Comparison of average values of data sets


I want to know if mean of A>B and A1, A2 are the two subsets of A. Similarily, B1, B2 are two subsets of B. Is the condition A1<B1 and A2<B2 mathematically possible?????
As I think it is not. I think that either both or at least one subset must have shown the same relationship in their average values as that of whole data set A and B.

It would be really helpful, if anyone can help me on this..
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Less is more. Stay pure. Stay poor.
Can you just run one-sided ttests. Though, I could be missing something in your description!
I run t-Test: Two-Sample Assuming Unequal Variances for all three data sets and found the following values:
1- A and B; p(two-tailed) = 1.19E-06
2- A1 and B1; p(two-tailed) = 3.24E-39
3- A2 and B2; p(two-tailed) = 2.16E-04

I want to share my excel file with you but not able to find the link for the attachment.
If you can help me on this also.