I was interviewing with a private equity focus consulting firm but failed the mode test. They asked all kinds of matching functions. What functions do I need to know in order to excel?

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The most common functions matching or using a match are MATCH, all the VLOOKUP, HLOOKUP, XLOOKUP.
For matching text it is FIND, REPLACE, and the regular expression add-in (need to use it with VBA)

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You can also use formula arrays if the match is complex:

{= IF(A1:A100<4,1,0) * IF(B1:B100= "dummy",1,0) }

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Well, reference functions (which I think is what you meant by match functions) are formulas in which you can directly or indirectly reference another value based on a criteria. The ones I know by the top of my head are:

=MATCH() - pls be aware index match is not a reference function per se
=VLOOKUP()
=HLOOKUP()
=XLOOKUP()
=XMATCH()
=OFFSET()
=FILTER()
=INDIRECT()

You can also do workarounds with =SUMPRODUCT() to transform it to a reference function - finance people use this trick quite often

Functions like =SEARCH(), =MID(), =SUMIFS(),=AGGREGATE() are not reference functions, however they use match process inside their logics

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