The following arithmetic equation is incorrect. Which two operation signs must be interchanged to make the statement 18 + 26 - 25 × 10 ÷ 5 = 42 true?

Introduction / Context:
This verbal reasoning question tests your understanding of arithmetic operations and operator precedence. You are told that the equation 18 + 26 - 25 × 10 ÷ 5 = 42 is incorrect and must decide which two operation signs should be interchanged so that the equation becomes a correct numerical statement. Problems like this commonly appear in competitive exams to check whether candidates can systematically test possibilities rather than guess.

Given Data / Assumptions:

• Given expression: 18 + 26 - 25 × 10 ÷ 5.
• We must interchange exactly two signs among +, -, × and ÷.
• Standard operator precedence applies: multiplication and division before addition and subtraction.
• The final value after the interchange must become 42.

Concept / Approach:
The key idea is to first evaluate the original expression with normal precedence to see how far it is from 42, then test the suggested interchanges from the options. Since only two signs are interchanged at a time, we can systematically substitute each pair and re-evaluate. This trial and improvement method is efficient when there are only a few given options.

Step-by-Step Solution:
Step 1: Evaluate the original expression: 18 + 26 - 25 × 10 ÷ 5.Step 2: Compute multiplication and division first: 25 × 10 = 250, then 250 ÷ 5 = 50.Step 3: Now we have 18 + 26 - 50 = 44 - 50 = -6, which is clearly not 42.Step 4: Test the pair "- and +" interchanged: replace every + with - and every - with +, giving 18 - 26 + 25 × 10 ÷ 5.Step 5: Evaluate this new expression: 25 × 10 ÷ 5 = 250 ÷ 5 = 50; then 18 - 26 + 50 = -8 + 50 = 42, which matches the required result.

Verification / Alternative check:
We can briefly check another option, for example interchanging ÷ and ×. That would produce 18 + 26 - 25 ÷ 10 × 5, which simplifies to 18 + 26 - 12.5 = 31.5, not 42. Similar checks show that no other interchange gives 42. Thus the only successful swap is between the plus and minus signs.

Why Other Options Are Wrong:

• + and ÷: leads to a different value, not 42.
• ÷ and x: also fails to yield 42 when the expression is evaluated.
• x and -: still does not give the target value.
• ÷ and -: again results in an incorrect total.

Common Pitfalls:
Candidates often ignore operator precedence and compute strictly from left to right, which gives wrong intermediate values. Another common mistake is to interchange signs only at one place instead of at all occurrences. It is important to apply each interchange globally across the expression and then evaluate using correct arithmetic rules.

Final Answer:
To make the equation correct, the plus and minus signs must be interchanged, so the correct pair is "- and +".