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705-805 Level|   Non-Math Related|         
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GMAT Club Olympics 2024 (Day 6): Andrea, Christiane, Demi, Iris 15 Jul 2024, 21:00
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Bunuel
Andrea, Christiane, Demi, Iris, Paulina, and Zozibini are six contestants in a reality TV show. On a special two-hour episode, some of these contestants will perform. Andrea must perform if either Christiane or Paulina performs. Paulina must perform if Demi performs. Demi must perform if either Iris or Zozibini performs. There are no other restrictions.

Select Demi performs for the minimum number of contestants who must perform in the special two-hour episode if the episode includes Demi’s performance and select Zozibini performs for the minimum number of contestants who must perform in the special two-hour episode if the episode includes Zozibini’s performance.

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­Given-
Andrea must perform if either Christiane or Paulina performs
Paulina must perform if Demi performs.
Demi must perform if either Iris or Zozibini performs

If Demi performs then min of others to perform are-Andrea ,Paulina, Demi so min is 3

If Zozibini performs then min of others to perform are-Andrea ,Paulina, Demi, Zozibini so min is 4 

Ans is 

If Demi performs then min of others to perform are-Andrea ,Paulina, Demi so min is 3

If Zozibini performs then min of others to perform are-Andrea ,Paulina, Demi, Zozibini so min is 4 
 
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GMAT Club Olympics 2024 (Day 6): Andrea, Christiane, Demi, Iris Updated on: 16 Jul 2024, 07:41
Originally posted by Gemmie on 15 Jul 2024, 21:33.
Last edited by Gemmie on 16 Jul 2024, 07:41, edited 1 time in total.
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­Andrea must perform if either Christiane or Paulina performs.
If A => C or P

Paulina must perform if Demi performs.
If P => D

Demi must perform if either Iris or Zozibini performs
If D => I or Z

So we have

(A) <== (C)
      or
     <== (P) <== (D) <== (I)
                                or
                                <== (Z)



---------

If D => P => A
==> total 3

If Z => D => P => A
==> total 4­
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GMAT Club Olympics 2024 (Day 6): Andrea, Christiane, Demi, Iris 15 Jul 2024, 21:36
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Quote:
­Andrea, Christiane, Demi, Iris, Paulina, and Zozibini are six contestants in a reality TV show. On a special two-hour episode, some of these contestants will perform. Andrea must perform if either Christiane or Paulina performs. Paulina must perform if Demi performs. Demi must perform if either Iris or Zozibini performs. There are no other restrictions.

Select Demi performs for the minimum number of contestants who must perform in the special two-hour episode if the episode includes Demi’s performance and select Zozibini performs for the minimum number of contestants who must perform in the special two-hour episode if the episode includes Zozibini’s performance.
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It is given that:-

C or P -> A must

D -> P must

I or Z -> D must

If demi performs => Either I or Z would have performed, and P w=must also perform, which means A must perform. Total = 4.

If Zozibini perfroms => D must => P must => A must => Total = 4

Hence, the answer for both parts is 4.
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GMAT Club Olympics 2024 (Day 6): Andrea, Christiane, Demi, Iris 15 Jul 2024, 22:31
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When Demi performs
Demi-Paulina-Andrea (Minimum -3)

When Zobini performs
Zobini-Demi-Paulina-Andrea (Minimum-4)

IMO 1-3 ,2-4
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GMAT Club Olympics 2024 (Day 6): Andrea, Christiane, Demi, Iris 15 Jul 2024, 22:32
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Answer - D:3 Z:4

A must perform if C/P performs.
P must perform if D performs.
D must perform if I/Z performs.

D performs: Minimum people that will perform if D performs.
D performs, therefore P must perform.
P performs, therefore A must perform.
Therefore minimum ADP (3 people) will perform.

