You are given a question and two statements. Identify which of the statements is/are sufficient to answer the question. Question: Nayan has 4 caps of 3 different colours. How many blue caps does he have? Statements: 1. Nayan has 2 white caps. 2. The number of blue caps he has is the same as that of white caps.

You are given a question and two statements. Identify which of the statements is/are sufficient to answer the question. Question: Nayan has 4 caps of 3 different colours. How many blue caps does he have? Statements: 1. Nayan has 2 white caps. 2. The number of blue caps he has is the same as that of white caps. Correct Answer Statements 1 or 2 alone are sufficient.

The two colours mentioned in this question are blue and white. Let us assume the third colour to be black.

  • Statement 1: Nayan has 2 white caps

Given: Nayan has 4 caps of 3 “different” colours.
Thus, we have the following combination: 

  • Case 1) 2 white caps and 1 blue cap

[ alt="F1 Archana 30-12-21 Saivita D1" src="//storage.googleapis.com/tb-img/production/21/12/F1_Archana_30-12-21_Saivita_D1.png" style="width: 311px; height: 42px;">

  • Case 2) 2 white caps and 2 blue caps.

[ alt="F1 Archana 30-12-21 Saivita D2" src="//storage.googleapis.com/tb-img/production/21/12/F1_Archana_30-12-21_Saivita_D2.png" style="width: 311px; height: 42px;">

This is not possible as 4 caps should have 3 different colours.

  • Case 3) 2 white caps and 2 black caps

[ alt="F1 Archana 30-12-21 Saivita D3" src="//storage.googleapis.com/tb-img/production/21/12/F1_Archana_30-12-21_Saivita_D3.png" style="width: 311px; height: 42px;">

  • This is not possible as 4 caps should have 3 different colours.
  • Thus, we can eliminate cases 2 and 3.
  • Therefore, Nayan has 1 blue cap.
  • Hence, statement 1 alone is sufficient to answer the question.

 

  • Statement 2: The number of blue caps he has is the same as that of white caps.
  • Case 1) 1 white cap and 1 blue cap

This will imply that the remaining 2 caps are black

[ alt="F1 Archana 30-12-21 Saivita D4" src="//storage.googleapis.com/tb-img/production/21/12/F1_Archana_30-12-21_Saivita_D4.png" style="width: 311px; height: 42px;">

  • Case 2) 2 white caps and 2 blue caps.

 

  • This case is not possible because there should be 3 different colours.
  • Therefore, Nayan has 1 blue cap. Hence, statement 1 alone is sufficient to answer the question.

Hence, statement 1 or 2 alone is sufficient to answer the question.

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