Analyzing the Numerical Relation Problem

The question asks us to identify the logic connecting pairs of numbers and then apply that same logic to a third number to find its related counterpart. We are given two examples:

• 15 is related to 29
• 22 is related to 43

We need to find the number related to 35 using the identical logic.

Identifying the Logic in Numerical Relations

Let's examine the relationship between the first pair, 15 and 29.

We can try common arithmetic operations. How can we get from 15 to 29?

• Addition: $15 + x = 29 \implies x = 29 - 15 = 14$. So, the logic could be adding 14.
• Multiplication: $15 \times x$ is unlikely to directly give 29 as 29 is not a multiple of 15. However, we could multiply and then add or subtract.
  • Maybe multiplying by a small integer? Let's try multiplying by 2: $15 \times 2 = 30$. This is close to 29. If we subtract 1 from 30, we get 29. So, the potential logic is multiplying by 2 and subtracting 1.

Testing the Identified Pattern with the Second Pair

Let's test the potential logic (multiply by 2, then subtract 1) on the second pair, 22 and 43.

According to the logic, if we start with 22, we should perform the operation:

$22 \times 2 - 1$

Calculation:

• $22 \times 2 = 44$
• $44 - 1 = 43$

The result 43 matches the number given as related to 22. This confirms that the logic "multiply by 2 and subtract 1" is the correct pattern for this problem.

Applying the Logic to Find the Related Number for 35

Now that we have established the consistent logic, we apply it to the number 35 to find its related number.

Using the logic "multiply by 2 and subtract 1":

$35 \times 2 - 1$

Calculation:

• First, multiply 35 by 2: $35 \times 2 = 70$
• Next, subtract 1 from the result: $70 - 1 = 69$

So, following the same logic, 35 is related to 69.

Checking Options and Final Answer

We compare our calculated result, 69, with the provided options:

Our calculated value, 69, matches Option 2.

Revision Table: Key Concepts

Additional Information: Types of Number Logic Problems

Numerical relation problems often involve finding patterns based on various mathematical operations. Some common types of logic include:

• Simple arithmetic operations (addition, subtraction, multiplication, division).
• Combinations of operations (e.g., multiply and add, divide and subtract).
• Squaring or cubing numbers.
• Working with number properties (e.g., prime numbers, odd/even numbers).
• Positional value operations in multi-digit numbers.

Solving these problems requires systematic testing of different possibilities and verifying the consistency of the potential logic across all given examples.