Solving the Number Analogy: Finding the Related Pair

This question asks us to identify the relationship between the first pair of numbers and then apply that same relationship to find the missing number in the second pair. The given analogy is 15 : 256 :: 18 : ?

We need to find the pattern connecting 15 and 256. Once we understand this pattern, we can use it to find the number related to 18.

Analyzing the First Number Pair: 15 and 256

Let's look at the relationship between 15 and 256. We can try different mathematical operations:

• Is 256 a multiple of 15? \(256 \div 15\) is not an integer.
• Is there a simple addition or subtraction? \(256 - 15 = 241\).
• What about squaring? \(15^2 = 15 \times 15 = 225\). This is close to 256. The difference is \(256 - 225 = 31\).
• Let's consider operations involving the number 15. What if we add or subtract a small number from 15 before squaring?
• Let's try adding 1 to 15: \(15 + 1 = 16\). Now let's square 16: \(16^2 = 16 \times 16\).

Calculating \(16^2\):

We can calculate \(16^2\) as follows:

So, we found the relationship: The second number is the square of the first number plus one. That is, \(256 = (15 + 1)^2\).

The pattern appears to be \((\text{First Number} + 1)^2 = \text{Second Number}\).

Applying the Pattern to the Second Pair: 18 and ?

Now, we apply the same pattern to the second pair. The first number is 18. The pattern is \((\text{First Number} + 1)^2\).

So, the missing number is \( (18 + 1)^2 \).

This means we need to calculate \(19^2\).

Calculating \(19^2\):

We can calculate \(19^2\) as follows:

Alternatively:

So, the missing number is 361.

Checking the Options

Let's compare our result with the given options:

• Option 1: 360
• Option 2: 361
• Option 3: 261
• Option 4: 461

Our calculated number, 361, matches Option 2.

Conclusion

The relationship between the numbers in the analogy is that the second number is the square of the first number plus one. Applying this pattern to the second pair, we find that the missing number is 361.

The related number pair is 18 : 361.

Number Analogy Revision Table

Additional Information on Number Analogies and Patterns

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

• Arithmetic Operations: Addition, subtraction, multiplication, division.
• Squaring and Cubing: Numbers might be squares or cubes, or operations might involve squares or cubes of the given numbers.
• Operations with Constants: Adding, subtracting, multiplying, or dividing by a fixed number.
• Operations with Modifications: Operations involving (number + 1), (number - 1), (number/2), etc.
• Digit Operations: Sum of digits, product of digits.
• Prime Numbers or Composite Numbers: The relationship might involve properties of the numbers like being prime or composite.

To solve number analogy problems, practice identifying various numerical patterns. Try to break down the numbers and see how they relate through basic or slightly more complex mathematical operations. Sometimes, looking at the numbers relative to perfect squares or cubes can reveal the pattern quickly, as seen in this problem.