QUESTION

# If P represents the set of factors of 36 and Q represents the factors of 48, then if P $\bigcap$ Q = K, and sum of all elements of K is s, then the value of $\dfrac{s}{4}$ is?

K = P $\bigcap$ Q = {1, 2, 3, 4, 6, 12}
Since, we are asked to find the sum of all elements of K, we have, 1 + 2 + 3 + 4 + 6 + 12 = 28. Thus, the value of s is 28. The value of $\dfrac{s}{4}$ is 7.
Note: It is important to know while solving the problem is to forget, 1 as the factor of both these numbers (by definition, the factor of a number includes 1 and the number itself apart from all the other divisors). We should also remember the common notations (related to the question in hand) of sets such as $A\bigcup B$ (represents the union of all elements of two sets) and $A\bigcap B$ (represents the intersection of elements of two sets, as done in this problem).