Logical Structure

GMAT LogicWe’ve covered, in an earlier blog post, how to deal with the simplest formal logic statement: If X, then Y.  But what happens when our necessary or sufficient factors become more complicated?  Let’s look at a couple of examples, using the idea of a vegetable salad.  The simplest statement and its contrapositive might look like this:

If the salad has lettuce, then it has tomatoes.
If the salad has no tomatoes, then it has no lettuce.

Now let’s add more vegetables (and more complicated logic):

If the salad has lettuce or spinach, then it has tomatoes and peppers.

Here’s an important idea: when you are forming a contrapositive, you already know that the necessary and sufficient factors are switched around and negated.  But now you also have to remember that “and” becomes “or,” and vice versa.  So the statement above becomes:

If the salad has no tomatoes or no peppers, then it has no lettuce and no spinach.

I find it extremely helpful to individually negate each element of the statement; otherwise, it’s easy to get confused. ...

GMAT SC LogicThe single-most crucial type of Sentence Correction error, Modifiers, Comparisons, and Verb Tenses all share one thing in common: you do not  need to be an expert editor to recognize that this sentence is illogical!  The introductory phrase in this sentence, “the single-most type…” is clearly meant to describe one item, but the rest of the sentence lists three.  This does not make logical sense!  Technically you’d call this a modifier error, in that the modifying phrase to begin the sentence – recognizable because it begins the sentence, is separated by a comma, and does not include its own subject and verb (note: these aren’t essential characteristics of any modifier, but they are one surefire way to identify a commonly-occurring type of modifier in which SC errors often crop up) – does not logically modify the noun that follows.

If you want to get really technical, it is an appositive modifier (a noun phrase used to describe another noun), but the GMAT will never require you to describe the...

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