Question

Three Vice Presidents (VP) regularly visit the plant on different days. Due to labour unrest, VP (HR) regularly visits the plant after a gap of 2 days. VP (Operations) regularly visits the plant after a gap of 3 days. VP (Sales) regularly visits the plant after a gap of 5 days. The VPs do not deviate from their individual schedules. CEO of the company meets the VPs when all the three VPs come to the plant together. CEO is on leave from January 5 to January 28, 2012. Last time CEO met the VPs on January 3, 2012. When is the next time CEO will meet all the VPs?

• A. February 6, 2012
• B. February 7, 2012
• C. February 8, 2012
• D. February 9, 2012
• E. None of the above

Hint:

When periodic events have “gaps,” convert each to a true period \((k+1)\), then take the LCM to find simultaneous occurrences. Finally, apply any exclusion windows (like leave/blackout dates).

Answer 1

The Correct Option is C

Step 1: Interpret “gap of \(k\) days” as visiting every \((k+1)\)th day.
\(\Rightarrow\) HR: every \(2+1=3\) days; Operations: every \(3+1=4\) days; Sales: every \(5+1=6\) days.
Step 2: All three visit together every \(\mathrm{LCM}(3,4,6)=12\) days. Since they last met on Jan \(3\), the common-visit days are:
\(3\) Jan, \(15\) Jan, \(27\) Jan, \(8\) Feb, \(\dots\)
Step 3: The CEO is on leave from Jan \(5\) to Jan \(28\). Hence the meetings on Jan \(15\) and Jan \(27\) cannot happen for the CEO. The next available common-visit date after the leave is \[\boxed{8~\text{Feb}~2012}\].