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Get the Specs: Tackling the Rules
So now we know what kind of game we’re dealing with and who the characters are
and what you’ll be doing with them. Now it’s time to tackle the rules, which
specifically spell out how the characters interact. The rules lay
down the specs that you’ll need to follow when tackling each question.
Keep in mind that the rules apply to all of the questions in the
question set, except for rare questions that specifically add a new
rule or omit or modify an existing rule. In those cases, the rule change applies
only to that particular question.
Some rules are complicated, and these are the ones you’ll need to spend the
most time learning how to handle. However, don’t overlook the conventional rules
that appear in many games. While these are fairly straightforward, you still need to
quickly recognize their implications. Many games are ruined by careless
misinterpretations of what appear on the surface to be simple rules, so it’s worth
taking a look at these before tackling the tough stuff.
Conventional Rules
Direct Positive
A Direct Positive rule explicitly tells you something that must be the
case. Here are examples of Direct Positive rules for each of the game types
discussed above, beginning with the Ordering game.
Art Lectures: Ordering
Here you’d go right ahead and place a Q under number 5 in your
initial sketch. The logical implications are that Q cannot go anywhere
else, and no other artwork can take space 5.
P Q R S T V W
In Ordering games, a special case of this rule can occur when a
character is directly assigned to either end of the sequence, since that
creates additional implications. For example, if a rule stated that the
lecture on artwork S must be delivered first, then the additional
implication is that no lecture precedes the lecture on S, and that S’s
lecture does not come after any others. Conversely, if S’s lecture was
assigned to space 7, no lecture can come after S’s, and S’s lecture
cannot come before any others. Note also that a Direct Positive rule can
be stated in the negative, for example: “No lecture is delivered later
in the week than the lecture on artwork K.” Different wording, same
result. We know exactly in this case where lecture K is—last, which
means seventh. Any rule that allows you to write a character directly
into your blueprint is a Direct Positive.
Let’s now see what a Direct Positive would look like in the
context of our Choosing game.
Maggie’s Courses: Choosing
In this case you’d go right ahead and put an F into one of the
three slots in your blueprint. The logical implication is that only two
spots remain to be filled.
B C E F H L P
Let’s try the same with our Placing game.
Economic Seminars: Placing
This tells you to place an L in the free trade column. Nothing in
the introduction to this game suggests that employees must only
participate in one seminar, so we can’t tell yet whether Lee
participates in venture capital as well. But we do know that at least
one middle manager participates in free trade, since Lee is defined as
such in the intro.
Now let’s wrap up Direct Positives with our Linking
scenario.
Birthday Party: Linking
If you were keeping track of the information using a table, you’d
place a check in the box intersecting G and S. If you’re using a list
instead, you’d simply write an S above or below G in your cast of
characters. Since the game stipulates that each child eats either pizza
or a sandwich, the implication of this rule is that Gillian does not eat
pizza.
Direct Positive rules and their implications
are fairly simple, but they are often used as the starting point for
longer chains of reasoning. Don’t overlook them or underestimate
their importance.
Direct Negative
A Direct Negative rule explicitly tells you something that CANNOT be
the case. Here are examples of Direct Negatives for each of the major game
types, based on the same game introductions utilized above.
Art Lectures: Ordering
Writing “no Q” above the fifth slot in your blueprint for this
Ordering game would suffice to represent this rule. This tells us that Q
must be somewhere else. Sometimes the negative will include multiple
spots in the sequence. For example: “The lecture on artwork Q will not
be delivered second or fifth.”
Moving on, you generally won’t see a Direct Negative in a Choosing
game, since there would be no reason to include a character in the game
that can never be chosen. For example, in the game in which Maggie is to
choose three of the seven available courses, it would make no sense to
see a rule that says “Maggie will not choose literature.” If she can
never choose it, why include literature in the first place? Direct
Negative rules do apply perfectly well, however, to Placing
games.
Economic Seminars: Placing
Since each employee must participate in at least one seminar, this
rule allows you to deduce that Lee must participate in the venture
capital seminar.
Turn negatives into positives whenever
possible! When told what CANNOT be true of a particular character,
see if you can bounce that information off the other game parameters
to deduce something that MUST be true.
You may come across Direct Negative rules in Linking games as
well.
Birthday Party: Linking
Following the advice to turn negatives into positives, you’d
deduce that Gillian must therefore eat pizza, since sandwich and pizza
are her only options.
