19 boys turn out for playing hockey. Of these, 11 are wearing hockey shirts and 14 are wearing hockey pants. There are no boys without shirts and/or pants. What is the number of boys wearing full uniform?
- (a) 3
- (b) 5
- (c) 6 ✓ UPSC's answer
- (d) 8
Why the answer is (c)
• Total number of boys is 19.
• Number of boys wearing hockey shirts is 11.
• Number of boys wearing hockey pants is 14.
• Using the principle of inclusion-exclusion, the number of boys wearing both shirts and pants (full uniform) is calculated as: (Shirts + Pants) - Total Boys.
• Calculation: 11 + 14 - 19 = 25 - 19 = 6.
• Therefore, 6 boys are wearing the full uniform.
Why the other options are wrong
- (a) 3
- Option 3 is incorrect because the sum of shirts and pants (25) exceeds the total boys (19) by 6, not 3.
- (b) 5
- Option 5 is incorrect because the arithmetic calculation 11 + 14 - 19 yields 6, not 5.
- (d) 8
- Option 8 is incorrect because the arithmetic calculation 11 + 14 - 19 yields 6, not 8.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2018, held on 3 June 2018. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.