Unplugged Prep

Logic Games: Before, After, But Not Both

This post will explain a more difficult rule of this type in the 4th game of PrepTest 52 (September 2007).

PrepTest 52, Game 4

Let’s look at the 4th rule of the 4th game in PrepTest 52. The game starts, “A bread truck makes exactly one delivery…”

4th rule of the game:

“Either Malpighi’s delivery is earlier than Harris’s or it is later than Kanzaki’s, but not both.”

This means that either both variables come before M, or both come after M.

(Keep in mind one of the game’s other limitations, which is that no two variables can occur simultaneously – they must all occur at different times.)

1st possibility:

M’s delivery comes earlier than H’s.

If M’s delivery earlier than H’s, then M’s delivery is not later than K’s.

This means that if M’s delivery is earlier than H’s, then M’s delivery is also earlier than K’s.

Therefore, M is before both H and K:

2nd possibility:

M’s delivery is later than K’s.

If M’s delivery is later than K’s, then K’s delivery is before M’s.

If K’s delivery is before M’s, then H’s delivery must also be before M’s.

Therefore, H and K are both before M:


These are the only two possibilities, so just write them along with your other rules:


Each valid scenario (ordering of the variables) will feature one of these possibilities or the other.


Read the other parts of the series

Part 1: Conditional Sequencing

Part 3: Before, After, But Not Both | PT53