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# If M is a negative integer and K is a positive integer,

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Intern
Joined: 02 Sep 2018
Posts: 43
If M is a negative integer and K is a positive integer,  [#permalink]

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11 Sep 2018, 07:13
00:00

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 100% (01:51) wrong based on 4 sessions

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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
Intern
Joined: 14 Aug 2018
Posts: 20
Location: United States (WA)
GMAT 1: 670 Q43 V40
GMAT 2: 750 Q47 V47
GPA: 3.3
WE: Education (Education)
Re: If M is a negative integer and K is a positive integer,  [#permalink]

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11 Sep 2018, 07:57
1
This is just a test of whether you know some properties of standard deviation.

Property 1: Standard deviation is 0 if and only if all of the members of the set are equal to one another.
Property 2: Standard deviation is always positive EXCEPT if Property 1 applies (all members of the set are equal to one another)

Why? You calculate standard deviation by squaring then square rooting a bunch of numbers (Plus a few more steps) (purposely non-exact - I'll follow up on this in a second). The result of the square root of a squared term is always positive (none of the other steps ever change this).

As you know, the GMAT isn't a test of your ability to calculate but rather your ability to think. Pro tip - if you find yourself calculating standard deviation you've indubitably missed an easier, faster solution. Of the three standard deviation questions in the problem solving section of the 2019 OG, none requires calculation. 68 can be solved by estimation, 151 involves three impossible answer choices (probably strategically best to guess between the remaining two), and 166 is really just quick algebra.
_________________

Jayson Beatty
Indigo Prep
http://www.indigoprep.com

Math Expert
Joined: 02 Sep 2009
Posts: 50613
Re: If M is a negative integer and K is a positive integer,  [#permalink]

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11 Sep 2018, 07:58
parijit 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

Discussed here: https://gmatclub.com/forum/if-m-is-a-ne ... 26819.html
_________________
Re: If M is a negative integer and K is a positive integer, &nbs [#permalink] 11 Sep 2018, 07:58
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