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# M25 Q10 Data Sufficiency Problem

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M25 Q10 Data Sufficiency Problem [#permalink]  13 Mar 2009, 10:29
Set T consists of a certain number of even integers divisible by 3. Is standard deviation of T positive?

1. All elements of set T are positive
2. The range of set T is 0

[Reveal] Spoiler: OA
B

Source: GMAT Club Tests - hardest GMAT questions

Can anyone explain this? Thanks!
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Re: M25 Q10 Data Sufficiency Problem [#permalink]  16 Mar 2009, 08:28
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jenyang5268 wrote:
M25, Q10 Data Sufficiency:

Set T consists of a certain number of even integers divisible by 3. Is standard deviation of T positive?

S1) All elements of set T are positive
S2) The range of set T is 0

Can anyone explain this? Thanks!

S1) All elements of set T are positive. - In this case you can have either 0 or positive, SD. (example: (3,3) or (3,6) and so it is not sufficient).

S2) The range of set T is 0, range is (max - min) and so it is zero only if max and min are same (example: 3, 3, 3, 3 set, in this case range will be zero and so standard deviation will be zero too and so S2) answer this question and sufficient.
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Re: M25 Q10 Data Sufficiency Problem [#permalink]  06 Jan 2010, 04:55
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Expert's post
Some tips:

SD\geq0, Standard deviation ALWAYS greater or equal to zero.

Standard deviation equals to zero if and only set consists of identical number(s) (special case set has only one element), eg {2,2,2,2}{-5,-5}{3}.

Range=0 --> SD=0, as when range=0 either we have the set of identical elements or set has only one element.
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Re: M25 Q10 Data Sufficiency Problem [#permalink]  05 Apr 2009, 09:30
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jenyang5268 wrote:
M25, Q10 Data Sufficiency:

Set T consists of a certain number of even integers divisible by 3. Is standard deviation of T positive?

S1) All elements of set T are positive
S2) The range of set T is 0

Can anyone explain this? Thanks!

It should be B however set T cannot have elements other than that are divisible by 3.

Remeber: SD and range can never be -ve.

1: The elements in set T could be [2, 3, 4, 5] or [3, 6, 9, 12, 15] or [3, 3, 3, 3, 3]. The SD could be 0 or +ve.
2: If the range of the set T is 0, then the elements in set T could be [-3, -3, -3, -3] or [3, 3, 3, 3, 3] or [6, 6, 6, 6, 6]. in any case the SD is 0, which is not a positive. Hence suff..
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Re: M25 Q10 Data Sufficiency Problem [#permalink]  16 Mar 2011, 04:29
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Yalephd wrote:
What does the abbreviation -ve mean?

GMAT TIGER wrote:
jenyang5268 wrote:
M25, Q10 Data Sufficiency:

Set T consists of a certain number of even integers divisible by 3. Is standard deviation of T positive?

S1) All elements of set T are positive
S2) The range of set T is 0

Can anyone explain this? Thanks!

It should be B however set T cannot have elements other than that are divisible by 3.

Remeber: SD and range can never be -ve.

1: The elements in set T could be [2, 3, 4, 5] or [3, 6, 9, 12, 15] or [3, 3, 3, 3, 3]. The SD could be 0 or +ve.
2: If the range of the set T is 0, then the elements in set T could be [-3, -3, -3, -3] or [3, 3, 3, 3, 3] or [6, 6, 6, 6, 6]. in any case the SD is 0, which is not a positive. Hence suff..

-ve: Negative. All numbers less than 0 on the number line.
+ve: Positive. All numbers greater than 0 on the number line.

Standard Deviation can never be -ve. It can be 0 or +ve.

Set contains certain number of even integers. Integers should be divisible by 6. Set can have -12,0,6,12,18

5 numbers; all even and divisible by 3.

1. All elements are +ve.

"6,12,18" will result in +ve standard deviation
"6,6,6" will result in 0 standard deviation because all numbers are equal.

