M25 Q10 Data Sufficiency Problem

jenyang5268 · **Posted:** Fri Mar 13, 2009 10:29 am

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!

patedhav · **Posted:** Mon Mar 16, 2009 8:28 am

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!

Answer is B).

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.

GMAT TIGER · **Posted:** Sun Apr 05, 2009 9:30 am

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..

fluke · **Posted:** Wed Mar 16, 2011 4:29 am

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"

RahlowJenkins · **Posted:** Tue Mar 17, 2009 8:46 am

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

gmatdreamz · **Posted:** Fri Mar 20, 2009 12:09 pm

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

Economist · **Posted:** Thu Mar 26, 2009 5:25 am

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!

Economist · **Posted:** Sun Apr 05, 2009 2:17 am

Hi jenyang5268, wat is OA?

wilbase · **Posted:** Tue Jan 05, 2010 5:48 pm

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.

Bunuel · **Posted:** Wed Jan 06, 2010 4:55 am

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.

jqiang · **Posted:** Thu Mar 11, 2010 9:50 am

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.

bangalorian2000 · **Posted:** Fri Mar 12, 2010 4:58 am

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.

hardnstrong · **Posted:** Sun Mar 14, 2010 2:27 am

B is my answer

gmatbull · **Posted:** Thu Mar 18, 2010 9:19 am

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.

sidhu4u · **Posted:** Fri Mar 19, 2010 6:32 am

+1 for B with the above explanation.

mailpravs · **Posted:** Mon Sep 06, 2010 11:34 pm

B.

Yalephd · **Posted:** Wed Mar 16, 2011 4:19 am

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..

subhashghosh · **Posted:** Wed Mar 16, 2011 7:31 am

The answer is B.

rongali · **Posted:** Wed Mar 16, 2011 9:37 am

answer is B

rajeshaaidu · **Posted:** Wed Mar 16, 2011 8:08 pm

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!

Answer is B).

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.

Short and crisp explanation that too before OA. +1.

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M25 Q10 Data Sufficiency Problem

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