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A committee recently held a planning meeting for a craft fair. The committee decided that the fair would occur on a Tuesday and that a public discussion about the fair would be held sometime after, also on a Tuesday.
In the table, select for Fair a number of days between the planning meeting and the fair and select for Discussion a number of days between the planning meeting and the public discussion that would be jointly consistent with the given information, Make only two selections, one in each column.
260
271
296
306
311
Let's visualize this problem to make it crystal clear. We're dealing with scheduling events over time, so let's use a timeline:
Planning Meeting ----[X days]----> Fair (Tuesday) ----[Y-X days]----> Discussion (Tuesday)
Key Constraints:
We need to find two numbers from our choices [260, 271, 296, 306, 311] where both resulting days must be Tuesdays and the second number must be larger than first. If an event happens N days after the planning meeting and lands on a Tuesday, then both selections must be consistent with the SAME planning meeting day.
Let's assign days: Sunday=0, Monday=1, Tuesday=2, Wednesday=3, Thursday=4, Friday=5, Saturday=6.
For each choice:
260 days: \(260 \bmod 7 = 1\), planning meeting = Monday;
271 days: \(271 \bmod 7 = 5\), planning meeting = Thursday;
296 days: \(296 \bmod 7 = 2\), planning meeting = Sunday;
306 days: \(306 \bmod 7 = 5\), planning meeting = Thursday;
311 days: \(311 \bmod 7 = 3\), planning meeting = Saturday.
We notice that 271 and 306 both require the planning meeting to be on Thursday! Since \(271 < 306\), we can select Fair: 271 days after planning meeting and Discussion: 306 days after planning meeting.
This satisfies all constraints: both land on Tuesdays from same Thursday planning meeting and discussion is after fair.