Not sufficient.

2. The range of the set is 0.

If the range of a set is 0, all the elements are equal.

Set can be; -12,-12,-12. Standard deviation=0
Or
0,0,0. Standard deviation=0
Or
6,6,6. Standard deviation=0

Since, all the numbers of the set are equal, the standard deviation will be 0.
Sufficient.

Ans: "B"
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Re: M25 Q10 Data Sufficiency Problem [#permalink]  17 Mar 2009, 08:46
jenyang5268 wrote:
M25, Q10 Data Sufficiency:

Set T consists of a certain number of even integers divisible by 3. Is standard deviation of T positive?

S1) All elements of set T are positive
S2) The range of set T is 0

Can anyone explain this? Thanks!

Standard deviation = the square root of something that has been squared, which must be positive, unless of course it's zero.

S1 -- Insufficient. the SD could be 0 or some other number. 0 is not positive, so insufficent to answer the question.

Example --> if the set is {0,0,0,0} SD is zero. If the set is {2,4} SD is 1
S2 -- Sufficient. All the numbers in the set are the same, therefore SD is 0, there the answer is always no.

{0,0,0,0} SD is 0. {2,2} SD is 0....

B
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Re: M25 Q10 Data Sufficiency Problem [#permalink]  20 Mar 2009, 12:09
IMO, the answer should be A. Here's the reasoning :

1. They have clearly given that all the members of the set are positive. Hence, 0 is out (0 does not bear a sign). Even if the members of the set are negative, their deviation will always be +ve. Hence A is sufficient.

2. The members of the set could all be 0. Hence the deviation will be 0. At the same time, all the members of the set can be the same. e.g. 2. In such cases, the range will be 0. So option 2 does not give any additional information. The only scenario that the deviation will not be positive is if the deviation is 0 (in case of all zeros). Hence B is not sufficient.

Ans : A
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Re: M25 Q10 Data Sufficiency Problem [#permalink]  26 Mar 2009, 05:25
IMO C.
1) Set can be {6,6} or {6,9,12} so deviation can be 0 or some +ve num. Not suff.
2) Set can be {0,0} or {6,6} or {-6,0,6,9} => deviation can be zero,-ve or +ve.

Combining, all +ve even numbers divisible by 3 are there and all numbers are same. eg{6,6} => deviation is 0 which is not positive.

What is OA?
jenyang5268 wrote:
M25, Q10 Data Sufficiency:

Set T consists of a certain number of even integers divisible by 3. Is standard deviation of T positive?

S1) All elements of set T are positive
S2) The range of set T is 0

Can anyone explain this? Thanks!
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Re: M25 Q10 Data Sufficiency Problem [#permalink]  05 Jan 2010, 17:48
gmatdreamz wrote:
IMO, the answer should be A. Here's the reasoning :

1. They have clearly given that all the members of the set are positive. Hence, 0 is out (0 does not bear a sign). Even if the members of the set are negative, their deviation will always be +ve. Hence A is sufficient.

2. The members of the set could all be 0. Hence the deviation will be 0. At the same time, all the members of the set can be the same. e.g. 2. In such cases, the range will be 0. So option 2 does not give any additional information. The only scenario that the deviation will not be positive is if the deviation is 0 (in case of all zeros). Hence B is not sufficient.

Ans : A

1, Even if all members of the set are positive, the standard deviation can still be 0.
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Re: M25 Q10 Data Sufficiency Problem [#permalink]  11 Mar 2010, 09:50
RahlowJenkins wrote:
jenyang5268 wrote:
M25, Q10 Data Sufficiency:

Set T consists of a certain number of even integers divisible by 3. Is standard deviation of T positive?

S1) All elements of set T are positive
S2) The range of set T is 0

Can anyone explain this? Thanks!

Standard deviation = the square root of something that has been squared, which must be positive, unless of course it's zero.

