SAT Question of the Day Explained – January 16, 2014 – Math, Algebra, Absolute Value

Stay positive!Today’s SAT question of the day begins with two numbers, a, and b.  The difference between |a| and |b| is 5.  The answer choices provide four false statements and one potentially true statement.

To look at things a different way, a – b is 5 and neither a nor b can be negative.  This means that a has to be bigger than b, and that a has to be at least 5.  (Test it out: for example, if a was 2, could we subtract any positive number and get 5?  Nope.)

We have to choose an answer that fits with those two facts. The correct answer can’t suggest that a is not bigger than b, or that a is less than 5.  Check each answer choice:

  1. says that a < 5
  2. is a possibility – doesn’t contradict a >b and a greater than or equal to 5.
  3. does not say that a > b
  4. makes no sense in this situation, and still doesn’t say that the absolute value of a is grear than the absolute value of b
  5. says that a < 1

Done!  We found only one answer that’s a possibility, so we know which one to choose.

As a reminder, absolute value means the number of units between 0 and your number on a number line.  -3 is three units from 0, so its absolute value is 3.  -95 has an absolute value of 95…as does 95.  Absolute value notation looks like |x|, which reads “the absolute value of x”.