Three diffrent frequency cause occurance of beat

[somecelxis]

my ans is f Y = 260hz. but the ans is f Y= 252hz . am i wrong? why?
Since X is 256Hz., when sounded with Y 4 beats are produced, so Y is either sounding at 260 or 252Hz (+-4Hz).
When Z is sounded with X, 8 beats are heard, so Z is either 264 or 248Hz.(+-8Hz). my fZ is (264Hz.) now the f Y can be 260 or 252Hz (+-4Hz).
which one to choose?

 

[rude man]

Could be either 252 or 260.
Is there a second part that compares fY with fZ? That would resolve the ambiguity.

 

[somecelxis]

Could be either 252 or 260.
Is there a second part that compares fY with fZ? That would resolve the ambiguity.

no . that's the whole question. so it can be bith 260hz and 252hz?

 

[rude man]

no . that's the whole question. so it can be bith 260hz and 252hz?

Yes.