Again, these conventional rules aren’t rocket science, but if you
bollix one up, you’ll be in for a tough time. So it’s definitely worth
thinking through these basic implications before tackling the tougher
stuff. We continue our discussion of conventional rules with a slightly
more complex variety: rules that impose relationships between
characters.
Positive Relationship
A Positive Relationship rule creates a positive link between two
characters or aspects in the game. Here are examples of positive
relationships for each of the major game types, again beginning with
Ordering.
Art Lectures: Ordering
This rule creates a “cluster” out of characters Q and V. The word
“immediately” tells us that these two characters must be right next to
each other somewhere in the sequence, although we don’t yet know in what
order. “QV or VQ” is an effective way to shorthand this common Ordering
rule. Note that we also don’t know where in the ordering this cluster
will appear (first and second? fourth and fifth? sixth and seventh?
etc.), but the fact that it takes up a definite two-slot portion of real
estate will certainly come into play in your solution to many questions.
Clusters can consist of two, three, and even
four characters. Many games test your ability to space out such
clusters among the other characters without violating other rules.
Another common Positive Relationship Ordering rule specifies the
exact number of spaces between two characters. For example:
Here’s how you can shorthand this:
Q __ __ V
V __ __ Q
Yet another common Positive Relationship Ordering rule forces
characters before or after other characters but does not specify the
distance between them. Check out an example on the next page.
In this case, we can deduce for sure that Q can’t be first and V
can’t be last. Beyond that, we don’t know how many lectures come between
them. The rule is satisfied as long as V is before Q. Using “. . .” is a
good way to represent this:
V . . . Q
As we’ll see later on, it’s possible to form helpful deductions
when more than one rule like this shares a common character.
Choosing games are not good candidates for simple Positive
Relationship rules. We’ll see how the characters in Choosing games
interact positively and negatively when we get to Conditional rules. But
let’s move on to Placing games.
Economic Seminars: Placing
This tells us that J and M will be together at exactly one
seminar, but it does not tell us which one. However, as soon as we see
Jobson somewhere, we’d have to place Manute there too, and vice versa.
In addition, this implies that J and M cannot attend the other seminar.
Now let’s check out this kind of rule in our Linking
scenario.
Birthday Party: Linking
There are two first graders, and this rule sets up a positive
relationship between one of those first graders and pizza. Note that
this leaves open the possibility that the other first grader eats pizza
too. If the test makers wished to close off that possibility, they would
have written “Exactly one first grader eats pizza.”
Much as in Logical Reasoning and Reading Comprehension, precision
of language is a key component to Logic Games. Failing to grasp the
difference between “at least” and “exactly” spells doom in this section.
By now you probably sense that where there are positives, there
are likely to be negatives, and you wouldn’t be mistaken in that
assumption. Which brings us to our next category . . .
Negative Relationship
A Negative Relationship rule creates a negative link between two
characters or aspects in the game. As always, this is best understood in the
context of examples, so here goes.
Art Lectures: Ordering
This rule creates the opposite of a cluster:
space between characters. “No QV or VQ” would suffice to shorthand this
rule and would serve as a quick reminder that these two characters will
never occupy adjacent spaces. This means that as soon as we know where
one of them is, we know one or two places where the other character
CANNOT be: one spot off limits if the known character appears at either
end of the ordering and two spots off limits if the known character
appears in the interior of the ordering, with a space to the right and
left of it. Knowing the location of one of the characters could
therefore be used to determine where that other character
could be, or at least to narrow down the possibilities.
Characters in Choosing games may be characterized by Negative
Relationships, such as in the following scenario.
Maggie’s Courses: Choosing
Order doesn’t matter in a Choosing game, so we can simply
shorthand this rule as “No FE.” The implications are that if she chooses
French, she can’t choose English, and if she chooses English, she can’t
choose French. It is possible, however, for her to
reject both.
A key to Logic Games is understanding not
just what the rules forbid but also what they allow.
It’s time to get negative about Placing. Consider the
following.
Economic Seminars: Placing
This tells us that anywhere J is, M cannot be, and vice versa.
Since J and M must both appear somewhere, we can infer
from this rule that each one attends exactly one seminar. That’s because
if either attended both, they would have to be together in at least one
of them, in opposition to the rule. Note that we can’t tell yet which
employee attends which seminar. “No JM” will serves as a good enough
reminder until we receive more information that allows us to place them
definitively.
Let’s bring this rule category to a close with our final game
type, Linking.
