A common pattern of GMAT Data Sufficiency question concerns sequences — specifically, arithmetic sequences and geometric sequences. The good news is that unlike with GMAT problem solving questions concerning sequences, on GMAT data sufficiency questions you don’t actually have to solve anything! Remember, all you need to do is figure out whether or not you could solve for a particular term in a sequence, given the two statements. That makes life much easier, doesn’t it?
Here are a few tips for you about these types of data sufficiency questions. First, remember this general rule about approaching data sufficiencies: Before you launch into evaluating the statements and trying to determine whether or not you could answer the question given the two statements, always do a bit of “mental brainwork” first. Specifically, try to determine in advance what information, if it were given to you, would enable you to answer the question.
In other words, as it concerns data sufficiency sequence questions, what pieces of information would you need to be given in the statements to be able to find the missing term in a sequence (assuming that’s what the question is asking for)? And would it matter if the sequence were an arithmetic sequence vs. a geometric sequence?
First, a quick note about sequences. Let’s say I gave you this set of numbers:
1, 2, 3, 5, 8, 13, 21, 34
What do you think would be the next number in that sequence?
If you recognized this as the famous Fibonacci Sequence, nice work. The next number would be 55, because you simply add the two two preceding numbers in the sequence to get the next number in the sequence.
Knowing this rule, could you figure out the 100th number in that sequence? Of course. It might be annoying to sit there with a calculator and add numbers 100 times, but the point is that you could do it.
Now, what if I gave you this rule for a hypothetical sequence:
To find the next term in Sequence S, multiply the last number in the sequence by 2 and then divide that product by three.
Question: What is the 100th term in Sequence S?
You can’t find it, can you? Doesn’t the 100th term depend on the 1st term? In other words, using that sequence rule, wouldn’t the 100th term be very different if the first term in Sequence S were 10 versus if the first term were -20? Yes, of course.
The point is, to find the Nth term in any sequence (whether arithmetic or geometric), you need two bits of information:
- A reference term in the sequence (not necessarily the first term)
- The rule for finding the next term in the sequence
With that in mind, take a stab at the following GMAT data sufficiency practice question:
If sequence S has 100 terms, what is the 92nd term of S?
(1) The first term of S is -40.
(2) Each terms of S after the first term is 5 less than the preceding term.
What’s the answer?
Great job if you saw that the answer is C. Based on what we just learned about the two pieces of information we need to know in order to find the Nth term in a sequence, neither statement alone is sufficient to answer the question. Statement (1) gives us a starting point, but no rule about how to get to the next term. Therefore, we have no idea what the 92nd term would be. Likewise, Statement (2) gives us a nice rule to employ to find the subsequent terms in the sequence, but no reference term. Therefore, the 92nd term could be anything using that rule, depending on what the first term is.
Taken together, however, the two statements certainly provide enough information to determine the 92nd term in the sequence. Incidentally, what is the 92nd term? We don’t care! We simply care that we could find it, if we spent enough time with our calculator!
Bonus Data Sufficiency Practice Question
If the price of a candy bar is doubled, by what percent will sales of the candy bar decrease?
(1) For every ten cent increase in price, the sales will decrease by 5 percent.
(2) Each candy bar now costs 60 cents.
What did you get?
The answer is C. Great job if you got that.
Hopefully this problem looked very similar to the sequence example above. This pattern of data sufficiency question will appear often on the GMAT. It may appear as an actual sequence example, or it may appear in a form like this one where the logic is the same, but the example is slightly different.
Here, you should have noticed that Statement (1) alone is insufficient because there is no starting — or reference — price. This “rule” provided in Statement (1) is helpful, but not sufficient. If the candy bar is currently $1 and doubles to $2, that will be a very different reduction in sales, based on a percentage change, than if the candy bar starts at $2 and doubles to $4. (if you need to convince yourself, actually do the math).
Statement (2) gives us that starting price, but no “rule” about how much an increase in price will affect sales. Therefore, by itself, Statement (2) is insufficient.
Taken together, however, we have both a reference point and a rule, which are enough information to answer the question.
Keep your antennae up for this type of pattern of GMAT data sufficiency question, and you should be able to get all of these right on test day.
