In a company where the 2nd and 4th Saturdays and every Sunday are official holidays, how many working days are there in a 31-day month that begins on a Friday?

Introduction:
This is a typical calendar and working-days problem. We are given a particular pattern of holidays (second and fourth Saturdays plus every Sunday) and asked to count working days in a month with 31 days that starts on a Friday. Such questions test your ability to track weekdays across dates and to distinguish between holidays and working days carefully.

Given Data / Assumptions:
Length of the month = 31 days. The month begins on a Friday (day 1 is Friday). Holidays: 2nd and 4th Saturdays, and every Sunday. All other days are working days.

Concept / Approach:
First we assign weekdays to each date in the 31-day month starting from day 1 as Friday. Then we identify all Saturdays and Sundays. Among the Saturdays, only the 2nd and 4th Saturdays are holidays; the other Saturdays remain working days. All Sundays are holidays. Finally, we subtract total holidays from 31 to obtain the number of working days.

Step-by-Step Solution:
Step 1: Assign weekdays to dates. Day 1: Friday. Day 2: Saturday. Day 3: Sunday. Day 4: Monday, and so on, repeating every 7 days. Saturdays in the month: days 2, 9, 16, 23, 30. Sundays in the month: days 3, 10, 17, 24, 31. Step 2: Identify holidays. 2nd Saturday: day 9 (holiday). 4th Saturday: day 23 (holiday). All Sundays (3, 10, 17, 24, 31) are holidays. Total holiday Saturdays = 2. Total holiday Sundays = 5. Total holidays in the month = 2 + 5 = 7 days. Step 3: Compute working days. Total days in month = 31. Working days = 31 − 7 = 24 days.

Verification / Alternative check:
We can quickly verify by counting non-working dates: {3, 9, 10, 17, 23, 24, 31}. There are exactly 7 distinct holidays. All other dates (1, 2, 4, 5, 6, 7, 8, 11, ... , 30 except 30 being a working Saturday) are working days, giving 24 in total.

Why Other Options Are Wrong:
23: Would mean 8 holidays, but we found only 7. 22 or 25 or 26: Each of these implies miscounting either an extra holiday or missing one, often due to treating all Saturdays as holidays or forgetting a Sunday.

Common Pitfalls:
Candidates often mistakenly treat all Saturdays as holidays, or forget that only the 2nd and 4th Saturdays are off. Another common error is mis-aligning the weekdays after the first week and assigning wrong weekday labels to mid-month dates.

Final Answer:
The number of working days in such a month is 24.