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09 Jul 2025, 08:00
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Minimum: 3
Maximum: 17
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A certain website has a request threshold (RT), defined as the maximum number of requests it can handle in a single day. If the number of requests on a given day exceeds the RT, the site processes only the first RT requests. The remaining requests are not addressed and are permanently discarded.
During one week, from Monday to Sunday, the number of requests received on each day was as follows:
810, 790, 830, 823, 780, 795, 820
On exactly 4 out of the 7 days that week, there was at least one request that was not addressed.
On the following Monday, the site received 812 requests.
Based on this information, select the Minimum and the Maximum number of requests that could have been not addressed on that Monday. Make only two selections, one in each column.
| Minimum | Maximum | |
| 2 | ||
| 3 | ||
| 15 | ||
| 16 | ||
| 17 | ||
| 18 |
ShowHide Answer
Official Answer
Minimum: 3
Maximum: 17
09 Jul 2025, 08:30
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GMAT Club Official Explanation:
Given that on exactly 4 out of the 7 days there was at least one request that was not addressed, those must be the 4 days with the highest request counts: 810, 820, 823, and 830. This implies that RT must be less than 810, so RT ≤ 809.
The next highest value is 795, and since it occurred on the remaining 3 days (which had all requests addressed), we know that 795 ≤ RT.
Thus, the request threshold must satisfy: 795 ≤ RT ≤ 809.
If RT = 809, then out of the 812 requests on the following Monday, only 3 would not be addressed (the minimum possible).
If RT = 795, then 812 - 795 = 17 requests would not be addressed (the maximum possible).
General Discussion
09 Jul 2025, 08:21
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1. Understand the Request Threshold (RT)
The RT is the maximum number of requests the site can handle in a day.
If requests > RT, then requests - RT are discarded.
If requests <= RT, then 0 requests are discarded.
2. Analyze the First Week's Data
The requests for the week are: 810, 790, 830, 823, 780, 795, 820
We know that on exactly 4 out of 7 days, there was at least one unaddressed request. This means for these 4 days, the number of requests was greater than the RT. For the remaining 3 days, the number of requests was less than or equal to the RT.
Let's sort the requests in ascending order:
780, 790, 795, 810, 820, 823, 830
Since 4 days had unaddressed requests, it means the RT must be somewhere between the 3rd and 4th highest values in the sorted list.
If RT were 795 or less, then more than 4 days would have unaddressed requests.
If RT were 810 or more, then fewer than 4 days would have unaddressed requests.
Therefore, the RT must be a value between the 3rd and 4th highest requests that resulted in 4 days having unaddressed requests.
Let's consider the possible range for RT:
The 4 days with unaddressed requests must be the days with the highest request numbers. These are 830, 823, 820, and 810.
The 3 days with no unaddressed requests must be the days with the lowest request numbers. These are 780, 790, and 795.
This means:
RT must be less than 810 (because 810 had at least one unaddressed request). So, RT ≤ 809.
RT must be greater than or equal to 795 (because 795 had no unaddressed requests). So, RT ≥ 795.
Combining these, the possible range for RT is: 795≤RT≤809.
3. Calculate Minimum Unaddressed Requests on Monday
On Monday, the site received 812 requests. To find the minimum number of unaddressed requests, we need to use the highest possible RT within its determined range (795≤RT≤809).
Maximum possible RT = 809
Unaddressed requests = Total requests - RT
Unaddressed requests = 812 - 809 = 3
4. Calculate Maximum Unaddressed Requests on Monday
To find the maximum number of unaddressed requests, we need to use the lowest possible RT within its determined range (795≤RT≤809).
Minimum possible RT = 795
Unaddressed requests = Total requests - RT
Unaddressed requests = 812 - 795 = 17
Therefore, the minimum number of requests not addressed on Monday is 3, and the maximum is 17.
The final answer is
Minimum: 3, Maximum: 17
The RT is the maximum number of requests the site can handle in a day.
If requests > RT, then requests - RT are discarded.
If requests <= RT, then 0 requests are discarded.
2. Analyze the First Week's Data
The requests for the week are: 810, 790, 830, 823, 780, 795, 820
We know that on exactly 4 out of 7 days, there was at least one unaddressed request. This means for these 4 days, the number of requests was greater than the RT. For the remaining 3 days, the number of requests was less than or equal to the RT.
Let's sort the requests in ascending order:
780, 790, 795, 810, 820, 823, 830
Since 4 days had unaddressed requests, it means the RT must be somewhere between the 3rd and 4th highest values in the sorted list.
If RT were 795 or less, then more than 4 days would have unaddressed requests.
If RT were 810 or more, then fewer than 4 days would have unaddressed requests.
Therefore, the RT must be a value between the 3rd and 4th highest requests that resulted in 4 days having unaddressed requests.
Let's consider the possible range for RT:
The 4 days with unaddressed requests must be the days with the highest request numbers. These are 830, 823, 820, and 810.
The 3 days with no unaddressed requests must be the days with the lowest request numbers. These are 780, 790, and 795.
This means:
RT must be less than 810 (because 810 had at least one unaddressed request). So, RT ≤ 809.
RT must be greater than or equal to 795 (because 795 had no unaddressed requests). So, RT ≥ 795.
Combining these, the possible range for RT is: 795≤RT≤809.
3. Calculate Minimum Unaddressed Requests on Monday
On Monday, the site received 812 requests. To find the minimum number of unaddressed requests, we need to use the highest possible RT within its determined range (795≤RT≤809).
Maximum possible RT = 809
Unaddressed requests = Total requests - RT
Unaddressed requests = 812 - 809 = 3
4. Calculate Maximum Unaddressed Requests on Monday
To find the maximum number of unaddressed requests, we need to use the lowest possible RT within its determined range (795≤RT≤809).
Minimum possible RT = 795
Unaddressed requests = Total requests - RT
Unaddressed requests = 812 - 795 = 17
Therefore, the minimum number of requests not addressed on Monday is 3, and the maximum is 17.
The final answer is
Minimum: 3, Maximum: 17
