Question

If today is Saturday, then what day of the week will be the 999th day from today?
A) Wednesday
B) Tuesday
C) Thursday

Answer 1

Hint: We will use the division method which helps in breaking the sequence problem into a division where the large number is the dividend, which is divided by the other repetitive number called the divisor, to give a remainder also. We know that there are seven days in a week and so the day of the week repeats itself every 7th day. Thus, we need to divide 999 by 7 and the remainder will be the additional days.

Complete step-by-step solution:
Step 1: Now as we know a week has \[7\] days from Sunday to Saturday.
Now by dividing the number of days given with the number of days in a week, we will first calculate how many weeks are there in \[999\] days:
Number of weeks =\[\dfrac{{999}}{7}\]
\[ \Rightarrow {\text{Number of weeks}} = 142{\text{weeks and }}5{\text{days}}\]
From the above division result we get\[142\]complete weeks in \[999\] days plus remaining
\[5\] days.
Step 2: Now, for better understanding, we can take the below example:
If today is Saturday, then after \[7\] days it will be Saturday again.
(1) Now, by adding one day to Saturday, it will be the next day i.e. Sunday.
(2) Then, by again adding one day to Sunday or we can say two days on Saturday, the next day will come which is Monday.
(3) By adding one day on Monday or three days on Saturday we get Tuesday.
(4) By again adding one day on Tuesday or four days on Saturday we get Wednesday.
(5) Similarly, by adding one day on Wednesday and 5 days on Saturday we get Thursday.
(6) Again, adding one day on Thursday and six days on Saturday, the next day will be Friday.
(7) Finally, adding one day on Friday and seven days on Saturday, we will again get the same day which is Saturday.
Step 3: Now from the above step we can see that it’s a complete week of seven days which repeats itself after a certain time or we can say after seven days.
We have complete \[142\] weeks calculated in step no. 1, which means that after \[142\] weeks the same day repeats itself. Today is Saturday, then after \[142\] weeks it will Saturday again.
Now, we have \[5\] days extra after Saturday, so for calculating the \[999\] day we will simply add these \[5\] days on Saturday as shown below:
Saturday plus \[1\] day: Sunday
Saturday plus \[2\] days: Monday
Saturday plus \[3\] days: Tuesday
Saturday plus
\[4\] days: Wednesday
Saturday plus \[5\] days: Thursday.
So, our final answer is Thursday.
Thus, option (C) Thursday is correct.

Note: We can also use an alternate method wherein we can assign numbers to the days such as :
Saturday can become \[0\]
Sunday can become \[1\]
Monday can become \[2\]
Tuesday can become \[3\]
Wednesday can become \[4\]
Thursday can become \[5\]
Friday can become \[6\].
You should start on the given day as here we have started on Saturday.
From the same division method as given in step 1:
Number of weeks =\[\dfrac{{999}}{7}\]
\[ \Rightarrow {\text{Number of weeks}} = 142{\text{weeks and }}5{\text{days}}\]
The remaining five correspond to Thursday which is our final answer.