Seven persons — A, B, C, D, E, F, and G — live in a seven-floor building numbered from 1 (ground floor) to 7 (top floor). Each person likes a differen...

Seven persons — A, B, C, D, E, F, and G — live in a seven-floor building numbered from 1 (ground floor) to 7 (top floor). Each person likes a different color: Green, Red, Violet, Purple, Black, Pink, and White. The following conditions apply:

• G lives on an even-numbered floor and is three floors above the person who likes Black.
• The number of persons living above the one who likes Purple equals the number of persons living below the one who likes Black.
• C lives two floors above the person who likes White, who lives on an odd-numbered floor.
• C does not like Black.
• B lives two floors above the person who likes Violet.
• The person who likes Green lives just above the one who likes Pink.
• More than three persons live between E and F, and F lives just above D.

Which of the following statements is true?

I. G does not live on a prime-numbered floor.

II. A lives above the person who likes Red.

III. There is at least a two-floor gap between G and F.