This question is a logic puzzle where symbols 'C' and 'D' represent mathematical operations. We are given two equations and need to determine the operations to solve a third expression.

Analyzing the Logic Puzzle Equations

We are given the following equations:

1. $34 \text{ C } 59 \text{ D } 16 = -9$
2. $61 \text{ C } 32 \text{ D } 14 = 43$

We need to find the operations that 'C' and 'D' represent from standard mathematical operations like addition (+), subtraction (-), multiplication (×), or division (÷).

Identifying the Operations for C and D

Let's test simple combinations of operations for C and D using the first equation: $34 \text{ C } 59 \text{ D } 16 = -9$.

• If C is '+' and D is '-': $34 + 59 - 16 = 93 - 16 = 77$. This is not -9.
• If C is '+' and D is '+': $34 + 59 + 16 = 109$. This is not -9.
• If C is '-' and D is '+': $34 - 59 + 16 = -25 + 16 = -9$. This matches the result of the first equation!

This suggests that C represents subtraction (-) and D represents addition (+). Let's verify this hypothesis using the second equation: $61 \text{ C } 32 \text{ D } 14 = 43$.

Applying C as '-' and D as '+':

$61 - 32 + 14 = 29 + 14 = 43$.

This also matches the result of the second equation. Therefore, the operations are:

• C = Subtraction (-)
• D = Addition (+)

Solving the Target Expression

Now that we have identified the operations, we can solve the expression $58 \text{ C } 7 \text{ D } 11$.

Replace 'C' with '-' and 'D' with '+':

$58 - 7 + 11$

Perform the calculation step-by-step:

1. First, perform the subtraction: $58 - 7 = 51$
2. Next, perform the addition: $51 + 11 = 62$

The value of the expression $58 \text{ C } 7 \text{ D } 11$ is 62.

Comparing with Options

The calculated value is 62. Let's compare this with the given options:

• Option 1: 62
• Option 2: 64
• Option 3: 63
• Option 4: 59

The result 62 matches Option 1.

Revision Table: Logic Puzzle Operations

Additional Information: Solving Symbolic Logic Puzzles

Symbolic logic puzzles like this one require deductive reasoning to figure out the meaning of unknown symbols or operators based on given examples. Here are some tips for solving such puzzles:

• Analyze Given Equations: Carefully look at the input numbers and the output result in each given equation.
• Test Basic Operations: Start by testing simple arithmetic operations (+, -, ×, ÷) in place of the symbols.
• Consider Order of Operations: Remember the standard order of operations (BODMAS/PEMDAS), although in simple puzzles like this, operations are often performed left to right unless parentheses are implied by the symbols' positions. In this case, C and D are binary operators applied sequentially.
• Verify Hypothesis: Once you find a set of operations that works for one equation, test it against all other given equations to confirm your hypothesis.
• Apply to Target: Only after confirming the operations, apply them to the expression you need to evaluate.

These types of questions test your pattern recognition and logical deduction skills.