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# Set T consists of a certain number of even integers divisibl

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Set T consists of a certain number of even integers divisibl  [#permalink]

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Updated on: 22 Sep 2013, 22:22
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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

If SD is never <0, then the question statement should be correct irrespective of answer options.

1) Whether the SD=0 or SD>0, in either cases it is not -ve. Hence acc to me this statement should suffice. This is considering the fact that 0 is considered to be +ve. If 0 is not considered +ve then this option is incorrect.

2) 0 is neither +ve nor -ve. Hence 0 cannot be considered to be +ve. In this regards, option b cannot be the correct answer.

Please correct my understanding. This question is taken from the free Quants test provided by GMAT Club.

Originally posted by jeetparicha85 on 22 Sep 2013, 18:56.
Last edited by Bunuel on 22 Sep 2013, 22:22, edited 2 times in total.
Renamed the topic, edited the question, added the OA and moved to DS forum.
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Re: Set T consists of a certain number of even integers divisibl  [#permalink]

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22 Sep 2013, 22:21
jeetparicha85 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

If SD is never <0, then the question statement should be correct irrespective of answer options.

1) Whether the SD=0 or SD>0, in either cases it is not -ve. Hence acc to me this statement should suffice. This is considering the fact that 0 is considered to be +ve. If 0 is not considered +ve then this option is incorrect.

2) 0 is neither +ve nor -ve. Hence 0 cannot be considered to be +ve. In this regards, option b cannot be the correct answer.

Please correct my understanding. This question is taken from the free Quants test provided by GMAT Club.

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 cannot 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.

Ss for 0: 0 is neither positive nor negative integer.

Hope it's clear.

M25-10
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Re: Set T consists of a certain number of even integers divisibl  [#permalink]

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25 Apr 2015, 16:30
Hi All,

Many DS questions can be 're-written' to make the question easier to answer (this is referred to as finding the "question behind the question."). Here, since we're dealing with Standard Deviation and the question asks if the SD of a group of numbers is POSITIVE, the question behind the question is whether the numbers in the group are all the SAME number or if there are any variations in the numbers.

Fact 1: All of the numbers are positive.

If they're all the SAME number, then the answer to the question is NO.
If the group contains different numbers, then the answer to the question is YES.
Fact 1 is INSUFFICIENT

Fact 2: The range of the group is 0

If the range is 0, then all of the numbers are the SAME. Thus, the answer to the question is ALWAYS NO.
Fact 2 is SUFFICIENT

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right way to think of this DS?  [#permalink]

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13 Dec 2015, 12:24
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.

The explanation for it was as follows:
(1): if the set is {6} then SD is zero and if SD {6,12} then SD is greater than zero or positive so 1 is not sufficient which i agree on

Now if we move to (2): if the range of the set is zero then it has to be of one element or identical element so SD will always be zero. And as i studied before that 0 is not considered positive or negative so SD is not considered positive or negative so it cannot be positive which means yes

is that the approach to this problem?
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Re: right way to think of this DS?  [#permalink]

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13 Dec 2015, 12:32
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.

Target question: Is standard deviation of set T positive?

IMPORTANT: The standard deviation of any set is always greater than or equal to zero. So, either the standard deviation is zero or it's positive. The standard deviation will EQUAL ZERO if all of the numbers in the set are IDENTICAL. The standard deviation will BE POSITIVE if the numbers in the set are NOT IDENTICAL.

Statement 1: All elements of set T are positive
There are various sets of numbers that meet this condition. Here are two:
Case a: the numbers are {6, 12, 18}. Since the numbers are not all identical, the standard deviation is positive
Case b: the numbers are {6, 6, 6}. Since the numbers are identical, the standard deviation is zero. In other words, the standard deviation is not positive
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: The range of set T is 0
If the range = 0, then the numbers (or number) in the set are IDENTICAL, which means the standard deviation is zero.
In other words, the standard deviation is definitely not positive
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Cheers,
Brent
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Re: Set T consists of a certain number of even integers divisibl  [#permalink]

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13 Dec 2015, 12:34
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.

The explanation for it was as follows:
(1): if the set is {6} then SD is zero and if SD {6,12} then SD is greater than zero or positive so 1 is not sufficient which i agree on

Now if we move to (2): if the range of the set is zero then it has to be of one element or identical element so SD will always be zero. And as i studied before that 0 is not considered positive or negative so SD is not considered positive or negative so it cannot be positive which means yes

is that the approach to this problem?

Merging topics. Please refer to the discussion above.
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Re: Set T consists of a certain number of even integers divisibl  [#permalink]

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13 Dec 2015, 12:35
The explanation for it was as follows:
(1): if the set is {6} then SD is zero and if SD {6,12} then SD is greater than zero or positive so 1 is not sufficient which i agree on

Now if we move to (2): if the range of the set is zero then it has to be of one element or identical element so SD will always be zero. And as i studied before that 0 is not considered positive or negative so SD is not considered positive or negative so it cannot be positive which means yes

is that the approach to this problem?

That sounds like a valid approach.

Cheers,
Brent
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Re: Set T consists of a certain number of even integers divisibl  [#permalink]

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13 Dec 2015, 18:00
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

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.

In the original condition, when you should match with the number of equations but there are many variables, you also need many equations. For 1) 1 equation, For 2) 1 equation, which is likely to make E the answer. In 1) & 2), it is T={6,6,6} and SD=0, which is no and therefore sufficient. However, this question is also a statistics question which is one of the key questions. When applying 4(A) of the mistake type,
In 1), T={6,12} SD>0 -> yes but T={6,6} SD=0 -> no, which is not sufficient.
In 2), from range=MAX-min=0, MAX=min. Then all the numbers are the same. Since SD=0, it is no and therefore sufficient. That is, the answer is B. This type of question is very current.

-> For cases where we need 3 more equations, such as original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 80% chance that E is the answer (especially about 90% of 2 by 2 questions where there are more than 3 variables), while C has 15% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since E is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, C or D.
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Re: Set T consists of a certain number of even integers divisibl  [#permalink]

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29 Mar 2017, 09:35
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Re: Set T consists of a certain number of even integers divisibl   [#permalink] 29 Mar 2017, 09:35
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