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GMAT Club World Cup 2026 (Day 2): At a community art festival, 54

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okHedwig

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We know that 54 participated either in P, C or both (P= photography, C= ceramics)
And 18 did not sign up for P, So, C- (P and C both) = 18
Statement 1: 12 did not sign up for ceramic , which mean P-(P & C both) = 12
or, 12 + (P&C both) +18 = 54, or P&C both = 24. Sufficient
Statemnt 2: 42 signed for ceramics.
or, 42- (P & C both) = 18 or P & C both = 42-18 = 24. Suffiecnt
Hence. D

Bunuel

At a community art festival, 54 participants signed up for photography, ceramics, or both. If 18 of these participants did not sign up for photography, how many participants signed up for both photography and ceramics?

(1) Of the 54 participants, 12 did not sign up for ceramics.
(2) Of the 54 participants, 42 signed up for ceramics.

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Statement 1. 54-12-18 gives us the both. Suff
Statement 2. 42-18 gives us the both. Suf

Answer D

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Bunuel

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If we create a 2 * 2 Matrix

	Photgraphy	Not Photography
Ceramics	A	B	A + B
Not Ceramics	C	D	C + D
	A + C	B+D

A + B +C = 54
B = 18

A + C = 54 - 18 = 36

Question: A = ?

Statement 1:

From S1, we can conclude that C = 12

Hence we can find A. Sufficient.

Statement 2:

From S2, we can conclude that A + B = 42

C = 54 - 42 = 12

C is know, so we can find A.

Sufficient.

Option D

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Total Participants = 54
Everyone signed up for at least one activity, either Photography (P) or Ceramics (C).

Since 18 participants did not sign up for P, they must have signed up for C only.

Participants who signed up for P were = 54-18 = 36.

S1 --> 12 participants did not sign up for C. This means P only were = 12
This means Both = 36-12 = 24

S1 - Sufficient

S2 --> 42 signed up for C.
C = Only C + Both
42 = 18 + Both ----> Both = 24

S2 - Sufficient

Answer D - Both statements are individually sufficient.

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Each statement alone is sufficient.

P is Photography, C is ceramics, ~ is negation.

Total = 54
~P = 18

Option 1
~C = 12
both P&C = 54 - (18+12) = 24

Option 2
both P&C = C - (~P) = 42-18 = 24

Bunuel

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07 Jul 2026, 11:19

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I think the answer is E.

I did this with 2x2 matrix method. Since there are no person who doesn't do either of the activity. NP x NC = 0, and total = 54.

18 people did not do photography means, 36 people did photography.

Both the statements give the complimentary information which can be derived by using either of them, not sufficient enough to derive to an answer

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Using the formula of PUC=P+C-B. Where P is photography, C is Ceramics, and B is both. 18 of them did not sign up for photography hence there are 36 for ceramics only. Now first option says - out of 54, 12 did not sign up for ceramics, hence 42 is P. We have C and P and PUC value, plug into the formula and you get 24 as answer for both. Hence 1 is sufficient, now the next option is reverse, follow the same formula and you get 24 as unique answer. Hence D is the correct answer, as both are sufficient.

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The given question is related to set theory

It mentions that there are 2 art festivals = Photography and Ceramics

Refer to the attached image which mentions that c = 18 , a+b+ c= 54 since there are no people who don't participate and the Question is what is "b"

Accordingly, our options are as below:
Option (1) - > "a" = 12, Accordingly, since we have both a and c, we can find b and this option is Sufficient
Option (2) - > "b+c = 42", since we have the value of c, and we have an equation which mentions that b+c = 42, we can derive the value of b and hence this option is also Sufficient

Accordingly, our correct answer is Option D = Each Statement alone is Sufficient to answer the question

Attachments

photo_2026-07-08_00-07-51.jpg [ 111.79 KiB | Viewed 122 times ]

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Each statement alone is sufficient, hence answer is D.
Given is total = 54 ( a = only P, b = Both and c = Only ceramics)
We are also given that c = 18, hence, we know a + b = 54 - 18 = 36.

(1) 12 did not go for ceramics, hence, a = 12. We can calculate b from given information now. Thus, sufficient.

(2) 42 is into ceramics i.e. b + c = 42. We already know c = 18, hence, we can calculate b. Thus, sufficient.

