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If the average (arithmetic mean) of five consecutive negativ

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If the average (arithmetic mean) of five consecutive negativ

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If the average (arithmetic mean) of five consecutive negative integers is 2k - 1, what is the difference between the greatest and least of the five integers?


A. 4
B. 4k
C. 4k + 4
D. 4 - 4k
E. 4k^2 - 4k

OA A

Source: Magoosh

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BTGmoderatorDC wrote:
If the average (arithmetic mean) of five consecutive negative integers is 2k - 1, what is the difference between the greatest and least of the five integers?


A. 4
B. 4k
C. 4k + 4
D. 4 - 4k
E. 4k^2 - 4k
Source: Magoosh
We have a finite arithmetic sequence, hence the average of the 5 integers is their median, that is the third (middle) term.

Conclusion: the greatest is (2k-1) + 2 and the least is (2k-1) - 2 , and their difference (our FOCUS) is [(2k-1)+2]-[(2k-1)-2] = 4.


This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.

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BTGmoderatorDC wrote:
If the average (arithmetic mean) of five consecutive negative integers is 2k - 1, what is the difference between the greatest and least of the five integers?


A. 4
B. 4k
C. 4k + 4
D. 4 - 4k
E. 4k^2 - 4k
The value of k is irrelevant.
For any set of 5 consecutive integers, the difference between the greatest and least will always be 4.

The correct answer is A.

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