SOLUTION
Given the question in the image, the following are the solution steps to answer the question
STEP 1: Write the given details
[tex]n(G)=136,n(P)=128,n(A)=152,n(A\cap G)=52,n(A\cap P)=60,n(A\cap P\cap G)=30,n(P\cap G)=58[/tex]
STEP 2: Get the number of students that takes the subjects only
From the basic stuff, we have Number of candidates who had taken only each of the subjects
[tex]\begin{gathered} n(A\text{ only)=}n(A)-\lbrack n(A\cap P)+n(A\cap G)-n(A\cap P\cap G)_{}\rbrack \\ \Rightarrow152-\lbrack52+60-30\rbrack=152-82=70 \\ \\ n(G\text{ only)=}n(G)-\lbrack n(A\cap G)+n(P\cap G)-n(A\cap P\cap G)\rbrack \\ \Rightarrow136-\lbrack52+58-30\rbrack=56 \\ \\ n(P\text{ only)=}128-\lbrack58+60-30\rbrack=40 \end{gathered}[/tex]
STEP 3: Represent the values above on a Venn Diagram after getting the values
STEP 4: Find the total number of candidate that sat for the exam.
[tex]\begin{gathered} We\text{ su}m\text{ all the numbers in the Venn diagram to get the total number of candidates that sat for the exam} \\ We\text{ have:} \\ 70+22+30+30+28+56+40=276 \end{gathered}[/tex]
Hence, the total number of candidates that sat for the exam is 276
