In a group of six women, there are four dancers, four vocal musicians, one actress, and three violinists. Girija and Vanaja are violinists, while Jalaja and Shailaja do not know how to play the violin. Shailaja and Tanuja are dancers. Jalaja, Vanaja, Shailaja, and Tanuja are all vocal musicians, and exactly two of them are also violinists. If Pooja is the only actress, who among the following is both a dancer and a violinist?

Introduction / Context:
This logical reasoning puzzle is based on classification and deduction from multiple overlapping sets. We have six women and information about who is a dancer, vocal musician, violinist, and actress. The task is to combine all the given constraints and identify which person must certainly be both a dancer and a violinist. Such questions train the ability to track conditions and use elimination to reach a unique conclusion.

Given Data / Assumptions:

• There are six women: Girija, Vanaja, Jalaja, Shailaja, Tanuja, and Pooja.
• Total roles: four dancers, four vocal musicians, one actress, and three violinists.
• Girija and Vanaja are violinists.
• Jalaja and Shailaja do not play the violin.
• Shailaja and Tanuja are dancers.
• Jalaja, Vanaja, Shailaja, and Tanuja are all vocal musicians.
• Exactly two of these four vocal musicians (Jalaja, Vanaja, Shailaja, and Tanuja) are violinists.
• Pooja is the only actress.

Concept / Approach:
The key idea is to combine set membership information. We know how many people belong to each skill group overall, and we also know specific inclusions and exclusions. We must first identify all violinists, then intersect that set with the set of dancers. Any person who is certainly in both sets, regardless of other possibilities, is the required answer. Consistency with the total counts is also important, so we use the totals to confirm that no alternative assignment is possible.

Step-by-Step Solution:
Step 1: From the statement, Girija (G) and Vanaja (V) are violinists. So we already have two violinists: G and V.Step 2: Jalaja (J) and Shailaja (S) do not know how to play the violin, so they cannot be violinists.Step 3: The four vocal musicians are J, V, S, and Tanuja (T). Exactly two of these four are violinists.Step 4: Among these four vocal musicians, V is already known to be a violinist. Therefore, exactly one more among J, S, and T must be a violinist.Step 5: However, J and S are explicitly stated not to play the violin. Hence they cannot be the second violinist among this group.Step 6: Therefore, Tanuja must be the second violinist among the vocal musicians. So the three violinists overall are Girija, Vanaja, and Tanuja.Step 7: Shailaja and Tanuja are dancers. Therefore, Tanuja is both a dancer and a violinist. Shailaja is a dancer but not a violinist. Girija and Vanaja are violinists but are not forced by the statements to be dancers.Step 8: Hence the only woman who is certainly both a dancer and a violinist is Tanuja.

Verification / Alternative check:
Check the total counts. There are three violinists: G, V, and T. This matches the requirement of three violinists. Vocal musicians are J, V, S, and T, and among them, exactly two (V and T) are violinists, which also matches the given condition. There are four dancers, and we already know S and T are dancers, while the remaining two dancers can be selected from G, V, J, and P without affecting the conclusion about who must be both dancer and violinist. Every condition can be satisfied with Tanuja as a dancer and violinist, and no other person is forced into that combination by the data.

Why Other Options Are Wrong:

• Shailaja is definitely a dancer and a vocal musician, but she does not play the violin.
• Vanaja is definitely a violinist and a vocal musician, but she is not required to be a dancer by any statement.
• Girija is a violinist, but again there is no compulsion that she is a dancer.
• Pooja is identified as the actress. She need not be a violinist or a dancer based on the given information.

Common Pitfalls:

• Assuming that every violinist is also a dancer simply because there are many dancers and violinists.
• Overlooking the restriction that Jalaja and Shailaja do not play the violin and mistakenly assigning them as violinists.
• Ignoring the condition that exactly two among the four vocal musicians are violinists, which forces Tanuja to be a violinist.

Final Answer:
The woman who is both a dancer and a violinist is Tanuja.