Need help with formula to return text value based on a number in a range.

I have a trial balance with account numbers and a mapping file with account ranges and their corresponding description. So for example, if the GL account is between 100000 and 102042 it should be Cash. I want to create a formula that will look at each account in the TB and return the line description based on the range in the mapping file.

My files look something like this (in excel format)

Mapping File:
CASH & CASH EQUIVALENTS - Between 100000 and 102042
MARKETABLE SECURITIES - Between 102043 and 110999
Trial balance:
101108 Current RMB-COB Shan
102043 Other Investments

Is there a formula that I can use to determine if the account number falls within different ranges and if it does return the text description for that range. I have a 5000 account GL so doing it one by one is very time consuming.

I should have mentioned, I have a list of about 300 descriptions. So writing each one defeats the purpose of trying the formula. Is there a way to reference the range with the description?

Can't figure out how to post the actual spreadsheet as an example, so this screenshot is the best I can do (please tell me how to attach excel file, if that's possible)Capture.JPG

Thank you for your help so far. I'm not sure a Vlookup is going to get me where I need to be.

See attached file. On the second tab, I want column C to show me the description based on the first tab (col A) derived from the account number falling within the range for that description.

Wow, I guess I was expecting this to be more complex that it really is. I didn't think that a vlookup function would be able to determine if the number was within the given range. Thank you so much for your help.