In a coded arithmetic expression, the symbol # means subtraction, & means division, @ means addition and % means multiplication. Using these code meanings and normal operator precedence, what is the numerical value of 505 & 5 # 4 @ 20 % 5 ?

Introduction / Context:
This verbal reasoning question uses coded arithmetic symbols. Instead of the usual plus, minus, multiplication and division signs, it gives special symbols and asks you to decode and evaluate the expression. Such questions test whether you can correctly translate each symbol and then apply the normal rules of arithmetic operations and precedence to arrive at the final value.

Given Data / Assumptions:

• # means subtraction, so A # B means A - B.
• & means division, so A & B means A / B.
• @ means addition, so A @ B means A + B.
• % means multiplication, so A % B means A * B.
• Expression to evaluate: 505 & 5 # 4 @ 20 % 5.
• Normal arithmetic precedence applies: division and multiplication are evaluated before addition and subtraction, and operations of the same rank are evaluated from left to right.

Concept / Approach:
The key idea is to rewrite the coded expression into a standard arithmetic expression by replacing each symbol with its actual meaning. After decoding, you must apply the standard BODMAS or PEMDAS rule, where multiplication and division are done before addition and subtraction. Many mistakes in such problems come from doing operations strictly from left to right without respecting precedence. So the safe approach is: first decode all symbols, then clearly mark the division and multiplication operations, evaluate them, and finally perform the remaining addition and subtraction in order.

Step-by-Step Solution:
Step 1: Write the coded expression: 505 & 5 # 4 @ 20 % 5. Step 2: Replace each symbol with its true operation. & means division, so 505 & 5 becomes 505 / 5. # means subtraction, so # 4 becomes - 4. @ means addition, so @ 20 becomes + 20. % means multiplication, so 20 % 5 becomes 20 * 5. Step 3: The decoded expression is 505 / 5 - 4 + 20 * 5. Step 4: Apply precedence. First evaluate division and multiplication. 505 / 5 = 101. 20 * 5 = 100. Step 5: Substitute these results back: 101 - 4 + 100. Step 6: Now perform subtraction and addition from left to right. 101 - 4 = 97. 97 + 100 = 197.

Verification / Alternative check:
A quick check is to recompute 505 / 5 separately to be sure it is 101, because a division mistake at this point would change the entire answer. Another check is to note that the term 20 % 5 always means 20 multiplied by 5, so it must contribute a positive and relatively large value of 100 to the final sum. If you forget precedence and wrongly compute from left to right as ((505 / 5) - 4 + 20) * 5 or something similar, you would get a completely different result. Confirming that only 197 fits the correctly decoded and evaluated expression gives confidence in the answer.

Why Other Options Are Wrong:
Options 211, 210, 195 and 201 usually come from common calculation errors, such as doing subtraction and addition in the wrong order, miscomputing 505 / 5, or forgetting that multiplication must be done before addition. Since the correctly decoded expression and proper precedence clearly give 197, all other values are inconsistent with the given coding rule and arithmetic laws.

Common Pitfalls:
Students often decode the symbols correctly but then evaluate strictly left to right. Another frequent mistake is to treat the coded expression as if it were a puzzle about changing precedence. In this question, precedence is standard; only the symbols are remapped. Writing the intermediate expression 505 / 5 - 4 + 20 * 5 on paper and underlining the division and multiplication parts is a reliable way to avoid confusion. Careful stepwise evaluation prevents arithmetic slips in exam conditions.

Final Answer:
The value of the expression 505 & 5 # 4 @ 20 % 5 under the given code is 197.