A custom operation is defined so that 3 @ 3 * 3 = 3 and 48 @ 4 * 3 = 36. Using the same rule, what is the value of 91 @ 13 * 2?

Introduction / Context:
This is a compound custom operation question where the expression a @ b * c is evaluated according to a hidden rule. Two examples are given and you must find the result for a third expression. The goal is to discover how @ and * combine or what overall formula maps the three numbers to the given outputs. This type of problem is common in reasoning sections to test pattern recognition in arithmetic operations.

Given Data / Assumptions:

• 3 @ 3 * 3 = 3.
• 48 @ 4 * 3 = 36.
• We must evaluate 91 @ 13 * 2 using the same rule.
• The entire expression "a @ b * c" is treated as a single combined operation with a consistent underlying formula.

Concept / Approach:
We suspect that the operation "a @ b * c" corresponds to some simple combination of division and multiplication because the second example 48 @ 4 * 3 yields 36, which is also the value of (48 / 4) * 3. We test whether this rule also works for the first example and then apply it to the third expression. Once we have a consistent formula, we can confidently calculate the required value.

Step-by-Step Solution:
Step 1: Consider the second example: 48 @ 4 * 3 = 36. Step 2: Compute (48 / 4) * 3 = 12 * 3 = 36, which matches the given result. Step 3: Hypothesis: a @ b * c means (a / b) * c. Step 4: Check with the first example: 3 @ 3 * 3 should equal (3 / 3) * 3 = 1 * 3 = 3, which matches the given 3. Step 5: Since the rule holds for both examples, accept a @ b * c = (a / b) * c. Step 6: Now evaluate 91 @ 13 * 2: (91 / 13) * 2. Step 7: Compute 91 / 13 = 7. Step 8: Multiply by 2: 7 * 2 = 14.

Verification / Alternative check:
There is no simpler or alternative rule that satisfies both provided examples as neatly as (a / b) * c. For instance, a + b * c or a * b / c do not yield the given results simultaneously. Using (a / b) * c gives exactly 3 and 36 for the two examples, which is strong evidence in favour of this rule. Applying the same rule to 91, 13, and 2 yields 14, so we accept this as the correct answer.

Why Other Options Are Wrong:
Under the established rule, the result must be 14. Options A (4), B (8), C (10), and E (6) do not match the calculation (91 / 13) * 2 and therefore violate the operation definition that holds for all given examples. Since reasoning questions require a single consistent rule, any answer that breaks that rule is invalid.

Common Pitfalls:
A common mistake is to treat @ and * separately with arbitrary meanings or to guess a rule from only one example without verifying it against the second. Another error is miscalculating 91 / 13, which can lead to an incorrect final result. Always validate your assumed rule with all given expressions before applying it to the new one, and carefully perform the division and multiplication steps.

Final Answer:
Therefore, using the rule a @ b * c = (a / b) * c, we get 91 @ 13 * 2 = 14.