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15 Oct 2023, 03:22
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Fair: 271
Discussion: 306
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
70% (02:21) correct
30%
(02:34)
wrong
based on 2070
sessions
History
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Not Attempted Yet
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.
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.
| Fair | Discussion | |
| 260 | ||
| 271 | ||
| 296 | ||
| 306 | ||
| 311 |
ShowHide Answer
Official Answer
Fair: 271
Discussion: 306
15 Oct 2023, 09:27
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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.
Since both the fair and the discussion will be held on a Tuesday, there will be one or more weeks between the fair and the discussion.
Thus, since a week is 7 days long, the difference between the number of days between the planning meeting and the fair and the number of days between the planning meeting and the discussion must be a multiple of 7.
We can narrow down our choices by noticing that, since there will be fewer days between the planning meeting and the fair than between the planning meeting and the discussion, the lowest number among the choices could be selected only for the first column, and the highest number among the choices could be selected only for the second column.
Then, using that constraint to our advantage, we simply find two numbers such that the one in the second column is greater than the one in the first column by a multiple of 7.
We can methodically subtract each lower number from each higher number to find a difference that is a multiple of 7.
For instance:
271 - 260 = 11 not a multiple of 7
296 - 260 = 36 not a multiple of 7
etc.
Alternatively, we can scan the numbers to see whether we quickly see a pair that differs by a multiple of 7.
Either way, we will find that 306 - 271 = 35, which is a multiple of 7.
Correct Answer
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.
Since both the fair and the discussion will be held on a Tuesday, there will be one or more weeks between the fair and the discussion.
Thus, since a week is 7 days long, the difference between the number of days between the planning meeting and the fair and the number of days between the planning meeting and the discussion must be a multiple of 7.
We can narrow down our choices by noticing that, since there will be fewer days between the planning meeting and the fair than between the planning meeting and the discussion, the lowest number among the choices could be selected only for the first column, and the highest number among the choices could be selected only for the second column.
Then, using that constraint to our advantage, we simply find two numbers such that the one in the second column is greater than the one in the first column by a multiple of 7.
We can methodically subtract each lower number from each higher number to find a difference that is a multiple of 7.
For instance:
271 - 260 = 11 not a multiple of 7
296 - 260 = 36 not a multiple of 7
etc.
Alternatively, we can scan the numbers to see whether we quickly see a pair that differs by a multiple of 7.
Either way, we will find that 306 - 271 = 35, which is a multiple of 7.
Correct Answer
271, 306
08 Apr 2024, 23:11
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parkhydel
Fair would be on a Tuesday and Discussion on another Tuesday. Hence there will be an integer number of weeks (7 days or 14 days or 21 days etc) between the fair and the discussion. Of the given options, we need values that have a difference of a multiple of 7 between them. Note that the numbers themseleves needn't be multiples of 7 but they must have the same format e.g. 7a + 3 and 7b + 3. Then their difference will be a multiple of 7.
260 - We can write it as 7a + 1 (where 1 is the remainder when it is divided by 7)
271 - This is 11 more than 260 so it is 7b + 5.
296 - This is 25 more than 271 so it is 7c + 2.
306 - This is 10 more than 296 so it is 7d + 5. GOT IT!
We already have a 7b + 5 so the difference between these two, 271 and 306 will be a multiple of 7.
311 - This is 5 more than 306 so it is 7e + 3.
Answer: 271 and 306
Check out this video on division:
https://youtu.be/A5abKfUBFSc
