Question

If '×' = '−', '+' = '÷', '−' = '+', '÷' = '×', then which is valid?

• A. 12 − 4 × 2 + 1 = 7
• B. 10 + 2 − 4 × 1 = 8
• C. 16 ÷ 4 + 2 - 2 = 10
• D. 8 × 2 - 2 + 2 = 1

Answer 1

Answer:

B. 10 + 2 − 4 × 1 = 8

Methodology for Mathematical Operators Problems

• Step 1: Symbol Substitution: The fundamental approach is to replace the original mathematical operators with the newly defined signs provided in the question.
• Step 2: Follow BODMAS/PEMDAS: After substitution, the resulting expression must be solved strictly adhering to the BODMAS (Bracket, Of, Division, Multiplication, Addition, Subtraction) order of operations.
• Step 3: Verification: Evaluate each option by performing calculations one by one. The valid option will satisfy the equality given in the problem statement.

Rules Applied in this Specific Logic:

• Replace × with −
• Replace + with ÷
• Replace − with +
• Replace ÷ with ×

Example Calculation Process: If an option states '10 + 2', applying the rule, it becomes '10 ÷ 2', which equals 5. Proceeding this way for all given components determines the correctness of the equation.

Exam Tips:

• Always write down the new operators clearly before substituting to avoid confusion during calculation.
• Check the division operation first, as it often helps eliminate options quickly. If the division results in a non-integer when an integer is expected, that option is likely incorrect.
• Perform calculations systematically to avoid simple arithmetic errors, which are common in this topic.