Finding the Number Analogy Pattern

This question asks us to find a missing number based on a logical or arithmetic relationship between two pairs of numbers. The first pair is 15:8, and the second pair is 31:?. We need to figure out the rule connecting 15 to 8 and then apply the same rule to 31 to find the missing number.

Analyzing the First Pair (15:8)

Let's examine the relationship between the first number (15) and the second number (8) in the first pair.

• Subtraction: If we subtract a number from 15 to get 8, that number is \(15 - 8 = 7\). So, one possible rule is "subtract 7".
• Division/Addition: Let's try another common pattern. What if we add 1 to the first number and then divide by 2? \((15 + 1) / 2 = 16 / 2 = 8\) This rule perfectly matches the first pair.

The second rule, \(B = (A + 1) / 2\), seems more likely as it uses a combination of operations often found in these types of problems.

Applying the Pattern to the Second Pair (31:?)

Now, we apply the identified pattern, \(B = (A + 1) / 2\), to the second pair where the first number is 31.

1. Take the first number: 31.
2. Add 1 to it: \(31 + 1 = 32\).
3. Divide the result by 2: \(32 / 2 = 16\).

So, the missing number is 16.

Conclusion

The logical relationship is that the second number is obtained by adding 1 to the first number and then dividing the sum by 2. Applying this to 31, we get \((31 + 1) / 2 = 16\). Therefore, the missing number in the second pair is 16.