Birthday Party: Linking
In a simple Linking game like this one, a Negative Relationship
rule translates easily into a Positive rule. Since there are only two
food choices, eliminating pizza as an option for first graders means
that both first graders must eat sandwiches. In more complicated games,
negative rules still can be turned into positive statements, even if it
doesn’t result in a definite deduction. For example, if the food choices
included macaroni, then the implication of this negative rule would be
that each first grader must eat either a sandwich or macaroni.
It bears repeating: Whether dealing with a
Direct Negative rule, Negative Relationship rule, or any other
negative element of the more complex rules to come, always try to
turn negatives into positives. Negatives are nice, if that’s all you
can get. But when you can turn negatives into positives, that’s when
the games break wide open. Knowing what is is more
powerful than knowing what isn’t.
Number Rules
It’s very important to understand the numbers that govern each game.
Sometimes numerical information is included in the game introduction, while
other times it’s provided in the rules themselves. Let’s work through some
typical examples of Number rules, again beginning with the Ordering game type.
Art Lectures: Ordering
With seven lectures total, you’d be expected to take this to its
logical conclusion: Q’s lecture must be delivered first, second, or third.
Any later would violate the rule. Again, notice how they tell you one thing
but fully expect you to derive something more concrete from it.
Now take a look at how numbers may influence a Choosing
game.
Maggie’s Courses: Choosing
Here very important numerical information is provided in the first
sentence of the introduction itself, strictly defining the parameters of the
game. Maggie must choose exactly three of the available seven courses.
Numbers often come into play in Placing games too.
Economic Seminars: Placing
Very helpful information, since there are exactly four middle managers
total in the game. Since Jobson, Lee, Manute, and Orson are the only middle
managers, this rule tells us that three of them will participate in the
venture capital seminar while the other must sit in on free trade. No doubt
some of the questions will play off this breakdown, which you’ll need to
manipulate in various ways depending on information presented in the other
rules or the question stems.
Let’s see an example of how numbers may influence a Linking
game.
Birthday Party: Linking
The birthday party game contains numerical information right in the
introduction which, when combined with this number rule, yields a valuable
Game Breaker (something we’ll discuss in greater depth when we get to Step
3). There is only one second grader in the game, so the only way that
more second graders than first graders can eat pizza is
if no first graders eat pizza. So should you write down “No
first grade pizza”? No! Since there’s only pizza and sandwiches in this
game, “no pizza” means “sandwiches.” So the full implication of this number
rule is that the lone second grader must eat pizza, while both first graders
eat sandwiches.
Always drive the information as far as it will
go! People who do this usually do well on Logic Games, for the simple
reason that this is one of the major things that’s tested: the ability
to recognize proper logical implications.
Of course, Number rules come in all shapes and sizes, and you’ll be
seeing plenty of them in the pages ahead. Now, however, it’s time to turn
our attention to the more complicated rules standing between you and Logic
Games success.
While you’re expected to instinctively understand the types of
conventional rules discussed to this point, there are other kinds of rules
that require a bit more brainpower. Let’s jump right in with Positive
Conditionals.
Complex Rules
Positive Conditional
Positive Conditional rules consist of if/then statements and
statements that can be translated into if/then statements. These tend to
give many test takers trouble. Let’s see how these work, beginning with the
same Ordering game we’ve been using throughout.
Art lectures: Ordering
In our discussion of if/then statements in the Logical Reasoning
chapter, we invoked a technique called reverse and negate (referred to
by some as the “contrapositive”). Here’s how it works:
The statement “If X, then Y” is logically equivalent to the
statement “If NOT Y, then NOT X.” We first reverse the order of the
characters in the statement, and then we negate both terms to form a
statement that means the same as the original.
Try it out in the case of the Ordering rule above: First reverse
the terms to get “If V fifth, then Q third.” Then (and make sure to do
this second step!), negate both to get “If V is NOT fifth, then Q is NOT
third.” Is that logically equivalent to the original? You bet—for the
simple reason that Q third requires V fifth. If V is not fifth, yet Q is
still third, then we’d be in violation of the rule.
Here’s how you might shorthand this on the page:
If Q3, then V5
If V NOT 5, then Q NOT 3
Now let’s consider a rule that’s a bit more complicated.
In this case, if Q is third, then two specific things must happen.
What would violate this rule? If either thing didn’t
happen while Q was third—that is, if V is NOT fifth and/or S is NOT
seventh. Either occurrence, by itself, is enough to violate the rule. So
here’s how we could shorthand both the rule and its logical
implications:
If Q3, then V5 and S7
If V NOT 5 or S NOT 7, then Q NOT 3
Consider one last variation on this theme:
In this case, a combination of two conditions causes a third event
to occur. This means that if this third event does not
occur, then the original combination cannot occur
either. That means that either part of the combination could happen
without the other, or that neither part could occur, which is fine too.
