Both signs are ruled by Mercury, planet of intellect and communication, so their mental connection will be strong. However, Virgo is a practical earth sign while Gemini is an impulsive air sign. They'll have to constantly balance their differences, and their communicative natures will help them talk it through. If Gemini's constant hyperactivity and chatter doesn't exhaust Virgo, and Virgo's pickiness doesn't spoil Gemini's party, they can build something solid and nurturing. If Gemini dreams up the wild ideas, and Virgo makes sure the practical details are handled, they can make a solid team.
Neither sign likes to reveal their personal secrets upfront. They prefer to debate, talk about ideas, and get to know a person's mind before they let you into their hearts. As mutable signs, they're both comfortable with change, and can adapt to all types of situations and personalities. They love to analyze, solve puzzles, and dig up interesting factual tidbits—they may share a love of reading, crosswords and clever wordplays. The mechanics of anything fascinates both signs, and nothing escapes their highly observant (and often critical) eyes. If opinions were worth money, they'd both be tycoons.