In a certain code language for arithmetic operations, the following substitutions are used:\n\nThe plus sign (+) represents multiplication, the minus sign (-) represents addition, the multiplication sign (x) represents division and the division sign (÷) represents subtraction.\n\nUsing this code, find the value of the expression: 642 x 6 ÷ 25 + 4.

Introduction / Context:
This is a coded-operations question where each familiar arithmetic symbol has been assigned a different meaning. To obtain the correct numerical value, we must first decode the expression according to the given mapping and then evaluate it using standard arithmetic precedence rules.

Given Data / Assumptions:

• + means multiplication.
• - means addition.
• x means division.
• ÷ means subtraction.
• Expression to decode: 642 x 6 ÷ 25 + 4.
• We use the usual precedence of operations: division and multiplication before addition and subtraction.

Concept / Approach:
The method is to translate each coded symbol into its true operation and rewrite the expression entirely in normal arithmetic form. After that, we simplify step by step, following the correct order of operations. The final result is then compared with the answer options.

Step-by-Step Solution:
Step 1: Replace x with ÷, because x represents division. Step 2: Replace ÷ with -, because ÷ represents subtraction. Step 3: Replace + with ×, because + represents multiplication. Step 4: The coded expression 642 x 6 ÷ 25 + 4 becomes 642 ÷ 6 - 25 × 4. Step 5: Evaluate division and multiplication first. Step 6: Compute 642 ÷ 6 = 107. Step 7: Compute 25 × 4 = 100. Step 8: Now perform the subtraction: 107 - 100 = 7.

Verification / Alternative check:
We can recompute the division 642 ÷ 6 by checking 6 × 107 = 642, which confirms the quotient is correct. The multiplication 25 × 4 = 100 is straightforward. Since 107 - 100 = 7 exactly, the decoded and evaluated expression is reliable.

Why Other Options Are Wrong:
The answers 11, 64 and 18 would arise only if we misinterpreted one of the coded symbols or changed the order of operations, such as treating + as ordinary addition or performing addition before multiplication. Because our decoding is consistent with the rules given, these alternative values are not correct.

Common Pitfalls:
Students often forget to apply the mapping to every occurrence of the symbol, or accidentally mix original meanings with coded meanings. Another pitfall is ignoring precedence, for example subtracting 25 from 642 before dividing. Being systematic in substitution and evaluation is essential in such coded-operator questions.

Final Answer:
After decoding and simplifying, the value of the expression 642 x 6 ÷ 25 + 4 is 7, so option (d) is correct.