Hi Sabicha,

Slightly tricky question.

But here , definitely statement I cannot be sufficient.

Not necessarily statement I always means that average should be equal to median.

Lets say,

Set X = -6, 0,0, 1,2,3

here in this case mean = mode but not necessarily the median.

here the difference between median and mode is 0.5.

But as you mentioned, it could be equal as well.

Say, 2,2,2,2,2

here the difference between median and mode is 0.

So, statement I is insufficient.

Also, statement II is insufficient obviously, because not enough information.

Difference between any two integers is less than 3 means,

we can take,

like

Set X = 2,3,3,4, here median = mode. So difference is zero.

Set X = 2,3,4,4, here median not equal to mode. So difference is 0.5

But together it is sufficient,

Since the range is less then 3 and mean is equal to the mode, only way to pick the set is either symmetrical from mean or all the elements are same.

for example,

-1,0,0,1 so here mean is equal to the median which is in turn equal to mode. So difference is 0.

2,2,2,2,2 – we could have all elements same as well. So mean = median = mode.

So answer has to be C.

Hope this helps.