Z performs: Minimum people that will perform if Z performs.
Z performs, therefore D must perform.
D performs, therefore P must perform.
P performs, therefore A must perform.
Therefore minimum ADPZ (4 people) will perform.
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GMAT Club Olympics 2024 (Day 6): Andrea, Christiane, Demi, Iris 15 Jul 2024, 23:42
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Answer is c, d

From the ques, we know:
1. D > P
2. P/C > A
3. I/Z > D
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GMAT Club Olympics 2024 (Day 6): Andrea, Christiane, Demi, Iris 16 Jul 2024, 00:01
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Andrea, Christiane, Demi, Iris, Paulina, and Zozibini are six contestants in a reality TV show. On a special two-hour episode, some of these contestants will perform. Andrea must perform if either Christiane or Paulina performs. Paulina must perform if Demi performs. Demi must perform if either Iris or Zozibini performs. There are no other restrictions.

Given:
A must perfom if C/P performs;
P must perfom if D performs;
D must perfom if I/Z performs.

So, minimum number of constestants if D performs:
D + P (Must) + A (As P perfroms), Hence 3.

So, minimum number of constestants if Z performs:
Z + D + P (Must) + A (As P perfroms), Hence 4.
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GMAT Club Olympics 2024 (Day 6): Andrea, Christiane, Demi, Iris 16 Jul 2024, 00:11
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Bunuel
Andrea, Christiane, Demi, Iris, Paulina, and Zozibini are six contestants in a reality TV show. On a special two-hour episode, some of these contestants will perform. Andrea must perform if either Christiane or Paulina performs. Paulina must perform if Demi performs. Demi must perform if either Iris or Zozibini performs. There are no other restrictions.

Select Demi performs for the minimum number of contestants who must perform in the special two-hour episode if the episode includes Demi’s performance and select Zozibini performs for the minimum number of contestants who must perform in the special two-hour episode if the episode includes Zozibini’s performance.

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­Let,
Andrea = a
Christiane = c
Demi = d
Iris = i
Paulina = p
Zozibini = z

Who must perform        If any of these performs
a                                 c or p
p                                 d
d                                 i or z

Now if d performs then any one of i and z must have performed and after that p and a have to perform.
1st column: 3 (i/z, p, a)

Now if z performs then d, p and a must perform.
2nd column: 3 (d, p, a)
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GMAT Club Olympics 2024 (Day 6): Andrea, Christiane, Demi, Iris 16 Jul 2024, 00:55
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If Demi performs, the following chain reactions are triggered:

If Demi performs, Paulina must perform.
If Paulina performs, Andrea must perform (since Andrea must perform if Paulina or Christiane performs).
Therefore, the minimum number of contestants who must perform if Demi performs are:

Demi
Paulina
Andrea
Scenario 2: Zozibini performs
If Zozibini performs, the following chain reactions are triggered:

If Zozibini performs, Demi must perform.
If Demi performs, Paulina must perform.
If Paulina performs, Andrea must perform (since Andrea must perform if Paulina or Christiane performs).
Therefore, the minimum number of contestants who must perform if Zozibini performs are:

Zozibini
Demi
Paulina
Andrea
Using the provided image, we select the appropriate options for each scenario.

Selection for Demi performs:

Select Demi performs
Select Paulina performs
Select Andrea performs
Selection for Zozibini performs:

Select Zozibini performs
Select Demi performs
Select Paulina performs
Select Andrea performs
In summary:

For Demi performs: minimum 3 contestants (Demi, Paulina, Andrea)
For Zozibini performs: minimum 4 contestants (Zozibini, Demi, Paulina, Andrea)
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GMAT Club Olympics 2024 (Day 6): Andrea, Christiane, Demi, Iris 16 Jul 2024, 00:59
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­Andrea, Christiane, Demi, Iris, Paulina, and Zozibini are six contestants in a reality TV show. On a special two-hour episode, some of these contestants will perform. Andrea must perform if either Christiane or Paulina performs. Paulina must perform if Demi performs. Demi must perform if either Iris or Zozibini performs. There are no other restrictions.

Select Demi performs for the minimum number of contestants who must perform in the special two-hour episode if the episode includes Demi’s performance and select Zozibini performs for the minimum number of contestants who must perform in the special two-hour episode if the episode includes Zozibini’s performance.



Solution: Given that,
  • Andrea must perform if either Christiane or Paulina performs
  • Paulina must perform if Demi performs
  • Demi must perform if either Iris or Zozibini performs

Given that Demi performs:
  • If Demi performs, Paulina must perform
  • If Paulina performs, Andrea must perform

So, the minimum number of contestants who must perform if Demi performs is:
  • Demi
  • Paulina
  • Andrea
Therefore, the minimum number of contestants is 3.

