# Executive Assessment: Quant Strategies for Faster Solutions – Part 2:

by on November 4th, 2017

Last time, we talked about how to Test Cases on Data Sufficiency (DS) questions. (If you haven’t read the first installment yet, go do that now.) Today, you’re going to get a chance to test out your skills on a similar problem.

Here’s another Executive Assessment problem from the official free practice set (this one is labeled #7 in the DS set on the EA website, as of October 2017). Give yourself about 2 minutes to answer the question.

“If r and s are integers, is r divisible by 7?

“(1) The product rs is divisible by 7.

“(2) s is not divisible by 7.”

(Reminder: If you don’t know Data Sufficiency well enough yet to have memorized the answer choices, follow this link.)

Before we dive in, how comfortable are you feeling with the problem right now? If you feel just fine, keep going. If you’re not as confident, use the first installment of this series to remind yourself of the steps of the process. Check your work. See whether you want to change anything.

Then, when you’re ready, come back here.

Glance: DS. Words like integer, divisible by, product—these indicate a number properties type of question.

Let’s Read and get this thing Jotted down on paper.

Now what? Reflect & Organize.

Definitely number properties. Also, they never give real values for r and s but just keep talking and asking about properties of the two. That’s how I know I’m going to test cases to solve.

Glance at the statements again. To me, the second statement is easier (I have to deal with only one of the variables, not both), so I’d prefer to start with statement (2). My next step is to write down BD / ACE on my scrap paper and start working on that statement.

The question asks about r, but the statement tells me only about s. Without any additional information, I can’t figure out anything about r, so I don’t have to test anything yet. Statement (2) is not sufficient; cross off BD.

Next, take a look at statement (1). This one is more involved. Pick a value that makes statement (1) true and see what happens.

The product rs could be 7, for example. There are two possibilities from there: either r = 1 and s = 7 (in which case, r is not divisible by 7) or r = 7 and s = 1 (in which case, r is divisible by 7).

We’ve got a sometimes yes, sometimes no answer, so statement (1) is also not sufficient to answer the question. Cross off answer (A).

Now, reflect again for a second. Your next step will be to combine the two statements; before you do that, what did statement (1) tell you about the properties of r and s?

If the product rs is divisible by 7, then either r or s has to be divisible by 7. (They could also both be divisible by 7.)

Jot that down. Now, what did statement (2) say? Right, s is not divisible by 7.

If at least one has to be divisible by 7, but s is not, then r must be divisible by 7.

The correct answer is (C): Both statements together are sufficient (but neither statement is sufficient alone).