Is the standard deviation of A=0? 1) The minimum value of

I choose B.

A set should have distinct elements. So SD can not be zero

A. if 5 is minimum, then there should be a maximum value which different from 5. therefore there is/are some more values other than 5. so should be A.

Sorry Himalayan but I disagree, since:

MIN(5,5,5) = 5

MAX(5,5,5) = 5

I agree with KillerSquirrel.
The question does not specify that the minimum and maximum values are different. We cannot assume that they are different! They may be the same!

yah, I know. I was just using a logic cuz msrinath said E is not OA.

What then is the OA? And, most importantly, the OE if OA is not E.

Can't imagine any OA other than 'E'

would the real GMAT really have questions like this?

If the OA really is not E, then this is more of a verbal question than a quant question lol... it's more of a play on words than it is a question testing mathematical concepts.

St1:
Nothing useful.

St2:
Even more useless than St1.

Using both:
Nothing useful really comes out.

E.

No. This is not a GMAT question, if the answer's not E.

Please post the OE, if you have it.

This is a standard practice for GMAT 700+ questions, hiding information in plain sight. The hidden information here is that "A" is a set. As per the definition of sets, all the elements of a set are unique.
[ https://en.wikipedia.org/wiki/Set ]

Now having this information in hand, lets start analysing the given statements

1] minimum value of elements in set A is 5.
=> Set could be {5} or {5,6 ...}
In first case SD=0 [minimum=maximum since only one element]
In second case SD#0 since the numbers are different. So not sufficient

2] set A has 20 elements => A is a set AND it has more than 1 elements so it has 20 different elements and hence the SD cannot be 0. A positive "YES" to the asked question.

Choice B

OA is B

Is that definition actually given in any of the review books? The only book I have on hand at the moment is the OG Quantitative Review, which says, "In mathematics a set is a collection of numbers or other objects". It says nothing about all elements being unique. I'll be sure to check out my myriad of other books at home tonight to see if that definition is given anywhere. If not, then that is a horribly unfair GMAT question!

I have never read that the set contains unique elements.

The OG11 says - A set is a collection of numbers or objects. This doesn't mean that the numbers can't be same.

Can you please give some other authentic reference, which says the set consists of unique elements.

I wanna clarify it so that I can face the questions without doubt in mind.