In a certain coding pattern, the operator "@" acts on two numbers in such a way that 15@7 = 44, 5@4 = 18, and 6@17 = 46. Using the same hidden rule, what is the value of 17@4?

Introduction / Context:
This verbal reasoning question tests your ability to identify a hidden numerical pattern expressed through a special operator symbol. Instead of using the familiar arithmetic operators like plus or minus, the expression uses the symbol "@", and you must decode the rule from the given examples. Such questions are very common in coding decoding and arithmetic reasoning sections of competitive exams.

Given Data / Assumptions:
- The operator "@" connects two numbers using a consistent rule.
- We are told that 15@7 = 44, 5@4 = 18, and 6@17 = 46.
- We must use the same rule to find the value of 17@4.
- All calculations are assumed to follow normal arithmetic on whole numbers.

Concept / Approach:
The key idea is to look for a simple and consistent relationship between the two input numbers and the output. Common patterns include addition, subtraction, multiplication, division, or combinations such as 2 * (a + b), a + 2b, or similar forms. We test different patterns on all given examples and accept only the rule that works perfectly for each pair. Once identified, we apply that rule to the required pair 17 and 4.

Step-by-Step Solution:
Step 1: Check a simple sum: 15 + 7 = 22, but the result given is 44, which is exactly 2 * 22. Step 2: Test the same rule on the second example: 5 + 4 = 9. Then 2 * (5 + 4) = 2 * 9 = 18, which matches the given 18. Step 3: Test the rule on the third example: 6 + 17 = 23. Then 2 * (6 + 17) = 2 * 23 = 46, which matches the given 46. Step 4: Therefore, the rule is: a@b = 2 * (a + b). Step 5: Apply the rule to 17@4: 17 + 4 = 21, then 2 * 21 = 42.

Verification / Alternative check:
We have verified the rule against all three examples. Each pair of numbers follows the pattern a@b = 2 * (a + b) without any contradiction. Because three consistent examples support the same rule, it is highly reliable to apply this rule to 17 and 4. No other simple pattern such as a + 2b or 2a + b fits all examples so neatly.

Why Other Options Are Wrong:
- Option 36 would require 2 * (17 + 4) to be 36, but that would mean 2 * 21 = 36, which is incorrect.
- Option 40 suggests a different pattern, but 2 * (17 + 4) is not 40, so it does not follow the deduced rule.
- Option 49 does not arise from any simple combination of 17 and 4 that also matches the earlier examples, so it is inconsistent with the pattern.

Common Pitfalls:
Students often try patterns like a + b, a * b, or a + 2b and may abandon the problem too quickly if these first guesses do not work. Another mistake is to find a rule that fits only one or two examples but not all of them. Always verify your pattern against every given equation before using it to find the unknown value.

Final Answer:
Using the rule a@b = 2 * (a + b), we get 17@4 = 2 * (17 + 4) = 42. Therefore, the correct answer is 42.