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 ?
- (a) Jalaja
- (b) Pooja
- (c) Shailaja
- (d) Tanuja ✓ UPSC's answer
Why the answer is (d)
• The group consists of 6 women: Girija, Vanaja, Jalaja, Shailaja, Tanuja, and Pooja.
• Pooja is identified as the single actress, so she is not a dancer, vocal musician, or violinist.
• The remaining 5 women (Girija, Vanaja, Jalaja, Shailaja, Tanuja) must fill the roles of 4 dancers, 4 vocal musicians, and 3 violinists.
• It is given that Jalaja and Shailaja do not play the violin, so the 3 violinists must be chosen from Girija, Vanaja, and Tanuja.
• Since there are exactly 3 violinists and only 3 eligible candidates (Girija, Vanaja, Tanuja), all three must be violinists.
• Tanuja is explicitly stated to be a dancer, and since she is also one of the three violinists, she is certainly both a dancer and a violinist.
Why the other options are wrong
- (a) Jalaja
- Jalaja is explicitly stated not to know how to play the violin.
- (b) Pooja
- Pooja is the actress and therefore does not hold the roles of dancer or violinist.
- (c) Shailaja
- Shailaja is explicitly stated not to know how to play the violin.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2014, held on 24 August 2014. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.