Solving Mathematical Expressions with Operator Substitution

This question asks us to evaluate a mathematical expression where letters represent different arithmetic operations. We are given the mappings for each letter and the expression to solve. To find the answer, we need to replace each letter with its corresponding operation symbol and then calculate the result following the standard order of operations (BODMAS/PEMDAS).

Problem Analysis: Understanding the Operator Codes

The problem provides a simple code for mathematical operators:

• ‘A’ means ‘×’ (Multiplication)
• ‘B’ means ‘+’ (Addition)
• ‘C’ means ‘–’ (Subtraction)
• ‘D’ means ‘÷’ (Division)

The expression we need to evaluate using these codes is:

66 A 3 D 11 B 43 C 48 D 12

Operator Substitution

Now, let's substitute the letters in the given expression with the mathematical operators they represent:

\(66 \times 3 \div 11 + 43 - 48 \div 12\)

Order of Operations Explained (BODMAS/PEMDAS)

To correctly evaluate the expression, we must follow the order of operations. This order is commonly remembered using acronyms like BODMAS or PEMDAS.

• Brackets (or Parentheses)
• Orders (or Exponents)
• Division and Multiplication (from left to right)
• Addition and Subtraction (from left to right)

In our expression, we have multiplication, division, addition, and subtraction. We will perform division and multiplication first, from left to right, and then addition and subtraction, also from left to right.

Step-by-Step Calculation

Let's evaluate the expression \(66 \times 3 \div 11 + 43 - 48 \div 12\) step by step following the BODMAS rule:

1. Perform Division: We have two division operations: \(3 \div 11\) and \(48 \div 12\). We perform these from left to right. However, it's often clearer to perform multiplications and divisions as they appear from left to right together. Let's start with the division related to 48:
   • \(48 \div 12 = 4\)
   The expression becomes: \(66 \times 3 \div 11 + 43 - 4\)
2. Perform Multiplication and remaining Division (from left to right): Next, we address \(66 \times 3 \div 11\).
   • \(66 \times 3 = 198\)
   • The expression is now: \(198 \div 11 + 43 - 4\)
   • \(198 \div 11 = 18\)
   • The expression is now: \(18 + 43 - 4\)
3. Perform Addition and Subtraction (from left to right): Finally, we perform the addition and subtraction.
   • \(18 + 43 = 61\)
   • The expression is now: \(61 - 4\)
   • \(61 - 4 = 57\)

Result of the Expression Evaluation

Following the step-by-step calculation based on the order of operations, the value of the expression \(66 A 3 D 11 B 43 C 48 D 12\) is 57.

The final calculated value is 57.

Revision Table: Key Concepts

Additional Information: More on Operator Logic Problems

Problems like this, where symbols or letters represent operations, are common in quantitative aptitude and logical reasoning tests. They assess your ability to follow instructions precisely and apply basic mathematical rules. Sometimes, the operator meanings might be unconventional (e.g., ‘A’ might mean adding the square of the first number to the second). Always read the specific definition of each symbol or letter carefully before attempting to solve the expression.

Another variation involves changing the standard meaning of operators (e.g., '+' means subtraction, 'x' means division). In all cases, the key is careful substitution and then applying the correct mathematical order of operations.