In a particular numerical code, the expression 4 x 9 is equal to 25 and 7 x 4 is equal to 53. Using the same hidden rule or pattern, what should be the coded value of 9 x 4?

Introduction / Context:
This verbal reasoning question belongs to the coding pattern type, where numbers in an expression do not give the usual product but are transformed according to a hidden rule. The task is to discover that rule from the given examples and then apply it correctly to a new pair of numbers to get the required coded result.

Given Data / Assumptions:

• According to the code, 4 x 9 is written as 25.
• According to the same code, 7 x 4 is written as 53.
• We must find the coded value of 9 x 4.
• The symbol x in this context is part of the coding notation and does not necessarily mean ordinary multiplication.
• The rule must be consistent for all the given examples.

Concept / Approach:
To solve such pattern questions, we check simple operations like sums, differences, squares and combinations of these applied to the numbers on the left hand side. By comparing 4 and 9 leading to 25 and 7 and 4 leading to 53, we attempt to find a common rule that fits both. Once a rule is identified, we generalize it and then apply it to the new case 9 x 4.

Step-by-Step Solution:
Step 1: For 4 x 9, try the expression 4^2 + 9. Calculate 4^2 = 16, then 16 + 9 = 25. This matches the coded result.Step 2: For 7 x 4, test the same rule. Compute 7^2 = 49, then 49 + 4 = 53, which matches the second coded result.Step 3: Since both examples fit the rule value = first number squared plus second number, this pattern is most likely correct.Step 4: Apply the rule to 9 x 4. First compute 9^2 = 81.Step 5: Now add the second number: 81 + 4 = 85.Step 6: Therefore, in this code, 9 x 4 should be written as 85.

Verification / Alternative check:
To verify, you can test whether any simpler alternative rule, such as adding or multiplying the digits or reversing the numbers, could explain both given examples. None of those simple attempts produce 25 from 4 and 9 and 53 from 7 and 4 simultaneously. The rule first number squared plus second number remains the only consistent pattern, increasing confidence that 85 is the correct coded value for 9 x 4.

Why Other Options Are Wrong:
The option 81 is simply 9^2 and ignores the addition of the second number. The option 83 would correspond to adding 2 instead of 4, which does not match the established pattern. The option 88 does not fit any natural rule derived from the earlier equations. The option 89 similarly lacks justification from the given data. Only 85 follows the same transformation that converts 4 x 9 to 25 and 7 x 4 to 53.

Common Pitfalls:
Students may wrongly assume that x stands for multiplication and immediately compute 4 x 9 = 36 or 7 x 4 = 28 and then try to force a connection. Others may focus on the sum of digits or other unrelated patterns. Another common error is to find a rule that fits only one of the examples but not both. Always ensure that the discovered pattern works consistently for all given cases.

Final Answer:
Using the same rule that maps 4 x 9 to 25 and 7 x 4 to 53, the value of 9 x 4 is 85.