Bunuel

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18 has not signed up for photography, means they only signed up for ceramics

1) Means that 12 signed up only for photography. 54 - 18 - 12 = 24 people signed up for both - Sufficient!
2) 42 signed up for ceramics only AND ceramics&photography. 42-18 = 24 signed up for both - Sufficient!

That means both statements are sufficient alone - D

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Answer D: Both statements are lone sufficient to answer the question. First statement- means only photograph is 12 and from the standard statement only ceramics is 18. Both photograph and ceramics is 54-18-12=24. Second statement means ceramics is 42 and from the standard statement only ceramics is 18. So, both photograph and ceramics is 42-18=24.

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Bunuel

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Total participants given = 54
We can break this down as 54 = Photopgrahy only (P) + Ceramics only (C) + both P&C
18 people have not taken photography which means C = 18

Statement 1
It is given that 12 people have not taken ceramics
i.e. P = 12, and C = 18 (from above)
we know 54 = P + C + both
hence 54 = 12 + 18 + both
both = 24
Hence Statement 1 is sufficient

Statement 2
It is given that 42 people have taken ceramics
Hence C + both = 42,
Also we know that C = 18
hence 18 + Both = 42
both = 24
Hence Statement 2 is sufficient

As both statements are sufficient, Answer = D

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24 Participants signed up for both Photography and ceramics
Both statements alone are sufficient

did this by creating a ven diagram

54 - total , 18 - no photography so they are ceramic

1) of the 54 , 12 did not sign up for ceramics - 12 are photography

18 - C , 12 - P
18+12 - 54 = 24 (both)

2) of 54 , 42 signed up for ceramics

As we know 18 - Ceramic
so 42- 18 = 24 (both)

Bunuel

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Bunuel

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Total participants = 54

18 did not sign up for photography, so: Photography only + Both = 54 - 18 = 36

(1) 12 did not sign up for ceramics. So ceramics participants = 54 - 12 = 42. Statement 1 is sufficient. Eliminate BCE.

(2) 42 signed up for ceramics. This gives the same information as statement (1).

Using this:
Photography = 36
Ceramics = 42
Total = 54

Both = Photography + Ceramics - Total

Both = 36 + 42 - 54 = 24. Sufficient again.

Option D

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As per Q, ceramics = 18, and Photo + bOTH = 36
Then Statement 1: just photo = 12. Means, both = 36-12 . Sufficient.
statment 2: ceramics +both =42, means both=42-18 . Suffiencnt.
Hence option D.

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Here P is only Photography, C is only Ceramics and Both is signing up for both Photography and Ceramics

P+C+Both = 54 --->(a)
We need to solve for Both=?

!P = 18 => C+Both =36 --->(b)

Option 1)
!C=12 => P+Both=42 ----> (c)

Adding (b)+(c)
P+C+2.Both=78
From (a)
54+Both=78
Both=24

Option 2)
C+Both=42
We know !P=18 -> C=18
=>Both=42-18=24

Both options are independently sufficient, so Option D

Bunuel

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Only P+ both + only C = 54
Only C =18
Only P + both = 54-18= 36

1. Only P = 12
Then both = 54-18-12 ..Sufficient

2. C =40
18+both =40...Sufficient

Ans D

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Let photography only be P, Both be B & Ceramics only be C
The question says:
P+B+ C = 54
C = 18

Statement 1:
P=12
so 12 + B + 18 = 54
You can find B - hence sufficient

Statement 2:
C+B = 42
We know that C = 18
18 + B = 42
You can find B - hence sufficient

So answer choice D - Each alone is sufficient.

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there are 54 people. signed up for photography , ceramics or both. so there no one in neither of the category.

	photo	no photo	total
ceramics	x
no ceramics		0
total	36	18	54

we need to find x

S-1
no ceramics = 12. so ceramics =42.
this is sufficient enough here.
x= 24

S-2.
ceramics= 42, no ceramics = 12.
this is same as above.
so sufficient.

Option D

Bunuel

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Bunuel

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Starting

	No photo	Photo
No ceramics
Ceramics
Total	18	36	54

After 1:

	No photo	Photo
No ceramic		Z	12
Ceramics	x	y	42
Total	18	36	54

X+Y =42
Y+Z= 36

Y could be 24 or 36 and satisfy the equations. Not sufficient

2. This is the same info presented differently as one. Not sufficient

Using all the statements does not help since they are giving the same info. Answer is E.