Finding the Number Relation Pattern in Sets

The question asks us to identify the relationship between the numbers in the given sets, (12, 5, 29) and (19, 12, 50), and then find the option set that follows the same rule. We are told to treat the numbers as whole units, not breaking them down into individual digits.

Analysing the Given Number Sets

Let's look at the first set: (12, 5, 29). Let the numbers be A, B, and C respectively.

• A = 12
• B = 5
• C = 29

We need to find a mathematical operation or combination of operations involving A and B that results in C.

• Perhaps a combination of multiplication and addition/subtraction?
• Let's try multiplying A by a small number and adding or subtracting B or a multiple of B.
• If we try $A \times 2$: $12 \times 2 = 24$. To get 29, we need to add 5. Coincidentally, B is 5.
• This suggests a potential pattern: $A \times 2 + B = C$. Let's write this as $A \times 2 + B \times 1 = C$.

Now, let's test this potential pattern with the second set: (19, 12, 50). Here, A = 19, B = 12, and C = 50.

• Applying the pattern $A \times 2 + B \times 1 = C$:
• $19 \times 2 + 12 \times 1 = 38 + 12 = 50$.

The pattern $A \times 2 + B \times 1 = C$ holds true for both given sets.

Applying the Pattern to the Options

Now we will test each option set to see which one follows the pattern $A \times 2 + B \times 1 = C$.

Option 1: (8, 15, 21)

• A = 8, B = 15, C = 21
• Check the pattern: $A \times 2 + B \times 1 = 8 \times 2 + 15 \times 1 = 16 + 15 = 31$.
• The result 31 is not equal to C (21). So, this option does not follow the pattern.

Option 2: (16, 12, 34)

• A = 16, B = 12, C = 34
• Check the pattern: $A \times 2 + B \times 1 = 16 \times 2 + 12 \times 1 = 32 + 12 = 44$.
• The result 44 is not equal to C (34). So, this option does not follow the pattern.

Option 3: (15, 14, 44)

• A = 15, B = 14, C = 44
• Check the pattern: $A \times 2 + B \times 1 = 15 \times 2 + 14 \times 1 = 30 + 14 = 44$.
• The result 44 is equal to C (44). So, this option follows the pattern.

Option 4: (17, 11, 55)

• A = 17, B = 11, C = 55
• Check the pattern: $A \times 2 + B \times 1 = 17 \times 2 + 11 \times 1 = 34 + 11 = 45$.
• The result 45 is not equal to C (55). So, this option does not follow the pattern.

Based on the analysis, only Option 3 follows the number relation pattern identified in the given sets.

Conclusion on Set Relation

The pattern $A \times 2 + B \times 1 = C$ correctly describes the relationship between the numbers in the given sets. Option (15, 14, 44) is the only set among the options that follows this exact same number relation logic.

Revision Table: Key Concepts

Additional Information: Solving Number Analogy Questions

Number analogy questions test your ability to find patterns and apply them. Here are some tips:

• Look for simple operations first: Addition, subtraction, multiplication, division.
• Consider combinations: $A \times k \pm B$, $A \pm B \times k$, $A \times k_1 \pm B \times k_2$, etc., where k is a constant.
• Think about squares or cubes: $A^2 \pm B$, $A^2 \pm B^2$, etc.
• Look at the relationship between the first two numbers, the last two, or the first and last.
• Test your assumed pattern on all given sets (if more than one) before checking options.
• Carefully read any specific instructions, like the rule about using whole numbers as given in this question.

Practice with various types of number relation problems helps improve pattern recognition skills.