Today’s ACT question of the day is a math question about absolute value and number properties.  Remember the basic fact about absolute value: everything that comes out of the bars is either positive or 0.  Kind of like coming out of prison?

Anyhow.  If we have that fact with us, we can answer this question.

They want to know the values of a and b, if any, where a|b – 2| < 0.  Let’s deal with the absolute value part first:

If b = 2, everything is 0

if b is anything else, that part is positive.

Now a:

if a = 0, everything is 0

if a > 0 and b 2, everything is positive ( means “not equal to” in case you weren’t sure)

if a < 0 and b 2, everything is negative.

If you wanted to use numbers instead, you could pick a positive number and a negative number to stand in for a, and any number other than 2 to stand in for b.

We want everything to be negative, so that means:

b 2 and a < 0

Choice A fits the bill!

For more practice with absolute value, take a look at these problems.