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First, let’s place the {Abstract, Baroque} block. They must be together and cannot be in Gallery C. If they were in Gallery A, the remaining artworks {Cubist, Expressionist, Digital} would have to go into Gallery B to meet the three-item rule. This would put Cubist and Expressionist together, which is forbidden. Therefore, the {Abstract, Baroque} block must be in Gallery B.

So, Gallery B contains {Abstract, Baroque, and one other artwork}.
We know Folk is in Gallery C. The remaining artworks to place are {Cubist, Expressionist, Digital}.

The only option that works is placing Expressionist in Gallery A and Cubist in Gallery C. This leaves Digital to fill the last spot in Gallery B.

This gives the final valid arrangement:
Gallery A: Expressionist Only
Gallery B: {Abstract, Baroque, Digital}
Gallery C: Cubist and Folk only

This arrangement satisfies all the rules.

Thus, Gallery A = “Expressionist Only” and Gallery C = “Cubist and Folk only”.
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Correct Answer
  • Gallery A: Expressionist Only
  • Gallery C: Cubist and Folk only
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Gallery C has Folk
So we have 3 options for Gallery C
1) Cubist, Folk, Digital -> not possible because then Gallery B will also have 3 artworks and A will be empty
2) Cubist, Folk -> then Barique and abstract can not be in Gallery A as it will leave Gallery B with only 2 artwork. So gallery B will have Baroque and Abstract and along with them either Digital or Expressionist
So by going with the options, Gallery A will have Expressionist only and Gallery B will have Baroque, Abstract and digital
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Art Types:
Abstract
Baroque
Cubist
Digital
Expressionist
Folk

Clue 1: Gallery B has exactly 3 types
So B = ??? (must hold 3 types)

Clue 2: Baroque and Abstract are together, and not in C
So Baroque + Abstract must be together in A or B → Let’s place both in B (makes sense)

Clue 3: Cubist and Expressionist are in different galleries
A = Expressionist
C = Cubist
Satisfies this clue

Clue 4: Folk is in Gallery C

C = Folk and Cubist
Satisfies this clue

Remaining type: Digital
We need to assign Digital somewhere.

Already used:
A = Expressionist
C = Cubist + Folk

So B must be:
Abstract , Baroque , Digital
Satisfies Rule 1 (3 types in B)

Now every artwork is assigned once, and no gallery is empty.

Assignments:
Gallery A: Expressionist
Gallery B: Abstract, Baroque, Digital
Gallery C: Cubist, Folk

All 4 clues are satisfied.

Final Answer:
Gallery A: Expressionist only

Gallery C: Cubist and Folk only

This pair is jointly consistent with all the rules.
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Below attached picture contain my solution
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Art types: A,B, C, D, E, F

Gallery: GA, GB, GC

GB = 3 types of art
A, and B = together but not in GC
C and E are not together
F is in GC

GC for sure has F maybe C or E and maybe D

GB must have A and B and then either C or E
GA must be C or E and maybe D

Now looking at possible answers.

C, F, D - GC could be this. GA then just E
C, F - GC could be this then- would need E and D in GA doesnt work.
C - GC could do this then- Then would need E, F, D, in GC doesnt work
B, A, -in BA doesnt work
E - could work
F - Could be GC but then no option for GA

By Elimination.

Gallery A is Expressionist Only
Gallery C is Cubist, Folk, Digital.




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A national art exhibition features six different types of artwork: Abstract, Baroque, Cubist, Digital, Expressionist, and Folk. These artworks are divided among three galleries: Gallery A, Gallery B, and Gallery C. Each artwork type is displayed in exactly one gallery, and no gallery is empty.

The following rules apply:

  • Exactly three types of artwork are showcased in Gallery B.
  • The Baroque and Abstract artworks are displayed together in the same gallery, but not in Gallery C.
  • The Cubist artwork is displayed in a different gallery from the Expressionist artwork.
  • The Folk artwork is displayed in Gallery C.

