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07 Jul 2026, 23:28
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We can solve this problem in 3 different ways
1. Using Formulas
2. Venn Diagram
3. Matrix Diagram
Let's solve this using Formulas
P---- Photography
C---- Ceramics
U---- Union
n---- Intersection
Given that 54 participants signed up for photography, ceramics, or both.
We can infer that
- [ P U C ] == 54 and ...
- [ Not P n Not C] == 0
Given that 18 of these participants did not sign up for photography
[ Not P ] == 18, We can get [ P ] == 54 - 18 === 36
We have to find [ P n C ]
Formula: [ P n C ] === [P] + [C] - [P U C]
We have values of [P] and [P U C] substituting the values in above formula
[ P n C ] === 36 + [C] - 54 ...................(i)
Hence if we get the value of [C] then our question is sufficient.
---------------------------------------------------------------
Analysing statement 1 alone,
[Not C] == 12, Therefore we can get [C] == 54 - 12 == 42
Substituting in the main equation(i)
[ P n C ] === 36 + 42 - 54 ==== 24
Hence statement 1 alone is sufficient
------------------------------------------------
Analysing statement 2 alone,
[C] == 42
Substituting in the main equation(i)
[ P n C ] === 36 + 42 - 54 ==== 24
Hence statement 2 alone is sufficient
Answer D
1. Using Formulas
2. Venn Diagram
3. Matrix Diagram
Let's solve this using Formulas
P---- Photography
C---- Ceramics
U---- Union
n---- Intersection
Given that 54 participants signed up for photography, ceramics, or both.
We can infer that
- [ P U C ] == 54 and ...
- [ Not P n Not C] == 0
Given that 18 of these participants did not sign up for photography
[ Not P ] == 18, We can get [ P ] == 54 - 18 === 36
We have to find [ P n C ]
Formula: [ P n C ] === [P] + [C] - [P U C]
We have values of [P] and [P U C] substituting the values in above formula
[ P n C ] === 36 + [C] - 54 ...................(i)
Hence if we get the value of [C] then our question is sufficient.
---------------------------------------------------------------
Analysing statement 1 alone,
[Not C] == 12, Therefore we can get [C] == 54 - 12 == 42
Substituting in the main equation(i)
[ P n C ] === 36 + 42 - 54 ==== 24
Hence statement 1 alone is sufficient
------------------------------------------------
Analysing statement 2 alone,
[C] == 42
Substituting in the main equation(i)
[ P n C ] === 36 + 42 - 54 ==== 24
Hence statement 2 alone is sufficient
Answer D
07 Jul 2026, 23:44
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Given, Not both=0, total=54,not photo=18
Lets create a table, and update it
0,Ceramics,Not ceramics, total
Photo,?,?,36
Not Photo,18,0,18
total,?,?,54
How 36? its total-not photo
Now, statement 1, 12 did NOT sign up for ceramics
New table-
0,C,NC,T
P,X,12,36
NP,18,0,18
T,?,12,54
X+12=36
X=24
Hence Sufficient
statement 2,
0,C,NC,T
P,X,?,36
NP,18,0,18
T,42,?,54
X+18=42
X=24
Hence Sufficient
Thus each statement alone is suff
Answer D
Lets create a table, and update it
0,Ceramics,Not ceramics, total
Photo,?,?,36
Not Photo,18,0,18
total,?,?,54
How 36? its total-not photo
Now, statement 1, 12 did NOT sign up for ceramics
New table-
0,C,NC,T
P,X,12,36
NP,18,0,18
T,?,12,54
X+12=36
X=24
Hence Sufficient
statement 2,
0,C,NC,T
P,X,?,36
NP,18,0,18
T,42,?,54
X+18=42
X=24
Hence Sufficient
Thus each statement alone is suff
Answer D
07 Jul 2026, 23:47
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Total = 54 members
Only Ceramic (C) = 18
None (N)=0
Only Photography =A
Both =B
We can derive that Total= A + C + B - N
54=A+18+B-0
54=A+B+18
Statement 1: A=12
therefore 54=12+18+B
B=24, Sufficient
Statement 2: 42=B+18
therefore 54=A+42
A=12
, we can derive that 54=12+B+18
B=24, Sufficient
Therefore option D is answer
Only Ceramic (C) = 18
None (N)=0
Only Photography =A
Both =B
We can derive that Total= A + C + B - N
54=A+18+B-0
54=A+B+18
Statement 1: A=12
therefore 54=12+18+B
B=24, Sufficient
Statement 2: 42=B+18
therefore 54=A+42
A=12
, we can derive that 54=12+B+18
B=24, Sufficient
Therefore option D is answer