Given that Zozibini performs:
  • If Zozibini performs, Demi must perform
  • If Demi performs, Paulina must perform
  • If Paulina performs, Andrea must perform

So, the minimum number of contestants who must perform if Zozibini performs is:
  • Zozibini
  • Demi
  • Paulina
  • Andrea
Therefore, the minimum number of contestants is 4.




 ­
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GMAT Club Olympics 2024 (Day 6): Andrea, Christiane, Demi, Iris 16 Jul 2024, 01:06
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Given:
A must perform if either C or P performs
P must perform if D performs
D must perform if either I or Z performs

Min performers when D performs:
No pre-requisite for D, but if D does, P will also do
If P does then A will also do
Hence 3

Min Performers when Z performs:
If Z does then D will do
If D does then P will do
If P does then A will do
Hence 4
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GMAT Club Olympics 2024 (Day 6): Andrea, Christiane, Demi, Iris 16 Jul 2024, 01:07
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Bunuel
Andrea, Christiane, Demi, Iris, Paulina, and Zozibini are six contestants in a reality TV show. On a special two-hour episode, some of these contestants will perform. Andrea must perform if either Christiane or Paulina performs. Paulina must perform if Demi performs. Demi must perform if either Iris or Zozibini performs. There are no other restrictions.

Select Demi performs for the minimum number of contestants who must perform in the special two-hour episode if the episode includes Demi’s performance and select Zozibini performs for the minimum number of contestants who must perform in the special two-hour episode if the episode includes Zozibini’s performance.

­
 


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­Let the six contestants be denoted by their initials, A, C, D, I, P and Z respectively. From the conditions provided in the stimulus, we can write the following.
  • If either C or P, A must
  • If D, P must
  • If either I or Z or both, D must
  1. D Performs
    D leading to P leading to A/C
    Necessary minimum: 3
  2. Z Peforms
    Z leading to D/D and I, leading to P leading to A
    Necessary minimum: 4

 
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GMAT Club Olympics 2024 (Day 6): Andrea, Christiane, Demi, Iris 16 Jul 2024, 01:49
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Constraints:

1. Demi must perform if either Iris or Zozibini performs.
2. Paulina must perform if Demi performs.
3. Andrea must perform if either Christiane or Paulina performs.

If Demi performs, Paulina must also perform. If Paulina performs, Andrea must also perform.

Minimum number of contestants who must perform if Demi performs: 3

If Zozibini performs, Demi must also perform. if Demi performs, Paulina must also perform. If Paulina performs, Andrea must also perform.

Minimum number of contestants who must perform if Zozibini performs: 4

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GMAT Club Olympics 2024 (Day 6): Andrea, Christiane, Demi, Iris 16 Jul 2024, 01:58
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Criteria:
If Christiane or Paulina then Andrea
If Demi then Paulina
If Iris or Zozibini then Demi
Inference
If Demi then Paulina then Andrea
If Zozibini then Demi then Paulina then Andrea
 
Answer
- If Demi per performs then including her there will be atleast three contestants in the episode
- If Zozibini performs then including her there will be atleast four contestents in the episode
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GMAT Club Olympics 2024 (Day 6): Andrea, Christiane, Demi, Iris 16 Jul 2024, 02:15
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If the episode includes Demi’s performance, then Paulina must perform. If Paulina performs then Andrea must perform (so we have 3 as min number of contestants)
If the episode includes Zozibini's performance, then Demi must perform. If Demi performs, then Paulina must perform. If Paulina performs then Andrea must perform (so we have 4 as min number of contestants)

So, the answers are 3 and 4 for Demi performs and Zozibini performs respectively. 
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GMAT Club Olympics 2024 (Day 6): Andrea, Christiane, Demi, Iris 16 Jul 2024, 02:17
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­Based on the conditions given, we can determine the minimum number of contestants who must perform in the special two-hour episode as follows:

If Demi performs:

- Demi must perform (given)
- Paulina must perform (since Demi is performing)
- Andrea must perform (since Paulina is performing)
- Total: 3 contestants (Demi, Paulina, Andrea)

If Zozibini performs:

