In a coded arithmetic expression, # means subtraction, & means division, @ means addition and % means multiplication. Using these meanings and standard precedence, what is the value of 315 & 3 # 9 @ 4 % 6 ?

Introduction / Context:
This question continues the pattern of coded arithmetic expressions, where ordinary operators are replaced with special symbols. You must translate the expression 315 & 3 # 9 @ 4 % 6 into standard arithmetic and then evaluate it. These problems assess precision in decoding and in applying precedence rules during multi step calculations.

Given Data / Assumptions:

• & means division, so A & B represents A / B.
• # means subtraction, so A # B represents A - B.
• @ means addition, so A @ B represents A + B.
• % means multiplication, so A % B represents A * B.
• Expression to evaluate: 315 & 3 # 9 @ 4 % 6.
• Standard precedence: division and multiplication first, then addition and subtraction from left to right.

Concept / Approach:
As in previous coded arithmetic questions, you first decode each symbol into its true arithmetic meaning. Once the expression is written with ordinary operators, you handle division and multiplication before any addition or subtraction. Writing each intermediate result clearly is important to avoid mixing the operations and accidentally changing the intended computation.

Step-by-Step Solution:
Step 1: Start with 315 & 3 # 9 @ 4 % 6. Step 2: Replace & with /, # with -, @ with + and % with *. Step 3: The decoded expression becomes 315 / 3 - 9 + 4 * 6. Step 4: Evaluate division and multiplication first. 315 / 3 = 105. 4 * 6 = 24. Step 5: Substitute these into the expression: 105 - 9 + 24. Step 6: Now perform subtraction and addition from left to right. 105 - 9 = 96. 96 + 24 = 120.

Verification / Alternative check:
You can verify quickly by checking the extreme operations. The division 315 / 3 must give a round value of 105, otherwise you know an arithmetic slip has occurred. Since 4 * 6 is a simple multiplication equal to 24, combining 105, 9 and 24 is straightforward. If you mistakenly ignore precedence and compute 315 / (3 - 9 + 4) * 6 or any other rearrangement, you will not arrive at 120 and will conflict with the defined coding rule. Thus 120 is the only value consistent with both the decoding and standard arithmetic evaluation.

Why Other Options Are Wrong:
Options 190, 221 and 420 are typical of errors where candidates either add before multiplying or confuse which numbers are involved in division. Option 315 is the original number and might attract those who misread the problem as a trick. None of these values follow directly from the expression 315 / 3 - 9 + 4 * 6 with correct precedence. Since only 120 matches the exact evaluation, the other options must be rejected.

Common Pitfalls:
Students often rush through coded arithmetic and treat the symbols as if they were ordinary operators in their usual positions, without rewriting the expression. This leads to mixing old and new meanings. Another common pitfall is evaluating from left to right and ignoring the rule that division and multiplication come before addition and subtraction. To avoid these mistakes, always decode first, rewrite the expression, and then carefully apply the operation hierarchy.

Final Answer:
So, according to the given symbol meanings, the value of 315 & 3 # 9 @ 4 % 6 is 120.