Over the recent decades a new theoretical framework entitled cognitive diagnostic assessment (CDA) has gained a special status in the field of educational measurement as an approach to integrate cognitive theories with education. This framework provides formative diagnostic feedback through a fine-grained reporting of learners’ attribute mastery profiles which is necessary to respond to test items. The present study, through application of Polytomouse Deterministic Input, Noisy ‘ ‘ and’ ’ gate [de la Torre & Douglas, 2013], investigated the degree to which the items of a mathematical literacy test can provide diagnostically useful information. Mathematics literacy test was designed based on PISA framework considering social and cultural characteristics. The construction of 20-item test was based on six cognitive competencies. Through expert rating, a Q-matrix including six fundamental cognitive attributes consisting of communication, mathematizing, representation, reasoning and argument, devising strategies for solving problems andusing symbolic, formal and technical language and operations was developed and data collected from 700 15-year-old students. Using PGDINA model, model fit indicators, latent Class Probabilities, items’ parameters, and student’ s attributes profile were produced. Results indicated flexibilities of the PGDINA model and items can provide diagnostically useful information based on proposed model.