In a certain mathematical code, 13 # 9 is equal to 94 and 18 # 7 is equal to 100. Using the same hidden operation for the symbol #, what is the value of 24 # 6?

Introduction / Context:
Here the symbol # represents a special arithmetic operation that combines two numbers in a fixed way. We are given two examples and asked to extend the same pattern to a new pair of numbers. This tests pattern recognition and algebraic reasoning in coded operations.

Given Data / Assumptions:

• 13 # 9 = 94.
• 18 # 7 = 100.
• We must find 24 # 6.
• The operation # is the same in all three expressions.

Concept / Approach:
A common type of coded operation is of the form a # b = a * b minus or plus some function of a and b. We try a simple pattern: multiply the two numbers and then subtract the sum of the operands plus 1. If this rule fits both given examples exactly, we can safely apply it to 24 and 6 to get the required value.

Step-by-Step Solution:
Assume a # b = a * b − (a + b + 1). Test this rule with 13 # 9. Compute 13 * 9 = 117. Compute a + b + 1 = 13 + 9 + 1 = 23. Then 117 − 23 = 94, which matches the given value. Now test the same rule with 18 # 7. Compute 18 * 7 = 126. Compute a + b + 1 = 18 + 7 + 1 = 26. Then 126 − 26 = 100, which again matches the given value. Since the formula fits both examples, use it for 24 # 6. Compute 24 * 6 = 144. Compute a + b + 1 = 24 + 6 + 1 = 31. Therefore 24 # 6 = 144 − 31 = 113.

Verification / Alternative check:
We can verify that the rule always produces reasonable integers and is symmetric in a and b: swapping the operands does not change the result because multiplication and addition are both commutative. Both given cases perfectly match the rule, which gives us confidence in applying it to the third case.

Why Other Options Are Wrong:
Using the same formula, we do not obtain 121, 148 or 115. Those values would require different operations that do not simultaneously satisfy the conditions for both 13 # 9 and 18 # 7, so they are inconsistent with the provided examples.

Common Pitfalls:
Students sometimes guess based only on one example or use unrelated operations for each expression. In coded operations, it is essential to check that a single, simple rule works for all given cases before applying it more widely.

Final Answer:
Using the same coded rule, the value of 24 # 6 is 113.