Question

Today is Monday, what is the ${{100}^{th}}$ day for today?
A. Monday
B. Wednesday
C. Sunday
D. Saturday

Answer 1

Hint: Here, we are given that, today is Monday and we have to find ${{100}^{th}}$ day. For this, we will use modular arithmetic which is given as $a = b \left| m \right|$ which means that, when ‘a’ is divided by m, b is the remainder obtained. As days of the week are involved so, we will take 'a' as 7 and we have to find ${{100}^{th}}$ day, so we will take' as 100 and find the value of b which will give the number of days after Monday. We can then calculate using basic general knowledge.

Complete step-by-step solution
As we know a week has seven days in the order of Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, and Sunday. We have to find ${{100}^{th}}$ day from Monday. So, let us use modular arithmetic which is given as $a = b \left| m \right|$. Here, a will be a number of days in a week that is 7, so, a = 7, m = 100.
$7=b \left| 100\right|$.
As we know $100=7\times 14+2$.
So, 2 is the remainder.
Hence, we need to find a second day from Monday which we know will be Wednesday. Hence, option B is the correct answer.
The logic that we used here was that we calculated that, after 14 weeks (seven days in a week), we will get ${{98}^{th}}$ day which will be the same as Monday. Since, after every seven days, the same day repeats. So, after ${{98}^{th}}$ day to find ${{100}^{th}}$ day, we were left with 2 days, which gives us Wednesday as an answer.

Note: Students should not start counting the days as it will only waste time and cause confusion. They can calculate it orally by just using the logic that, after seven days, the same day comes, so they can just divide by seven and whatever remainder is obtained, that number of days from Monday will be the required answer.