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GMAT Club Olympics 2024 (Day 6): Andrea, Christiane, Demi, Iris

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tulee

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Bunuel

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We have
- 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 -> Paulina must perform -> Andrea must perform => 3 people
=> If Zozibini performs -> Demi must perform -> Paulina must perform -> Andrea must perform => 4 people

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If D happens then P, A and (either I or Z) would happen. => minimum 3 (Option C)
If Z happens then D, P and A would happen. => minimum 3 (Option C)

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

To find the answer, we back track from the requirement.

1- If Demi performs, Paulina must perform. If Paulina performs, Andrea must perform.
The minimum number of contestants who must perform in the special two-hour episode if the episode includes Demi’s performance = 3

2- If Zozibini performs, Demi must perform. If Demi performs, Paulina must perform. If Paulina performs, Andrea must perform.
The minimum number of contestants who must perform in the special two-hour episode if the episode includes Zozibini’s performance = 4

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Indicating everyone by their first letter.
If D performs, then as per the given constraints, P must perform and since P performs A also must perform. No one else is obligated to perform.
Hence If D performs minimum 3 person must perform.

If Z perfroms then D must perform. We already established that if D performs P and A also must perform, taking the total to 4 persons.

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15 Jul 2024, 10:38

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Rules.
if either Iris or Zozibini performs then Demi must perform.

if Demi performs then Paulina must perform.

if either Christiane or Paulina performs then Andrea must perform.

So if Z performs, then D, P and A must perform. hence min 4 performances.
And If D performs then P and A must perform. Hence 3 performances.

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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.

Ans.

A ∝ C or P
P ∝ D
D ∝ I or Z

So, If D performs => P performs =>A performs.
Also, If D performs => I or Z must have performed...

Total 4 contestants perform when D performs

And, If Z performs => D performs =>P performs =>A performs.

Total 4 contestants perform when Z performs

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If Demi performs:
Paulina must perform (since Paulina must perform if Demi performs).
Andrea must perform if Paulina performs (since Andrea must perform if either Christiane or Paulina performs).
Therefore, if Demi performs, Paulina and Andrea must also perform.

Thus, the minimum number of contestants who must perform if Demi performs is 3 (Demi, Paulina, Andrea).

If Zozibini performs:
Demi must perform (since Demi must perform if either Iris or Zozibini performs).
If Demi performs, Paulina must perform.
If Paulina performs, Andrea must perform.
Therefore, if Zozibini performs, Demi, Paulina, and Andrea must also perform.

Thus, the minimum number of contestants who must perform if Zozibini performs is 4 (Zozibini, Demi, Paulina, Andrea).

Conclusion
Demi performs: 3 contestants (Demi, Paulina, Andrea)
Zozibini performs: 4 contestants (Zozibini, Demi, Paulina, Andrea)

Ans C, D

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15 Jul 2024, 12:49

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For simplicity let's consider that
Andrea=A, Christiane=C, Demi=D, Iris=I, Paulina=P, and Zozibini =Z

We have the following conditions :
(1)C, P => A
(2)D=> P
(3)I, Z => D

if the episode includes Demi’s performance then systematically according to (2) P performes the A performs according to (1)
the minimum then is 2 when Demi performs

if the episode includes Zozibini’s performance then, D performs according to (3) then P performs according to (2) then A performs according to (1)
the minimum then is 3 when Zozibini performs

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15 Jul 2024, 13:03

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Andrea=A
Christiane= C
Demi= D
Iris= I
Paulina=P
Zozibini= Z

Possible performance
A must perform if C or P perform
P must perform if D perform
D must perform if I or Z perform

DEMI
If I performs D must perform, if D performs P must perform if P performs A must performs
IDPA( 4 PEOPLE)
If Z performs D must perform if D performs P must perform if P performs A must performs
ZDPA ( 4 PEOPLE)
If C performs A must perform, if If Z performs D must perform if D performs P must perform
CAZDP ( 5 PEOPLE)
If C performs A must perform, if If I performs D must perform if D performs P must perform
CAIDP ( 5 PEOPLE)

SO 4 people minimum will perform if D performs

ZOZIBINI

If Z performs D must perform if D performs P must perform if P performs A must performs
ZDPA ( 4 PEOPLE)
If C performs A must perform, if If Z performs D must perform if D performs P must perform
CAZDP ( 5 PEOPLE)

SO 4 people minimum will perform if D performs

SO 4 people minimum will perform if D performs

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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.

