about modulation

someone said(let's say the music is in C major. the examiner will play the C major chord at the very beginning. at this point, * REMEMBER THE C NOTE *!! then the examiner will start to play the music. when he stops, * REMEMBER THE ENDING CHORD (BASS) NOTE *!! let's say you hear the ending chord (bass) note is G. then you will know the answer is G chord, which is the DOMINANT KEY (5th note) of C major. )
But in the aural training in practice Book III (ABRSM) ,p.79, Q.5a,the starting key is G major and it ends in a dominant key, then i think it must be changed into D major, but why in the song there is G# and C#? That means it is changed into A major or D major?