When you search for a document using SharePoint Search, make use of Web Apps.
The results of your search term will present a shortlist. However, you may see a couple of possible documents that could be the one you are after.
Clicking on the document name will download the document to your desktop and open it using the correct Office application.
Clicking on the "View in Browser" link will open the document using Web Apps, on SharePoint.
It is faster to View in Browser to quickly check if the document is the one you are trying to find.