The only thing that couldn’t happen is both occurring if the third event
is missing. We can note this as follows:
If R2 and T4, then W5
If W NOT 5, then NOT BOTH R2 and T4
We can apply the same type of reasoning to our Choosing game
scenario.
Maggie’s Courses: Choosing
An interesting thing to note from this rule is that not every
conditional statement actually contains the words if
and then. Sometimes, as in this case, these words are
implied. First translate the rule into proper if/then form: Including
biology anytime history is included essentially means that if history is
included, then biology is included. The reverse and negate technique
works for any conditional statement, regardless of game type, so we can
apply it here to derive the rule’s logical equivalent: If no biology,
then no history. Here are both statements in shorthand form:
If H, then B
If NO B, then NO H
Now work through the Positive Conditional in our trusty Placing
game.
Economic Seminars: Placing
Here’s the shorthand of the original rule, plus the result of
reverse and negate:
If N ft, then J vc
If J NOT vc then N NOT ft
Since the only seminars are free trade and venture capital, we can
take this one step further:
If J ft, then N vc
Hopefully you’re getting the hang of working with Positive
Conditionals. Let’s try one more example in the context of our Linking
scenario.
Birthday Party: Linking
Here’s the shorthand of the original rule, plus the result of
reverse and negate:
If J pizza, then F nurs
If F NOT nurs, then J NOT pizza
Sounds reasonable, but you’d be negligent to leave it at that.
“Not nursery school” means first or second grade, and “not pizza” means
“sandwich,” so this last statement can be rewritten in the positive as:
If F 1st or 2nd, then J sandwich
With this info under our belts, how nice would it be for a
question to place Francie in first or second grade, and then ask what
must be true? “James does not eat pizza” would be a fine answer to allow
us to cash in on this work. Or the question might ask what CANNOT be
true, in which case “James eats pizza” would get the point. Anyway,
we’re getting a bit ahead of ourselves, since cashing in comes after
we’ve dissected the rules and tried our best to Search
for Game Breakers, Step 3 of our Essential Strategy. But you can see
where we’re heading. Let’s get back to the present discussion with a
look at the next complex rule type—Negative Conditionals.
Negative Conditional
Negative Conditional rules also consist of if/then statements and
statements that can be translated into if/then statements. However, unlike
Positive Conditionals, these specify that when one thing happens, another
thing doesn’t happen. Here are some examples for each of
the major game types.
Art lectures: Ordering
The key to using reverse and negate for Negative Conditional rules
is to remember that two negatives make a positive. In the Ordering rule
above, the negation of “V NOT fifth” is “V fifth.” So here’s how we can
shorthand the rule, and its logical implication:
If Q3, then V NOT 5
If V5, then Q NOT 3
Let’s apply this to one of the more complicated Ordering rules
discussed earlier:
Here’s a shorthanded version of the rule plus the result when we
apply reverse and negate:
If R2 and T4, then W NOT 5
If W5, then NOT BOTH R2 and T4
Negating a negative statement turns it into a
positive statement.
Try the next one based on our Choosing game intro.
Maggie’s Courses: Choosing
Here’s the rule and its logical equivalent in shorthand form:
If B, then No H
If H, then NO B
Notice that in this case the upshot is that biology and history
can never be included together in the group of courses Maggie selects.
Now try it with Placing.
Economic Seminars: Placing
Here’s the shorthand of the original rule, plus the result of
reverse and negate:
If Nft, then J NOT vc
If Jvc, then N NOT ft
Since in this case free trade and venture capital are the only two
seminars, we can take this one step further:
If Nft, then Jft
If Jvc, then Nvc
Bring it on home for Negative Conditionals with the Linking
scenario . . .
Birthday Party: Linking
Here’s the shorthand of the original rule, plus the result of
reverse and negate:
If J pizza, then F NOT nurs
If F nurs, then J NOT pizza
Can we take this one step further as well? Yup, and we should
since it’s always best to gather as much positive information as
possible. “Not nursery school” means first or second grade. “Not pizza”
means “sandwich.” So here’s our final understanding of this
rule:
If J pizza, then F 1st or 2nd
If F nurs, then J sand
Unless
Some rules are built around the word unless. On the
LSAT, you might see a rule indicating that a certain thing can’t happen
unless something else happens. Here’s an example.
