B. Let's wait 'til Mom gets home.
If you chose A, count yourself among the countless millions who have forgotten that the third word is actually not a whole word. The confusion stems from the relaxed way we speak. "Until," when said quickly, usually comes out sounding like "'ntil," or "til," hence the error.
B. Let's eat, Grandma.
You've seen this before, usually under the title, "Punctuation kills."
The first sentence is something a hungry cannibal would say. The second one lets Grandma know the speaker is hungry.
A. Safe deposit box.
"A" is the correct choice here. Again, lazy speech patterns have led to this extremely common mistake. The box in question is one that is located in a safe.
B. The P90X exercise regimen is the best I have ever done.
A "regime" is a form or mode of management, à la the "Hitler regime."
A "regimen" is a way of life, a prescribed course of medication, a practice. Even the best of writers get this one wrong, and it's sad, really. Writers should know better.
By the way, "regime" is pronounced re-JEME, not RAY-jeme -- unless, of course, you are French.
A. The answer lay in the many scribbles in his journal.
Unless an answer is a solid, there is no way for an answer to lay anywhere. The easiest way to remember when to use lay or lie is to think whether you are referring to an object. You lay down an object.
Other ways to remember correct usage:
People lie (lie down or utter fibs); chickens lay eggs.
The title to Eric Clapton's wonderful song, Lay Down Sally, should actually be Lie Down Sally, because he is referring to an action he wants her to perform. As written, he is actually telling someone to take hold of Sally and lay her body (the object) down.
Bob Dylan fans will also be sad to know that "Lay Lady Lay" is also incorrect on a couple of counts. One, "lay" should be "lie," and two, he's missing a comma before and after "Lady." Poor Bob. The song, however, is still wonderful.
Back in the '70s, a lot of us used to say, "Lay it on me, man." Well, our grammar was correct. "'It',in this case, is the object, even though it is figurative.