Select for Gallery A the set of artwork types displayed in Gallery A, and select for Gallery C the set of artwork types displayed in Gallery C, such that the two selections, from among the given options, would be jointly consistent with the information provided. Make only two selections, one in each column.
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R1 - Exactly three types of artwork are showcased in Gallery B.
Total artwork = 6
Artwork in B = 3

R2 - A and C can have (1,2) or (2,1) artworks only as Each artwork type is displayed in exactly one gallery, and no gallery is empty
R3 - The Baroque and Abstract artworks are displayed together in the same gallery, but not in Gallery C.
R4 - The Cubist artwork is displayed in a different gallery from the Expressionist artwork.
R5 - The Folk artwork is displayed in Gallery C.

Gallery AGallery C
X because of R1X because of R1Cubist, Folk, and Digital only
YesCubist and Folk only
X because of R5Cubist only
X because of R5Baroque and Abstract only
YesX because of R5Expressionist Only
Folk Only

Case 1: If C has F only, A can have either C or E not both. If A has C or E, B has A and B
Option C has Folk Only and A has Cubist only or Expressionist Only. But we don't know which one

Case 2: If C has Cubist and Folk only, then A has Expressionist Only. No other option. This is the answer

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A national art exhibition features six different types of artwork: Abstract, Baroque, Cubist, Digital, Expressionist, and Folk. These artworks are divided among three galleries: Gallery A, Gallery B, and Gallery C. Each artwork type is displayed in exactly one gallery, and no gallery is empty.

The following rules apply:

  • Exactly three types of artwork are showcased in Gallery B.
  • The Baroque and Abstract artworks are displayed together in the same gallery, but not in Gallery C.
  • The Cubist artwork is displayed in a different gallery from the Expressionist artwork.
  • The Folk artwork is displayed in Gallery C.

Select for Gallery A the set of artwork types displayed in Gallery A, and select for Gallery C the set of artwork types displayed in Gallery C, such that the two selections, from among the given options, would be jointly consistent with the information provided. Make only two selections, one in each column.
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Let's organize what we know about the six artwork types (Abstract, Baroque, Cubist, Digital, Expressionist, and Folk) and the three galleries:
* Gallery B must contain exactly 3 artwork types
* Baroque and Abstract must be displayed in the same gallery (either A or B, not C)
* Cubist and Expressionist must be in different galleries
* Folk artwork must be in Gallery C
Let's start by placing Folk in Gallery C since that's explicitly required.
Next, let's consider Baroque and Abstract. They must be together, and they can't be in Gallery C. So theye either both in Gallery A or both in Gallery B.
Since Gallery B must have exactly 3 types, let's explore both possibilities:
Possibility 1: Baroque and Abstract are in Gallery A
* Gallery A: Abstract, Baroque, possibly others
* Gallery B: Must have exactly 3 types from the remaining (Cubist, Digital, Expressionist)
* Gallery C: Folk, possibly others
But this won't work because we'd need to put all three remaining types (Cubist, Digital, Expressionist) in Gallery B, which would violate the rule that Cubist and Expressionist must be in different galleries.
Possibility 2: Baroque and Abstract are in Gallery B
* Gallery B: Abstract, Baroque, plus one more type (to make exactly 3)
* Gallery A: Some combination of remaining types
Gallery C: Folk, possibly others
For the third type in Gallery B, we can use either Cubist or Digital or Expressionist. Let's try each:
If Cubist is the third type in Gallery B:
* Gallery B: Abstract, Baroque, Cubist
* Gallery A: Digital, Expressionist (Expressionist can't be with Cubist)
* Gallery C: Folk
This doesn't match our options since Gallery A would have two types.
If Digital is the third type in Gallery B:
* Gallery B: Abstract, Baroque, Digital
* Gallery A: Either Cubist or Expressionist or both
* Gallery C: Folk, and possibly the remaining artwork
If Expressionist is the third type in Gallery B:
* Gallery B: Abstract, Baroque, Expressionist
* Gallery A: Digital, possibly Cubist (Cubist can't be with Expressionist)
* Gallery C: Folk, possibly Cubist
Looking at our options for Gallery A and Gallery C, we need to find a combination where Gallery A has just one type (Expressionist) and Gallery C has just one type (Folk).
This works if:
* Gallery A: Expressionist only
* Gallery B: Abstract, Baroque, and Cubist (exactly 3 types)
* Gallery C: Folk only
This arrangement satisfies all the conditions:
* Gallery B has exactly 3 types
* Abstract and Baroque are together (in B) and not in C
* Cubist (in B) and Expressionist (in A) are in different galleries
* Folk is in Gallery C
* Digital must be in Gallery A with Expressionist
Therefore, the correct selections are "Expressionist Only" for Gallery A and "Folk Only" for Gallery C.
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A national art exhibition features six different types of artwork: Abstract, Baroque, Cubist, Digital, Expressionist, and Folk. These artworks are divided among three galleries: Gallery A, Gallery B, and Gallery C. Each artwork type is displayed in exactly one gallery, and no gallery is empty.

