UPSC Prelims 2017 CSAT Paper II · Q29 of 79 Logical Reasoning medium

In a group of six women, there are four tennis players, four postgraduates in Sociology, one postgraduate in Commerce and three bank employees. Vimala and Kamla are the bank employees while Amala and Komala are unemployed. Komala and Nirmala are among the tennis players. Amala, Kamla, Komala and Nirmala are postgraduates in Sociology of whom two are bank employees. If Shyamala is a postgraduate in Commerce, who among the following is both a tennis player and a bank employee?

  1. (a) Amala
  2. (b) Komala
  3. (c) Nirmala ✓ UPSC's answer
  4. (d) Shyamala

Why the answer is (c)

• The six women are Vimala, Kamla, Amala, Komala, Nirmala, and Shyamala.

• Vimala and Kamla are the two bank employees.

• Amala and Komala are unemployed, so they are not bank employees.

• Komala and Nirmala are tennis players.

• Since Vimala and Kamla are the only bank employees, and Komala is unemployed, Komala cannot be a bank employee.

• Therefore, Nirmala must be the tennis player who is also a bank employee, as she is the only remaining tennis player who could be one of the two bank employees (Vimala or Kamla is not a tennis player based on the exclusion of others, but wait: Vimala and Kamla are bank employees. Komala and Nirmala are tennis players. Amala and Komala are unemployed. So Komala is not a bank employee. Nirmala is a tennis player. Is Nirmala a bank employee? The bank employees are Vimala and Kamla. This implies Nirmala is NOT a bank employee? Let's re-read carefully. 'Vimala and Kamla are the bank employees'. This is a definitive statement. 'Komala and Nirmala are among the tennis players'. 'Amala, Kamla, Komala and Nirmala are postgraduates in Sociology of whom two are bank employees'. The two bank employees among the Sociology PGs are Kamla and Nirmala? No, Vimala and Kamla are the bank employees. So Kamla is a bank employee. Is Vimala a Sociology PG? The list of Sociology PGs is Amala, Kamla, Komala, Nirmala. Vimala is not in this list. So Vimala is not a Sociology PG. But Vimala is a bank employee. The statement says 'of whom [the Sociology PGs] two are bank employees'. This implies two of {Amala, Kamla, Komala, Nirmala} are bank employees. We know Kamla is a bank employee. Who is the other? Amala and Komala are unemployed, so they are not bank employees. Therefore, Nirmala must be the second bank employee among the Sociology PGs. Thus, Nirmala is a bank employee. Since Nirmala is also a tennis player, she is both.

Why the other options are wrong

(a) Amala
Amala is unemployed, so she cannot be a bank employee.
(b) Komala
Komala is unemployed, so she cannot be a bank employee.
(d) Shyamala
Shyamala is a postgraduate in Commerce, not Sociology, and is not identified as a bank employee or tennis player in the constraints.

Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2017, held on 18 June 2017. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.

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