Analyze a Venn Diagram and Logical Puzzles

Problem Statement

Given the following information, how many students are studying physics? There are 227 students in total. An equal number of students are studying chemistry and physics. The Venn Diagram with three overlapping circles labeled P (Physics), C (Chemistry), and M (Math) has the following regions: Region P only: x; Region C only: y; Region M only: z; Region P and C (but not M): 12; Region P and M (but not C): 13; Region C and M (but not P): 14; Region P, C, and M: 15; Region outside all circles: 20. The total number of students studying Math (M) is 100. 78 88 98 108 Observe the following figures and find the missing value (?). The problem presents three columns of numbers where the top and bottom numbers are connected to the middle number. Column 1: Top 50, Middle 65, Bottom 30. Column 2: Top 45, Middle 10, Bottom 40. Column 3: Top 5, Middle ?, Bottom 2. 43 53 63 73 Given the logic in the upper sequence, determine the value of '?' in the lower sequence. Upper: ABC --[Square]--> EFGH --[Tria