Question

CSATMediumPrelims 2014Reasoning

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

Explanation

There are six women: Girija, Vanaja, Jalaja, Shailaja, Tanuja, and Pooja. Four dancers: Tanuja, Shailaja, and two others (yet to be determined). Four vocal musicians: Jalaja, Vanaja, Shailaja, and Tanuja. One actress: Pooja. Three violinists: Girija, Vanaja, and one other (yet to be determined). Girija and Vanaja are violinists. Jalaja and Shailaja do not play the violin. Shailaja and Tanuja are dancers. Jalaja, Vanaja, Shailaja, and Tanuja are vocal musicians, and two of them are also violinists. Given these conditions, we know:

Jalaja is a vocal musician but does not play the violin, so she cannot be a violinist. Shailaja is a dancer and a vocal musician, but she does not play the violin. Tanuja is a dancer, vocal musician, and must also be a violinist since there are only three violinists and Vanaja and Girija are already violinists. Vanaja is a violinist and a vocal musician. Pooja is the actress and does not fit into the dancer or violinist categories. From the above reasoning, Tanuja is the only person who is certainly both a dancer and a violinist.