One way in which the GMAT differs from most tests is that you only need to find the correct answer to the given question. There are absolutely no points for your development, your reasoning or indeed anything you decide to write down. This is completely contrary to much of what we learned in high school and university, where you could be rewarded for having the correct algorithm or approach even if you didn’t get the correct answer. On most math problems, if you got the wrong answer but demonstrated how you got there, you could at least get partial credit, especially if your approach was perfect but the execution lacked (like passing on the 1 yard line).
The GMAT will give you 100% credit for selecting the correct answer, even if you got there by flipping a coin, taking a wild guess or only selecting an answer choice based on the letters of your last name (I tend to pick either A or D if I’m making a complete guess). In class, I’ve asked many students how they get to the answer choice they provided me, and often their reasoning is wrong but they still land on the correct square. The GMAT has no way of differentiating sound logic from blind luck (or false positives, as they’re often called), so sometimes you get answers right purely by chance.
Of course, you can often determine which answer choice is correct without necessarily knowing exactly why. Especially on a multiple choice exam, you can often backsolve using the answer choices and find that answer choice A is correct even if the reasoning is hazy. On test day, there is no incentive to spending undue time to determine why the answer must be correct, no trophy for your approach. While preparing for the exam, you can certainly take time to investigate patterns and paradigms that seem to repeat regularly.
As a simple example, you probably know that a number is divisible by 3 if the sum of its digits is divisible by 3 (hence 93 or 1335 would be divisible by 3 because the sum of the digits is 12 in each case). You don’t necessarily need to know why; simply recognizing that it always works is enough on the GMAT.
However, sometimes it’s interesting to delve deeper into number properties as mathematics has so many interesting (well, interesting to me) properties that help you understand math better. Let’s look at an example:
If n is a prime number greater than 3, what is the remainder when n^2 is divided by 12?
This type of question shouldn’t take you too long to figure out. Even if the question seems somewhat arbitrary, it is simply asking you to take a prime number, square it, and divide the product by 12 to find the remainder. Picking any prime number (greater than 3) should solve this problem, but we’ll want to look at a few just to make sure the pattern holds.
Since the prime numbers 2 and 3 are excluded from consideration, we can begin at the next prime number, which is 5. 5^2 is 25, and 25 divided by 12 gives us 2 with remainder 1 (remember that the remainder is what’s left over after you find the quotient). Since we picked one prime number and got the result of 1, we could already select that answer choice and move on. However, it’s probably cautious to at least consider a couple of other options before hastily selecting answer choice B.
The next prime number would be 7, and 7^2 is 49. If you divide 49 by 12, you get 4, remainder 1. The pattern seems to hold. The next one is 11? 11^2 is 121, which divided by 12 gives 10, remainder 1. The pattern seems pretty solid here. Let’s pick a random bigger prime number just to be sure: say 31. 31^2 is 961, which divided by 12 gives 80, with remainder 1 again. At this point we’re pretty sure that the remainder will always be 1, and can pick answer choice B with confidence. (Feel free to do a dozen more if you’d like, it always holds).
Again, though, on test day, you might make this selection after checking only one or two numbers. But since we’re still preparing for the exam (if you’re reading this during your GMAT they will undoubtedly cancel your score), let’s dive into why this pattern holds. It certainly seems odd that for any prime number, this property will hold, especially considering that prime numbers can be hundreds of digits long.
To see why this holds, let’s consider what this pattern means. The square of the number n, less 1, is divisible by 12. This can be expressed as (n^2 – 1) is divisible by 12. This might remind you of the difference of squares, because it’s of the form n^2 – x^2, where x happens to be 1. We can thus transform this equation to: (n-1) * (n+1) is divisible by 12. This form will be more helpful in detecting the underlying pattern.
For a number to be divisible by 12, it must be divisible by 2, 2 and 3. If I were to take three consecutive numbers n-1, n and n+1, one of these three must necessarily be divisible by 3. Remember that multiples of 3 occur every third number, so it is impossible to go three consecutive numbers without one of them being a multiple of 3. And since n has been defined to be a prime number greater than 3, it cannot be n. Thus either n+1 or n-1 must be divisible by 3.
Similarly, if n is a prime greater than 3, then it must be odd. Clearly, then, n-1 must be even, and n+1 must be even. Since both of these numbers are divisible by 2, their product must be divisible by 4. This means that for any two numbers (n-1) * (n+1) where n is a prime greater than 3, the product will be divisible by 2, by 2 and by 3, and therefore by 12.
On test day, figuring out the correct answer to the question is your main priority (not taking too long and not soiling yourself are two other big ones). Recognizing a pattern and making a decision based on the pattern is sufficient to get the question right, but it’s an interesting exercise to look into why certain patterns hold, why certain truths are inescapable. There’s no trophy for understanding math properties (not even a Nobel Prize), but identifying things that must be true goes a long way towards getting the right answer.
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.