LSAT Logic Games: How to Use ‘But Not Both’

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In Logic Games, cute and cuddly “A must come before B” rules are often treated as cherished instructions. It makes sense; they’re simple, absolute, and easily diagrammed. They’re also more intuitively digestible than some of our more complex Logic Games rules.

But digesting complex carbs gives you fuel, while simple carbs give you a beer belly. Similarly, complex LG rules often unlock the game and propel you through the questions, whereas “A before B” rules… make you fat… (shush, no analogy is perfect).

One of the most useful complex relationships comes in the form of an exclusive disjunction. You remember these from Logical Reasoning: “Bubba buys either laundry detergent or a whole new wardrobe, but not both.”

For Logic Games, this is expressed in the form of “Either A comes before B, or B comes before C, but not both.” These rules, initially, should be written like this:

A — B
or
B — C
but not both

Be not afraid, for there are deductions to be had.

These are essentially conditionals; if one thing happens, then the other cannot happen. Let’s take the first relationship: A — B. Because of the “but not both,” we know that if A precedes B then it cannot be the case that B precedes C. In a One-to-One Ordering Game, that means that, in order to ensure that B does not precede C, we must have C precede B (because they cannot occupy the same space).

That’s huge for us. We know that both A and C precede B, so we should be diagramming with branches to reflect this relationship. The same goes for the other disjunct; if B comes before C, then we know that B must come before A.

Having done this, we’re left with a rule implying that either A and C both precede B, or else B precedes both A and C. Breathtakingly beautiful binary branches to better our brain-teaser.

So, that’s for Ordering Games. This rule also appears, however, on Grouping Games. Let’s consider an In-and-Out Grouping Game. If we’re selecting from among eight super heroes to create a five person Justice League delegation, we might say that either Superman or Batman must be selected. But not both; that would be overkill.

Just like with Ordering Games, we have to make a deduction. If Superman is in, then what do we know? We know that, based on our “but not both” rule, Batman must be out, and vice versa. If, for example, we have another rule that “If Batman is not in the delegation then Wonder Woman must be,” then this initial deduction will be very useful in allowing us to make a chain of rules (if Superman is in then Batman is out and Wonder Woman is in).

The trick is to look at these rules not as a bigger challenge, but as a bigger and better key. They don’t just lead to discrete deductions; often you’ll find that LSAC has hidden the whole solution behind these complex relationships, providing an extra incentive for you to go beyond simply transcribing the rules.

For more practice, check out the October 1993 Test, Game 2.

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