Aries are known for their fiery temper and their will to win. Because of their lack of planning skills
A Gemini would be cool under pressure, thus they would choose a long-range method like poisoning to kill someone.
Cancer would send the target a letter loaded with lethal anthrax since killing them would likely cause him more pain than the victim.
If a Virgo were to commit murder, they would most certainly do extensive planning and study beforehand.