GMAT Tip of the Week: Learning Math from Mathers

March has traditionally been “Hip Hop Month” in the GMAT Tip of the Week space, so with March only hours away and winter weather gripping the world, let’s round up to springtime and start Hip Hop March a few hours early, this time borrowing a page from USC-Marshall Mathers. There are plenty of GMAT lessons to learn from Eminem. He’s a master, as are the authors of GMAT Critical Reasoning, of “precision in language“. He flips sentence structures around to create more interesting wordplay, a hallmark of Sentence Correction authors. But what can one of the world’s greatest vocal wordsmiths teach you about quant?

On his latest album, Eminem talks about feeling like a “Rap God”. And while that track – 6,077 words in 6 minutes, or about 18 Reading Comprehension passages’ worth of words – is more dense than anything you’ll have to read for the GMAT, it supplies a few nuggets of wisdom that can dramatically increase your score, most notably this lyric in which he mocks other MCs who have accused him of being too mainstream, too pop:

“I don’t know how to make songs like that
I don’t know what words to use”
Let me know when it occurs to you
While I’m ripping any one of these verses that versus you

Now, while Em is mocking other emcees, he could very well be mimicking the way that the GMAT would mock *you* on certain problems. The GMAT is designed in large part to be a “quantitative reasoning” test as opposed to a “math” test, and leads a lot of students to stare at problems nervously saying, essentially, “I don’t know how to solve problems like that; I don’t know what tools to use”. All the while, the 75-minute section clock ticks down and the GMAT sits back, smirking, thinking “let me know when it occurs to you how to solve this problem that versus you”.

In other words, difficult GMAT problems are often difficult because people waste a lot of time sitting scared not knowing how to get started. And in many of those cases, the way to get started is to go much more “mainstream” than you’d think. Consider this example:

With # and & each representing different digits in the problem below, the difference between #&& and ## is 667. What is the value of &?


(A) 3
(B) 4
(C) 5
(D) 8
(E) 9

Now, many would look at this problem and think “I don’t know how to solve problems like that…”, as it’s not a classic “Algebra” problem, but it’s not a straight-up “Subtraction” problem, either. It uses the common GMAT themes of Abstraction and Reverse-Engineering to test you conceptually to see how you think critically to solve problems. And in true Eminem-mocking form, the key to a complicated-looking problem like this is a lot more mainstream than it is advanced. You have to just get started playing with the numbers, testing possibilities for # and & and seeing what you learn from it.

When GMAT students lament that “I don’t know what tools to use” to start on a tough problem, they’re often missing this piece of GMAT wisdom – *that’s* the point. You’re supposed to look at this with some trial-and-error like you would in a business meeting, throwing some ideas out and eliminating those that definitely won’t work so that you can spend some more time on the ones that have a good chance. In this case, throw out a couple ideas for #. Could # be 5? If it were, then you’d have a number in the 500s and you’d subtract something from it. There’s no way to get to 667 if you start smaller than that and only subtract, so even with pretty limited information you can guarantee that # has to be 6 or bigger.

And by the same logic, try a value like 9 for #. That would give you 900-and-something, and the most that ## could be is 99 (the largest two-digit number), which would mean that your answer would still be greater than 800. You need a number for # that allows you to stay in the 667 range, meaning that # has to be 6 or 7. That means that you’re working with:

6&& – 66 = 667


7&& – 77 = 667

And just by playing with numbers, you’ve been able to take a very abstract problem and make it quite a bit more concrete. If you examine the first of those options, keep in mind that the biggest that & can be is 9, and that would leave you with:

699 – 66 = 633, demonstrating that even at the biggest possible value of &, if # = 6 you can’t get a big enough result to equal 667. So, again, by playing with numbers to find minimums and maximums, we’ve proven that the problem has to be:

7&& – 77 = 667, and now you can treat it just like an algebra problem, since the only unknown is now 7&&. Adding 77 to both sides, you get 7&& = 744, so the answer is 4.

More important than this problem, however, is the takeaway – GMAT problems are often designed to look abstract and to test math in a different “order” (here you had two unknowns to “start” the problem and were given the “answer”), and the exam does a masterful job of taking common concepts (this was a subtraction problem) and presenting them to look like something you’ve never seen. The most dangerous mindset you can have on the GMAT quant section is “I don’t know how to solve problems like this” or “I’ve never seen this before”, whereas the successful strategy is to take a look at what you’re given and at least try a few possibilities. With symbol problems (like this), sequence problems, numbers-too-large-to-calculate problems, etc., often the biggest key is to go a lot more mainstream than “advanced math” – try a few small numbers to test the relationship in the problem, and use that to narrow the range of possibilities, find a pattern, or learn a little more about the concept in the problem.

If your standard mindset on abstract-looking problems is “I don’t know how to solve problems like that”, both Em and the G-Em-A-T are right to chide you a bit mockingly, as that’s often the entire point of the problem, to reward those who are willing to try (the entrepreneurial, self-starter types) and “punish” those who won’t think beyond the process they’ve memorized. Even if you don’t become a GMAT God, if you follow some of Eminem’s lessons you can at least find yourself saying “Hi, my name is…” over and over again at b-school orientation.

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By Brian Galvin