The following rules apply:

  • Exactly three types of artwork are showcased in Gallery B.
  • The Baroque and Abstract artworks are displayed together in the same gallery, but not in Gallery C.
  • The Cubist artwork is displayed in a different gallery from the Expressionist artwork.
  • The Folk artwork is displayed in Gallery C.

Since there are total 6 artwork and 3 are displayed in Gallery B and no gallery is empty, there are 1 artworks in Gallery A & and 2 artworks Gallery C or vice versa.
Cubist, Folk, and Digital only option is NOT possible for either of the galleries.

Since the Folk artwork is displayed in Gallery C, it has 2 options,
1. Folk only
2. Cubist and folk only

1. Folk only
Gallery ABaroque and Abstract only
Gallery BCubist, Digital, Expressionist - Not possible
Gallery CFolk only

2. Cubist and folk only
Gallery AExpressionist Only
Gallery BBaroque, Abstract, Digital
Gallery CCubist & Folk only


Select for Gallery A the set of artwork types displayed in Gallery A, and select for Gallery C the set of artwork types displayed in Gallery C, such that the two selections, from among the given options, would be jointly consistent with the information provided. Make only two selections, one in each column.

Gallery AGallery C
Expressionist OnlyCubist & Folk only
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    Folk => C (As per Rule 4), so Gallery C must include Folk.Baroque + Abstract => Gallery B (not C), and Gallery B must have exactly 3 types.The remaining types are Cubist, Digital, and Expressionist.If Gallery C = {Cubist, Folk}, that leaves Digital and Expressionist for Galleries A and B.Gallery B already has Baroque+Abstract and adds Digital to reach 3.That leaves Expressionist alone => goes to Gallery A.This configuration meets all rules:
  • Gallery B has 3 types.
  • Baroque & Abstract stay together outside C.
  • Cubist ≠ Expressionist.
  • No gallery is empty.
  • All six types are used.
So the only valid pair is:
  • Gallery A: Expressionist only
  • Gallery C: Cubist and Folk only
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Bunuel
 


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A national art exhibition features six different types of artwork: Abstract, Baroque, Cubist, Digital, Expressionist, and Folk. These artworks are divided among three galleries: Gallery A, Gallery B, and Gallery C. Each artwork type is displayed in exactly one gallery, and no gallery is empty.

The following rules apply:

  • Exactly three types of artwork are showcased in Gallery B.
  • The Baroque and Abstract artworks are displayed together in the same gallery, but not in Gallery C.
  • The Cubist artwork is displayed in a different gallery from the Expressionist artwork.
  • The Folk artwork is displayed in Gallery C.

Select for Gallery A the set of artwork types displayed in Gallery A, and select for Gallery C the set of artwork types displayed in Gallery C, such that the two selections, from among the given options, would be jointly consistent with the information provided. Make only two selections, one in each column.
Lets explore the column for possibilities of gallery C
If I try to fit F + C + D into Gallery C, Gallery A will be left empty or gallery B will be < 3 , eliminate

If Gallery C has F+C,
Gallery B can have A+B+D
Gallery C can have E

This combination fulfills all criterias.
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let art work be
a,b,c,d,e,f
Galleries be A,B,C

condition is Each artwork type is displayed in exactly one gallery, and no gallery is empty.
[*]Exactly three types of artwork are showcased in Gallery B.
[*]The Baroque and Abstract artworks are displayed together in the same gallery, but not in Gallery C.
[*]The Cubist artwork is displayed in a different gallery from the Expressionist artwork.
[*]The Folk artwork is displayed in Gallery C.



