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

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Bunuel

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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.

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Bunuel

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GMAT Club Official Solution:

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?

Since all 54 participants signed up for photography, ceramics, or both, any participant who did not sign up for photography must have signed up for ceramics only.

So the 18 participants who did not sign up for photography signed up for ceramics only.

The question asks for the number of participants who signed up for both photography and ceramics.

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

Since all participants signed up for at least one of the two activities, these 12 participants signed up for photography only.

Therefore:

Both = Total - Ceramics only - Photography only = 54 - 18 - 12 = 24

Sufficient.

(2) Of the 54 participants, 42 signed up for ceramics.

Of these 42 participants, 18 signed up for ceramics only.

Therefore:

Both = 42 - 18 = 24

Sufficient.

Answer: D.

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ankushsambare

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07 Jul 2026, 08:20

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Given:
Total : 54
Photography = 54-18 = 36
Use: Both = Photography + Ceramics - Total
1. Ceramics = 54-12 = 42
Both = 36+42 = 24
Sufficient
2. Ceramics = 42
Sufficient
Answer: D

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Here's my solution for this question

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IMG_20260707_205048.jpg [ 509.5 KiB | Viewed 1726 times ]

rajdeep212003

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I got option choice D as a correct answer
— here, 54 = p , c or both ( x ) so if 18 of them is not P, then P =54 - 18 = 36 , total = P + C - x ,, 54 = 36 + c - x ,, x = c - 18
Now ,, statement one 12 not into c ,, C an= 54 -12 = 42 so now x = 42 so here x = 42 - 18 = 24 sufficient !!

And ,, statement two say c = 42 so x = 42 ( c) -18
So this one is also sufficient!!

As both statement is sufficient, I got option choice d !!

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Answer: D) Each statement alone is sufficient.

The prompt gives us:
P + C + PnC = 54
C = 18, so P + PnC = 36
We need to find PnC

Statement (1): P = 12, so 12 + PnC = 26 -> PnC = 24
Statement (2): PnC = Signed up for Ceramics - Didn't sign up for Photography = 42 - 18 = 24

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07 Jul 2026, 08:31

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Total = 54 who signed up for ceramics / photography / both.

18 didnt sign up for photography meaning they only signed up for ceramics ONLY. We need to find photography + ceramics, we already have only ceramics.

Statement 1: 12 didnt sign up for ceramics - so they signed up for photography only. 54-12-18 = 24, SUFFICIENT

Statement 2: 42 signed up for ceramics, we already know only ceramics is 18. 42-18 = 24. Sufficient.

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Photography | No photography| Total
Ceramics | | 18 |
No ceramics. | | 0 |
Total. | 36 | 18 | 54

Before going into the statements, this is what we already know:

1. Total participants= 54
2. Every participant either takes photography or ceramics or both. That means there are 0 participants who dont take either of them.
3. There are 18 participants who do not take photography.
4. that also gives me 36 participants who take photgraphy.
5. Which in turn tells me that there are 18 participants who take ceramics but not photography.

Statement 1:
12 did not sign up for ceramics. Sufficient (once we plug in the values in the chart above. )

Statement 2:
42 signed up for ceramics. Sufficent (once we plug in the values in the chart above)

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07 Jul 2026, 08:33

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given: Total=54=P+C+PC (none=0)
C=18

To find: both =PC

1) P=12 subtituting in equation, we can find PC..so thsi is sufficient

2) C+PC=42 we know C=18 so we can find PC this is also sufficient

Hence D is the answer

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07 Jul 2026, 08:33

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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.

	Photography	~Photography	Total
Ceramics	x = ?
~Ceramics		0
Total	54-18=36	18	54

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

	Photography	~Photography	Total
Ceramics	x = ?	42-x	54-12=42
~Ceramics	36-x	x-24=0	12
Total	54-18=36	18	54

x-24=0; x = 24
24 participants signed up for both photography and ceramics
Sufficient

(2) Of the 54 participants, 42 signed up for ceramics

	Photography	~Photography	Total
Ceramics	x	42-x	42
~Ceramics	36-x	x-24=0	54-42=12
Total	54-18=36	18	54

x-24=0; x = 24
24 participants signed up for both photography and ceramics
Sufficient

IMO D

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07 Jul 2026, 08:34

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Let only photography be a & only ceramics be b and both be c,
thus given that
eq 1: a+b+c = 54
eq 2: c = 18
statement 1:
eq 3: a= 12, thus using eq 3 & eq 2 in eq 1, we can get value of b. thus solved.
statement 2:
eq 4: b+c = 42, this using eq 2 in rq 3, we can get value of b. thus solved.

Hence both statements alone is sufficient to solve it.

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07 Jul 2026, 08:36

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Statement (1): Of the 54 participants, 12 did not sign up for ceramics.
This means 12 people signed up for only photography ($\text{Only P} = 12$).
Plugging this into our main formula:
$54 = 12 + 18 + \text{Both}$
$54 = 30 + \text{Both}$
$\text{Both} = 24$
Since we can find a single definitive value, Statement (1) is Sufficient.

Statement (2): Of the 54 participants, 42 signed up for ceramics.
The total number of people taking ceramics includes both those taking only ceramics and those taking both classes.
$\text{Total C} = \text{Only C} + \text{Both}$
$42 = 18 + \text{Both}$
$\text{Both} = 24$
Since we can find a single definitive value, Statement (2) is Sufficient.

