150- At minimum, how many subsets must be chosen from the set $\{7, \ldots, 3, 2, 1\}$ so that we are certain that two subsets share a common element?
(4) $46$ (3) $45$ (2) $64$ (1) $65$
Place for Calculations
%% Page 10
Control Code: 122 A
Download of questions and descriptive answer keys of the national entrance exam from the Riazi Sara website
www.riazisara.ir
National University Entrance Exam for Universities and Higher Education Institutions of the Country --- Year 1401
Mathematical and Technical Sciences Group Specialized Exam

Notes	Response Time	To Question No.	From Question No.	Number of Questions	Subject
70 questions	50 minutes	190	151	40	Physics
80 minutes	30 minutes	220	191	30	Chemistry

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A project team of 100 people has a certain number of projects, and everyone in the team will be assigned to some of these projects. It is desired that everyone in the team works on an equal number of projects, but no two people work on exactly the same projects. This condition cannot be satisfied if everyone works on 3 projects, but it can be satisfied if everyone works on 4 projects.
Accordingly, how many projects does the team have?
A) 6
B) 7
C) 8
D) 9
E) 10