The question is from CAT Calendars. How many years it takes to have the birthday on one particular day in a week? CAT exam is known to test on basics rather than high funda ideas. CAT also tests multiple ideas in the same question, and 2IIMs CAT question bank provides you with CAT questions that can help you gear for CAT Exam CAT 2019. Set Theory (especially constructing venn diagrams) is a frequently tested topic. Make sure you know the basics from this chapter.

Question 4: John was born on Feb 29^{th} of 2012 which happened to be a Wednesday. If he lives to be 101 years old, how many birthdays would he celebrate on a Wednesday?

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Starts Sat, April 27th, 2019

Let us do this iteratively. Feb 29^{th} 2012 = Wednesday => Feb 28^{th} 2012 = Tuesday

Feb 28^{th} 2013 = Thursday (because 2012 is a leap year, there will be 2 odd days)

Feb 28^{th} 2014 = Friday, Feb 28^{th} 2015 = Saturday, Feb 28^{th} 2016 = Sunday, Feb 29^{th} 2016 = Monday

Or, Feb 29^{th} to Feb 29^{th} after 4 years, we have 5 odd days.

So, every subsequent birthday, would come after 5 odd days.

2016 birthday – 5 odd days

2020 birthday – 10 odd days = 3 odd days

2024 birthday – 8 odd days = 1 odd day

2028 birthday – 6 odd days

2032 birthday – 11 odd days = 4 odd days

2036 birthday – 9 odd days = 2 odd days

2040 birthday – 7 odd days = 0 odd days. So, after 28 years he would have a birthday on Wednesday

The next birthday on Wednesday would be on 2068 (further 28 years later), the one after that would be on 2096. His 84th birthday would again be a leap year.

Now, there is a twist again, as 2100 is not a leap year. So, he does not have a birthday in 2100. His next birthday in 2104 would be after 9 odd days since 2096, or 2 odd days since 2096, or on a Thursday.

From now on the same pattern continues. 2108 would be 2 + 5 odd days later = 7 odd days later. Or, 2108 Feb 29^{th} would be a Wednesday.

So, there are 4 occurrences of birthday falling on Wednesday – 2040, 2068, 2096 and 2108.

The question is **"How many birthdays would he celebrate on a Wednesday?"**

Choice B is the correct answer.

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