If a + b means a - b; a - b means a × b; a × b means a ÷ b; a ÷ b means a + b, then what is the value of 10 + 30 - 100 × 50 ÷ 25? (Operations are to be replaced simultaneously)
- (a) 15
- (b) 0
- (c) -15
- (d) -25 ✓ UPSC's answer
Why the answer is (d)
• The problem states that operations are replaced simultaneously, so we first translate the entire expression using the given mappings: '+' becomes '-', '-' becomes '×', '×' becomes '÷', and '÷' becomes '+'.
• The original expression is 10 + 30 - 100 × 50 ÷ 25.
• Applying the substitutions: 10 becomes 10, '+' becomes '-', 30 becomes 30, '-' becomes '×', 100 becomes 100, '×' becomes '÷', 50 becomes 50, '÷' becomes '+', and 25 becomes 25.
• The new expression is 10 - 30 × 100 ÷ 50 + 25.
• Following the standard order of operations (BODMAS/PEMDAS), we perform multiplication and division from left to right: 30 × 100 = 3000, then 3000 ÷ 50 = 60.
• The expression simplifies to 10 - 60 + 25, which equals -50 + 25 = -25.
Why the other options are wrong
- (a) 15
- Option (a) 15 is incorrect because it likely results from ignoring the order of operations or miscalculating the division step.
- (b) 0
- Option (b) 0 is incorrect because the arithmetic sum of the transformed terms does not cancel out to zero.
- (c) -15
- Option (c) -15 is incorrect because it stems from an error in the final addition or subtraction step after simplifying the multiplication and division.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2024, held on 16 June 2024. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.