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Update statement with CASE and banding

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Hello Folks,

I am stuck and am going nowhere.
I have two tables

MinuteCategory
------------------

Minute

MinuteCategory

MinuteLookup

--------------------

MinuteCategoryId (surrogate key)
MinuteLow
MinuteHigh

MinuteCategory

Sample from Minute Lookup table ..

11 15<15 min
216 30<30 min
331 45<45 min
446 60<60 minutes
561 75<1 hour 15 minutes
.
.
.
.
.. . . . . 
I am trying to update the MinuteCategory column in the MinuteCategory table using the MinuteLookup table.
For example if the minute = 33 then the corresponding lookup value would be 3 (from the lookup table), because the 
33rd minute falls in between 31 min and 45 min and the corresponding surrogate key is 3
Is this possible with an Update statement in SQL? The only thing i can think of is use case statement as the join key between

the two tables but i don't think it's going to work :(

UPDATE

SET MinuteCategory = ml.MinuteCategoryId

FROM MinuteCategory mc join MinuteLookup ml on mc.Minute = 

CASE WHEN mc.Minute between ml.MinuteLow and ml.MinuteHigh THEN ml.MinuteCategoryId ELSE NULL

END

Would appreciate any help.

SS


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