The scoring algorithm on the GMAT is such that in order to achieve a high score on the test you have to be getting hard questions right. As most people understand, the number of questions that you get right is not the major factor…your score is based on the level of difficulty of the questions that you are able to answer correctly. But how do you answer hard GMAT questions correctly?
First of all, it is helpful to consider what makes a hard question “hard.” I often like to ask my tutorees this question and I usually get answers like “the Math is very difficult” or “the wording of the question is tricky.” These can certainly be aspects of hard questions but at their core what makes hard questions hard is that most people get them wrong. Obviously the GMAT writers have a very good sense for whether a question will be easy or hard when they are writing it, but the real test comes when the question is introduced as an experimental question. If most people get the question right, it is an easy question and if most people get it wrong it is a hard question. It’s as simple as that.
This raises an interesting dilemma. If the way to get a high score on the GMAT is to answer hard questions correctly and if a hard question is one that, by definition, most people get wrong, how can you answer questions correctly that most people get wrong? Well, if we are talking about Quant questions you really have 2 choices. Either be better at Math than almost everyone who takes the test or find ways to approach the questions that deviate from what most people would do. Think of it this way: if on a particular question you do what everyone else is doing you will be just as likely as they are to get the question wrong, unless you are better than them at the very same approach. And if the question is very hard then you need to be better than maybe 80 or 90 percent of test takers (many of whom are very, very good at Math).
If, however, you take a more creative approach and differentiate yourself not by your pure Math ability but by being a more creative problem solver, you put yourself in a position to get hard questions right that most people will get wrong (including people who may be better than you at Math). You can essentially sidestep what makes the question so difficult for most people in the first place by approaching it in a novel and unconventional way.
Since rewarding good quantitative reasoning and creative problem solving is at the heart of what the GMAT does, there are many, many official GMAT questions that would illustrate this point – so many that I don’t even know where to start! One example that I often like to use with students is the below question:
The above question can be approached in a number of ways. The most obvious method and the method that most people choose is to use algebra. But the algebra is pretty difficult on this question. Well, it’s not that difficult if you spot how to do it, but most people really don’t know how to do it and so they go round and round with algebra until it is clear that they are not going to get to the answer in a reasonable amount of time. That is why this question would be considered difficult – most people don’t know how to approach it so most people get it wrong.
But there is another way. You could just pick numbers. If you’ve had some practice picking numbers on other questions, this becomes a layup of a question when approached in this way. As long as we satisfy the first 2 equations we can pick whatever values we want and then just answer the question (numerically, not in terms of a and b). So if we make x=3 and y=2, then a=5 and b=1. Now we just answer the question – what does 2xy equal? Well, 2(3)(2)=12. Now we just need to find which answer equals 12 when we plug our values of a and b (5 and 1) into the answer choices. Choice A equals 12 and none of the other answers do, so the answer is A.
That could almost be done in one’s head without writing anything down – I am not suggesting you do that, but the question becomes so easy and so straightforward that it clearly ceases to be a hard question. So why is it considered a hard question? Because almost nobody would approach the question in that way and when approached algebraically the question is significantly more difficult. I must admit that the fact that most people would us algebra here still surprises me a little bit because to me it is pretty intuitive to pick numbers on a question like this (but of the hundreds of people I have done this question with, very few of them have picked numbers). And I am not saying that there is anything wrong with doing the algebra. I would be comfortable doing the algebra on this question as well and if it is perfectly clear to you how to solve it algebraically then that is certainly an acceptable approach too. But personally I would CHOOSE to pick numbers because it would be clear to me how easy the question would become if I took that approach.
To be clear, it should be understood that the test itself is designed to reward creative problem solving and good, clever quantitative reasoning, not the ability to regurgitate Math formulas and reflexively apply methods in an automatic way. So by taking a more creative, strategic approach to the questions you are actually aligning yourself with what the test largely seeks to measure. I have found over the years that convincing people of this fact is one of the necessary steps in getting people to become better GMAT problem solvers. Too many people see the test as a measure of their pure Math ability and therefore misunderstand the true nature of the test.
So, as you elevate your GMAT game and start to encounter those harder Quant questions just remember that what makes those questions hard is that most people get them wrong. And the reason that most people get them wrong is not a lack of Math ability but an inability to approach the problems in creative and effective ways. As you practice try to cultivate an ability to think outside the box and flex your problem solving and reasoning muscles more than your pure Math muscles.