Which of the following pairs of elements could possibly be in the same group? x has a 1+ ion; y has a 1- ion. x tends to form a 2+ ion; y tends to gain two electrons. x will tend to gain one electron; y has eight valence electrons. x has an atomic number 15; y forms a 3- ion.

Let's eliminate these one by one.
The first pair would not be the same, as X would most likely be in group IA, and Y would be in group VIIA, because of their tendency to gain and lose electrons.
The second pair would also violate the same rule, but X would most likely be in group IIA, and Y would most likely be in group VIA.
The third pair would not be the same, as X is most likely in group VIIA, and since Y has eight valence electrons, it is most likely a noble gas.
The final pair has X with atomic number 15, making it phosphorous. Phosphorous wants to gain 3 electrons to have a full octet of 8 outer "valence" electrons, and Y would also like to gain 3 electrons. This means it is possible that the final pair would be in the same group.