An international exhibition is inaugurated on January 26th of a leap year, which falls on … — State PSC Exam

An international exhibition is inaugurated on January 26th of a leap year, which falls on a Thursday. The closing ceremony is scheduled for October 15th of the same year. On what day of the week will the closing ceremony take place?

Answer: Monday / monday

Answer

Monday

The total number of days elapsed from January 26th to October 15th in a leap year is exactly

263

days. Dividing

263

7

gives

37

full weeks and a remainder of

4

odd days. Counting

4

days forward from Thursday results in Monday.

Step-by-Step Solution

Calculate the remaining days in January and note the full days in the intervening months.

January:

5

days (

31 - 26

). February:

29

days (since it is a leap year). March:

31

, April:

30

, May:

31

, June:

30

, July:

31

, August:

31

, September:

30

To find the total number of days elapsed between January 26th and October 15th, we must sum the relevant days in each month.

Add the days of the final month (October) to the sum of the previous months.

5 + 29 + 31 + 30 + 31 + 30 + 31 + 31 + 30 + 15 = 263

days.

This calculation yields the exact number of days that pass from the inauguration to the closing ceremony.

Divide the total number of elapsed days by

7

to find the remainder (odd days).

263 \div 7 = 37

with a remainder of

4

days.

Since the days of the week repeat every

7

days, only the remainder affects the final day of the week.

Count

4

days forward from the starting day (Thursday).

Thursday

+ 1 =

Friday,

+ 2 =

Saturday,

+ 3 =

Sunday,

+ 4 =

Monday.

Adding the odd days to the initial day correctly determines the final day of the week.

Key Concept

Calculating elapsed days across multiple months and using the concept of odd days (modulo 7 arithmetic) to determine the exact day of the week.

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