GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 17 Jun 2019, 08:01

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

Author Message
TAGS:

### Hide Tags

Manager
Joined: 07 Nov 2009
Posts: 229
If M is a negative integer and K is a positive integer  [#permalink]

### Show Tags

31 Jan 2012, 00:08
2
1
19
00:00

Difficulty:

65% (hard)

Question Stats:

55% (01:32) correct 45% (01:48) wrong based on 659 sessions

### HideShow timer Statistics

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
Math Expert
Joined: 02 Sep 2009
Posts: 55635
If M is a negative integer and K is a positive integer  [#permalink]

### Show Tags

31 Jan 2012, 00:56
15
10
rohitgoel15 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

Important note: SD is always >=0. SD is 0 only when the list contains all identical elements (or which is same only 1 element).

So the answer is clearly E, none.

To elaborate more: Standard deviation shows how much variation there is from the mean, how widespread a given set is. So, a low standard deviation indicates that the data points tend to be very close to the mean, whereas high standard deviation indicates that the data are spread out over a large range of values. So, basically we can say that it in a sense measures the distance and the distance cannot be negative. Also if you look at the formula for the standard deviation you'll see that it's square root of some number (variance) and the square root can never be negative.

Check this for more: math-standard-deviation-87905.html

Hope it helps.
_________________
##### General Discussion
Senior Manager
Joined: 23 Oct 2010
Posts: 340
Location: Azerbaijan
Concentration: Finance
Schools: HEC '15 (A)
GMAT 1: 690 Q47 V38
Re: M is a negative integer and K is a positive integer  [#permalink]

### Show Tags

31 Jan 2012, 00:57
1
1
SD cant be negative. SD=0 if all the numbers are the same, or it is only one number in the set

So,E is the answ

hm...cant be before Bunuel trying, but still cant be hehe
_________________
Happy are those who dream dreams and are ready to pay the price to make them come true

I am still on all gmat forums. msg me if you want to ask me smth
Manager
Status: MBA Aspirant
Joined: 12 Jun 2010
Posts: 134
Location: India
WE: Information Technology (Investment Banking)
Re: M is a negative integer and K is a positive integer  [#permalink]

### Show Tags

31 Jan 2012, 21:36
Thanks Bunnel and Rohit for this good post and explanation
Director
Joined: 14 Dec 2012
Posts: 741
Location: India
Concentration: General Management, Operations
GMAT 1: 700 Q50 V34
GPA: 3.6
Re: If M is a negative integer and K is a positive integer  [#permalink]

### Show Tags

12 Aug 2013, 03:49
rohitgoel15 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

SD is always positive ...hence E.

IF the question would have been that what could be themedian.in that case answer would be C.
_________________
When you want to succeed as bad as you want to breathe ...then you will be successfull....

GIVE VALUE TO OFFICIAL QUESTIONS...

learn AWA writing techniques while watching video : http://www.gmatprepnow.com/module/gmat-analytical-writing-assessment
Intern
Joined: 02 Aug 2015
Posts: 1
Re: If M is a negative integer and K is a positive integer  [#permalink]

### Show Tags

26 Aug 2015, 19:36
Bunuel wrote:
rohitgoel15 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

Important note: SD is always >=0. SD is 0 only when the list contains all identical elements (or which is same only 1 element).

So the answer is clearly E, none.

To elaborate more: Standard deviation shows how much variation there is from the mean, how widespread a given set is. So, a low standard deviation indicates that the data points tend to be very close to the mean, whereas high standard deviation indicates that the data are spread out over a large range of values. So, basically we can say that it in a sense measures the distance and the distance cannot be negative. Also if you look at the formula for the standard deviation you'll see that it's square root of some number (variance) and the square root can never be negative.

Hope it helps.

_________________________________________________________________________________________

Hi,

I understood that SD cant be negative,
but SD can be zero, because SD <= 1/2 Range and if the range of a set is ZERO then SD will also be ZERO (I read this somewhere).

Math Expert
Joined: 02 Sep 2009
Posts: 55635
Re: If M is a negative integer and K is a positive integer  [#permalink]

### Show Tags

26 Aug 2015, 23:47
gaganjyot11 wrote:
Bunuel wrote:
rohitgoel15 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

Important note: SD is always >=0. SD is 0 only when the list contains all identical elements (or which is same only 1 element).

So the answer is clearly E, none.

To elaborate more: Standard deviation shows how much variation there is from the mean, how widespread a given set is. So, a low standard deviation indicates that the data points tend to be very close to the mean, whereas high standard deviation indicates that the data are spread out over a large range of values. So, basically we can say that it in a sense measures the distance and the distance cannot be negative. Also if you look at the formula for the standard deviation you'll see that it's square root of some number (variance) and the square root can never be negative.

Hope it helps.

_________________________________________________________________________________________

Hi,

I understood that SD cant be negative,
but SD can be zero, because SD <= 1/2 Range and if the range of a set is ZERO then SD will also be ZERO (I read this somewhere).

SD is 0 only when the list contains all identical elements (or which is same only 1 element).

