OG 2020: Question No. 322
In the figure above, if A, B, and C are the areas, respectively, of the three nonoverlapping regions formed by the intersection of two circles of equal area, what is the value of B + C?
- A + 2B + C = 24
- A + C = 18 and B = 3
| Source | OG 2020 |
| Type | Data Sufficiency |
| Topic | Geometry |
| Sub-Topic | Circle |
| Difficulty | Medium |
Solution
Steps 1 & 2: Understand Question and Draw Inferences
In this question, we are given
- A diagram of two circles, intersecting at two distinct points.
- The areas of the three nonoverlapping regions are denoted as A, B, and C.
- The individual areas of the two circles are equal.
We need to determine
- The value of B + C.
As the individual areas of both circles are equal, we can say
- A + B = B + C
Or, A = C
As we cannot infer any further information from the question stem, let us now analyse the individual statements.
Step 3: Analyse Statement 1
As per the information given in statement 1, A + 2B + C = 24
We also know that A = C.
- Hence, we can write C + 2B + C = 24
Or, 2B + 2C = 24
Or, B + C = 12
As we can determine the value of B + C, statement 1 is sufficient to answer the question.
Step 4: Analyse Statement 2
As per the information given in statement 2, A + C = 18, and B = 3.
We also know that A = C.
- Hence, we can write C + C = 18
Or, C = 9
From this statement, we know the value of B and can determine the value of C.
- Therefore, we can determine the value of B + C.
Hence, statement 2 is sufficient to answer the question.
Step 5: Combine Both Statements Together (If Needed)
Since we could determine the answer from either of the statements individually, this step is not required.
Hence, the correct answer is option D.
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