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GMAT Club Olympics 2025 (Day 8): A certain website has a request

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10 Jul 2025, 04:07

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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.

Sorting the requests given: 830,823,820,810,795,790,780

As indicated above by red color, the top 4 days had requests rejected, and green days(3) had no rejected requests.

On the day with 812 requests:
For Min rejected requests, we need to make the RT as max => 810-1 = 809. (If it was any higher say 810, then the rejected days initially given would become 3 instead of 4)
This makes the min rejected requests = 812-809 = 3

Now, for Max rejected requests, we need to make RT as min => 795. (if it was any lower say 794, then the rejected days initially given would become 5 instead of 4)
This makes the max rejected requests = 812-795 = 17

So the Min and Max values are 3 and 17 respectively.

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10 Jul 2025, 04:18

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The request threshold must be between 795 (included) and 810 (not included, so 809) in order that Monday(810), Wednesday(830), Thursday(823) and Sunday(820) can be the days with at least one request that was not addressed.

Maximum if threshold=795: 812-795=17
Minimum if threshold=809: 812-809=3

Minimum=3
Maximum=17

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10 Jul 2025, 04:44

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Excess requests are discarded, so 4 out of 7 days have seen at least 1 request discarded, so on the following monday we have at least 1 request discarded.

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10 Jul 2025, 04:44

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ordered list: 780, 790, 795, 810, 820, 823, 830

On exactly 4 out of the 7 days that week, there was at least one request that was not addressed: means that 795<=RT<=809

If RT=809, Minimum is 812-809=3
If RT=795, Maximum is 812-795=17

Minimum=3 and Maximum=17

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10 Jul 2025, 04:57

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Final answer minimum= 3
Maximum= 16

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10 Jul 2025, 05:09

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Checking the numbers, RT must be between 795 and 810.
795 is included and 810 is not included (if included, this only produces 3 days with discarded requests)

Maximum is when RT is minimum (795): 812-795 = 17
Minimum is when RT is maximum (809): 812-809 = 3

The right answers:
Minimum=3
Maximum=17

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10 Jul 2025, 05:17

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For minimum, let's take the set of 4 as maximum four : 830, 823, 820, 810. From this, if some of 812 has been discarded then, that would be 812-810 = 2.
For maximum, let's take the set of 4 as minimum four : 780, 790, 795, 810. From this, if some of 812 has been discarded then, that would be 795-810 = 17.

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10 Jul 2025, 05:32

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Number of requests in the days with all the requests addressed: 780, 790, 795
Number of requests in the days with at least one request not addressed: 810, 820, 823, 830

795 <= threshold < 810
795 <= threshold <= 809

Minimum = 812-809 = 3
Maximum = 812-795 = 17

Correct answers: Minimum=3 and Maximum=17

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10 Jul 2025, 05:43

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Mon(810), Tue(790), Wed(830), Thu(823), Fri(780), Sat(795), Sun(820)

arranging in increasing order we get 780,790,795,810,820,823,830

Mon, Sun, Thu, Wed are possible days on which at least one request that was not addressed

for minimum requests to be discarded on next Monday take RT = 809 , this will satisfy the above condition

on next monday total number of req = 812

min discarded requests = 812-809 = 3

for maximum requests to be discarded on next Monday take RT = 795

max discarded requests = 795-812 = 17

Bunuel

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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.

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10 Jul 2025, 06:38

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From the information provided we can conclude that all 780, 790 and 795 requests were addressed and some of the 810, 820. 823 and 830 were not

To fit the criteria we can safely say that the least number of addressed requests in a day is 795 while the most request addressed is 810-1= 809. The latter ensures that there was at least one request that was not addressed for 810, 820. 823 and 830 .
Based on the above the following Monday Min possible unaddressed requests can be computed as 812-809= 3
and Max value of unaddressed requests can be computed as 812-795= 17

Bunuel

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810, 790, 830, 823, 780, 795, 820

