Tackling Exponents in Data Sufficiency Questions
However, refreshing yourself with the rules of exponents will enable you to move through these questions confidently.
Let’s look at the following example from the Economist GMAT Tutor:
If and are integers, what is the value of ?
As always, look at statement (1) first. Because the bases are different, the only way that these terms can be equal is if each exponent is equal to 0, since any number raised to the 0 power is equal to 1:
Therefore, we can equate each exponent to 0, giving us:
If this is the case, then in either situation, we have . As such, and could be anything, as long as they have the same value. Therefore, Stat. (1) is insufficient.
Now let’s look at statement (2).
The easiest way to deal with exponent questions involving an equation is if either the bases on both sides of the equal sign are the same, or the exponents on both sides of the equal sign are the same. It is usually easier if you make the bases equal. Let’s do that here.
Now, we can equate the exponents:
→ For the 3s, we have:
→ For the 5s, we have:
We have a value for , and as such, Stat.(2) is sufficient. The answer is B.
Notice this question, which looked challenging at first glance, becomes easier if you work step by step through it using all the rules at your disposal.
. Secondly, make bases or exponents the same.
Following these rules will save you time. There are so many exponent questions on the GMAT that involve making the bases the same or making the exponents the same that to do so should be your first reaction when you see such questions.
This post appeared first on the Economist GMAT Tutor blog.