The question asks us to identify a set of numbers from the options that shares the same relationship as the given sets: (9, 18, 324) and (14, 11, 308). The rule states that operations must be performed on the whole numbers themselves, not their individual digits.

Analyzing the Relationship in the Given Sets

Let's examine the numbers in the first given set: (9, 18, 324).

• First number: 9
• Second number: 18
• Third number: 324

We need to find a mathematical relationship between these numbers. Let's try common operations:

• Sum of the first two: $9 + 18 = 27$. Is 27 related to 324? $324 / 27 = 12$. So, $(9+18) \times 12 = 324$. This factor of 12 seems arbitrary.
• Product of the first two: $9 \times 18 = 162$. Is 162 related to 324? $162 \times 2 = 324$. This looks promising. Let's see if this rule holds for the second set.

Now let's examine the second given set: (14, 11, 308).

• First number: 14
• Second number: 11
• Third number: 308

Let's apply the potential rule we found: Third number = (First number $\times$ Second number) $\times$ 2.

Calculate (First number $\times$ Second number) $\times$ 2:

$(14 \times 11) \times 2 = 154 \times 2 = 308$.

This matches the third number in the set (14, 11, 308). So, the relationship is indeed: Third number = (First number $\times$ Second number) $\times$ 2.

Applying the Relationship to the Options

Now we will apply this rule to each of the given options to see which one follows the same pattern.

Option 1: (7, 12, 168)

• First number: 7
• Second number: 12
• Third number: 168

Calculate (First number $\times$ Second number) $\times$ 2:

$(7 \times 12) \times 2 = 84 \times 2 = 168$.

The calculated value (168) matches the third number in the set (168). This option follows the relationship.

Option 2: (14, 15, 320)

• First number: 14
• Second number: 15
• Third number: 320

Calculate (First number $\times$ Second number) $\times$ 2:

$(14 \times 15) \times 2 = 210 \times 2 = 420$.

The calculated value (420) does not match the third number in the set (320). This option does not follow the relationship.

Option 3: (8, 13, 206)

• First number: 8
• Second number: 13
• Third number: 206

Calculate (First number $\times$ Second number) $\times$ 2:

$(8 \times 13) \times 2 = 104 \times 2 = 208$.

The calculated value (208) does not match the third number in the set (206). This option does not follow the relationship.

Option 4: (11, 12, 268)

• First number: 11
• Second number: 12
• Third number: 268

Calculate (First number $\times$ Second number) $\times$ 2:

$(11 \times 12) \times 2 = 132 \times 2 = 264$.

The calculated value (264) does not match the third number in the set (268). This option does not follow the relationship.

Conclusion

Based on our analysis, only the set in Option 1, (7, 12, 168), follows the same mathematical relationship where the third number is equal to twice the product of the first two numbers.

Let's summarize the check:

Revision Table: Number Analogy Concepts

Additional Information: Solving Number Series and Analogies

Number analogy questions are a common type in reasoning tests. They require you to observe the relationship within a given set of numbers and apply that relationship to other sets. Here are some tips for solving such problems:

• Examine the Given Sets Carefully: Look for patterns involving addition, subtraction, multiplication, division, squaring, cubing, square roots, cube roots, or combinations of these operations.
• Focus on Pairs or Triples: The relationship might be between the first two numbers, the last two, or all three.
• Test Potential Rules: Once you think you've found a rule based on the first given set, immediately test it on the second given set (if provided) to confirm its validity.
• Apply the Rule to Options: Work through each option, applying the established rule to see which one fits.
• Consider Multiple Steps: Sometimes the relationship involves more than one step, like multiplying two numbers and then adding or subtracting another value, or multiplying by a constant factor.
• Check Constraints: Always pay attention to any specific instructions, like the one in this problem about not breaking down numbers into digits.

Practicing different types of number analogy problems helps in quickly identifying common patterns and relationships.