When you set up the algebra (Rate = Distance / Time), you’ll end up with:

Rate upstream = (v – 3) = 90 / (T + ½)

Rate downstream = (v + 3) = 90 / T

Now here, you have two equations and two variables, so the algebra is looking up. That means that you can solve for each variable. So in sort of classic algebraic style, your first move may well be to get rid of the denominators by multiplying both sides of each equation by its denominator (or many GMAT students will have this already, preferring the RT = D equation). But watch where that will let you down, using the upstream equation:

(v – 3)( T + ½) = 90

You know algebra well enough to see that this leads you down the quadratic route and will stick you not just with two variables, v and T, but with a combined vt term. The “normal” algebraic method is a dead end! But at this point backsolving is a little bit of a mess, too, as if you were to start in the middle and plug in 2.3 for C you’ll have denominators of 2.8 and 2.3 – those don’t make for clean work. So what are you to do?

Here’s where some AI can kick in – elite test takers will see that they can back the algebra up a step and try a new route. If multiplying out those denominators creates uglier math, what if you just leave them be and combine the two equations as given:

Rate upstream = (v – 3) = 90 / (T + ½)

Rate downstream = (v + 3) = 90 / T

Subtract the first from the second:

– (v – 3) = -[90 / (T + ½)]

(v + 3) = 90 / T

6 = 90 / T – 90/(T + ½)

Now you have just one equation and one variable, but again the math is ugly (how do you find a common denominator out of this?). Again, Artificial Intelligence isn’t binary (“this is an algebra problem…must do algebra”) but involves taking steps that maximize your likelihood of success.

The answer choices give you several possible values of T, and you should note that what you’re supposed to do with T is include it in two denominators, ending with a result of a single-digit integer (6). What does that tell you? You probably want a pretty clean number in that denominator. And only one answer choice is “clean”: 2.5. So plug that in and see where it takes you. Does:

6 = 90/2.5 – 90/3 ?

6 = 36 – 30?

Yes – so the answer must be 2.5. But more important is the takeaway – there’s no “one way” to do a rate problem involving algebra. You need to go to your toolkit and be ready to use multiple devices at multiple steps, including:

**Algebra** (but once you see an ugly quadratic you may need to change course)

**Backsolving** (but not immediately, so you need to have the flexibility to keep the answer choices nearby as you delve into algebra)

**Factors/Multiples** (once it comes time to backsolve, do so efficiently by predicting which answer choices even have a chance. 90/2.3 would be the same as 900/23, which won’t give you a clean number at all. But 90/2.5, that has a chance…)

Difficult GMAT problems don’t necessarily have one blueprint just as the problems of the future can’t be solved simply by binary logic. Tech firms are doubling down on artificial intelligence and business schools are looking for a version of that, too – consider those Harvard and Stanford MBA graduates from even six years ago. When they studied business there was no such thing as a social media strategy or a mobile app. Top b-schools can’t just binary-program their students for success in the future; they need to train them like programmers are developing AI, by giving them frameworks via which to assess and choose options to maximize the likelihood of success. To identify which students are likely to be receptive to that, that’s part of the GMAT’s job. Which is why this kind of thinking, akin to Artificial Intelligence, is so crucial for those looking to achieve high scores on this test.

And you can do one better than Artificial Intelligence – you have actual intelligence! So put it to use – while you can certainly program yourself with plenty of rules and formulas that will help you on the GMAT, simply doing so is typically not enough for those attempting to score in the top 10 percent. So remember that your job isn’t to program yourself solely with if/then binary logic, but rather to seek out that mental agility that comes from having flexible approaches to use as you attempt to maximize your chances for success. As you study, take note not just of “the way to do this problem,” but more of the general themes and strategies that you’ve had to apply in different ways. To prove to the computer-adaptive test administration and scoring that you’re in the top 10% of “GMAT intelligence,” steal a page from that computer’s future and train yourself to think in the way of Artificial Intelligence. AI, as they say, is the answer.

*Brian Galvin is Director of Academic Programs at Veritas Prep, a GMAT prep and graduate school admissions consulting provider. This is his second column for Poets&Quants.com. His contrarian views appear monthly.*

**DON’T MISS: THE NEW-GEN GMAT TEST: THE VIEW OF TWO B-SCHOOL DEANS or WHY YOU SHOULD DITCH YOUR GMAT GOALS**