S1 -- Insufficient. the SD could be 0 or some other number. 0 is not positive, so insufficent to answer the question.

Example --> if the set is {0,0,0,0} SD is zero. If the set is {2,4} SD is 1
S2 -- Sufficient. All the numbers in the set are the same, therefore SD is 0, there the answer is always no.

{0,0,0,0} SD is 0. {2,2} SD is 0....

B

The definition SET in mathematics (according to wikipedia ) is:
A set is a collection of distinct objects, considered as an object in its own right.

Note the word "DISTINCT", in the set given example the elements are identical, thus this doesn't fit the definition of a set.

So, the answer should be B, since the elements in the set should be multiples of 6, and they must be distinct.

S1 alone: They can be {6} or {6,12,18}, in the first case SD is 0 and in the second case SD is positive

S2 alone: Range = 0 implies that the max element = min element in the set, since the elements are distinct, the set contains only one element. The SD in that case will always be 0, so not positive.
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Re: M25 Q10 Data Sufficiency Problem [#permalink]  12 Mar 2010, 04:58
jenyang5268 wrote:
Set T consists of a certain number of even integers divisible by 3. Is standard deviation of T positive?

1. All elements of set T are positive
2. The range of set T is 0

[Reveal] Spoiler: OA
B

Source: GMAT Club Tests - hardest GMAT questions

Can anyone explain this? Thanks!

Its B.

Stmt 1: SD can be +ve or zero so can't decide on SD hence insufficient.
Stmt 2: Range is zero so SD has to be zero so sufficient.
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Re: M25 Q10 Data Sufficiency Problem [#permalink]  18 Mar 2010, 09:19
jenyang5268 wrote:
Set T consists of a certain number of even integers divisible by 3. Is standard deviation of T positive?

1. All elements of set T are positive
2. The range of set T is 0

1. 0, 0, are even integers divisible by 3. SD = 0
Also, 0, 6 are even integers divisible by 3. SD is +ve
considering both cases, stmt1 is INSUFF

2. The sets {-6, -6}, {0, 0}, and {12, 12} all have range 0. Irrespective of whether the elements
are +ve or -ve, a unique value in the set gives SD 0.....so, SUFFICIENT
Hence, OA = B.
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Re: M25 Q10 Data Sufficiency Problem [#permalink]  16 Mar 2011, 04:19
What does the abbreviation -ve mean?

GMAT TIGER wrote:
jenyang5268 wrote:
M25, Q10 Data Sufficiency:

Set T consists of a certain number of even integers divisible by 3. Is standard deviation of T positive?

S1) All elements of set T are positive
S2) The range of set T is 0

Can anyone explain this? Thanks!

It should be B however set T cannot have elements other than that are divisible by 3.

Remeber: SD and range can never be -ve.

1: The elements in set T could be [2, 3, 4, 5] or [3, 6, 9, 12, 15] or [3, 3, 3, 3, 3]. The SD could be 0 or +ve.
2: If the range of the set T is 0, then the elements in set T could be [-3, -3, -3, -3] or [3, 3, 3, 3, 3] or [6, 6, 6, 6, 6]. in any case the SD is 0, which is not a positive. Hence suff..
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Re: M25 Q10 Data Sufficiency Problem [#permalink]  24 Mar 2012, 05:59
patedhav wrote:
jenyang5268 wrote:
M25, Q10 Data Sufficiency:

Set T consists of a certain number of even integers divisible by 3. Is standard deviation of T positive?

S1) All elements of set T are positive
S2) The range of set T is 0

Can anyone explain this? Thanks!

S1) All elements of set T are positive. - In this case you can have either 0 or positive, SD. (example: (3,3) or (3,6) and so it is not sufficient).

S2) The range of set T is 0, range is (max - min) and so it is zero only if max and min are same (example: 3, 3, 3, 3 set, in this case range will be zero and so standard deviation will be zero too and so S2) answer this question and sufficient.

why are we asuming that the set contains only positive integers while evaluating st 2.
for example: set can be {-6, 3,3, 6} in this case range is 0 but sandard daviation is ont.

