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GMAT Tip: Inequalities…and then some…(Part 1)

When it comes to tricky quantitative questions, inequalities take the prize for serving as one of the biggest deceivingly easy questions. Test takers should just treat inequalities as algebraic “equal to” equations with just a < or > symbol in place of the = sign, right?

If only it was so simple. Inequalities are designed to assess your critical thinking skills, working beyond solving for a value of a variable to considering the range of variable possibilities. Furthermore, inequalities questions are set up as data sufficiency questions the majority of the time. Smart test takers know to be on their toes.

Let’s start with a 500 level quantitative inequality question:

Is n between 0 and 1?

Statement 1: n^2 < n
Statement 2: n^3 > 0

Start by evaluating the question. What does it mean when n is between 0 and 1? It means n is not an integer. It is also a positive fraction or decimal, such as ½ or 0.25.

Now that we know what we are working with, so let’s move on to Statement 1. What would make n^2 less than n?

The variable n cannot possibly be a negative number, because by squaring it n becomes a positive number.

The only way the n^2 could be less than n is if n was a fraction, like ½. When ½ is squared (½ * ½) it becomes ¼, which is smaller than ½.

Indeed, Statement 1 is sufficient to prove that n lies between 0 and 1.

Okay, so next up is Statement 2, where n^3 > 0. If we have the same mindset as Statement 1, we work to assess the options.

If n^3 is greater than 0, then it cannot possibility be negative. But, then, does n definitely lie between 0 and 1?

Not necessarily. The expression n^3 means that, sure, if n = ½ then (½)^3 is ⅛ and therefore greater than 0. The variable n could also be 1, or 2, which would make n^3 greater than 0, but not a fraction or decimal.

Statement 2 is not sufficient. The correct answer to this question is (A).

When looking at inequality questions, the key to getting the right answer is being flexible in your thinking.

But inequalities are rarely this simple. Often, these trickster questions are complicated by absolute value, multiple variables, and square roots.

How do we tackle those questions? Check out Part 2 in next week’s post.

The above GMAT Tip comes from Veritas Prep. Since its founding in 2002, Veritas Prep has helped more than 100,000 students prepare for the GMAT and offers the most highly rated GMAT Prep course in the industry.

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