Hans is considering purchasing each of six items arranged from left to right on a shelf at the travelers' warehouse—a razor, a stereo, a television, a UV lamp, a video camera, and a watch. Each of these items is powered either by batteries or by an adapter, but not by both. The following conditions apply:
- The UV lamp is either the leftmost or the rightmost item on the shelf.
- No item powered by batteries is adjacent to any other item powered by batteries.
- The watch is powered by batteries.
- The fourth item on the shelf is not powered by an adapter.
- The razor, which is powered by batteries, is to the left of the watch, and to the right of the video camera and the stereo.
Which of the following could be true?(A) The UV lamp is the sixth item on the shelf.
(B) The razor is the third item on the shelf.
(C) The fifth item on the shelf is powered by batteries.
(D) The stereo is powered by batteries.
(E) Both the UV lamp and the video camera are powered by batteries.