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Shrey1
Harry (Training for Youth Olympics, First-generation American, Soccer) could be added to Either Day since -
1. adding Harry will not make more than 2 players playing Soccer
2. adding Harry to Day 1 will satisfy the condition of having at least 4 players training for Youth Olympis in 1 day.
3. adding Harry to Day 2 will satisfy the condition of having majority minority community students


Michelle (Training for Youth Olympics, European American, Tennis) could be added to Neither Days since -
1. adding Michelle to Day 1 will break the condition of 2 players playing Tennis
2. adding Michelle to Day 2 will break the condition of having majority minority community students

So, the answer would be E, A
­Why is Chloe not for neither day? Badminton and majority will break both days' rules. 

Chloe can fit into the first day based on Youth Olympics criteria, but not the second day

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­Day A: at least 3 must be 1st gen Am.; Native Am.; Afri. Am.; or Hispanics
Day B: at least 4 must be training for Olympics

No more than 2 sports on the same days

D1.........................................D2
3/4 Olympics............................2/4 Olympics
Day B (at least 4 Olympics).......Day A (at least 3 minority communities)
...............................................2 EU + 1 Afr. Am. + 1 1st gen Am.
2 Tennis...................................2 Badminton

=> For Either day: 3 requirments
+ must be Olympics
+ must be from minority community
+ must not Tennis or Badminton

Michelle (Training for Youth Olympics, European American, Tennis)
Ben (Training for Youth Olympics, European American, Soccer)
Frank (Not training for Youth Olympics, Native American, Ice Hockey)
Chloe (Training for Youth Olympics, European American, Badminton)
Harry (Training for Youth Olympics, First-generation American, Soccer)


=> For Neither day: 2 requirements
+ Not training for Olympics or Tennis
+ Not minor comm or Badminton

Michelle (Training for Youth Olympics, European American, Tennis)
Ben (Training for Youth Olympics, European American, Soccer)
Frank (Not training for Youth Olympics, Native American, Ice Hockey)
Chloe (Training for Youth Olympics, European American, Badminton)
Harry (Training for Youth Olympics, First-generation American, Soccer)­
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=> For Neither day: 2 requirements
+ Not training for Olympics or Tennis
+ Not minor comm or Badminton
Can you explain how you arrived at this logic?
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Day 1 already has 2 Tennis players (Margery and Lana). Adding a third Tennis player would violate “no more than two in the same sport,” so anyone who plays Tennis is out for Day 1.

Day 2 already has 2 Badminton players (Nora and Marty). Adding a third Badminton player would violate the same rule, so anyone who plays Badminton is out for Day 2.

Therefore, a “neither-day” candidate can be eliminated by either:
  • Failing the minority requirement on Day 1 or by playing Tennis,
    and
  • Failing the Youth-Olympics requirement on Day 2 or by playing Badminton.
DhanyaAbhirami
Gemmie
=> For Neither day: 2 requirements
+ Not training for Olympics or Tennis
+ Not minor comm or Badminton
Can you explain how you arrived at this logic?
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This solution is super clear for me, thx.
Gemmie
­Day A: at least 3 must be 1st gen Am.; Native Am.; Afri. Am.; or Hispanics
Day B: at least 4 must be training for Olympics

No more than 2 sports on the same days

D1.........................................D2
3/4 Olympics............................2/4 Olympics
Day B (at least 4 Olympics).......Day A (at least 3 minority communities)
...............................................2 EU + 1 Afr. Am. + 1 1st gen Am.
2 Tennis...................................2 Badminton

=> For Either day: 3 requirments
+ must be Olympics
+ must be from minority community
+ must not Tennis or Badminton

Michelle (Training for Youth Olympics, European American, Tennis)
Ben (Training for Youth Olympics, European American, Soccer)
Frank (Not training for Youth Olympics, Native American, Ice Hockey)
Chloe (Training for Youth Olympics, European American, Badminton)
Harry (Training for Youth Olympics, First-generation American, Soccer)


=> For Neither day: 2 requirements
+ Not training for Olympics or Tennis
+ Not minor comm or Badminton

Michelle (Training for Youth Olympics, European American, Tennis)
Ben (Training for Youth Olympics, European American, Soccer)
Frank (Not training for Youth Olympics, Native American, Ice Hockey)
Chloe (Training for Youth Olympics, European American, Badminton)
Harry (Training for Youth Olympics, First-generation American, Soccer)­
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The subtle caveat in this question is the only reason it is considered 805+ level.

It mentions that on one of the two days, a majority of the competitors will need to be from one of the minority communities - this could mean either day at this point. So does one more requirement mentioned in the passage - that the other day will have at least 4 students undergoing Youth Olympics training. If you look closely at the provided schedule, you will notice that only day 1 has a chance of having at least 4 Youth Olympic trainees if one more Youth Olympic trainee is added from the set of additional students. This means that we need to utilise the minority consideration for day 2.

This means that Chloe does make the cut on day 1 since she's a Youth Olympics trainee, and she can't be rejected on day 1 for being from a majority community for the above reason. (I am specifying Chloe because I am sure many of us, including me, picked her for 'neither')

With that out of the way, the question is pretty straightforward. Michelle plays tennis, and there are already 2 tennis players on day 1. And Michelle is European American and including her on day 2 would mean that there wouldn't be a majority of minority students. Hence, Michelle can't be picked for either day.

Harry’s inclusion on Day 1 would mean four Youth Olympic trainees and only two soccer players on day 1. So, Harry can make it on day 1. Harry’s inclusion on Day 2 would mean that there will be three from minority communities and two soccer players. Therefore, Harry can make it on day 2 as well and hence, Harry can go on either day.
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