unlike the credit allowed by the examining board in the Abramson case, in accordance with the rules promulgated prior to the date the examination was held. Adoption of the formula by the commission in the instant proceeding is, therefore, neither unlawful, arbitrary, nor capricious.
The application is accordingly denied and the stay heretofore granted to the petitioners is vacated. Settle order.