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If the average (arithmetic mean) of seven consecutive integers is k + 2, then the product of the greatest and least integer is
Title
Mean is k plus 2
Your Result
Correct
Difficulty
Hard
Your Pace
1:40
Others' Pace
2:23
Video Explanation
Text Explanation
For any collection of evenly spaced numbers, the mean and median are always equal. Because this is set with seven members, an odd number of elements, the median is the middle number, the 4th number on the list: there are three numbers on the list below it and three above it. Thus, (k + 2) is the mean as well as the median, the middle or 4th number on the list. Since there are only seven numbers, we can simply write them out:
{k – 1, k, k + 1, k + 2, k + 3, k + 4, k + 5}
The least, three lower than the median, is (k – 1).
The greatest, three higher than the median, is (k + 5).
Their product is:
product = (k – 1)(k + 5) = k2 + 4k – 5
Answer = (E)
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