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x = both
P + C - x = 54

As C - x = 18 then:
P + 18 = 54
P = 36

The equation is:
x = P + C - 54 = 36 + C - 54 = C - 18

(1)
not C = 12 -> C = 54 - 12 = 42
x = C - 18 = 24

Sufficient

(2)
C = 42
x = C - 18 = 24

Sufficient

IMO D
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Total Participants = 54
# of participant for Photography = P, Ceramic = C, both = x, None = 0 since question mentions people participate in P, C, or both
Given 18 didn't participate in photography, which means this includes C but excludes the common part x, so C-x = 18

Solving using Venn Diagram below. Answer D)
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total = 54 = photography + ceramics - both
ceramics = only ceramics + both = 18 + both

54 = photography + (18 + both) - both = photography + 18
photography = 36

both = photography + ceramics - 54 = 36 + ceramics - 54 = ceramics - 18

(1)
only photography = 12
photography = only photography + both
36 = 12 + both
both = 24

Condition sufficient

(2)
ceramics = 42
both = ceramics - 18 = 42 - 18 = 24

Condition sufficient

Answer D
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from the question we get
18 people did ceramics since
now from. 1
12 signed up for photography
so 12+18 + both Pand C =54
sufficient
also
in 2
42+ Ponly =54
P only= 12
again similarly how we solved 1 we can get both P and C as 30 here again
so (D) Each statement alone is sufficient
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There are 3 types of people
1. Sign up only photo -> a
2. Sign up only ceramics -> b
3. Sign up for both -> c

We're given b = 18. And we know a + b + c = 54

Investigate
(1) Give a = 12 -> know a, b solve for c -> ENOUGH
(2) Give b+c = 42 -> know b -> solve for c -> ENOUGH

So, D.
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From the question itself we are given total number and neither, from both of the statements we can only find the number for total ceramics we do not have any details to find the subsets behind ceramic and photographic therefore both of these answers are insufficient.
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PhotographyNo PhotographyTotal
CeramicX42
No Ceramic12
Total361854

The prompt provides the overall total value (54) and the total of 18 for the no photography column. This values confirms 36 as the value for the photography column.

We need to find the value for x. We need a value of one of the cells in the table aside total row/ column values.
Statement provides another row total, there are multiple values that can hold for this. not sufficient.
Statement 2provides another row total, there are multiple values that can hold for this, not suuficient.

Cosindering both statement, only row and column total are available, multiple values can hold. not suuficient
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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p: photography
c: ceramics
b: both

p + c - b = 54

c - b = 18 -> c = 18 + b

Sustituting:
p + c - b = p + 18 + b -b = p + 18 = 54
p = 36

(1)
p - b = 12
b = p - 12 = 36 - 12 = 24

Condition (1) is sufficient

(2)
c = 42
36 + 42 - b = 54
b = 78 - 54 = 24

Condition (2) is sufficient

The answer is D
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photography + ceramics - both = 54

onlyceramics = ceramics - both = 18

photography + 18 = 54
photography = 36

(1)
onlyphotography = photography - both = 12
36 - both = 12
both = 24

Sufficient

(2)
ceramics = 42
ceramics - both = 18
42 - both = 18
both = 24

Sufficient

The correct answer is D
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Photography only = p
ceramics only = c
both = x
p+x+c = 54
c = 18

option 1
p = 12
x = 24
Statement 1 is sufficient

option 2
x+c = 42 , therfore x = 24.

Statement 2 is sufficient

option D is correct answer, both are correct independently.
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We are given:
Total =54
Total = Photography(P) + Ceramics(C) -Both(B)
In this case neither =0.
And 18 didn't participate in P.
That means total who participated in P = 54-18 = 36.

Stmt I:
Didn't participate in C =12
Participated in C = 42

Now using the formula :
Total -Neither = P+C -Both
54-0=36+42-Both
=> Both = 24.
Sufficient

Stmt II:
This is the same as the information given in Statement I
42 participated in Ceramics = 12 didn't participate in it.

Sufficient

ANSWER: D
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I first started by establishing the information I knew before looking at the additional statements. There are 54 participants and 18 of them did not sign up for photography. Since all participants are in photography, ceramics, or both, that means those 18 are taking ceramics.

I look at this formula as I am solving this problem

54 = P (photography) + C (ceramics) + B (both)

With the 18 in Ceramics we now have:

54 = P + 18 + B

without looking at any statements.

