If the average (arithmetic mean) of five consecutive negativ

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 âˆ’ 4k

OA A

Source: Magoosh

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fskilnik@GMATH: GMAT Instructor; Posts: 1449; Joined: Sat Oct 09, 2010 2:16 pm; Thanked: 59 times; Followed by:33 members

by fskilnik@GMATH » Sun Dec 09, 2018 6:37 am

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 âˆ’ 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.

Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pm; Location: New York, NY; Thanked: 13060 times; Followed by:1906 members; GMAT Score:790

by GMATGuruNY » Sun Dec 09, 2018 6:49 am

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 âˆ’ 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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Scott@TargetTestPrep: GMAT Instructor; Posts: 7243; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Mon Mar 18, 2019 5:35 pm

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 âˆ’ 4k

OA A

Source: Magoosh

We are asking for the range of the 5 consecutive integers. It's a fact that the range of a set of n integers is always n - 1. For example, in the set of {2, 3, 4, 5, 6, 7}, there are 6 consecutive integers, we see that the range is 7 - 2 = 5, which is 1 less than the number of consecutive integers. Therefore, in a set of 5 consecutive integers, whether they be positive or negative, the difference between the greatest and least integers, i.e., the range, is 4.

Answer: A

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770

by Brent@GMATPrepNow » Tue Mar 19, 2019 4:49 am

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 âˆ’ 4k

OA A

Source: Magoosh

Let x = the 1st (smallest integer)
So, x+1 = the 2nd integer
x+2 = the 3rd integer
x+3 = the 4th integer
x+4 = the 5th integer (greatest integer)

What is the difference between the greatest and least of the five integers?
Difference = ( x+4) - x = 4

Answer: A

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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