The marks scored in an examination are converted from 50 to 10 for the purpose of internal assessment. The highest marks were 47 and the lowest were 14. The difference between the maximum and the minimum internal assessment scores is

### Concept & Formula When a set of values is scaled by a constant factor, the difference between any two values in the set is also scaled by that exact same factor. $$ \text{Scaled Difference} = \text{Original Difference} \times \text{Scale Factor} $$ ### Step-by-Step Solution * **Scale Factor:** The base marks are converting from 50 to 10. * Scale Factor = $\frac{10}{50} = \frac{1}{5}$. This means every score is divided by 5. * **Original Difference:** Calculate the difference between the highest and lowest original marks. * Original Maximum = 47, Original Minimum = 14. * Original Difference = $47 - 14 = 33$. * **Calculation:** Apply the scale factor to the original difference. * Scaled Difference = $33 \times \frac{1}{5} = \frac{33}{5}$ * Scaled Difference = $6.6$ ### Exam Strategy & Shortcut Instead of converting both the maximum and the minimum scores individually ($\frac{47}{5} = 9.4$ and $\frac{14}{5} = 2.8$) and then subtracting them ($9.4 - 2.8 = 6.6$), it is vastly faster to subtract the raw scores first ($33$) and divide by the scale factor once ($\frac{33}{5} = 6.6$). ### Common Pitfall Converting the individual numbers first. While mathematically correct, dealing with decimals like $9.4$ and $2.8$ under time pressure invites subtraction errors. Stick to integers as long as possible before dividing. ### Final Answer **Therefore, the correct answer is 6.6.**