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

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sonit1987

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07 Jul 2026, 08:59

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suppose:
a- only photography
b- only ceramics
c-both
then a+b+c =54( given)
18 did not signup for photography.. it simply means they only signup for ceramics, so we know b=18
( note all 54 participants signup for at least one otherwise they would not have come this is basic assumption)

from statement-1:
12 did not signup for ceramics. it again simply means they signup for photography only. a=12
now a+b+c=54
12+18+c=54
c=24
statement-1 sufficient

Statement-2:
42 signup for ceramics. this means b+c =42
we already have b=18 from main argument
so 18+c=42
c=24

statement-2 is also sufficient
Ans:D

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07 Jul 2026, 08:59

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tt p=54
cat- P, C, both
neither g - 0
18p - not sign P so 18 ppl did C
Statement 1
Of 54, 12 not C
if 12 not C then MUST P only
both = ttl-only P - only c
b= 54-12-18 = 24
sufficient

Statement 2
of 54, 42 are C
C = only C + both
only C = 18
ttl C = only c + both
42 = 18+both
both=42-18=24
sufficient

ans D each is sufficient

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07 Jul 2026, 08:59

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lets consider P-photography, C-ceramic, and x-both.
So given is, all P+x= 54-18 = 36 so we can find only c so only C would be 54-(P+x) = 54-36 = 18.
1) 12 did not sign C so all C+x= 54-12= 42, so x = 42-18 = 24 sufficient
2) 42 is given as all C+x= 42 so x =42-18= 24, sufficient.
So answer would be D.

Bunuel

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07 Jul 2026, 09:03

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Worth drawing out a rough venn, i find it useful.

18 who didnt sign up for photo, means they went for ceramics only.

So even before looking at the options, write down the following

P(P) + P(C) +P(both) = 54

Now option1:
Gives us the second variable so we can rearrange to get both as 24

Now option 2:
the ceramics section is a total 42 and we know it includes people who also do both, so 42-ceramics only = both, 42-18 = 24 for both. So statement D

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Total Paricipants= 54
No. of participants that did not sign up for photography=18----> that means 54-18=36 participants signed up for photography
We can put it like this:
Number of people who signed up for both photography and ceramics=no. of people signed for photography+no. of people signed for ceramics- total ( subtracting total removes the double count and only gives the overlap)

1) 12 did not sign up for ceramics
54-12=42 people signed up for ceramics ---> plugging this into the above formula we get
Both=36+42-54=24 This makes statement 1 sufficient

2) 42 signed up for ceramics
Both=36+42-54=24 This makes statement 2 also sufficient.

Since both statements are sufficient answer is D- Each Statement alone is sufficient

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07 Jul 2026, 09:08

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Let p represents the participants in photography and c represents the participants in ceramics. Let x be the participants who are in both photography and ceramics.
We know that 18 did not participate in photography, so 36 participated in photography. Since all participated in at least one, number of participants are 0 for neither p and neither c. Refer the image attached.

Statement 1:
12 did not sign up for ceramics.
We can calculate x as 36-12 = 24. Sufficient

Statement 2:
42 signed up for ceramics
This gives x+18 = 48
x=24
Sufficient.

Hence, each statement alone is sufficient

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07 Jul 2026, 09:09

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As per the diagram,
a = photography only
b = both photography and ceramics
c = ceramics only

Q.stem has given a+b+c = 54 and c = 18 and has asked for b.

St1: Of the 54, 12 did not sign for ceramics
This means they signed up only for photography, which means a = 12. From question a+b+c = 54, 12+b+18 = 54, b=24. SUFFICIENT

St2: Of the 54, 42 signed up for ceramics
This means 42 includes both only ceramics (c) and both ceramics and photography (b). b+c = 42. From question, c=18. Hence b=24. SUFFICIENT

Final answer is option D

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07 Jul 2026, 09:10

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Total people 54
photography P
ceramics C
both B

we know 18 did not sign up for photography

therefor P = 54 - 18 = 36

since everyone signed up for photo, ceramins or both

54 = 36 + C - Both

Both = 36 + C - 54

Statement 1
12 did not sign up for ceramics. C = 54 - 12 = 42

Both = 36 + 42 - 54 = 24

Therefor statement 1 is sufficient

Statement 2
42 signed up for ceramics

Both = 36 + 42 -54 = 24 Sufficient

Answer D

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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.

we can solve this with 2x2 matrix

----P----NP----total
C-- x---- ------
NC-- --- --0--
tot-- --- --- --54
54 total participants who signed up for photography , ceramic or both
participants both who did not sign up for photo is '0'
target is determine value of x i.e. both photography & ceramic

#1
out of 54 participants , 12 did not sign up for ceramics
---P---NP---total
c-- 24--- 18---42
nc--12--- 0--- 12
---36----18---54
'24' is both photography & ceramics ; sufficient
#2
out of 54 participants , 42 signed up for ceramics

---P---NP---total
c---24---18---42
nc--12---0---12
-----36---18---54

'24; is both photography & ceramics ; sufficient

OPTION D is correct

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07 Jul 2026, 09:14

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Total participants = 54
Ceramic participants = 18

Statement 1 :- Photography participants = 12, so participants signed up for both = 54 - 18 -12 = 24
Statement 2 :- Ceramics + Both = 42 , so Both = 42 - 18 = 24
Both are correct and individually sufficient