1st - Demi performs for the minimum number of contestants who must perform in the special two-hour episode if the episode includes Demi’s performance
If demi then Paulina, and if Paulina then Andrea.
Therefore, when Demi performs for the minimum number of contestants who must perform in the special two-hour episode if the episode includes Demi’s performance - 3
Option C.

2nd - Zozibini performs for the minimum number of contestants who must perform in the special two-hour episode if the episode includes Zozibini’s performance.
If Zozibini then Demi and if Demi then Paulina, and if Paulina then Andrea.
Therefore, Zozibini performs for the minimum number of contestants who must perform in the special two-hour episode if the episode includes Zozibini’s performance. - 4
Option D.

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For Demi to perform, Iris or zozibini must perform. So 1 from here. And Demi herself. So minimum 2 performances.
Zozibibi can perform independently. So only 1 performance.

Answer 2 & 1

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Show Spoiler

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Bunuel

This question was provided by Experts' Global
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Andrea [A], Christiane [C], Demi [D], Iris [I], Paulina [P], Zozibini [Z] are six contestants.

On a special two-hour episode, some of these contestants will perform. Some mean anyone from 1 to 6 will perform.

A must perform if either C or P performs
P must perform if D performs
D must perform if either I or Z performs

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?
If D performs, then P must perform . If P performs A must perform.
so D, P, A .

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?
if Z performs, D must perform. and If D performs P must perform . If P performs A must perform
so Z, D, P, A. Hence 4 is the minimum number of contestants

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15 Jul 2024, 15:02

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Demi = 2
Z-3

Given
If C or P--> must A
If I or Z --> must D
If D--> must P

Minimum for D is
Let D perform
so P must perform
if P --> A must perform
So, it is 2 folks

Minimum for Z
if Z-> D must
If D-> P must
If P --> A must
So, 3 folks

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Bunuel

This question was provided by Experts' Global
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Working backwards, let's map out our restrictions that we will follow:

Iris OR Zozobini -> Demi -> Paulina

Christiane OR Pauline -> Andrea (note that I didn't put this above because Demi performing does not mean that Christiane MUST perform).

If Demi performs

Demi -> Paulina -> Andrea so the answer here is 3.

If Zozibini performs

Zozobini -> Demi -> Paulina -> Andrea so the answer is 4.

Therefore, the minimum number of contestants who MUST perform if Demi performs is 3 and if Zozibini performs is 4.

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Let's analyze the conditions given:

If either Christiane or Paulina performs, Andrea performs
If Demi performs, Paulina performs.
If either Iris or Zozibini performs, Demi performs.

Case 1: Demi performs
According to the conditions:

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

This gives us a minimum of 3 contestants performing.
Remember, If X is true, then Y does not imply that if Y is true, then X is true. It is not the logical converse.

Case 2: Zozibini performs

If Zozibini performs, then Demi must also perform.
If Demi must perform, So Paulina performs.
If Paulina performs, Andrea performs.

This gives us a minimum of 4 contestants performing.

Summary of Minimum Performers:
If Demi performs: 3 contestants
If Zozibini performs: 4 contestants

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According to the text there are 3 chains:

Iris -> Demi -> Paulina -> Andrea

Zozibini -> Demi -> Paulina -> Andrea

Christiane -> Andrea

Minimum number of contestants if Demi performs:
Demi -> Paulina -> Andrea (3)

Minimum number of contestants if Zozibini performs:
Zozibini -> Demi -> Paulina -> Andrea (4)

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Question Stem:
1. If C or P perform -> A must perform
2. If D performs -> P must perform
3. If I or Z perform -> D must perform

Min For D -> D performs, hence P reforms, hence A perform - total 3 performances
Min for Z -> Z performs, hence D performs, hence P performs, hence A performs - total 4 performances.

Demi performs: 3
Zozibini performs: 4

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In both cases the answer is 4.

Demi --> 1 performer is Demi, who only perform if I or Z (this count as one). Since Demi performed, Paulina has to, and since Paulina perform, Andrea also performs. That is 4 performers

Z --> Same case as before

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15 Jul 2024, 19:52

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if D performs -> P performs
if P performs -> A performs
So 2 exclusing D

if Z performs-> D performs
if D performs-> P performs
if P performs-> A performs

So 3 exclusing Z

Ans BC