Explanation of the Number Analogy Problem

The question asks us to find a missing number in a sequence based on a specific relationship observed in other number pairs. The format is $A:B :: C:D :: E:F$. We are given $6:16 :: 7:? :: 5:13$. We need to find the value represented by '?' based on the relationship between the first pair (6 and 16) and the third pair (5 and 13).

Analyzing the Relationship in the Given Pairs

Let's examine the relationship between the numbers in the known pairs:

• Pair 1: 6 and 16
• Pair 3: 5 and 13

We need to find a consistent mathematical rule that transforms the first number into the second number for both pairs.

Identifying the Mathematical Pattern

Let's analyze the first pair: 6 and 16.

Consider the first number as $X$ and the second number as $Y$. We are looking for a function $Y = f(X)$.

One possible relationship is multiplication and addition/subtraction.

Let's try the rule $Y = 3X - 2$.

Checking Pair 1 (6 and 16):

Substitute $X=6$ into the formula:

$$Y = 3 \times 6 - 2$$

$$Y = 18 - 2$$

$$Y = 16$$

This matches the second number in the first pair.

Checking Pair 3 (5 and 13):

Substitute $X=5$ into the formula:

$$Y = 3 \times 5 - 2$$

$$Y = 15 - 2$$

$$Y = 13$$

This matches the second number in the third pair.

Since the rule $Y = 3X - 2$ works for both given pairs, we can confidently use it to find the missing number.

Solving for the Missing Number

Now, let's apply the identified rule $Y = 3X - 2$ to the middle pair, where the first number is 7.

Here, $X=7$. We need to find $Y$.

$$Y = 3 \times 7 - 2$$

$$Y = 21 - 2$$

$$Y = 19$$

The missing number is 19. This corresponds to Option 4.