Whenever tackling GMAT Quantitative section, we always encourage students to ask the essential self-reflection question “why am I here?”
We mean with respect to each quantitative question, not necessarily pondering why you decided to spend at Saturday morning taking a GMAT exam or why we exist on this very planet…. well, you are welcome to do that, of course, but you may find that your test timer has reached zero very quickly!
Perhaps a more appropriate way of looking at it is to consider what the GMAT has placed within the question, and how that is designed to achieved the end goals of leveraging assets, critically thinking, and logically reasoning that you are being assessed for overall.
Getting a solid handle on what type of question you are facing and what types of concepts you need to consider is a great first start towards organizing your approach to the right answers. Am I looking at a problem solving or data sufficiency problem? Does the problem integrate the area of a triangle? Is the problem asking for a remainder?
Again, remember the GMAT is not assessing your ability to do math. You need to continue to ask the question “why am I here?” as you work through the problem, allowing it to evolve as you progress towards the right answer. Did they throw a curveball with percent in a ratio data sufficiency question? If so, why did the GMAT decide to throw that curveball your way?
Understanding the relationship between all the steps and pieces of a GMAT quantitative question is important to help you towards your final question, “did I give the GMAT what they were looking for?”
Consider a question that is designed to make sure you lose sight of knowing why you are here: If xy is not equal to zero, is 1/x + 1/y = 16? Statement 1: x + y = 16xy Statement 2: x = y
First, we need to make sure we understand what we are being asked to assess. Is the reciprocal of x + y – two unknown variables – equal to 16?
Without knowing those two variables, it is impossible to know if whether or not the reciprocal of x + y adds up to 16. As this is a data sufficiency question, we would expect an answer that would either provide the variables x and y and/or establish a relationship within a statement that helps us determine whether or not 1/x + 1/y = 16. If we don’t get this information in either or with both statements, then the answer is (E).
In assessing Statement 1, if x + y = 16xy we should first determine how we manipulate the equation in the question to include an “xy,” which is done by finding the like denominator (and it becomes clear the GMAT is testing your understanding of rules of addition). So, y/xy + x/xy = 16 x + y / xy = 16 If we replace x + y with 16xy, then 16xy / xy = 16 16 = 16 as we are able to cancel out xy (xy/xy = 1)
Statement 1 is sufficient. However, Statement 2 is where many students start to lose sight of what the GMAT is looking to assess in this question. The first step we take, if x = y is to place this into the equation: 1/x + 1/x = 16 2/x = 16
And from there, many students take this next step: 2 = 16x 2/16 = x 1/8 = x
And solving for x feel that Statement 2 is also sufficient, thereby selecting the incorrect answer of (D).
But, in fact, the correct answer to this question is (A) – only Statement 1 is sufficient. The question asked us if 1/x + 1/y = 16, not to solve for or determine what x is if 1/x + 1/y = 16.
Making sure you continue to pause and assess “why you are here” is absolutely key to getting the right answer of many GMAT quantitative questions. Don’t fall into their trap of trying to “just do math” versus assessing what should be the right answer. | 
