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# DS: STDs (m08q09)

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Retired Moderator
Joined: 18 Jul 2008
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28 Nov 2008, 13:54
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Set $$T$$ consists of odd integers divisible by 5. Is standard deviation of $$T$$ positive?

1. All members of $$T$$ are positive
2. $$T$$ consists of only one member

[Reveal] Spoiler: OA
B

Source: GMAT Club Tests - hardest GMAT questions

On a side note, when a question tells you a set S has numbers x,y,z - do we assume that x y z will always be different numbers? or can they be the same number, but repeated 3 times.

REVISED VERSION OF THIS QUESTION IS HERE: ds-stds-m08q09-73347-20.html#p1210600
Manager
Joined: 19 Feb 2009
Posts: 55

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02 Apr 2010, 12:16
4
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Statement 1 : All members of T are positive
We have two possibilities here

Case a) all the members are same
=> e.g T= {5,5,5} = {5} (Since by definition a 'Set' is a unique collection of objects.)
=> S.D = 0

Case b) all the members are different
=> e.g. T = {5,15,25}
=> S.D. = some positive number.

Since statement 1 is giving two possibilities , its Not Sufficient

Statement 2 : Set T consists of only one member
=> Since its only one member , S.D. =0
Hence Statement 2 is Sufficient

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Joined: 12 Jul 2009
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02 Apr 2010, 08:28
2
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B.

For A, we can't say that the SD will always be +ve as it can be 0 as in the case of B.
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Posts: 3357
Location: New York City
Schools: Wharton'11 HBS'12

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29 Nov 2008, 20:01
1
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i get B

SD of 1 object is 0
Senior Manager
Joined: 01 Feb 2010
Posts: 264

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02 Apr 2010, 09:57
1
KUDOS
Set $$T$$ consists of odd integers divisible by 5. Is standard deviation of $$T$$ positive?

1. All members of $$T$$ are positive
2. $$T$$ consists of only one member

[Reveal] Spoiler: OA
B

Source: GMAT Club Tests - hardest GMAT questions

On a side note, when a question tells you a set S has numbers x,y,z - do we assume that x y z will always be different numbers? or can they be the same number, but repeated 3 times.

1: Not enough as all members can be same in that case SD is 0 which is not +ve but in other case when all numbers are +ve and different SD will be +ve hence insufficient.
2: Enough as SD is zero which is not +ve hence suffcient.
Math Expert
Joined: 02 Sep 2009
Posts: 39695

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11 Apr 2013, 05:51
1
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Expert's post
thaihoang305 wrote:
snkrhed wrote:
I'm not going to go into "how to solve" since many others are do it much better than I do.

I think for this question the key factors to know are:
1) definition of standard definition
2) definition of "0"

remember, when all numbers are the same or if there is one number in the set, the standard deviation is 0.
0 is not a positive integer. (positive integer is > 0).

Sorry but is there some mistake here.
Thought this helpful set of Bunuel

math-number-theory-88376.html

Then positive number is a real number greater than 0
And 0 is not negative or positive number. Then in (2) SD = 0 => Why 0 is a positive number.

I find out this revise of Bunuel
ds-stds-m08q09-73347-20.html#p1210600
He also says the answer is B.
Could anyone here explain for me?

From (2) we get that SD=0, thus the answer to the question "is SD positive" is NO, which makes the second statement sufficient.
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Joined: 02 Nov 2008
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28 Nov 2008, 16:27
Standard deviation is always postivie . It's a average distance from mean. Distance can't be negative

1 - Suff
2- St dev is 0 - Suff

D
Manager
Joined: 27 May 2008
Posts: 199

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28 Nov 2008, 19:53
Correct HG , SD is always positive

Also to answer the side note question

we cant assume that x y z will always be different numbers or they are the same number.
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Joined: 29 Aug 2007
Posts: 2473

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29 Nov 2008, 23:39
Did you type correctly? Y should be T, correct?
"Set T consists of odd integers divisible by 5" and "T consists of only one member" in statement 2 are also inconsistant.

1: Anyway, statement 1 is not helpful in finding SD.
2: Statement 2 is definitely helps to get the SD, which is 0 in this case as the SD of an element is 0.

Set Y consists of odd integers divisible by 5. Is standard deviation of T positive?

1) All members of T are positive
2) T consists of only one member

On a side note, when a question tells you a set S has numbers x,y,z - do we assume that x y z will always be different numbers? or can they be the same number, but repeated 3 times.

For your side question, can you post the question if you have? Because a question with context would be very useful in anylizing the issue on hand.

IMO, real gmat test do not offer such a confused context.
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30 Nov 2008, 09:37

However, isn't all STDs positive? so wouldn't A) answer the question "Is Standard deviation of T positive?"

