Seven distinct positive integers have a mean of and a median of . What is the greatest possible value of the largest integer?
Answer and explanation
Correct answer: D.
- Step 1: With integers having a mean of , their total sum is . Arrange them in ascending order: , where the median is .
- Step 2: To maximize the largest integer , minimize all other integers to the smallest possible distinct positive values: set , , , and immediately above the median set , .
- Step 3: Calculate : .
Answer
.
Why not the others: repeats integers instead of requiring distinct positive values; over-allocates values to smaller integers; neglects the median constraint; assigns non-distinct minimum values.
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