Set T consists of a certain number of even integers divisible by 3. Is

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

Answer = B
Cheers,
Brent

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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