Hello GMAT aspirants! It's Murtuza Gadiwala here, your 99th percentile GMAT instructor. Today, I want to demystify a type of GMAT question that often looks more complex than it truly is: Sequence Questions. You know the ones – they're filled with "n"s and "n-1"s and often seem very mathematical. While they might appear daunting, trust me, they are usually quite straightforward. The secret? Just get started!
Generate the first few terms, and a clear pattern is almost guaranteed to emerge. Let’s dive into a specific Data Sufficiency example, a question type that now features in the GMAT Focus Edition's Data Insights section, to show you exactly what I mean.
$$ s_n = \frac{1}{n} - \frac{1}{n+1} $$
Is the sum of the first k terms greater than 9/10?
(1) k > 10
(2) k < 19
Unpacking the Sequence: Discover the Pattern
The first thing I always recommend my students do is to simply start writing down the first few terms. This small step is often the breakthrough you need. Let's try it together.
Interactive Term Generator
Because all the intermediate terms cancel, the sum of the first 'k' terms (Sₖ) simplifies dramatically. The `-1/2` cancels, the `-1/3` will cancel, and so on, until only the very first and very last parts remain. The general formula for the sum is:
$$ S_k = 1 - \frac{1}{k+1} $$
This simple formula, discovered just by writing out a few terms, is the key to solving the problem efficiently.
Solving the Data Sufficiency Question
The question is: Is Sₖ > 9/10? Or, rephrased using our formula: Is 1 - 1/(k+1) > 9/10? Let's test the statements.
Statement (1): k > 10
Statement (2): k < 19
The Final Verdict
Based on our interactive analysis, Statement (1) alone is sufficient because it always yields a "Yes". Statement (2) is not sufficient because it yields both "Yes" and "No" answers. Therefore, the answer to this Data Sufficiency question is A.
The biggest takeaway here, as with many GMAT Quant problems, is to conquer your initial intimidation. Don't worry about how complex a sequence might appear. Just get started! Write down those first three or four terms, observe how they interact, and you'll often find a simple, clear pattern that makes the rest of the problem-solving process fall into place.