Logical Reasoning | Formal Logic Inference Questions

My students know I'm not a fan of diagramming most Logical Reasoning questions. However, some questions just beg to be diagrammed. These questions tend to be formal logic inference questions and sufficient assumption (justify) questions.

In this blog post, I'll cover one Logical Reasoning question that should be easy but gives many test-takers a lot of difficulty when they're first starting Logical Reasoning:

It's PrepTest 30 (December 1999), Section 2, Question 18 (page 59 in Next 10). It's about inspired musical performances, good show, etc.

First sentence:
This part of the stimulus is pretty straightforward and contains clear indicator words (If...then), so we can diagram this as:

IP --> GS

Second sentence:
This one's a bit nasty, as it contains the word "unless." It's a clear example where putting the "unless" translation technique into practice comes in handy.

Take the word "unless" to introduce the necessary condition and negate the other part of the clause to make it the sufficient condition.

"NOT GS" becomes "GS" and is the sufficient condition part of this conditional statement.

"SL" becomes our necessary condition, giving us:

GS --> SL

Instead of writing it down separately (as I just did), I would immediately connect this with the first sentence, giving us:

IP --> GS --> SL

Third sentence:
This one has less obvious indicator words than the first sentence does.

"To be" is the sufficient condition indicator. You may know this more commonly as "in order to be", but this meaning is the same.

"Must" is our necessary condition indicator.

This can be diagrammed as:

SL --> MR

As with the second sentence, instead of writing down the new information separately, I would it immediately connect it with what we already have, giving us a long chain (and its contrapositive):

LSAT PrepTest 30, Section 2, Question 18

Attacking the answer choices:
Just check each of the answer choices against the appropriate chain. You'll find that the wrong answer choices are all mistaken negations of one chain and mistaken reversals of the other.

I would not actually diagram or write anything out for any of the answer choices. Instead, I would just read each choice and mentally check it against the choices. It's faster, and you'll find that you don't actually need to write anything out.

Choice B: NOT GS --> NOT MR
Choice C: MR --> IP
Choice D: NOT GS --> NOT MR
Choice E: SL --> IP

Yes, choices B and D are identical - they're just presented differently (D has the word "unless" in it).

What LSAC is likely to ask in a question like this, and why:
The remainder of this blog post is not a description of how I would actually approach this question (or questions of this type). I already covered that above.

I'll number the variables for easy reference:
LSAT PrepTest 30, Section 2, Question 18, Numbered

When asking us what "must be true," LSAC is not likely to ask about any variables that are adjacent to each other (consecutively numbered / touching).

Someone who hadn't connected the sentences into conditional chains would still be able to answer that questions, and LSAC loves it when you're able to connect things.

This means that the correct answer is not likely to be any of the following:

1 requires 2
2 requires 3
3 requires 4
5 requires 6
6 requires 7
7 requires 8

LSAC also isn't likely to ask us anything about the first chain (the variables numbered 1-4).

Asking about the first chain wouldn't require you to have taken the contrapositive. LSAC loves the contrapositive more than milk and cookies. It just makes them so happy.

This means we're likely to deal with the second chain (the contrapositive) - the one with all the negatives.

With the first chain out of the way, our remaining options are:

5 requires 7
6 requires 8
5 requires 8

Sure enough, the answer is 6 requires 8.


  1. Hey Steve,

    Im all out of ideas man. I posted a comment about a couple of weeks ago when you were discussing the Feb LSAT. I've been focussing mainly on Logical Reasoning for now. So I've done all the LR section from Preptests 36 to 43 now. Gone over the Logical Reasoning bible and applying the concepts. Im focussing mainly on accuracy for the time being and hope that I can cut down the time. The problem is that its taking about an avg of 53 min to complete the sections with about 5-6 wrong answers. I dont really know how I'd be able to bring this time down while maintaining/improving accuracy. Any tips? Also, Im having a terrible time doing Inference/Must be True questions. Its really annoying for me to know that Im sacrificing time to get the questions right but I get almost every single one of these question wrong. For example on Preptest 43, Section 3 question 21, why can't the answer be C instead of B? I've done everything I can, I dont know what else I can do to improve my chances for the Feb LSAT. Im sure its not the number of preptests you do, cuz in total I've gone through around 30 of them - 10 more actual, The Next 10 and 39 to 45...Im clueless.


  2. Hey Ali...i had that problem initially at first..but one thing I did was sit my lsats down and try to apply the concepts to real life. i felt totally bummed when it would take me a long time to do lsats...but when I cam back to it a few weeks later, my score jumped significantly...
    and I looked at the question for u...you can tell off the back that the correct answer is B. I thought this was tricky at first but hear me out...the answer is not A because of what the stimulus says, and since some is the logical opposite of none, some can mean all...and the stimulus says that there were at least some who were NOT active in the artistic circle (at least one) since some can me 100% a is wrong. C is wrong because it could be true but it does not have to be. The stimulus says that the two events took place the the same time, but it did not say that the participants of the two events participated independent of each other. Look again at the last sentence...it starts with at least some (1%-100%), which means that at least one of the people participated in both events, so it must be true that at least one person from the art circle received a certificate , but it also must be true that at least some people were not in both groups because the last sentence says "here are at least some spring cleanup
    participants who are not active in the town’s artistic
    circles." Sorry for the long explanation...but once it clicked..i was excited to explain it.

  3. great post steve, thanks!

  4. Do certain words in this question, namely "any" and "no," and the phrase "there are" change the diagram?

    For example,
    Any (even 1 single) IP --> GS --> (at least 2) SL --> (at least 2) MR
    EVERYONE NOT MR (as in not even one person MR) --> EVERYONE NOT SL (as in not even one person SL) --> NOT GS --> NOT (even 1) IP

    I bring this up because answer choices (B) and (D) seem to be a little different from each other.

    Above, answer choice (B) is diagrammed as: NOT GS --> NOT MR

    Doesn't B really say: NOT GS --> EVERYONE NOT MR
    This clearly goes in the opposite direction from the diagram for the contrapositive, so (B) is clearly wrong. But both NOT GS and EVERYONE NOT MR show up in the diagram.

    What about (D)? Above, it's diagrammed (using the conversion method for "unless") as NOT GS --> NOT MR

    What about this approach?
    As stated: GS unless SOME (at least 2) NOT MR
    Conversion: NOT GS --> SOME (at least 2) NOT MR

    This still goes in a direction opposite to the diagram for the contrapositive, but also appears to introduce another error, i.e., "SOME (at least 2) NOT MR" has been substituted for "EVERYONE NOT MR."

    Is this correct, and does the LSAT ever ask you to make a distinction in diagrams between "everyone" (or "all") and "some" (or at least one)?


  5. Now, now, I think it may be a bit extreme to say the LSAC loves contrapositives more than milk and cookies.

    Okay, maybe not.

    I know all of this stuff, danggit, and I diagram most (like 98%) questions correctly. I made an "A" in Symbolic Logic and loved derivations (not more than milk and cookies though). I truly believe my processing speed is not as sharp, as I also found it a problem that I read slow in college.

  6. Steve, When doing this question, if we see A and recognize it as the correct answer, do you recommend that we read the rest of the answer choices or move on to the next question right away?