If M is a negative integer

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CSASHISHPANDAY: Senior | Next Rank: 100 Posts; Posts: 84; Joined: Sat Jun 18, 2011 9:50 pm; Location: New Delhi; Thanked: 35 times; Followed by:3 members; GMAT Score:800

If M is a negative integer

by CSASHISHPANDAY » Mon Dec 03, 2012 9:22 pm

If M is a negative integer and K is a positive integer, which of the following could be the standard deviation of a set {-7, -5, -3, M, 0, 1, 3, K, 7}

I. -1.5 II. -2 III. 0
(A) I only (B) II only (C) III only (D) I and III only (E) None

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Source: Beat The GMAT — Problem Solving | Mon Dec 03, 2012 9:22 pm

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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 » Mon Dec 03, 2012 9:42 pm

CSASHISHPANDAY wrote:If M is a negative integer and K is a positive integer, which of the following could be the standard deviation of a set {-7, -5, -3, M, 0, 1, 3, K, 7}

I. -1.5 II. -2 III. 0
(A) I only (B) II only (C) III only (D) I and III only (E) None

Nice question. I like how the information regarding M and K is totally superfluous

Okay, first we need to recognize that the standard deviation of any set of numbers will always be greater than or equal to zero.

So, the standard deviation can never equal -1.5 or -2.

Also, the only time that the standard deviation equals zero is when all of the numbers in the set are equal. Since the numbers in this set are not all equal, the standard deviation cannot be zero.

If the standard deviation cannot equal -1.5, -2, or 0, the correct answer here is E

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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CSASHISHPANDAY: Senior | Next Rank: 100 Posts; Posts: 84; Joined: Sat Jun 18, 2011 9:50 pm; Location: New Delhi; Thanked: 35 times; Followed by:3 members; GMAT Score:800