Running and thoughts along the way
Cutting an apple with a cheap, flimsy, plastic, serratedknife is both difficult and messy.
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I too have applied brute force to cut an apple with a disposable knife. It's really not worth the effort unless you enjoy juicy pulpy fragments of apple. Here is my recipe for a delicious apple at work. Start with a red delicious (of course, the only kind) and cut into four quarters using a sharp paring knife brought from home. Peel and core each section, and then liberally apply cinnamon to each. I use approximately one tablespoon per quarter. This makes for a gritty, but deliciously tasty treat.
I'm partial to apple and peanut butter myself. I usually have a paring knife at work, but I brought it home one day and forgot to bring it back.