She needs a pen, pencil, and an answer sheet." Is this grammatically?
It is, though for the sake of style consistency, I would add another a before pencil. The comma after pencil is an example of the Oxford comma - some will argue that its not necessary, as it is clearly understood that these are three separate items in most circumstances without it. Others, including myself, will say you should make a habit of using one anyway, in case one of the more unusual examples comes up, one famous one being the sentence The highlights of his global tour include encounters with Nelson Mandela, an 800-year-old demigod, and a dildo collector. Take out the final comma, and the meaning could be significantly misconstrued