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)
Correct Answer: Option D
Explanation
First, I will perform 'Step-by-Step Substitution' [20] to decode the expression based on the rules: '+' becomes '-', '-' becomes '×', '×' becomes '÷', and '÷' becomes '+'.\n\nThe original expression is:\n$10 + 30 - 100 \\times 50 \\div 25$\n\nApplying the changes simultaneously [31]:\n$10 - 30 \\times 100 \\div 50 + 25$\n\nNow, I must apply the 'Order of Operations (BODMAS)' [10]. The context warns us about the 'linear trap'—solving from left to right would give $-15$ (Option C), which is incorrect [15].\n\nStep 1: **Division** ($100 \\div 50$)\n$100 \\div 50 = 2$\nThe equation becomes: $10 - 30 \\times 2 + 25$\n\nStep 2: **Multiplication** ($30 \\times 2$)\n$30 \\times 2 = 60$\nThe equation becomes: $10 - 60 + 25$\n\nStep 3: **Addition and Subtraction**\nWe can simply process the integers now:\n$10 - 60 = -50$\n$-50 + 25 = -25$\n\nThe correct value is -25.
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