Which of the following serial dilutions contains an incorrect factor?

In evaluating the serial dilutions presented, each dilution should represent a consistent method of ratio reductions that maintain a proportional factor. When assessing the sequence of ratios, the goal is to ensure that each subsequent dilution is a systematic progression from the previous one.

The first choice demonstrates a proper doubling pattern: 1:4 leads to 1:8, which is a further halving, and subsequently to 1:16, maintaining the structure of being proportional and consistent with dilutions.

The second choice adheres to the same logic where 1:1 to 1:2 indicates a doubling, followed by 1:4 which is again consistent within that pattern.

The third choice represents a series where the initial dilution of 1:5 is not valid as it does not logically progress to 1:15 and then to 1:45 through a consistent factor. The correct approach here would involve using a common factor or ratio that is uniform for each step.

However, in examining the last choice, the dilution factors of 1:2 to 1:6 and then to 1:12 do not follow a consistent multiplying or dividing factor as expected. While the numerical progression seems reasonable, the multiplicative relationships do not maintain the expected