Number Relationship Pattern Explained

The question presents a number analogy problem. We are given a pair of numbers (\(25:30\)) that follow a specific logical or arithmetic relationship. Our task is to identify this pattern and apply it to find the missing number in the second pair (\(36:?\)).

Analyzing the First Pair (\(25:30\))

Let's examine the relationship between the first number, \(25\), and the second number, \(30\). We observe that \(25\) is a perfect square: \(25 = 5^2\) Now, let's see how \(30\) relates to \(25\). The difference is \(30 - 25 = 5\). Interestingly, this difference, \(5\), is the square root of the first number, \(25\). \( \sqrt{25} = 5 \) So, the relationship appears to be: The second number is obtained by adding the square root of the first number to the first number itself. \( \text{Second Number} = \text{First Number} + \sqrt{\text{First Number}} \) Let's verify this for the first pair: \( 30 = 25 + \sqrt{25} \) \( 30 = 25 + 5 \) \( 30 = 30 \) The pattern holds true for the first pair.

Applying the Pattern to the Second Pair (\(36:?\))

Now, we apply the same identified pattern to the second pair, where the first number is \(36\). Using the formula: \( \text{Missing Number} = 36 + \sqrt{36} \) First, find the square root of \(36\): \( \sqrt{36} = 6 \) Now, add this result to \(36\): \( \text{Missing Number} = 36 + 6 \) \( \text{Missing Number} = 42 \)

Therefore, the missing number in the second pair is \(42\). Comparing this with the given options, we find that option 2 matches our result.