Question 687·Hard·Math

The mean is the total divided by the count, so multiply the mean by the count to work backward. Type $11(60)$ in Desmos; it shows $660$, the total of the original scores.

The new mean covers 12 scores, so type $12(62)$ on the next Desmos line. It shows $744$, the new total. The median is the middle of an ordered list; $55$ and $57$ don't give you either total.

Let $x$ be the added score. All the old scores remain, so only $x$ fills the gap between the totals:

Don't divide that gap by $12$: it belongs to one new score, not to each score in the set.

Type $660+x_1\sim744$ in Desmos. Use $x_1$ for the unknown and $\sim$ to ask Desmos to find the value that makes both sides equal. Under PARAMETERS, it shows $x_1=84$. The additional test score is $84$. Choice D.

If the added score were $60$, the mean would stay $60$. Instead, all 12 scores share a mean increase of $62-60$. Type $12(62-60)$ in Desmos; it shows $24$. The added score must be $24$ above $60$.

Type $60+24$ on the next line; Desmos shows $84$. So the additional score is $84$. Choice D.