M25 Q10 Data Sufficiency Problem

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


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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.

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

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

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?

Hi jenyang5268, wat is OA?

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..

1, Even if all members of the set are positive, the standard deviation can still be 0.

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.

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.

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.

B is my answer

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.

+1 for B with the above explanation.