#"Option 1"# is contraindicated. No data are conveyed with respect to solubility.
#"Option 2"# is contraindicated, by the very terms of the question. Why?
#"Option 3"# is again contraindicated, by the very terms of the question. Why?
And this leaves #"Option 4"# as the only horse running. We started with #AY_2#. In solution this speciated to give discrete particles of (arguably) #A^(2+)# and #2xxY^(-)#; of course the charge could have been the other way round.
In solution #"b"# there was no association between cation and anion. When a strong electrolyte dissolves in water it speciates to give its constituent ions. Solutions #"a"# and #"c"# still showed associated ions. Why?
Real examples of #"Option 4"# could include #CaCl_2#, and #Na_2SO_4#, i.e. consider the following equation representing their dissolution, are as follows:
#CaCl_2(s) rarr Ca^(2+) + 2Cl^-#
#Na_2SO_4(s) rarr 2Na^+ + SO_4^(2-)#
This is a good and hard question designed to make you really think. I certainly had to do so!
