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imaityaroy
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To get a job at Company X, an applicant must be recommended by 28 Jun 2026, 06:38
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Hi mx39,
Great explanation, thanks alot.

I have one doubt,(# entities in no group), how did you know this group is 0?

I did not get the explanation of 'In this case (# entities in no group), they are all assigned a group, so that's one less thing to worry about.'
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To get a job at Company X, an applicant must be recommended by Updated on: 14 Jul 2026, 02:31
Originally posted by atharvadixit on 14 Jul 2026, 01:07.
Last edited by Bunuel on 14 Jul 2026, 02:31, edited 1 time in total.
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KarishmaB

Hey Karishma, thanks for all the support towards this community. I just have one quick question - in the video explanation, you started with the minimum sets, but in this particular question, you're starting with the maximum ones. Why? And how do we determine which methodology to go with?
KarishmaB

­Max min in overlapping sets is discussed here: https://youtu.be/oLKbIyb1ZrI

Start with the largest set and put it down: 20. We have 10 remaining.
When we put down 17, we avoid overlap so 10 go to the remaining and 7 overlap with the 20 set.
When we put down 15, to avoid overlap, we put all 15 (shaded region) on the 23 where there is no overlap. Hence minimum overlap of all three is 0.

Attachment:
Screenshot 2024-06-24 at 2.35.11 PM.png

Answer (A)

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KarishmaB
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To get a job at Company X, an applicant must be recommended by 14 Jul 2026, 03:47
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It doesn't matter what you start with - either will give you the same answer. Just that having a plan helps.

atharvadixit
KarishmaB

Hey Karishma, thanks for all the support towards this community. I just have one quick question - in the video explanation, you started with the minimum sets, but in this particular question, you're starting with the maximum ones. Why? And how do we determine which methodology to go with?

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To get a job at Company X, an applicant must be recommended by 14 Jul 2026, 03:54
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You’re awesome. You cleared a very big gap in my conceptual understanding of min-max sets today. Thank you!!


KarishmaB
It doesn't matter what you start with - either will give you the same answer. Just that having a plan helps.

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To get a job at Company X, an applicant must be recommended by 09 Aug 2026, 10:28
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3 sets + asking minimum in ALL 3 → MAX(0, A+B+C−2N)
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To solve this one you can look for the extreme cases. For all 3 to be approved it must be that the worst case scenario group must overlap with the largest group.
Take 15 and 17, since they are the smallest and therefore will have the smallest overlap.
15 and 17 in a group of 30 are guaranteed to have a minimum overlap of 2.
Worse case is 2.

Now, do those 2 people HAVE to be part fo the 20 that 3 approved?
No.
We don't know who 3 approved, just that it was 20 people. Those 20 could overlap with 1 and 2, but it doesn't have to be true that those who were approved by both 1 and 2 must be approved by 3.
Answer = 0
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I didn't understand this part "When we put down 15, to avoid overlap, we put all 15 (shaded region) on the 23 where there is no overlap", which 23 are you referring to? KarishmaB
KarishmaB

­Max min in overlapping sets is discussed here: https://youtu.be/oLKbIyb1ZrI

Start with the largest set and put it down: 20. We have 10 remaining.
When we put down 17, we avoid overlap so 10 go to the remaining and 7 overlap with the 20 set.
When we put down 15, to avoid overlap, we put all 15 (shaded region) on the 23 where there is no overlap. Hence minimum overlap of all three is 0.

Attachment:
Screenshot 2024-06-24 at 2.35.11 PM.png

Answer (A)

­
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KarishmaB
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To get a job at Company X, an applicant must be recommended by 17 Aug 2026, 05:30
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Make the diagram along. Make a rectangle (Total set) of 30. This is Total.
Put down the 20 circle. There are 10 remaining in the rectangle.
Put down 17 circle such that all 10 remaining are included and 7 overlap with the previous 20 circle.
So now all 30 are in at least 1 circle. 7 are in overlap region and the other 23 (13 + 10) do not have any overlap. So 23 have no overlap.
So put down 15 somewhere in this 23 region.

Here is a video explaining this: https://anaprep.com/sets-statistics-min-max-in-sets/


GulfTube
I didn't understand this part "When we put down 15, to avoid overlap, we put all 15 (shaded region) on the 23 where there is no overlap", which 23 are you referring to? KarishmaB

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