For statement 1 if 12 did not sign up for ceramics then all 12 did photography giving us:

54 = 12 + 18 + B

Then you can solve for the number of people in photography and ceramics which is 24, so Statement 1 is sufficient.

For statment 2, 42 signed of for ceramics. This includes people who did both and those who only signed up for ceramics so we can set this up as:

42 = C + B, we now C is 18 so 42 - 18 = 24 who take both. Stement 2 is also sufficient. The answer is Each statement alone is sufficient.
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The question states that PUC = 54 (eq 1) and C - P^C = 18 (eq 2) [here I am using U for union and ^ for intersection]

1) 12 did not sign up for ceramics, therefore, P - P^C = 12 (eq 3)
adding eq 2 and eq 3 we get -> P + C - 2P^C = 30 (eq 4)
we know that PUC = P + C - P^C = 54 (from eq 1)
if we subtract eq 4 from the above equation, P^C = 24 which is our answer. So (1) is sufficient

2) 42 signed up for ceramics, therefore, C = 42, putting this into eq 2 -> 42 - P^C = 18
thus, P^C = 24 which is our answer, (2) sufficient.

D - each statement alone is sufficient.

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.

 


This question was provided by GMAT Club
for the GMAT World Cup Competition

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⚠️ Important: GMAT Club does not allow AI-generated posts. AI-generated solutions are not eligible for kudos, and users who post them may face moderation action, including a ban.
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Total participants = 54
Since all 54 signed up for either one or both options, all 54 are part of at least one group.

Of these 54, 18 did not sign up for photography - which means n(ceramics only)=18
This means number of people who signed up for photography only or both n(photography only)+n(both)=54-18=36

We have to find out n(both).
From the above, n(both)=36 - n(photography only)

(1) 12 did not sign up for ceramics, hence they signed up for photography only.
n(photography only)=12
n(both)=36-12=24
Sufficient alone.

(2) 42 signed up for ceramics, thus n(ceramics only)+n(both)=42
We know n(ceramics only)=18
Thus, n(both)=42-18=24
Sufficient alone.

Therefore, option D.
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Consider the following table based on the information given in the prompt:
Photography Not Photography Total
Ceramics | X Y
Not Ceramics | A B
Total | 18 54

We need to find X.
Basis above table, we can also find X + A = 36 = participants taking photography. Thus, X = 36 - A

1) This says A + B = 12. Since we don't know B, we cannot find A, and thus also not X. Thus, Insufficient.
2) This implies X + Y = 42. Since we don't know A or Y, we cannot find X. Thus, Insufficient.
1) + 2)
A + B = 12
X + Y = 42
Y + B = 18
A + X = 36

While all totals are available, there is no way for us to identify A / B / X / Y individually.
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.

 


This question was provided by GMAT Club
for the GMAT World Cup Competition

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Let A represent the number of participants that only signed up for Photography
Let B represent the number of participants that signed up for both Ceramics and Photography. We need to find out the value for B
Let C represent the number of participants that only signed up for Ceramics

According to the question: A + B + C = 54 and C = 18

=> A + B = 36

Now lets look at each statement individually
Statement 1 says A = 12 => B = 36 - 12 = 24
Statement 2 says B + C = 42 => B = 42 - 18 = 24

Since both statements give us a definitive answer. The correct option is 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.

 


This question was provided by GMAT Club
for the GMAT World Cup Competition

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1. Decode the Main Clues
Before looking at the statements, let's figure out what we already know from the prompt:

Total = 54: Everyone signed up for Photography, Ceramics, or both. This means 0 people signed up for neither.

18 did not take Photography: Since nobody is taking neither class, these 18 people must be taking Ceramics only.

So, our starting board looks like this:

Ceramics only = 18

Photography only = ?

Both = ?

Total = 54

Now, let's look at the statements to see if we can find the "Both" group.

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

If they didn't sign up for ceramics, they must be taking Photography only.

Now we have the missing pieces:
Photography only (12) + Ceramics only (18) + Both = 54 total.

30 + Both = 54, which means Both = 24.

Statement (1) is sufficient.

3. Check Statement (2)
"Of the 54 participants, 42 signed up for ceramics."

The "Total Ceramics" group is made up of two types of people: those taking Ceramics only and those taking Both.

We already know 18 people are taking Ceramics only.

Ceramics only (18) + Both = Total Ceramics (42).

18 + Both = 42, which means Both = 24.

Statement (2) is sufficient.

Since we can solve the problem using either clue completely on its own, each statement alone is enough to get the answer!
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