The data of different natural numbers 4, 7, 10, 14, 2x+3, 2x+5, 22, 23, 30, 50 are in ascending order. How many possible values are there for the median of the data for various values of x?

  1. A. Only one value
  2. B. Only two values
  3. C. Only three values
  4. D. Five values

Correct Answer: D. Five values

Explanation

Since there are 10 numbers, the median is the average of the 5^{\text{th}} and 6^{\text{th}} terms: \frac{2x+3 + 2x+5}{2} = 2x+4. For ascending order of distinct natural numbers, 14 \lt 2x+3 and 2x+5 \lt 22. Thus 11 \lt 2x \lt 17. The possible integer values for 2x are 12, 13, 14, 15, 16. This gives 5 possible values for the median.

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