The question asks us to find the number that is related to the third number (13) in the same way that the second number (441) is related to the first number (22).

We need to identify the relationship or pattern between the first pair of numbers, 22 and 441. Once we find this relationship, we will apply the same rule to the third number, 13, to find the missing fourth number.

Finding the Relationship in Number Analogy

Let's look at the numbers 22 and 441. We need to think about common mathematical operations or patterns that might connect them.

• Could it be addition, subtraction, multiplication, or division? These simple operations don't directly give 441 from 22.
• Let's consider squares or cubes.
  • The square of 22 is $22^2 = 484$. This is close to 441, but not exactly.
  • Let's look at numbers close to 22. What about 21 or 23?
  • The square of 21 is $21^2 = 441$. This matches the second number exactly.

So, the relationship seems to be that the second number is the square of the number that is one less than the first number. In mathematical terms, if the first number is $N$, the second number is $(N-1)^2$.

Applying the Relationship to the Third Number

Now, we apply this same relationship to the third number, which is 13.

According to the pattern, the missing fourth number should be the square of the number that is one less than the third number (13).

Third number = 13

Number one less than the third number = $13 - 1 = 12$

The missing number is the square of 12.

Calculation: $12^2 = 12 \times 12 = 144$.

Conclusion

The relationship between 22 and 441 is $(22-1)^2 = 21^2 = 441$. Applying the same logic to 13, we get $(13-1)^2 = 12^2 = 144$.

Therefore, the missing number in the analogy 22 : 441 :: 13 : ? is 144.

Number Analogy Revision Table

Additional Information on Number Relationships

Number analogy questions test your ability to find patterns and relationships between numbers. Common relationships include:

• Basic arithmetic operations (addition, subtraction, multiplication, division).
• Squares, cubes, or other powers.
• Square roots or cube roots.
• Operations involving digits of the number (e.g., sum of digits, product of digits).
• Prime numbers, composite numbers.
• Even or odd numbers.
• Consecutive numbers.
• Combinations of the above operations.

Solving these types of questions requires practice in observing numbers and testing potential relationships quickly.