Understanding the Number Analogy Problem

This question asks us to identify a pattern or logical relationship between pairs of numbers and then apply that same relationship to find a missing number. The structure is given as Number1 : Number2 :: Number3 : Number4 :: Number5 : ?.

In this specific problem, we have the following number series:

$$ 8:14::13:24::9:? $$

We need to find the relationship between the first pair (8 and 14) and the second pair (13 and 24). Once we determine this relationship, we will apply it to the third pair (9 and the unknown number) to find the missing value.

Analyzing the Number Relationships

Let's examine the relationship between the numbers in the first two pairs:

• First Pair (8 : 14):
  • Difference: $14 - 8 = 6$.
  • Let's check if multiplying the first number by 2 and subtracting 2 works: $ (8 \times 2) - 2 = 16 - 2 = 14 $. This relationship holds true.
• Second Pair (13 : 24):
  • Let's test the relationship discovered from the first pair, which is $ \text{Number} \rightarrow (2 \times \text{Number}) - 2 $.
  • Applying this to 13: $ (13 \times 2) - 2 = 26 - 2 = 24 $. This relationship also holds true for the second pair.

Since the relationship $ \text{Result} = (2 \times \text{Input}) - 2 $ works for both the first and second pairs, we can confidently apply it to find the missing number.

Applying the Logic to Find the Missing Number

Now, we apply the established relationship $ \text{Result} = (2 \times \text{Input}) - 2 $ to the third pair, where the input number is 9.

• Third Pair (9 : ?):
  • Using the formula: $ (9 \times 2) - 2 $.
  • Calculation: $ 18 - 2 = 16 $.

Therefore, the missing number in the series is 16.

Evaluating the Options

Let's compare our result with the given options:

The calculated missing number, 16, corresponds to Option 2.