Maggie’s Courses: Choosing
To say that biology is not selected unless history is selected is
the same as saying that biology requires history:
If B, then H
To which we can now apply reverse and negate:
If NO H, then NO B
Notice that the selection of history does not
guarantee the selection of biology—it merely makes it
possible. There’s no equivalency beginning “If H . . .” because if
history is selected, biology may be selected, but it
need not be. All we know for sure from this “unless” rule are the two
if/then statements listed above.
Either
Some rules contain the word either. Here are a few
examples to chew on for the Ordering and Choosing game varieties.
Art Lectures: Ordering
The implications are that if some lecture beside T’s lecture is
first, T’s must be sixth, and if some lecture beside T’s lecture is
sixth, T’s must be first.
Here’s another way either can be used in an
Ordering rule:
In this case, it makes sense to jot down T/V above the third slot
in your blueprint. As soon as you see one of those characters in some
other spot, you can pencil the other character into spot 3.
Now see how either plays out in the context of a
Choosing example.
Maggie’s Courses: Choosing
That means that a group with communications but not philosophy is
okay. A group with philosophy but not communications is also okay. A
group with both communications and
philosophy is also okay.
Wait a minute—that seems counterintuitive to many, since the rule
seems to say that we need either one or the other. However, on the LSAT
the idea “but not both” will be included in the rule if the intention is
that both characters cannot be included in the group. The only thing
that violates the rule as stated above is a group of chosen courses that
includes neither communications nor philosophy.
If you’re having trouble interpreting a rule,
think about what scenarios would violate that rule.
That should help you zero in on what the rule really means and how
it will play out throughout the game.
Only If
An “only if” statement can be turned into an if/then statement by
placing the “then” after the “only” term. For example, consider the
following Placing rule.
Economic Seminars: Placing
There are two parts of an “only if” statement: the part attached
to the “only if” phrase (here, K vc) and the other condition in the
statement (here, O ft). This other condition—in this case, Orson joining
free trade—relies on the “only if” condition. Here, that means that if
Orson participates in free trade, then King must participate in venture
capital; the “only if” phrase in the statement demands this. So we can
turn this “only if” statement into a standard if/then statement, like
so:
If O ft, then K vc
In fact, we can even derive a general rule from this: For any
“only if” statement, throw an “if” in front of the other condition and a
“then” in front of the condition associated with the “only if” phrase
and you’ll end up with a valid statement in the form of “If X, then Y.”
It sounds confusing, but go back to look how we applied this rule to the
example above and it should eventually click. The beauty of restating
the “only if” statement as an if/then statement is that now we can apply
reverse and negate to yield yet another valid statement:
If K NOT vc, then O NOT ft
Do we stop there? No! Remember to translate negatives into
positives whenever possible. Since the only choices in this game are
free trade and venture capital, we can get rid of the two NOTs:
If K ft, then O vc
That’s a lot of information derived from a seemingly innocuous
“only if” rule, but that’s what Logic Games success is all
about.
If and Only If
What if we add an “if” to the “only if” statement? Let’s use the same
Placing rule to find out.
Economic Seminars: Placing
The interpretation of the “only if” part of the rule remains the
same as what we just deduced:
If O ft, then K vc
If K ft, then O vc
However, we must also take the “if” part into account:
If K vc, then O ft
Using reverse and negate and translating negatives to positives
yields:
If O vc, then K ft
Here’s the difference: The “only if” rule allows for the
possibility that King and Orson participate together in the seminar on
venture capital. The “if and only if” version of the
rule does not allow for this possibility. It forces these two employees
to split up, no matter what. The test makers don’t use “if and only if”
very often, but they have in the past, and nothing stops them from doing
so in the future. Your confidence will increase when you go into the
test feeling as if you’re ready for anything they may throw your way.
That does it for Step 2, Get the Specs. The specs of the game are
mainly spelled out in the rules, although some important specifications,
especially number information, may be included in the introduction as
well. The line between what we call Conventional and Complex rules may
blur in cases. For example, some Conditional rules may become simple to
you with practice, while a Number rule may throw you for a loop. Don’t
get hung up in the terminology—just study the categories above until
these kinds of rules discussed, and their logical equivalencies, make
sense and become second nature to you. Hopefully, even the toughest of
rules will seem conventional to you by test day. The examples above
cover the majority of rule scenarios you’ll come across, but you’ll
likely encounter variations and combinations as well. You’ll get plenty
of practice working with rules from the eight games in this book. Extend
what you learn from this section, and from those eight games, to every
practice game you try.
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