Vlookup or serarch or index

My table is as such:
Column B: Names
Column E: Remainder
Column K: Criteria is True or False.

I need a formula that searches for TRUE in column K and finds the lowest number in column E (some FALSE numbers are lower though) and returns with the name in column B.

Can anyone help? Thank you in advanced.

This should work for you:

=INDEX(B2:B6,MATCH(MINIFS(E2:E6,K2:K6,"True"),E2:E6,0))

=INDEX(Table1[NAME],MATCH(MINIFS(Table1[REMAINDER],Table1[BUDDY],"True"),Table1[REMAINDER],0))

This is what it changes to when I put all the rows in, but it gives me a #NAME? error




EDIT: When I click on evaluate it comes back as:

=INDEX($B$5:$B$93,MATCH(MINIFS(Table1[REMAINDER],Table1[BUDDY],"True"),Table1[REMAINDER],0))

with the italics and underlines.
Clicking evaluate once more gives
=INDEX($B$5:$B$93,MATCH(#NAME?(Table1[REMAINDER],Table1[BUDDY],"True"),Table1[REMAINDER],0))

Ah, I have 2010 version. :/

Anyone know? :/