Operator re-mapping and evaluation: If K denotes "×", B denotes "÷", T denotes "−", and M denotes "+", then evaluate: 40 B 8 T 6 M 3 K 4 = ?

Difficulty: Easy

Correct Answer: 11

Explanation:


Introduction / Context:
This problem tests symbolic substitution and correct use of operator precedence (BODMAS/PEMDAS). We replace the given letters with their intended arithmetic operators and then evaluate with standard precedence rules.


Given Data / Assumptions:

  • K → × (multiplication), B → ÷ (division), T → − (subtraction), M → + (addition).
  • Expression: 40 ÷ 8 − 6 + 3 × 4.
  • Use standard precedence: × and ÷ before + and −; evaluate left to right within the same precedence tier.


Concept / Approach:
First perform division and multiplication, then handle addition/subtraction. Parentheses are not present, so no grouping overrides the default precedence.


Step-by-Step Solution:

Replace symbols: 40 B 8 T 6 M 3 K 4 → 40 ÷ 8 − 6 + 3 × 4. Compute ÷ and ×: 40 ÷ 8 = 5; 3 × 4 = 12. Now evaluate: 5 − 6 + 12 = (5 − 6) + 12 = −1 + 12 = 11.


Verification / Alternative check:
Reordering incorrectly (left-to-right without precedence) would give a wrong value; a quick calculator check with the same precedence confirms 11.


Why Other Options Are Wrong:
Values like 19 or 23 arise from ignoring precedence (e.g., adding before multiplying). −31 is the result of multiplying both 4 and 8 before subtracting from 7-like patterns, which do not apply here.


Common Pitfalls:
Misreading K as division or treating all operations strictly left-to-right. Always apply ×/÷ before +/− unless parentheses dictate otherwise.


Final Answer:
11.

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