The equation 12 - 6 × 5 + 20 ÷ 4 = 31 is incorrect. If the arithmetic signs in this expression are coded so that two of them are interchanged, which pair of signs must be swapped to make the equation mathematically correct?

Introduction / Context:
This problem tests understanding of operator precedence and logical adjustment of arithmetic signs. The equation is currently false, and the task is to identify which two operators must be interchanged so that the left hand side evaluates exactly to 31. These kinds of puzzles are common in aptitude tests to examine both calculation skills and logical reasoning about symbol manipulation.

Given Data / Assumptions:

• Original expression: 12 - 6 × 5 + 20 ÷ 4.
• Right side of the equation is 31.
• We may interchange exactly two signs from among plus, minus, multiplication and division.
• Arithmetic precedence (multiplication and division before addition and subtraction) must still be followed after any interchange.

Concept / Approach:
Instead of guessing randomly, test each suggested pair of signs systematically. For each option, substitute the new signs into the expression, then evaluate using correct precedence to see if the result equals 31. Since the numbers remain the same, only the operations change. The correct pair will produce an exact match with the right side of the equation.

Step-by-Step Solution:
Step 1: Evaluate the original expression: 12 - 6 × 5 + 20 ÷ 4. Step 2: Compute 6 × 5 = 30 and 20 ÷ 4 = 5. The expression becomes 12 - 30 + 5 = -13, which is not 31. Step 3: Option A suggests interchanging + and ÷. This turns the expression into 12 - 6 × 5 ÷ 20 + 4. Step 4: Evaluate option A: 6 × 5 = 30, 30 ÷ 20 = 1.5, so 12 - 1.5 + 4 = 14.5, not 31. So option A is incorrect. Step 5: Option B suggests interchanging + and ×. Now × becomes + between 6 and 5, and + becomes × between 5 and 20. The expression becomes 12 - 6 + 5 × 20 ÷ 4. Step 6: Evaluate option B: 5 × 20 = 100 and 100 ÷ 4 = 25. The expression simplifies to 12 - 6 + 25 = 6 + 25 = 31. Step 7: Since this equals 31, option B works. We do not need to test the remaining options for equality, though they can be checked to confirm they fail.

Verification / Alternative check:
To verify, we may also check quickly that options C and D do not produce 31. Changing - and + only rearranges addition and subtraction signs and cannot correct the large negative result fully. Swapping ÷ and × similarly yields different products and quotients but does not hit 31 exactly. Therefore, only swapping the plus and multiplication symbols leads to the accurate evaluation, confirming that option B is unique and correct.

Why Other Options Are Wrong:
When testing option A, the result is 14.5. Option C yields a different integer but not 31, and option D also fails to reach 31 after applying proper precedence. In each of these cases, numerical evaluation directly exposes the discrepancy from the target value, so they must be rejected.

Common Pitfalls:
Some candidates forget to apply precedence after swapping operators and instead compute strictly from left to right. Others might misinterpret "interchange" as changing only one occurrence of a sign instead of both. It is important to alter every instance of the two specified operators in the expression and then recompute using the usual arithmetic rules.

Final Answer:
The equation becomes correct when the plus and multiplication signs are interchanged, so the required pair of signs is + and ×.