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Re: M25 Q10 Data Sufficiency Problem [#permalink]  24 Mar 2012, 06:13
Expert's post
nishtil wrote:
patedhav wrote:
jenyang5268 wrote:
M25, Q10 Data Sufficiency:

Set T consists of a certain number of even integers divisible by 3. Is standard deviation of T positive?

S1) All elements of set T are positive
S2) The range of set T is 0

Can anyone explain this? Thanks!

S1) All elements of set T are positive. - In this case you can have either 0 or positive, SD. (example: (3,3) or (3,6) and so it is not sufficient).

S2) The range of set T is 0, range is (max - min) and so it is zero only if max and min are same (example: 3, 3, 3, 3 set, in this case range will be zero and so standard deviation will be zero too and so S2) answer this question and sufficient.

why are we asuming that the set contains only positive integers while evaluating st 2.
for example: set can be {-6, 3,3, 6} in this case range is 0 but sandard daviation is ont.

One note: the range of {-6, 3, 3, 6} is 12 not 0.
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Re: M25 Q10 Data Sufficiency Problem [#permalink]  24 Mar 2012, 09:49

S1) All elements of set T are positive. - In this case you can have either 0 or positive, SD. (example: (3,3) or (3,6) and so it is not sufficient).

S2) The range of set T is 0, range is (max - min) and so it is zero only if max and min are same (example: 3, 3, 3, 3 set, in this case range will be zero and so standard deviation will be zero too and so S2) answer this question and sufficient.[/quote]

why are we asuming that the set contains only positive integers while evaluating st 2.
for example: set can be {-6, 3,3, 6} in this case range is 0 but sandard daviation is ont.

One note: the range of {-6, 3, 3, 6} is 12 not 0.[/quote]

Miss that point.... thanks bunuel..
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Re: M25 Q10 Data Sufficiency Problem [#permalink]  27 Mar 2012, 02:46
Expert's post
Set T consists of a certain number of even integers divisible by 3. Is standard deviation of T positive?

The standard deviation of a set 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 can not be negative, which means that the standard deviation of any set is greater than or equal to zero: SD\geq0.

Next, the standard deviation of a set is zero if and only the set consists of identical numbers (or which is the same if the set consists of only one number).

(1) All elements of set T are positive --> set T can be {6, 6} so with the standard deviation equal to zero or {6, 12} so with the standard deviation more than zero. Not sufficient.

(2) The range of set T is 0 --> in order the range to be zero set T should have all identical elements, which means that the standard deviation of the set is zero. Sufficient.

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Re: M25 Q10 Data Sufficiency Problem [#permalink]  30 Mar 2012, 18:42

It is asking us if the standard deviation is positive. But (within the definition of "standard deviation"), isn't it a given that it already is positive?
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Re: M25 Q10 Data Sufficiency Problem [#permalink]  31 Mar 2012, 00:43
Expert's post
restore wrote:

It is asking us if the standard deviation is positive. But (within the definition of "standard deviation"), isn't it a given that it already is positive?

So, as you can see the standard deviation of any set is greater than or equal to zero: SD\geq{0}.

PS questions on SD with various tips: ps-questions-about-standard-deviation-85897.html

Hope it helps.
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Re: M25 Q10 Data Sufficiency Problem [#permalink]  18 Apr 2013, 00:52
Set T consists of a certain number of even integers divisible by 3. Is standard deviation of positive?

1. All elements of set T are positive
2. The range of set T is 0

Case 1:
as SD>= 0, Hence for all positive numbers we can have 2 SD, 0 or +ve. Hence Insufficient

Case 2:
range = 0 => all elements are same hence SD = 0, Sufficient

Hence IMO B
Re: M25 Q10 Data Sufficiency Problem   [#permalink] 18 Apr 2013, 00:52
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