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parkhydel
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A committee recently held a planning meeting for a craft fair. The com 15 Oct 2023, 03:22
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Fair: 271 Discussion: 306
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45% (medium)

Question Stats:

70% (02:24) correct 30% (02:38) wrong based on 3091 sessions

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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.
Fair Discussion
260
271
296
306
311
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Fair: 271 Discussion: 306
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A committee recently held a planning meeting for a craft fair. The com 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
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271, 306
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A committee recently held a planning meeting for a craft fair. The com 08 Apr 2024, 23:11
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parkhydel
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.
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­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
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A committee recently held a planning meeting for a craft fair. The com 16 Feb 2024, 04:54
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Hi, Marty Thanks for the answer. Although I have a a query : shouldnt the number of days between two tuesdays be 7K+6?
MartyMurray
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
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271, 306
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A committee recently held a planning meeting for a craft fair. The com 31 May 2024, 23:27
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My approach is,
1. Fair (number of days between the planning meeting & the fair) must be smaller than Discussion (number of days between the planning meeting and the public discussion)
2. Both the the fair and the public discussion are on a Tuesday

As a result the difference between the values selected must be divisible by 7 / a multiple of 7. Best to do the quick math starting from Fair being 260, then 271 (at which we get the answer), at 296, at 306 there isn't much mental math to do at that point (can do if there is time to check).
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A committee recently held a planning meeting for a craft fair. The com 22 Jan 2025, 22:24
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Hi Marty

Thank you for the very elegant solution.

I have a question on why we are saying that there would be fewer days between Planning meeting and fair versus Planning meeting and Public discussion.

Shouldn't the order be: Planning Meeting -> Public Discussion ->Fair, where you plan invite a public discussion and based on engagement hold the fair. So there are less days between meeting and discussion versus planning and fair, in this answer set in my understanding the fair happens 271 days after meeting whereas the discussion happens 306 days later, by which time the fair is already over.
MartyMurray
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
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271, 306
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A committee recently held a planning meeting for a craft fair. The com 05 Mar 2025, 19:19
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SirSanguine
Hi, Marty Thanks for the answer. Although I have a a query : shouldnt the number of days between two tuesdays be 7K+6?
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The number of days between a Tuesday and another Tuesday is 6.

However, the number of days between a particular day and two different following Tuesdays will be a multiple of 7 because one Tuesday is 7 days later than another Tuesday since the first Tuesday will be counted in the days between the initial day and the second Tuesday.
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devarpanc
Hi Marty

Thank you for the very elegant solution.

I have a question on why we are saying that there would be fewer days between Planning meeting and fair versus Planning meeting and Public discussion.

Shouldn't the order be: Planning Meeting -> Public Discussion ->Fair, where you plan invite a public discussion and based on engagement hold the fair. So there are less days between meeting and discussion versus planning and fair, in this answer set in my understanding the fair happens 271 days after meeting whereas the discussion happens 306 days later, by which time the fair is already over.
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Interesting question.

Normally, we'd expect a public discussion of an event to be held before the event, rather than after it. At the same time, it is possible for such a public discussion to be held after the event.

So, in answering a GMAT question like this one, we have to be careful to note what the passage says rather than go with what's normal.

In this case, the passage says the following:

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.
Although "sometime after" could somehow mean "sometime after the committee first met," the more logical meaning is "sometime after the fair."

After all, there's no reason to say that the discussion will be held "sometime after the committee met" since that fact is a given. Also, the sentence lists the fair first and the discussion second, indicating in another way that the fair will occur first and the discussion later.

So, even though we might expect the discussion to occur before the fair, our best move is to go with the idea that the discussion will occur after the fair.
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Since 260 is the smallest and divisible by 10, I will subtract 260 from others to get the numbers that in the multiplication table (less than 100), for easy calculation.

260 - 0
271 - 11
296 - 36
306 - 46
311 - 51

Then I see that the two numbers 11 and 46 when divided by 7 have a remainder 4. So their difference will be divisible by 7.

Or we also easily find the difference of two numbers among the five smaller numbers, 46-11=35, that is divisible by 7.
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A committee recently held a planning meeting for a craft fair. The com 03 Apr 2026, 23:23
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If you are fast with calculation it wouldn't take more than few seconds to quickly stumble upon the right combo of multiples of 7 which is what is needed. The thing is to not get fazed by the initial few if one misses maybe thinking that the approach is wrong IMO.
parkhydel
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.
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A committee recently held a planning meeting for a craft fair. The com 27 Jul 2026, 19:01
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For this one I looked at the difference of days between the two numbers. If the difference was divisible by 7, it means that the two numbers were the ones that were right. Since the two meetings are on tuesday, it means that the spacing must be divisible by 7 days.
parkhydel
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.
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