_________________
Board of Directors
Joined: 17 Jul 2014
Posts: 2547
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30
GPA: 3.92
WE: General Management (Transportation)
Re: If M is a negative integer and K is a positive integer  [#permalink]

### Show Tags

04 Dec 2015, 19:05
good one..very tricky
SD can never be negative, thus I and II out
SD will be 0 only when all the elements of the set are equal. thus, in our case, it can't be 0.
if m is -1 and k is 5, then SD would be between 1 and 2.
Intern
Joined: 31 Jan 2018
Posts: 16
Re: If M is a negative integer and K is a positive integer  [#permalink]

### Show Tags

18 Feb 2018, 02:07
-1.5,-2 cannot be the standard deviation,Because standard deviation can never be a negative number. SD>=0
SD=0 only when all the terms are equal.Irrespective of M and K all terms are not equal.So SD cannot be equal to 0 also.
Intern
Joined: 09 Jun 2016
Posts: 21
Re: If M is a negative integer and K is a positive integer  [#permalink]

### Show Tags

17 Jun 2018, 23:09
Bunuel wrote:
So, basically we can say that it in a sense measures the distance and the distance cannot be negative.

Hope it helps.

Hi Bunuel , understand that SD is always greater than or equal to 0. But you say that the square root can never be negative, there always seems to be some confusion regarding this. Can you please direct me to any material which helps in understanding when to consider +/- {square root} and when not to?
_________________
..................................................................................................................
micro-level speed, macro-level patience | KUDOS for the post ,shall be appreciated the most
Math Expert
Joined: 02 Sep 2009
Posts: 55635
Re: If M is a negative integer and K is a positive integer  [#permalink]

### Show Tags

17 Jun 2018, 23:16
abhishek911 wrote:
Bunuel wrote:
So, basically we can say that it in a sense measures the distance and the distance cannot be negative.

Hope it helps.

Hi Bunuel , understand that SD is always greater than or equal to 0. But you say that the square root can never be negative, there always seems to be some confusion regarding this. Can you please direct me to any material which helps in understanding when to consider +/- {square root} and when not to?

What is confusing there? Yes, SD as well as the even roots (such as square root of a number) is 0 or positive.
_________________
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9325
Location: Pune, India
Re: If M is a negative integer and K is a positive integer  [#permalink]

### Show Tags

18 Jun 2018, 00:12
1
abhishek911 wrote:
Bunuel wrote:
So, basically we can say that it in a sense measures the distance and the distance cannot be negative.

Hope it helps.

Hi Bunuel , understand that SD is always greater than or equal to 0. But you say that the square root can never be negative, there always seems to be some confusion regarding this. Can you please direct me to any material which helps in understanding when to consider +/- {square root} and when not to?

Also, check out this post:
https://www.veritasprep.com/blog/2016/0 ... oots-gmat/
_________________
Karishma
Veritas Prep GMAT Instructor

Intern
Joined: 09 Jun 2016
Posts: 21
Re: If M is a negative integer and K is a positive integer  [#permalink]

### Show Tags

20 Jun 2018, 22:15
VeritasPrepKarishma wrote:
abhishek911 wrote:
Bunuel wrote:
So, basically we can say that it in a sense measures the distance and the distance cannot be negative.

Hope it helps.

Hi Bunuel , understand that SD is always greater than or equal to 0. But you say that the square root can never be negative, there always seems to be some confusion regarding this. Can you please direct me to any material which helps in understanding when to consider +/- {square root} and when not to?

Also, check out this post:
https://www.veritasprep.com/blog/2016/0 ... oots-gmat/

Thanks. This was the confusion!
_________________
..................................................................................................................
micro-level speed, macro-level patience | KUDOS for the post ,shall be appreciated the most
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 2888
Re: If M is a negative integer and K is a positive integer  [#permalink]

### Show Tags

20 Jun 2018, 22:36

Solution

Standard deviation formula is the mean of square of difference between mean and each element of the set which can either be positive or 0.

Thus, SD can either be 0 or positive.
Now, standard deviation is 0 when x= x ̅ or when mean and all the elements of the set are equal.
However, in the set {-7, -5, -3, M, 0, 1, 3, K, 7} all the elements of the given set are not equal.
Thus, none of the given number can be the mean of the set {-7, -5, -3, M, 0, 1, 3, K, 7}.
Hence, the correct answer is option E.

_________________
CEO
Joined: 12 Sep 2015
Posts: 3777
Re: If M is a negative integer and K is a positive integer  [#permalink]

### Show Tags

11 Sep 2018, 10:10
Top Contributor
rohitgoel15 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

Property 1: The standard deviation of a set of values is always greater than equal to 0
Property 2: If all values in a set are equal, the standard deviation of the set equals 0
Property 3: If the values in a set are NOT all equal, the standard deviation of the set is greater than 0

Now examine the statements...
I. -1.5 standard deviation cannot be negative.
II. -2 standard deviation cannot be negative.
III. 0 since the values are not all equal, the standard deviation cannot be zero.

Cheers,
Brent
_________________
Test confidently with gmatprepnow.com
Re: If M is a negative integer and K is a positive integer   [#permalink] 11 Sep 2018, 10:10
Display posts from previous: Sort by