In a dataset of 5 distinct positive integers, the mean is 12, the median is 10, and the mode does not exist. If the smallest integer is 4, what is the greatest possible value of the largest integer?
Answer and explanation
Correct answer: B. 30
- Step 1: Let the sorted integers be . Total sum is .
- Step 2: Given and median . To maximize , minimize and : minimum and minimum .
- Step 3: Sum of first four integers: . Therefore maximum .
Answer
30.
Why not the others: '28' unnecessarily increases intermediate integers; '25' under-optimizes the distribution; '35' would force the sum to exceed 60.
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