Logic Problems

Logic problems on the SAT usually require you to do some math in addition to applying logic.  They come with three statements, and ask you which combination is true.

Here’s an example.

Assume that a and b are non-zero real numbers so that (b<a<frac ab)  Which of the following statements must be true?

I. (b^2>a)
II. (b<1)
III. (a>0)

A)  I only 
B)  I and II only 
C) II only 
D) II and III only 

Strategy:

  1. Distinguish exactly what the problem is asking. Does it say something should be true or something must be true?
  2. Be sure to underline and follow any rules/parameters given in the question.
  3. If dealing with relationships between variables, test each answer choice with numbers. For this method, you want to use several numbers that are different (positive, negative, and fractions) to be sure you thoroughly understand the relationship.

Back to our example:

First, notice the wording.  It does not say “could be true”, it says “must be true”.  

Now, we have some variables but no numbers, so let’s try inserting our own numbers.

We can start by making b = (v) and a = 1.  This works in our inequality in the question, and disproves statement I. With these values, which follow the rule in the question, (b^2<a). This eliminates A) and B).

Now let’s try and follow the rules and disprove III. Let’s make b = -4 and a = -2. This would make (frac ab=frac12), so we’ve successfully followed the inequality rule in the question. And a is clearly less than 0. So we’ve eliminated III and answer choice D).

Leaving us with the correct answer: C).