Hence (D) EACH statement ALONE is sufficient.

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statement 1.png [ 9.09 KiB | Viewed 1331 times ]

statement 2.png [ 9.3 KiB | Viewed 1327 times ]

BrownBearBR

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07 Jul 2026, 08:37

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Answer here is D.
We can use Venn Diagrams here for easier calculation.

Since the statement clearly says that 55 people wither signed for P or C or both, none = 0. (That is there are no participants who signed for neither).

Statement 1 says out of 54 participants, 12 did not sign up for ceramics. Which means 12 only signed up for photography. In our original statement we have 18 people who did not sign up for photography. Which means these 18 people only signed up for ceramics. Hence if x is people who signed for both P and C, then 12 + x + 18 = 54. x = 24. This is sufficient.

In Statement 2, we are given 42 people signed up for ceramics. Which is only ceramics + both (ceramics + photography). Since from the original statement we know, only ceramics is 18, we can calculate the value for both P& C. This is sufficient.

Hence each statement alone is sufficient. Answer is D.

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07 Jul 2026, 08:38

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I tried using the 2x2 matrix method for this:

The matrix was as follows (the info given in question stem is in bold):

Photography. Not Photography. Total
Ceramics

Not Ceramics _12_

Total _36_ _18_ _54_

Statement 1: 12 did not sign up for ceramics (highlighted in italics in the above matrix):
This helps us with Also the number of people who signed up for the Ceramics class as 54-12 = 42
However, this still leaves us with a lot of possibilities for people who signed up for both classes. Hence, statement one is not enough. cross out A and D

Statement 2: 42 signed up for ceramics.
This statement pretty much gives us the same information as the Statement 1. Hence, it is not enough as well. Cross out B

Both statements combined still give us no additional information. Hence cross out C as well.

Answer is (E)

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Given -
18 participants did not sign up for photography and since everyone signed up for something, these 18 must belong only to the ceramics group.

Ceramics Only = 18

Statement 1 -
Of the 54 participants, 12 did not sign up for Ceramics. If 12 people did not sign up for Ceramics, they must belong only to the Photography group.

Photography Only = 12

We know the total is 54.

Photography Only + Ceramics Only + Both = Total

12 + 18 + Both = 54

Both = 24

So statement 1 is sufficient.

Statement 2 -
Of the 54 participants, 42 signed up for Ceramics.

The total number of participants who signed up for Ceramics is the sum of those who did "Ceramics Only" and those who did "Both".

Total Ceramics = Ceramics Only + Both
42 = 18 + Both
Both = 24

So statement 2 is also sufficient.

So we can conclude that each statement alone is sufficient, so D is our answer

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07 Jul 2026, 08:41

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Let x be participants signed up for both P & C
1.12+x+18=54 -> x=24
2. 48=x+18 -> x =30
I don't see 4 answers but I guess answer is we can get the answer with each statement alone -> D

Bunuel

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07 Jul 2026, 08:51

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i am going with option d. as we are given that either they are in photography, ceramic and both and we are given that there is total 54 participants and 18 did not sign up for P so they exclusively did for C then as they can't be in both.
option A says that 12 didn't sign up for C so they exclusively did for P then as they can't be in both, so we now know the participants exclusively for both C & P hence subtracting them gives the number for both.
option b states that 42 signed up for C and we are given the exclusive no. of C that is 18 so the rest indicates participants in both hence D.

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07 Jul 2026, 08:52

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Make a cross 4x4 table
Statement 1 will not give definate answer ---so cancel AD
Statement 2- will give definate answer of 24 people that signed up for both
Hence, B

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07 Jul 2026, 08:53

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easy to solve using venn diagram, let P = only photography, C = only ceramics, B = both (count of students)

P + C + B = 54
Also, if 18 did not sign for photography means only ceramics, C = 18. Then, P + 18 + B = 56 => P + B = 36. Now, question is what is the value of B?

Option 1) 12 did not sign for ceramics, means only photographic students (P) = 12. Putting in equation above gives 12 + B = 36 => B = 24 (Sufficient)
Since option 1 is sufficient, our answer choices will be either A or D. Let's evaluate option 2 now.

Option 2) 42 signed for ceramics, it means B + C = 42. We already know that C = 18, so B = 42 -18 = 24 (Sufficient)

Our answer choice is D

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07 Jul 2026, 08:56

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Bunuel

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Analysing the question, we get
Only ceramics = 18 ---- (*)
Only Ceramics + Both + Only Photography = 54
Further, 18 did not sign up for photography, so only ceramics is 18 (as they did not sign up for photography, we will remove both and only photography) ----- (1)

Now we know that: Both + Only Photography = 54 - 18 = 36 (From 1) ---- (2)

Statement 1
12 did not sign up for ceramics are only photography folks; same logic as (1)
So we now know only photography and inputting the value in (2) will give us the value for both
Both + 12 = 36
Both = 24; hence, Sufficient

Statement 2
42 signed up for ceramics means the ones who signed up only for ceramics and who signed up for both
Inputting this into the (*) equation, we get
Only ceramics + Both = 42
18 + Both = 42
Both = 24; Sufficient

Therefore, (D) Both individually sufficient