Evenly spaced set

[vinni.k]

I just want to confirm my knowledge on the evenly spaced sets.

A set of numbers in which each number is a set distance, or increment, from the next. 1, 4, 7, 10 is an evenly spaced set with an increment of 3.

The arithmetic mean (average) is equal to the median. The set comprising 1, 2, 3, 4, and 5 has a mean of 3 and a median of 3.

So following numbers are all evenly spaced set:-

Set of odd numbers {1,3,5,7,9} --> increment of 2
Set of even numbers {2,6,8,10} --> increment of 2
Multiple of 15 {15,30,45,60} --> increment of 15

What about these sets. Are these also evenly spaced sets ?

{1,1,1,1} --> there is no increment
{3,3,3,3}
{0,0,0,0}

There is no increment, and as per definition each number is a set distance or increment. Hence, we cannot consider them as evenly spaced ?

Please correct me if i am wrong.

[Brent@GMATPrepNow]

/b]

{1,1,1,1} --> there is no increment
{3,3,3,3}
{0,0,0,0}

There is no increment, and as per definition each number is a set distance or increment. Hence, we cannot consider them as evenly spaced ?

Please correct me if i am wrong.

Those are also evenly spaced.
The increment = 0

Also, notice that for each set, the median = mean

Cheers,
Brent

[vinni.k]

Thanks Brent

[ceilidh.erickson]

Yes, these are evenly spaced, as Brent has pointed out. I don't recall ever seeing a GMAT problem that dealt with an all-same-value set as being evenly spaced (this would strike me as too much of a "gotcha"), so I doubt you'd ever encounter this issue. I could imagine a DS question for which you could use an all-same set as an example to prove a statement insufficient... but in all likelihood, this isn't a rule that you'll need to commit to memory.