Number Analogy: 6 : 5 :: 8 : ?

This problem involves finding a missing number in a sequence based on a logical relationship, known as a number analogy. The format is A : B :: C : ?, meaning the relationship between A and B should be the same as the relationship between C and the unknown number (?). Here, A=6, B=5, C=8, and we need to find ?.

Pattern Analysis: First Pair (6 and 5)

We first look for a connection between 6 and 5.

Possible relationships include:

• Subtraction: $6 - 1 = 5$. The difference is 1.
• Division: $6 / (6/5) = 5$. The ratio is $6/5 = 1.2$.
• Other mathematical operations.

The simplest relationship, subtraction ($6 - 1 = 5$), is often the intended pattern in such questions.

Logic Application: Second Pair (8 and ?)

Now, we apply the discovered pattern to the second pair, 8 and the unknown number (let's call it $x$).

Test 1: Applying Constant Difference

If the relationship is a constant difference of 1, we would expect $8 - x = 1$. This leads to $x = 7$. However, 7 is not listed as an option (Options are 2, 6, 12, 4).

Test 2: Applying a Sequential Difference

Let's consider that the difference might change sequentially. The difference in the first pair (6, 5) is 1. A logical progression is for the difference to increase. If the difference increases by 1, the difference for the second pair (8, $x$) would be $1 + 1 = 2$.

Using this difference of 2:

We set the equation $8 - x = 2$.

Solving for $x$: $x = 8 - 2$ $x = 6$

Result Verification

The result $x = 6$ is one of the provided options.

This suggests the pattern is: The first number minus a value equals the second number. The value subtracted increases by 1 for each subsequent pair. Pair 1: $6 - 1 = 5$ Pair 2: $8 - 2 = 6$ The sequence of subtrahends is 1, 2, which follows a clear logical progression.

Final Answer

Based on the analysis of the sequential difference pattern, the questioned number is 6.