I. Roman numeral Quant problems aren’t a whole lot of fun.
II. A lot of my students choose to skip them entirely, which is much smarter than wasting five minutes wondering what to do!
III. However, it’s possible to turn this rare and tricky problem type into an opportunity.
Reason 1: They’re always easier than they look.
Roman numeral problems are a little bit like Data Sufficiency problems. The difficulty usually doesn’t come from the math itself; it comes from complicated logic and deliberately obscure writing. You should always start a tricky-looking Data Sufficiency problem by
translating and
simplifying the problem, and you can do the same on Roman numeral problems.
Here’s a problem:
At first glance, this problem is a mess. If you simplify the problem before you begin approaching it, though, you’ll discover a much easier problem underlying it. Start with the question stem, just like in Data Sufficiency:
Then, simplify the statements, starting with the first:
The first statement actually simplifies to exactly what you’re given in the question itself, so it must be true. As an exercise, simplify the second statement in the same way. It simplifies to
ad >
bc, which
isn’t true.
At this point, you know that the right answer must include I, and it can’t include II. You could move on and simplify the third, much more complex statement, but do you really have to?
Reason 2: There’s partial credit.
Well, not technically. But take another look at those answer choices.
You can actually eliminate all but two of them. Only (B) and (E) meet the criteria of including Roman numeral I, but not including Roman numeral II. If you’re quick enough with algebra, you could get to this point 1 minute into the problem — and
a 50/50 guess after 1 minute beats a definitive answer after 3 minutes, when it comes to maximizing your final score. Since Roman numeral problems often have one or two statements that are much simpler than the others, they represent a fantastic opportunity to take a
good guess quickly.
But if you’ve got plenty of time to solve a Roman numeral problem all the way through, what do you do?
Reason 3: Testing easy cases works really well.
As mentioned above that the difficulty of Roman Numeral problems doesn’t usually come from the math. When you test cases, you’ll rarely be tripped up by tough arithmetic or lengthy calculations. Plus, problems are often designed so that it’s clear what cases you should test. When they aren’t, you can sometimes get enough information by just testing a simple case at random. Try that approach with the third statement.
Since
ad < bc, choose the following values:
a = 1 b = 2
d = 1 c = 2
Then, plug those values into statement III:
Since that isn’t true, statement III doesn’t
have to be true. The correct answer to the problem is
(B) I only. The thing to notice here is how straightforward it was to test that case — and how, unlike in Data Sufficiency, testing just one case sometimes gives you all the information you need.
What to do next
Roman numeral problems are rare on the CAT. There’s no reason to spend hours studying them, since you might see a single one on any given Quant section. That said, they’re sometimes easier than they look! After reading this article, you have all of the basic tools you need to approach most Roman numeral problems.
