The mean of 20 numbers is zero. At most, how many of them can exceed zero?
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Answer: D. 19
Explanation
The mean of twenty numbers is zero, which means the mathematical sum of all twenty numbers must equal zero. To maximize the count of positive numbers, the remaining numbers must be made as negative as possible. Setting nineteen numbers to positive one and one number to negative nineteen keeps the sum at zero. The arithmetic mean is calculated by dividing the sum of a dataset by the total number of items. A zero mean implies that positive deviations from zero are exactly balanced by negative deviations. Extremal problems require pushing variable constraints to their absolute maximum or minimum limits.
Data analysts examine zero-mean datasets when studying standardized scores and normalized test distributions. Financial portfolio returns often average out to zero over cyclical market adjustment periods. Logical deduction puzzles test a student's ability to reason about mathematical constraints and extremes. Option A assumes incorrectly that no numbers can be positive when the mean is zero. Option B underestimates the maximum possible count by restricting positive numbers arbitrarily. Option C represents half the dataset size, but more than ten numbers can easily be positive.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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