Bunuel

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07 Jul 2026, 09:18

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What we know:
P + C + P intersection C(call it x) = 54 and not P = 18. We can use venn diagram to see:
Statement 1: not C = 18
x+ not P + not C = 54(total), as we have not C and not P. Therefore, we can get x. so options ACD remains.
Statement 2: C = 42
C = x + not P, we know C and not P, so we can find out x. Therefore, both statements alone can solve the problem. Answer(D)

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07 Jul 2026, 09:19

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07 Jul 2026, 09:20

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Examining the stem-
Let's say,
Participants that participated in ONLY photography = P
Participants that took part in ONLY ceramics = C
Participants that took part in both = X

Therefore, P+C+X=54

Since, 18 did not sign up for photography at all, it means they signed up for only Ceramics.
Therefore, C = 18.
We need to find 'X'

Statement 1-
Since these participants (12) did not sign up for Ceramics at all, they signed up for only Photography.
Therefore, P = 12
(imp- Here this logic works only because the statement explicitly says 'out of these 54'. Questions might try to trick you by saying participants in general, and refer to participants that have participated for other things)
P+C+X=54
18+12+X=54
We can get 'X'
Data is sufficient.

Statement 2-
Since 42 signed up for Ceramics,
C + X = 42
Therefore, 18+X=42
(C was given to us in the question stem itself)
We can find 'X'
Therefore, data is sufficient.

Answer: D. Both statements are alone sufficient.

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07 Jul 2026, 09:21

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From both the options answer cannot be derived.

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07 Jul 2026, 09:23

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The total people signed for photography, ceramaics or both is 54.
18 did not sign for photography= 18 only cermaics. The need is to get both ceramics and photography.
a) 12 didnt signup for ceramics= only photography
12+18+ both C&P=54: both C&P= (54-30=24)-- A is sufficient.
b)42 signed up for ceramic: only ceramic +both cermaic and photography.
42=18+both C&P: both C&P=42-18=24--- B is sufficient.
Answer-D HEnce each statement alone is sufficient on its own

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07 Jul 2026, 09:24

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The answer is D.

With double overlapping set questions, I have seen the two main approaches to these problems be either a venn diagram or a double set matrix. Personally, I always do the double set matrix because it is what I am used to.

So we create a table and we know we are looking for the part of the 54 which signed up for both. Note the implicit restriction in the question which suggests that the number of the 54 who signed up for neither is 0.

1) 12 did not sign up for ceramics, so we know the number which did. Combined with the fact that we know how many signed up for and did not sign up for photography, this is enough to answer the question. Sufficient.

2) 42 signed up for ceramics, so we know the number which did not sign up for ceramics. The statements are providing the same information. The answer is D.

Whenever you see two statements providing the same information or no new information, the answer will be D or E.

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07 Jul 2026, 09:32

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This is probable one of the easiest DS questions. It is given that there are 54 people signing up for either ceramics (C), photography (P) or both (B). Now it say. 18 did not sign up for P, which means P= 54-18 = 36, so wkt the Total = 54 = P + C - B = 36 + C - B
, here there is no neither option as everyone has signed up for either P or C.

Statement 1: 12 did not sign up for Ceramics, so C= 54-12 = 42
54 = 36 + 42 - B --> B= 24 (Statement 1 is sufficient)
Keep A and D

Statement 2: 42 signed up for ceramics. As we can see again it mentions that C= 42 and hence the answer B= 24 again
So Statement 2 is sufficient as well.

Hurrayyyyyy Answer is D (Both the statements are individually sufficient)

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07 Jul 2026, 09:33

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Right choice is D (Each statement alone is sufficient)

As per the statement, all 54 participant have participated in at-least one activity. With this understanding, 18 didn't signup for photo, they sign up for ceramics. It also means that (54-18) 36 people signup for photo (it can also include both photo plus ceramics)

Coming to statement 1:
Out of 54, 12 didn't signup for ceramics. Means 12 signed up for only photo. So, we have information as below
Only photo: 12, Only ceramics: 18, Both are remaining (54-18-12) 24

Statement 2:
Out of 54, 42 signed up for ceramics. We know that only ceramics is 18. So, (42-18) 24 signed up for both.

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07 Jul 2026, 09:38

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Bunuel

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There are a total of 54 people, and everyone took at least 1 class.
P -> only photograph, B -> both, C -> ceramics
Let's say 54 = P + B + C
and C=18, so P + B = 54-18 = 36.
statement (1) Sufficient
P = 12, P + B = 36
12 + B = 36 => B = 24
statement (2) Sufficient
B + C = 42
B + 18 = 42 => B = 24

Option D, Each statement ALONE is sufficient.

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07 Jul 2026, 09:39

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This problem can be easily solved by using VENN diagram.

From statement 1 , out of 54 participants 18 people were not in the photography group . So they are in ceramics group.12 people are not in ceramics group . Hence , they are in photography group. [ 18+12]= 30 people were those people we wasn't interested in signing up for both group . Rest [ 54-30] =24 people signed up for both group . So, statement one is sufficient alone to ans the question .

From statement 2, 42 participants out of 54 took part in ceramic, among which 18 didn't sign up for photography . so , only [ 42-18]=24 signed for both photography and ceramics. Statement 2 is also sufficient alone to solve the asked question .

so , both statement alone is sufficient to find out how many participants signed up for both ceramics and photography.