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10 Jul 2025, 06:42

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If in 4 days out of the seven, atleast 1 request was not addressed, then the 4 days according to requests are - >
810, 820, 823, 830.
The smallest number of requests are on the day with 810 requests.
The maximum request threshold can be 809. If it's more than 809, that would mean there are 3 days out of the 7 on which atleast 1 request was not addressed, which is not possible. Therefore, RT can't be more than 809.
The minimum number of requests not addressed on monday are 812-809 = 3
The day with the smallest number of requests after the day with 810 requests had 795 requests.
The minimum request threshold can be 795, because if it's lower than 795, that would mean there are 5 days out of the 7 in which atleast 1 request was not addressed, which is not possible.
The maximum number of requests not addressed on monday = 812-795 = 17

UfuomaOh

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10 Jul 2025, 06:57

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The question gives us the order received from monday to Sunday. It states that on exactly 4 out of the 7 days that week, there was at least one request that was not addressed. Meanwhile it has a request threshold and if that threshold is exceeded, the site processes only the first RT request.

On the following Monday, the site received 812 requests. What is the minimum and maximum quantity of order that would not have been processes

To know this we have to know the RT and also apply information that states that 4 out of the 7 days of that week had at least one order that was not processed

So arranging the order quantity from ascending to descending we have

780, 790, 795, 810, 820, 823, 830

So the minimum order is between 795 and 810
796<=RT<= 809

if RT= 796
Minimum order not treated

812-809= 3

Maximum order not treated

812-796=16

GarvitGoel

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10 Jul 2025, 06:59

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Option B and Option E are the correct answers.

First lets understand the information given in the question before trying to solve it.

So the question starts by telling us that "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". Then it gives us the request history of a week, from Monday to Sunday: 810, 790, 830, 823, 780, 795, 820. After which it tells us that "On exactly 4 out of the 7 days that week, there was at least one request that was not addressed". Then it ends the question by telling us that "On the following Monday, the site received 812 requests" and asks us to select the Minimum and Maximum that could not have been addressed on that Monday.

So as the question tells us that on exactly 4 out of the 7 days that week there were atleat on request that was not address by the site. Form this information we can easily conclude that RT must be somewhat between 795≤RT≤809. Now lets understand how we got this range: So lets say if the RT is ≤795 then it would mean that either we have identified the correct value of RT or either there were atleast 4 days on which the [color=#0f0f0f]at least one request that was not addressed. Which we know is not the case as per the information mentioned in the question and same is the reason for ≤809 that's why we are just considering the range of values for RT.[/color]

Now as the question asks us the value of minimum and maximum requests that were not addressed by the site.

To answer the first part of the question i.e. the minimum number of requests which were not answered by the site we need to maximize the value of RT which will be 809, beyond this RT cannot have any other value.
=>Minimum requests not addressed = 812 - RT
=>Minimum requests not addressed = 812 - 809
=>Minimum requests not addressed = 3 (Option B)

And for answering the second part of the question i.e. maximum number of requests which were not answered by the site for this we need to minimize the value of RT which will be 795, below this RT cannot have any other value.
=>Maximum requests not addressed = 812 - RT
=>Maximum requests not addressed = 812 - 795
=>Maximum requests not addressed = 17 (Option E)

So from the above calculations and answers we can conclude that the minimum and maximum number of requests that could have been not addressed on that Monday are 3(Option B) and 17(Option E) respectively.

Bunuel

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810, 790, 830, 823, 780, 795, 820

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10 Jul 2025, 07:04

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Lets put the number of requests in ascending order first : 780, 790, 795, 810, 820, 823, 830

For exactly 4 out of 7 days to exceed the limit, the RT should be somewhere more than 794 and less than 810. This is because
> for a limit of 794, there are 5 days when this limit is exceeded : 795, 810, 820, 823 and 830
> for a limit of 810, there are only 3 days when limit is exceeded : 820, 823, 830
> anything below 794, will cause 5 or more than 5 days to exceed limit
> anything above 809 will cause 3 or less than 3 days to exceed limit

But if RT is within the range 795-809, there will be exactly 4 days where this is exceeded : 810, 820, 823, 830

Now we have 812 requests on Monday.
For minimum requests to be exceeded, we should take the upper limit of the range 795-809 , which is 809. If 809 is the RT, then 812-809= 3 requests will be discarded.