For the side note question, I posted the question in this link:
7-p544767?t=73389#p544767

Notice how X and Y even though different variables, can take on the same value (both x and y = 4), as per the OE in the post. I'm wondering if this is can be the case in the real GMAT.

Btw, this was a gmat club test question.

GMAT TIGER wrote:
Did you type correctly? Y should be T, correct?
"Set T consists of odd integers divisible by 5" and "T consists of only one member" in statement 2 are also inconsistant.

1: Anyway, statement 1 is not helpful in finding SD.
2: Statement 2 is definitely helps to get the SD, which is 0 in this case as the SD of an element is 0.

Set Y consists of odd integers divisible by 5. Is standard deviation of T positive?

1) All members of T are positive
2) T consists of only one member

On a side note, when a question tells you a set S has numbers x,y,z - do we assume that x y z will always be different numbers? or can they be the same number, but repeated 3 times.

For your side question, can you post the question if you have? Because a question with context would be very useful in anylizing the issue on hand.

IMO, real gmat test do not offer such a confused context.
Director
Joined: 21 Dec 2009
Posts: 583
Concentration: Entrepreneurship, Finance

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07 Apr 2010, 08:57
(1) 1: SD = 0; 1, 15, 15: SD = some +ve value............Insuff
(2) -15: SD = 0; 15: SD = 0 as well. In all cases,
for any single digit, SD = 0 - NOT positive.
Hence, B
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Intern
Joined: 09 Mar 2010
Posts: 38
Concentration: Technology, General Management
Schools: McCombs '14

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14 Apr 2010, 02:43
The question is if it's positive or not.
From both the statements we can make out if its positive or not.
Stat 1: always +ve
Stat 2: always 0 - Not positive.
So we can conclude both the statements alone are suffice.
option D,
Please let me know if im wrong.
Intern
Joined: 09 Mar 2010
Posts: 38
Concentration: Technology, General Management
Schools: McCombs '14

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14 Apr 2010, 02:54
gmatbull wrote:
(1) 1: SD = 0; 1, 15, 15: SD = some +ve value............Insuff
(2) -15: SD = 0; 15: SD = 0 as well. In all cases,
for any single digit, SD = 0 - NOT positive.
Hence, B

> odd integers divisible by 5 are 5,15,25,35,45
mean = 25
S.D = ((20^2 + 10^2 + 0^2 + 10^2 + 20^2) /5)^(1/2) which is always positive.

case 2. say -5,-15,25,35,45
mean = 13
S.D = +ve in any case.

So option 1 is always +ve.
CIO
Joined: 02 Oct 2007
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14 Apr 2010, 03:12
S1 is not sufficient. Consider Set T consisting of the same number elements ([4, 4, 4], for example). Then SD = 0. You can see more details in this post above:
ds-stds-m08q09-73347.html?view-post=709035#p709035
kalrac wrote:
The question is if it's positive or not.
From both the statements we can make out if its positive or not.
Stat 1: always +ve
Stat 2: always 0 - Not positive.
So we can conclude both the statements alone are suffice.
option D,
Please let me know if im wrong.

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Joined: 16 Nov 2010
Posts: 1663
Location: United States (IN)
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06 Apr 2011, 05:10
The answer is B. (1) is insufficient as we don't know if all elements are same or different. (2) says there is only 1 element, so SD = 0, which is a definitive answer.
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Director
Joined: 01 Feb 2011
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23 Apr 2011, 15:51
1. Not sufficient.

as we dont whether the elements of the set are same or diff

if same , SD =0 => is not greater than 0

if different , SD >0

2. Sufficient.

as there is only one element, SD =0.

Manager
Joined: 20 Dec 2010
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01 Jul 2011, 15:49
Terrific question...

Fell for the trap answer D....

Statement 1 presents a double case...It can be +ve or zero!

Brilliant question!
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10 Apr 2012, 06:36
amod243 wrote:
Statement 1 : All members of T are positive
We have two possibilities here

Case a) all the members are same
=> e.g T= {5,5,5} = {5} (Since by definition a 'Set' is a unique collection of objects.)
=> S.D = 0

Case b) all the members are different
=> e.g. T = {5,15,25}
=> S.D. = some positive number.

Since statement 1 is giving two possibilities , its Not Sufficient

Statement 2 : Set T consists of only one member
=> Since its only one member , S.D. =0
Hence Statement 2 is Sufficient

Best answer to a tricky question!
Fell into the trap and didn't consider the difference between 'positive' and positive or null'...
This one goes on my error log.
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Intern
Joined: 01 Apr 2012
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10 Apr 2012, 06:55
nice explanation....
Intern
Joined: 11 Jan 2012
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10 Apr 2012, 09:59
I think language for 1 is not clear.
It can be zero or +ve.

For 2 always zero

So B it is
Re: DS: STDs (m08q09)   [#permalink] 10 Apr 2012, 09:59

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# DS: STDs (m08q09)

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