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?
- A. Only one value
- B. Only two values
- C. Only three values
- 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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