Grades 9-10 Video Solutions 2010-Levels 9&10 Video Solutions 2010 problem15

Video Transcription

Question number 15, a certain month had three Tuesdays that fell on even-numbered days. What day of the week was the 21st of that month?  So let's just see what happens if we try to construct a month with four Tuesdays and we know that some Tuesdays, in fact three of them, have to fall on even-numbered days.  So let's just say that Tuesday would be the 1st. If it's the 1st, then also the 8th, and then the 15th, and I move here from one number  to the next just by adding 7, and then 15 plus 7 would give us the 22nd, and then also the 29th of the month. And so we have here 1, 2 even-numbered days.  So this is not such a month. Let's try and see what happens if we have Tuesdays beginning with the 2nd.  So if the 2nd is a Tuesday, then also the 9th is a Tuesday, the 16th would be a Tuesday plus 7, the 23rd would be a Tuesday, and then the 30th would be a Tuesday.  And so here we have 1, 2, and 3 Tuesdays. And that is, in fact, the only way we can get three even-numbered days to be Tuesdays in a month.  So here we know that the 23rd is a Tuesday, so we can then see what happens on the 21st. So we have the 23rd, that's a Tuesday, the 22nd before that would be a Monday, and the  21st would have to be a Sunday. And so we have found what happens on the 21st, it is in fact a Sunday, and that gives us choice E over here for question 15.

Video Summary

The video transcript discusses a problem-solving exercise related to determining the weekday of the 21st in a month with specific conditions. The problem states the month has three Tuesdays on even-numbered days. By calculating potential starting days for Tuesdays, it deduces that if Tuesday falls on the 2nd, then the 9th, 16th, 23rd, and 30th also are Tuesdays, meeting the criteria. Thus, if the 23rd is a Tuesday, the 21st is deduced to be a Sunday. Hence, the correct answer is Sunday, choice E.

Keywords

problem-solving

weekday determination

Tuesdays

21st

Sunday