Question Type: Arithmetic Reasoning

Step-by-step Solution:

The given equation is: \(56 - 74 \times 17 + 391 \div 23 = 1297\)

Let's evaluate the equation using the standard order of operations (BODMAS/PEMDAS):

1. Division: \(391 \div 23 = 17\)
2. Multiplication: \(74 \times 17 = 1258\)
3. Subtraction and Addition: \(56 - 1258 + 17 = -1185\)

The result is -1185, which is not equal to 1297. We need to interchange two signs to make the equation correct.

Let's try interchanging the '+' and '-' signs:

\(56 + 74 \times 17 - 391 \div 23 = ?\)

1. Division: \(391 \div 23 = 17\)
2. Multiplication: \(74 \times 17 = 1258\)
3. Addition and Subtraction: \(56 + 1258 - 17 = 1297\)

The equation now holds true: \(1297 = 1297\)

Why other options are incorrect:

• Option 1 (\(\div\) and \(\times\)): Interchanging these would significantly alter the result and not lead to 1297.
• Option 3 (\(\times\) and \(-)\): This would result in a large negative number.
• Option 4 (\(\div\) and +): This would also result in a value far from 1297.

Core Logic/Pattern: The core logic is to systematically try interchanging the arithmetic operators to find a combination that satisfies the equation. The order of operations must be carefully followed.

Therefore, the correct answer is to interchange the '+' and '-' signs.