---A------B-------C
--e------abc-----f


Gallery A ; Expressionist Only
Gallery C ; Folk Only
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A national art exhibition features six different types of artwork: Abstract, Baroque, Cubist, Digital, Expressionist, and Folk. These artworks are divided among three galleries: Gallery A, Gallery B, and Gallery C. Each artwork type is displayed in exactly one gallery, and no gallery is empty.

The following rules apply:

  • Exactly three types of artwork are showcased in Gallery B.
  • The Baroque and Abstract artworks are displayed together in the same gallery, but not in Gallery C.
  • The Cubist artwork is displayed in a different gallery from the Expressionist artwork.
  • The Folk artwork is displayed in Gallery C.

Select for Gallery A the set of artwork types displayed in Gallery A, and select for Gallery C the set of artwork types displayed in Gallery C, such that the two selections, from among the given options, would be jointly consistent with the information provided. Make only two selections, one in each column.
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Information given:
- 6 artworks: Abstract, Baroque, Cubist, Digital, Expressionist, Folk
- Galleries: A, B, C
- Rules:
- Each artwork type is displayed in exactly one gallery
- No gallery is empty
- Gallery B has exactly 3 artworks
- Baroque & Abstract must stay together, and not in C
- Cubist & Expressionist must be in different galleries
- Folk must be in Gallery C

Question:
- Pick one valid option for Gallery A and one for Gallery C, so that both options together fit all the rules

Solution:
- All process of elimination can be used, starting with gallery C (given that it must contain at least Folk)

- Option: Folk only
- C would have 1 artwork, so 5 left
- B must have 3, so A must have 2
- Baroque & Abstract must be together, must go to A
- Leftover: Cubist, Digital & Expressionist, must go to B
- This would place Cubist & Expressionist in same gallery, invalid

- Option: Cubist only
- Folk must be in C, invalid

- Option: Baroque & Abstract only
- Baroque & Abstract can't be in C, invalid

- Option: Expressionist only
- Folk must be in C, invalid

- Option: Cubist, Folk, digital
- C = 3 artworks, 3 left for A and B
- B must have 3, so 0 left for A
- No gallery can be empty, invallid

- Option: Cubist and Folk only
- C = 2 artworks, 4 left
- B must have 3, A must have 1
- Baroque & Abstract must be together, must go to B
- Baroque, Abstract, Digital to B
- Leftover, expressionist, goes to A
- Valid

Answer: Gallery A, expressionist only, Gallery C, cubist and folk only
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A national art exhibition features six different types of artwork: Abstract, Baroque, Cubist, Digital, Expressionist, and Folk. These artworks are divided among three galleries: Gallery A, Gallery B, and Gallery C. Each artwork type is displayed in exactly one gallery, and no gallery is empty.

The following rules apply:

  • Exactly three types of artwork are showcased in Gallery B.
  • The Baroque and Abstract artworks are displayed together in the same gallery, but not in Gallery C.
  • The Cubist artwork is displayed in a different gallery from the Expressionist artwork.
  • The Folk artwork is displayed in Gallery C.

Select for Gallery A the set of artwork types displayed in Gallery A, and select for Gallery C the set of artwork types displayed in Gallery C, such that the two selections, from among the given options, would be jointly consistent with the information provided. Make only two selections, one in each column.
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Types of Artworks: A, B, C, D, E, F
Galleries: GA, GB, GC

1st rule: GB has 3 exhibits. That means GA has 2 exhibits or 1 exhibit, and GC has 1 exhibit or 2 exhibits, respectively.
2nd rule: A+B belong in the same Gallery, but not in GC.
3rd rule: C and E belong in different galleries.
4th rule: GC has F exhibit.

From above, we get:
If GA has exhibit A+B and GC has exhibit F, GB would have other exhibits C, D and E. But, we know C and E are in separate exhibits.
So, GB has to have the exhibit A+B.

Hence,
GA: 2 or 1
GB: 3 : A+B
GC: 1or 2: F

According to given options first can be eliminated as GC cannot have 3 exhibits.

2nd selection states C+F,
GA: 1 : E or D
GB: 3 : A+B+ D or E
GC: 2 : F+C
5th selection for GA aligns well with this option.

3rd selection states C only
GA: 1 : C
GB: 3 : A+B+ D or E
GC: 2 : F+ D or E
Non of the given selections align for GC so this can be eliminated.

