BACKSOLVE
One of the answer choices has to be the correct answer, so you can sometimes just try them
out. Since the answer choices are generally in numerical order, start with (B) or (D). If it
doesn’t work, you might at least know whether you’re looking for something bigger or
something smaller. At most you only have to try the middle number of the remaining
choices. Note: Often you don’t have to try all the answer choices when backsolving.In this case, the base on the left is 9, and the base on the right is 27. They’re both powers of 3, so
express both sides as powers of 3:
Now that both sides have the same base, you can simply set the exponent expressions equal and
solve for n:
Then plug in −3 for n in the final expression:
The answer is (D).
Note that Backsolving would work here if we were solving for n, but it doesn’t work because of the
added expression to evaluate. Don’t depend on backsolving too much. Lots of math questions can’t
be backsolved at all, and many that can are more quickly solved by a more direct approach.