Question

3) \$(3 \\# 4),(3 \\# 4) \$(4 \$ 4)]\( is equal to : (a) 1234 (b) 1236 (c) 1335 (d) none of these # \)\operatorname{Max}[(2 \\# 3) \$(3 \\# 4),(3 \\# 4) \$(4 \$ 4)]$ is equal to : (a) 1234 (b) 1236 (c) 1335 (d) none of these

Short answer

Answer: (d) none of these

Step-by-step solution

Define the Operators

In this problem, we are given two operators: "\(\\#\)" and "$\$$". The "\(\\#\)" operator is defined as the concatenation of two numbers. For example, \(2 \\# 3 = 23\). The "\(\$$" operator is defined as the addition of two numbers. For example, \)2 \$ 3 = 5$.

Apply the Operators to the Given Expression

Now that we understand the operators, let's apply them to the given expression: (2 \(\\#\) 3) \(\\_\) (3 \(\\#\) 4),(3 \(\\#\) 4) \(\\_\) (4 $\\$ 4) Using the "\(\\#\)" operator: 23 \(\\_\) 34, 34 \(\\_\) (4 $\\$ 4) Using the "$\$$" operator: 57, 34 \(\\_\) 8

Simplify the Expression

Now, let's simplify the expression further: 57, 42

Determine the Maximum Value

Now that we have the simplified expression, we need to find the maximum value: \(\operatorname{Max}(57, 42) = 57\)

Compare the Maximum Value to the Given Options

Now let's compare the maximum value obtained to the given options: (a) 1234 (b) 1236 (c) 1335 (d) none of these Since the maximum value we obtained (57) is not equal to any of the given options (a), (b), or (c), the correct answer is (d) none of these.

Key concepts

Mathematical Operators

Mathematical operators are symbols or words used to denote an operation between numbers or variables. These operators serve as instructions to perform specific mathematical processes. For instance, in this exercise, we are introduced to custom operators: "\#" and "\\(".

Here's a breakdown of each operator as defined in this problem:

• The "\#" operator instructs us to concatenate two numerical values. For instance, concatenating 3 and 4 results in 34.


• The "\\)" operator represents addition, meaning the sum of two numbers. Thus, for numbers 3 and 4, applying the "\$" operation results in 7.

Understanding these operators is crucial as they dictate the processes you follow to solve the problem. Knowing the function of each symbol or term enables clear and logical steps in any calculation.

Problem Solving

Problem solving in mathematics involves understanding the problem, applying relevant operations, and simplifying the expression to reach a solution.

In our exercise, the problem-solving process unfolds as follows:

• Understand the Problem: Become familiar with the custom operators \# and \\(, knowing that they denote concatenation and addition respectively.


• Apply the Operations: Begin by using the \# operator: concatenate 2 and 3 to form 23, and 3 and 4 to create 34. Next, apply the \\) operator, adding numbers as needed.


• Simplify the Expressions: Follow the properly defined operations to reduce complex expressions, like resulting in 57 and 42 from the given problem.

Each step is vital to navigating the problem correctly and efficiently. This structured approach aids in comprehending not only this specific mathematical problem but also allows tackling more complex tasks.

Maximization in Mathematics

Maximization in mathematics refers to finding the largest possible value within a set or expression. It's often a target operation, especially in problems asking for the 'maximum' value among numbers.

In this particular task, after evaluating and simplifying the expression using given operators, we found ourselves comparing two values: 57 and 42.

• Identify Available Values: After simplification, pick the values calculated in the expression.


• Compare Values: Evaluate which among these holds the highest value; in simple numeric terms, 57 surpasses 42.

With 57 recognized as the larger number here, it becomes integral to the final answer determination. While this value doesn't match any of the provided options, understanding maximization's role is crucial in making conclusions about any numeric comparison or decision-making task in mathematics.