In the following expression, each question mark must be replaced by one mathematical operator so that the entire inequality becomes correct: 27 ? 9 ? 18 ? 24 ? 12. Which of the following sets of operators, when placed in order in the blanks from left to right, makes the expression true?

Introduction / Context:
This problem asks you to choose a sequence of standard arithmetic operators that will make a given expression correct. The expression contains four blanks, each to be filled with one operator from the chosen option. Some options use equality, others use inequality signs like greater than or less than. The question tests how well you can apply operator precedence and compare the values of expressions on different sides of a relational symbol such as > or <.

Given Data / Assumptions:

• Base expression with blanks: 27 ? 9 ? 18 ? 24 ? 12.
• Each option gives four operators to insert from left to right.
• Option A: ÷, +, = and +.
• Option B: ÷, x, < and +.
• Option C: ÷, x, > and +.
• Option D: +, ÷, = and ÷.
• Standard operator precedence (multiplication and division before addition) applies once operators are inserted.

Concept / Approach:
The strategy is to test each option by inserting its operators into the blanks and then simplifying the resulting expression. Because some options use equality and others use inequality, we must calculate the left and right sides of any relation and check whether the relation holds. Rather than doing complex algebra, we simply follow arithmetic rules carefully. The correct option will be the one where the entire statement is true. If more than one looks possible, rechecking calculations usually reveals where a mistake has occurred.

Step-by-Step Solution:
Step 1: Test option C because it uses both ÷ and x, which seem natural candidates. Inserting these gives 27 ÷ 9 x 18 > 24 + 12. Step 2: Evaluate the left side with precedence. First compute 27 ÷ 9 = 3. Step 3: Next compute 3 x 18 = 54. So the left side is 54. Step 4: Now evaluate the right side: 24 + 12 = 36. Step 5: Compare the two sides: 54 > 36 is a true statement. Step 6: Therefore, option C produces a correct inequality. Step 7: Briefly check that the other options fail. For example, option B would give 27 ÷ 9 x 18 < 24 + 12, which simplifies to 54 < 36, a false statement. Step 8: Option A results in 27 ÷ 9 + 18 = 24 + 12, or 3 + 18 = 36, that is 21 = 36, which is false. Step 9: Option D gives 27 + 9 ÷ 18 = 24 ÷ 12, or 27 + 0.5 = 2, which is 27.5 = 2, again false.

Verification / Alternative check:
Once option C is shown to work, it is good practice to double check the arithmetic. Recomputing 27 ÷ 9 as 3, then 3 x 18 as 54, and 24 + 12 as 36, again confirms that 54 is greater than 36. Since none of the other options produce a true equality or inequality, option C is uniquely correct. There is no hidden trick or additional rule beyond ordinary arithmetic precedence here.

Why Other Options Are Wrong:
Option A fails because the two sides of the equality are 21 and 36, which are not equal. Option B fails because 54 is not less than 36. Option D fails because 27.5 is not equal to 2. These incorrect options highlight the importance of applying precedence rules correctly and not simply inserting operators that look appealing without checking the resulting statement thoroughly.

Common Pitfalls:
A frequent pitfall is evaluating from left to right without giving priority to multiplication and division. For instance, if someone treated 27 ÷ 9 x 18 as (27 ÷ 9) x 18 they are actually still applying correct precedence, but mistakenly doing 27 ÷ (9 x 18) would give a wrong result. Another common mistake is misreading the inequality signs and assuming < when > is required. Carefully rewriting each candidate expression and simplifying step by step helps avoid these issues.

Final Answer:
The set of operators that makes the expression correct is ÷, x, > and + (option C).