Discussion

The median of the numbers 8, 11, 13, 15, x+1, x+3, 30, 35, 40, 43 is 22. What is the value of x?

Answer: C

Correct answer: 20

There are ten values, already in ascending order, so the median is the mean of the 5th and 6th.

\[\frac{(x+1) + (x+3)}{2} = \frac{2x+4}{2} = x + 2\]

Setting this equal to the given median:

\[x + 2 = 22 \quad\Longrightarrow\quad x = 20\]

Substituting back, the list reads 8, 11, 13, 15, 21, 23, 30, 35, 40, 43, which is indeed in order, and the middle pair 21 and 23 averages to 22.

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