- Zozibini performs (given)
- Demi must perform (since Zozibini is performing)
- Paulina must perform (since Demi is performing)
- Andrea must perform (since Paulina is performing)
- Total: 4 contestants (Zozibini, Demi, Paulina, Andrea)

Therefore, the correct answers are:

- Demi performs: 3
- Zozibini performs: 4
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GMAT Club Olympics 2024 (Day 6): Andrea, Christiane, Demi, Iris 16 Jul 2024, 02:46
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Bunuel
Andrea, Christiane, Demi, Iris, Paulina, and Zozibini are six contestants in a reality TV show. On a special two-hour episode, some of these contestants will perform. Andrea must perform if either Christiane or Paulina performs. Paulina must perform if Demi performs. Demi must perform if either Iris or Zozibini performs. There are no other restrictions.

Select Demi performs for the minimum number of contestants who must perform in the special two-hour episode if the episode includes Demi’s performance and select Zozibini performs for the minimum number of contestants who must perform in the special two-hour episode if the episode includes Zozibini’s performance.

­
 


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­
For Demi :

Demi perform.
Paulina have to perform (because Paulina have to perform if Demi performs).
Andrea have to perform (because Andrea have to perform if Paulina performs)Zozibini Performs:


  1. Zozibini have to perform.
  2. Demi have to perform (because Demi have to perform if Zozibini performs).
  3. Paulina have to perform (because Paulina have to perform if Demi performs).
  4. Andrea have to perform (because Andrea have to perform if Paulina performs).
Minimum
so for Demi - 3
Zozibini = 4
 
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GMAT Club Olympics 2024 (Day 6): Andrea, Christiane, Demi, Iris 16 Jul 2024, 02:54
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­Question stem gives us following details:
There are six contestants - Andrea, Christiane, Demi, Iris, Paulina, and Zozibini
Andrea must perform if either Christiane or Paulina performs. 
Paulina must perform if Demi performs. 
Demi must perform if either Iris or Zozibini performs.

This can be simpliefied as, 

Iris or Zozibini -> Demi -> Paulina -> Andrea

Now, we need to find minimum number of contestants who must perform in the special two-hour episode if the episode includes Demi’s performance or Zozibini peforms.

For Demi,
If Demi performs than Paulina must perform. And if Paulina performs than Andrea must perform. 
Remmeber that Demi must perform if either Iris or Zozibini performs but it doesn't mean that Demi cannot perform if either of two don't peform. 
We need to find minimum.

So, total for Demi = Demi + Paulina + Andrea = 3

For Zozibini,
If Zozibini performs than Demi must perform. 
If Demi performs than we know Paulina and Andrea will perform as established in answer for Demi.

So total for Zozi = 1 + 3 = 4

Final answer - 
3 for Demi and 4 for Zozi­
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GMAT Club Olympics 2024 (Day 6): Andrea, Christiane, Demi, Iris 16 Jul 2024, 03:05
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Bunuel
Andrea, Christiane, Demi, Iris, Paulina, and Zozibini are six contestants in a reality TV show. On a special two-hour episode, some of these contestants will perform. Andrea must perform if either Christiane or Paulina performs. Paulina must perform if Demi performs. Demi must perform if either Iris or Zozibini performs. There are no other restrictions.

Select Demi performs for the minimum number of contestants who must perform in the special two-hour episode if the episode includes Demi’s performance and select Zozibini performs for the minimum number of contestants who must perform in the special two-hour episode if the episode includes Zozibini’s performance.

 
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­Performs               Must perform
    C/P                           A
      D                            P
    I/Z                            D

If D performs, P must perform and if P performs, A must perform.
So total must performances  = D, P, A = 3

Demi Performs = 3

If Z performs, D must perform, Rest is same as above.
So total performances = Z, D, P, A = 4

Zozibini performs = 4
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GMAT Club Olympics 2024 (Day 6): Andrea, Christiane, Demi, Iris 16 Jul 2024, 03:09
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let Andrea=A performs either Christiane or Paulina performs so, the probability is 2/6=1/3
Christiane=C
Demi=D performs either Iris or Zozibini performs so, the probability is 2/6=1/3
Iris=I
Paulina = P performs only Demi performs so, the probability is 1/6
Zozibini = Z
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