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Default LOOKUP or IF-THEN stmt - which one?

First, I apologize for the vague Subject, but I'm not sure what I need here....

I need to have a formula to look at two values and determine the result
based on the where the value falls in a range...

Column A
(A1) - 39,841
(A2) - 20,623
(A3) - 24,496
(A4) - 23,909

Column B
(B1) - 1,749
(B2) - 635
(B3) - 1,142
(B4) - 965

IF the number in A2 is between 38000 and 40000
OR
If the number in B2 is between 2000 and 2150
THEN "B1" should be the result in C2

IF the number in A2 is between 20000 and 37999
OR
If the number in B2 is between 1000 and 1999
THEN "B2" should be the result in C2

(I will need to repeat this pattern a couple more times as well)

I used =LOOKUP(B2,{0;10000;20000;38000},{"B4";"B3";"B2";" B1"}) to get a
result on the first set of criteria, but I just can't seem to figure out how
to get the formula to look at the second set of criteria as an OR.

Please let me know if you have any suggestions as soon as possible, as I'm
trying to get a report out yet this afternoon.

Thanks very much in advance,
Jessica
 
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