The term “market structure” describes how a firm or a group of firms relate to each other and to the consumers who purchase the firms’ product. The factors that “determine” market structure are really located in the nature of the product being produced, and the distribution channel for such product. You've got the four categories right [1. Pure Competition, 2. Monopolistic Competition, 3. Oligopoly, and 4. Pure Monopoly], so it's just a matter of figuring out what McGraw-Hill sells, right?
Sometimes it's a little tricky because in a lot of cases the way each market category is defined produces a little overlap. For example, in monopolistic competition, there are a large number of firms producing fairly differentiated products. The apparel and furniture industries are normally grouped under this market structure. McGraw-Hill is a publishing company. There are a lot of firms that produce books and other forms of print and non-print information. You MIGHT say that different "books" are differentiated from each other, just as different chairs or kinds of blue jeans are, but publishers normally DON'T compete based on market differentiation, like brand awareness. Most of the time we don't really know who published the book we're reading... So I'd rule out monopolistic competition.
They're certainly not a pure monopoly. Those kinds of companies are things like utilities (electrical and cable TV suppliers).
They don't seem to be like an oligopoly either. In that case, you have a small number of firms that produce really similar products. There are dozens of different kinds of breakfast cereal, but in reality they are all made by only a few firms in the US.
What's left? You "guessed" it correctly - - PURE COMPETITION. That kind of market structure is characterized as one where many firms all produce a relatively standardized product. Agriculture is often sited as an example, where many different “firms” (farms) produce what is essentially the same product. Entry to the purely competitive market is generally unrestricted meaning that, in theory, acquiring the infrastructure needed to begin operating as a firm is not considered so formidable an undertaking to prevent a decision to do so. Firms in a purely competitive market are said to be “price takers” in that a single firm cannot influence the overall market price.
This describes the publishing industry pretty well. All firms produce a more-or-less standard product (books, magazines). You don't need all that much to get into the publishing business... a photocopier and some content will do so almost anybody can get into the business (but that's no guarantee anybody will want to buy what you write!). And while your favorite bookstore might have a "sale," it's not normally that one particular publisher is able to just decide to influence price.
So I think your answer makes sense. Pure competition.
Finished my MBA recently, and we had to plow through this in the economics course.