4th selection. Already established A+B belong to gallery GB.

6th selection.
GA: 1 : E+D or C+D
GB: 3 : A+B+ D or E
GC: 2 : F
Neither is an option.

Hence, Answer is GA: Expressionist Only and GC: Cubist and Folk only.

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A national art exhibition features six different types of artwork: Abstract, Baroque, Cubist, Digital, Expressionist, and Folk. These artworks are divided among three galleries: Gallery A, Gallery B, and Gallery C. Each artwork type is displayed in exactly one gallery, and no gallery is empty.

The following rules apply:

  • Exactly three types of artwork are showcased in Gallery B.
  • The Baroque and Abstract artworks are displayed together in the same gallery, but not in Gallery C.
  • The Cubist artwork is displayed in a different gallery from the Expressionist artwork.
  • The Folk artwork is displayed in Gallery C.

Select for Gallery A the set of artwork types displayed in Gallery A, and select for Gallery C the set of artwork types displayed in Gallery C, such that the two selections, from among the given options, would be jointly consistent with the information provided. Make only two selections, one in each column.
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A national art exhibition features six different types of artwork: Abstract, Baroque, Cubist, Digital, Expressionist, and Folk. These artworks are divided among three galleries: Gallery A, Gallery B, and Gallery C. Each artwork type is displayed in exactly one gallery, and no gallery is empty.

The following rules apply:

  • Exactly three types of artwork are showcased in Gallery B.
  • The Baroque and Abstract artworks are displayed together in the same gallery, but not in Gallery C.
  • The Cubist artwork is displayed in a different gallery from the Expressionist artwork.
  • The Folk artwork is displayed in Gallery C.

Select for Gallery A the set of artwork types displayed in Gallery A, and select for Gallery C the set of artwork types displayed in Gallery C, such that the two selections, from among the given options, would be jointly consistent with the information provided. Make only two selections, one in each column.
It can be deduce that Gallery B contains Baroque and Abstract and Digital, implies Three artworks is satisfied and also Expressionist and cubist not in same gallery is satisfied.Folk is in Gallery C
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Gallery A ->
Gallery B -> 3 types of artwork
Gallery C -> Folk artwork is displayed

Baroque and Abstract always displayed together. This means it can either be in Gallery A, Gallery B or Gallery C
The Cubist artwork is displayed in a different gallery from the Expressionist artwork.

So if Baroque and Abstract are displayed in Gallery A, then Cubist, Digital and Expressionist will have to be included in Gallery B which contradicts
If Baroque and Abstract are displayed in Gallery C, then Gallery B will have 2 artworks and hence not fulfill our criteria

So Baroque and Abstract must be displayed in Gallery B

Gallery A ->
Gallery B -> Baroque, Abstract
Gallery C -> Folk artwork is displayed

If we keep Cubist in A, Expressionist will be either in B or C
If we keep Cubist in B, Expressionist will be either in A or C
If we keep Cubist in C, Expressionist will be either in A or B

Keeping Cubist in C, expressionist in A and Digital in B we can fulfill the criteria

So in Gallery A - > Expressionist Only
In Gallery C -> Cubist and Folk

Bunuel
 


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A national art exhibition features six different types of artwork: Abstract, Baroque, Cubist, Digital, Expressionist, and Folk. These artworks are divided among three galleries: Gallery A, Gallery B, and Gallery C. Each artwork type is displayed in exactly one gallery, and no gallery is empty.

The following rules apply:

  • Exactly three types of artwork are showcased in Gallery B.
  • The Baroque and Abstract artworks are displayed together in the same gallery, but not in Gallery C.
  • The Cubist artwork is displayed in a different gallery from the Expressionist artwork.
  • The Folk artwork is displayed in Gallery C.

Select for Gallery A the set of artwork types displayed in Gallery A, and select for Gallery C the set of artwork types displayed in Gallery C, such that the two selections, from among the given options, would be jointly consistent with the information provided. Make only two selections, one in each column.
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if we check column start from Mid

If A is cubist only, then C must be folk, expressionist. (This is not an option for C, as only cubist and folk only and folk Only are given).

If A is expressionist Only, then C must be folk, cubist. This matches the option cubist and folk only. and other three for B
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