Question

The month of July has 31days. Find the greatest number of possible Saturdays that can occur.
a) 5
b) 4
c) 3
d) None

Answer 1

Hint: In this question, we need to find the greatest number of possible Saturdays that can occur. As in a week, which consists of seven days, only one Saturday can occur, we have to first divide the total number of days 31 by 7 to find the total number of complete weeks in July and as in the remaining number of days each day can occur only once, we can adjust the starting date to be a Saturday to get the answer as the sum of the number of total weeks and 1.

Complete step by step solution:
We know that there are seven days in a week…………………….(1.1)
It is given that the month of July has 31 days, thus from (1.1), we see that the maximum number of weeks in July should be the quotient when we divide 31 by 7
Thus, number of weeks in July= $\dfrac{31}{7}=\dfrac{7\times 4+3}{7}=4+\dfrac{3}{7}.........................(1.2)$
Therefore, the number of complete weeks in July should be equal to 4 and there are three additional days in July……………………….(1.3)
Therefore, as one Saturday will occur in each week, there must be 4 Saturdays in July without considering the additional 3 days. However, as we are asked to find the maximum number of possible Saturdays, we can consider the situation where one of the additional days is a Saturday……………(1.4)
Thus, the total number of Saturdays in July= Total number of complete weeks + 1 Saturday from the additional days= 4+1=5
Thus, the required answer is 5.

Note: We should note that it is not necessary that in each year, July will have 5 Saturdays. However, as there are 4 complete weeks, there should be at least 4 Saturdays. However, some months may have the $5^{th}$ Saturday depending on the position of the additional 3 days.