For maximum requests to be exceeded, take the lower limit of the range 795-809, which is 795. If 795 is the RT, then 812-795= 17 requests will be discarded

Hence minimum = 3, maximum = 17

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10 Jul 2025, 07:06

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There were 3 days out of the 7 when all requests were addressed.
If we sort the requests in ascending order
780, 790, 795, 810, 820, 823, 830
It has to be the days when the requests were 780, 790, and 795.
Why?
If the RT were 810, then it would mean that there were 4 days during which all requests were addressed. RT has to be less than 810 and greater than or equal to 795

Now on next Monday, when the requests were 812, to get
1. The minimum number of requests that were not addressed, we have to take the maximum possible value for RT, which is 809. In this case, it would mean that 3 requests went unaddressed.
2. The maximum number of requests that were not addressed, we have to take the minimum possible value for RT, which is 795. In this case, it would mean 17 requests went unaddressed.

Minimum - 3, Maximum - 17.

Bunuel

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810, 790, 830, 823, 780, 795, 820

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10 Jul 2025, 07:09

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Arrange the no. of requests in ascending order: 780,790,795,810,820,823,830

The highest 4 among the list were not addressed entirely.

795<=RT<810

Max request discarded = 812-795 = 17
Min req discarded = 812-809 = 3

Bunuel

This question was provided by GMAT Club
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810, 790, 830, 823, 780, 795, 820

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10 Jul 2025, 07:34

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Arranging he requests in ascending order:
780, 790, 795, 810, 820, 823, 830.
On exactly 4 of the 7 days, at least one request was not addressed. The threshold could have been <=809.
If threshold was 795, still the situation would be satisfied.
On the following Monday, 812 requests were received.
With RT=795, requests not addressed = 17. (maximum)
With RT=809, requests not addressed = 3.

Minimum: 3
Maximum: 17

Bunuel

This question was provided by GMAT Club
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810, 790, 830, 823, 780, 795, 820

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Updated on: 10 Jul 2025, 08:12

Originally posted by eshika23 on 10 Jul 2025, 07:42.
Last edited by eshika23 on 10 Jul 2025, 08:12, edited 2 times in total.

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Lets first arrange the RT in Ascending order

780,790,795,810,820,823,830

4 out of 7 days atleast one request was discarded. This means atleast one, it can be more but atleast 1 is discarded. So last 4 Might be when atleast 1 request is discard.

795 requests are as far as we know can be proceeded.

On following monday 812 requests were there

So minimum requests that could be denied are:
we know atleast one request was denied when 810 requests where there so with 812 requests 3 requests minimum will be rejected.
And if we assume only 795 requests were allowed and rest were denied so 812-795=17 requests max can be rejected.

Minimum: 3 Max:17

Bunuel

This question was provided by GMAT Club
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810, 790, 830, 823, 780, 795, 820

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10 Jul 2025, 07:44

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Over 7 days, the number of requests received each day is 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.
We need to find the Minimum and the Maximum number of requests that could have been not addressed on that Monday

Lets arrange the requests in ascending order
=> 780, 790, 795, 810, 820, 823, 830

Given that on exactly 4 days, the requests exceeded RT, the cutoff is between 795 and 809 inclusive

So,
Maximum RT that still gives exactly 4 days of overload = 809 (810, 820, 823, 830 would still exceed it)
Minimum RT that still gives exactly 4 days of overload = 795 (810, 820, 823, 830 would still exceed it)

So the RT range possible is between 795 to 809

Now we need,
Minimum number of requests that could have been not addressed on that Monday is when RT is maximum
=> RT = 809
=> Minimum unaddressed requests= 812 - 809 = 3

Maximum number of requests that could have been not addressed on that Monday is when RT is minimum
=> RT = 795
=> Maximum unaddressed requests = 812 - 795 = 17

Minimum = 3
Maximum = 17

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10 Jul 2025, 07:52

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On exactly 4 out of the 7 days that week, there was at least one request that was not addressed:
Top 4 are: 830, 823, 820, 810, atleast 1 request was not addressed.
The requests during days that were all addressed = 795, 790, 780
Maximum threshold = 809
Minimum threshold = 796

On monday - 812 were received
Minimum number of unaddressed requests = 812 - 809 = 3
Maximum number of unaddressed requests = 812 - 796 = 17

Bunuel

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810, 790, 830, 823, 780, 795, 820

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