Question

Jim was born on 29 February 2016, which was a Monday. How old will he be the next time his birthday falls on a Monday?

• A. 5
• B. 4
• C. 8
• D. 9

Answer 1

The correct option is A 5

Any day of the week repeats itself after seven days.

For example:

1 April 2022 is a Friday.

$1+7=8$

Hence, 8 April 2022 will also be a Friday.

Generalising this, we find that this is true for any number that is a multiple of 7.

Hence, 1 + 7k will be a Friday for any integer of value k.

We know that:

$Numberofdaysinayear=365Numberofdaysinaleapyear=366$

We can rewrite these numbers as:

$365=364+1=7\left(52\right)+1366=364+2=7\left(52\right)+2$

Hence, if 21 April 2022 is a Thursday, then as 2023 is not a leap year. So, we have:

$21April2023=21April2022+365=21April2022+7\left(52\right)+1=\underset{–}{Thursday+7\left(52\right)}+1=\underset{–}{Thursday}+1=Friday$

On the other hand, 2024 is a leap year. So, we have:

$21April2024=21April2023+366=21April2023+7\left(52\right)+2=\underset{–}{Friday+7\left(52\right)}+2=\underset{–}{Friday}+2=Sunday$

Hence, after every normal year, the same date will fall one day later.

Further, after every leap year, the same date will fall two days later.

Now, Jim was born on 29 February. As 29 February only appears on leap years, we instead observe the days on which 28 February falls over the years.


So, 28 February 2021 falls on a Sunday.

Hence, 29 February 2021 will be a Monday, which will be the first time that Jim will celebrate his birthday on a Monday after his birth.

In 2021, Jim will be 5 years old as shown in the table.

Therefore, Jim will be 5 years old the first time he celebrates his birthday on a Monday since his birth.