Understanding 1337 GMAT Logic

One of the most difficult tasks on the GMAT is to properly interpret what the question is really asking. The GMAT is loaded with dense terminology, accurate but irrelevant prose and confusing technical jargon (and that’s just the instruction page!) The verbiage is dense on purpose, with the deciphering of the information part of the skills being tested. And since this task only gets more challenging as you get more tired throughout the exam, it’s important to recognize the vocabulary used on the GMAT. To borrow from geek culture, you need to understand the GMAT 1337 speak.

For those unfamiliar with 1337, it is known as “leet” or “leetspeak” wherein English alphabet letters are replaced by the number that resembles them the most. It uses 1 for L, 3 for E and 7 for T, allowing the number 1337 to stand in for leet, cacographic shorthand for “elite”. (Think of it as pig Latin for the 21st Century). In essence, some people have devised a sublanguage of English that is hard to read for the average person, but very easy to understand for anyone versed in the language’s rules. The same logic can be applied on GMAT questions.

Many terms that you’ll encounter on the GMAT are commonplace in math milieus, but most GMAT students don’t spend much time in such environments. Almost all students have also learned many of the terms long ago, like quotient and decimal, but have since forgotten their definitions because they don’t use them in everyday situations. Other concepts, like Data Sufficiency, only really exist on the GMAT and are not used in the same manner in the real world. This melange of issues can sometimes make it feel like the exam is speaking a language you don’t.

The ideal situation would be to avoid encountering any new or exotic word on test day, which hopefully means you’ve seen all of them during your test preparation. Moreover, simply understanding what each individual word means isn’t enough either, the entire meaning of the sentence must be clear in order to get the correct answer. As always, practice makes perfect, so let’s look at a sample GMAT problem and put the pieces together:

If R and S are positive integers, can the fraction R/S be expressed as a decimal with only a finite number of nonzero digits?

(1)    S is a factor of 100

(2)    R is a factor of 100

(A)   Statement 1 alone is sufficient but statement 2 alone is not sufficient to answer the question asked.

(B)   Statement 2 alone is sufficient but statement 1 alone is not sufficient to answer the question asked.

(C)   Both statements 1 and 2 together are sufficient to answer the question but neither statement is sufficient alone.

(D)   Each statement alone is sufficient to answer the question.

(E)    Statements 1 and 2 are not sufficient to answer the question asked and additional data is needed to answer the statements.

For many students, a question worded in this way is dreadful. The question is asking about two positive integers, R and S, and what happens if we divide one by the other. Could the resulting fraction be expressed as a decimal, and if so, would that decimal have a finite number of nonzero digits?

Let’s tackle these issues one at a time. If we divide R by S, could the fraction be written as a decimal? Yes, say the fraction were 2/3, this could be rewritten as 0.666… However this decimal would go on forever with 6’s, as opposed to the fraction 2/4 which would be rewritten as 0.500 and would stop there. The second part of this question is asking us to make this distinction: does the number continue on forever or does it have a finite number of digits after which it is completed. A number like 2/3 continues with an infinite number of 6’s, whereas 2/4 culminates in a finite number of nonzero digits.

Once you understand exactly what the question is asking for, it becomes much simpler to answer it. We can answer “no” if we find a decimal that goes on to infinity (and beyond). We can answer “yes” if the decimal ends at a specific point. We can determine a few simple examples in our heads (1/3, ½, ¾, etc) and then look at statement 1.

Statement 1 tells us that integer S (the denominator) is a factor of 100. A factor means that I can divide 100 by an integer and get another integer, so 1, 2, 4, 5, 10, 20, 25, 50 and 100 are all factors of 100. It wouldn’t take too long to test that every one of these nine numbers, as the denominator, will end in a finite point. Logically, this is because the prime factorization of 100 is 2^2 * 5^2, and therefore all the factors of 100 will be some multiples of 2’s and 5’s, both of which are finite decimals (0.5 and 0.2, respectively). Try as you might, any numerator over 2 will end in x.0 or x.5, and any numerator over 5 will end in x.0, x.2, x.4, x.6 or x.8 (next five series of X-box consoles?). Since it is impossible to get an infinite decimal with these denominators, statement 1 will be sufficient to say the decimal will definitely end.

Statement 2 tells us that integer R (the numerator) is a factor of 100. This means that R can be the same 9 options we had for statement 1 (1, 2, 4, 5, 10, 20, 25, 50 and 100), but it doesn’t provide the same amount of help as defining the denominator does. If the numerator is 1, then the denominator can be 2 (finite) or 3 (not finite) and I’d have completely different answers. For the same reason that the numerator didn’t matter in statement 1, it doesn’t matter in statement 2, either.

If statement 1 gives us a definitive answer and statement 2 can go either way, then the correct answer to this question must be answer choice A. However getting the right answer is dependent on first understanding the question being asked. Just as with any language, maximum exposure will lead to maximum comprehension and retention, even if sometimes the terms seem peculiar. Remember that if you speak the GMAT’s language on test day, you’re more likely to get a 1337 score.

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Ron Awad is a GMAT instructor for Veritas Prep based in Montreal, bringing you weekly advice for success on your exam.  After graduating from McGill and receiving his MBA from Concordia, Ron started teaching GMAT prep and his Veritas Prep students have given him rave reviews ever since.