“Real knowledge is to know the extent of one’s ignorance.” – Confucius
Talk to friends who are just starting out on the path to the GMAT, and you will hear resounding gripes and grievances of, “I had no idea how much I didn’t know.” Most people in this position have been in the workforce for three to five years, have had great career success and felt confident enough in their own intellect to make a $100,000 investment (i.e. business school). So, naturally, it can bruise the ego when you’re reintroduced to rusty concepts, such as geometry and quadratics, which seem a lot harder than in high school.
But the GMAT isn’t testing the same type of geometry and quadratics you did in high school, and, quite frankly, you probably don’t know how to do the kind of math the sacred 700+ GMAT score requires. It’s not a test of your computational abilities – if it were that easy, the average student wouldn’t dish out $1,000 or more on test prep. The test makers use familiar concepts but make them much more difficult with one purpose in mind: to assess your ability to think through problems (similar to those you’ll meet in the business world) quickly, accurately and efficiently. Consider the following problem:
If x is a positive integer, is (x)(x+2)(x+4) divisible by 12?
(1) x² + 2x is a multiple of 3
(2) 3x is a multiple of 2
The set-up of a Data Sufficiency question alone is something unique to the GMAT. You are given a question stem (the phrase above the two statements) and you must determine whether or not the information in either, both combined or neither of the statements is sufficient to solve the problem. This type of critical thinking is not about simply solving the problem but determining the minimal unknown data you would need to be able to solve it.
Given ten minutes you might be able to come up with an answer using your memory of high school math, but under time restrictions of 1½ to 2 minutes per question, it’s not enough to know how to do the math eventually – you need to know how to do the math efficiently. Here’s a breakdown of the strategic thinking and approach that will get to the answer quickly and confidently:
Analyze the Question
What is the question type?
o This is a Data Sufficiency question
o Within the Data Sufficiency question type, there are two sub-types: Yes/No and Value. This is a Yes/No question type – always yes, divisible by 12 or always no, not divisible by 12
What is the area of knowledge being tested?
o Our familiarity with Number Properties
State the Task
We need to find out if the information in the statements is sufficient to determine whether the statement (x)(x+2)(x+4) will always – or always not – be divisible by 12.
Whenever you see “divisible by” you should automatically break the number in question (in this case, 12) down to its prime factors. This is a pattern recognition that will help you ultimately save time on similar questions on test day. Getting the number in question to its prime factors will allow you to see if those same prime factors are present in the statement at hand much more easily. If they are, then any additional factors are only multiplying 12 by a greater amount. This is the type of strategic thinking you will need on the GMAT, rather than the long division you were taught in high school.
For example: 12 = 2 x 2 x 3, so we know that in order for the statement (x)(x+2)(x+4) to be divisible by 12 it must include those same prime factors. Any additional factors in the makeup of (x)(x+2)(x+4) will only be multiplying 12 by a greater amount (and therefore will still be divisible by 12).
Now that we understand the basic goal of this problem is to find out if there is a 2 x 2 x 3 somewhere in the statement (x)(x+2)(x+4), we have a much clearer picture of the exact information we are looking for as we go into evaluating the statements.
Statement (1) says that x² + 2x is a multiple of 3. The “x²” here should be a red flag that you will need to factor out the quadratic (x)(x+2)(x+4) to get it into the same terms. By multiplying the first two sets of parenthesis we get (x² + 2x)(x+4). Look familiar? So now we know that the first parenthesis is a multiple of 3 (one of our prime factors we are looking for) – great. But we still know nothing about the second set of parenthesis (x+4). If (x+4) includes a 2 x 2 then we will have all three prime factors needed. But if it does not, then it will not be a multiple of 12. Since we have no way of knowing, Statement (1) is insufficient.
Remember to never let any information you gained from Statement (1) influence your decision as you move on to evaluate – separately – Statement (2).
Statement (2) says that 3x is a multiple of 2. We know that 3 is not a multiple of 2, so that means that x must be. Let’s start simply with x = 2. If we plug that back into our original statement we have (2)(2+2)(2+4) = (2)(4)(6) = 2 x 2 x 2 x 2 x 3. We have all prime factors (2 x 2 x 3) to make this number divisibly by 12, and any larger multiple of 2 that x could equal would only make the multiplication of 12 larger (and still yes, always divisible by 12). Statement (2) is sufficient and we are ready to confidently move on to the next problem.
As you can see, the type of math that you will need to ace the GMAT is more about strategy and pattern recognition than it is doing the math itself. All of the numbers we were working with in this example were very small and easily manageable. However, if you didn’t have the strategies and shortcuts, you would be stuck working with much larger numbers and taking much more time than you should be.
Needless to say, the test prep process can be very discouraging as you realize that the standard math you learned in high school won’t cut it. Unfortunately for some the GMAT can become a major obstacle, and unless you are a genius, it is most probable that you will be met with self-doubt along the way. But as Confucius was so astute to point out, “Real knowledge is to know the extent of one’s ignorance.” The realization of how much we do not yet know can discourage us. But if you want to be successful on the GMAT, it is that same discouragement that gives definition to your areas of opportunity for better understanding – and ultimately – to that prized 700+ test score.
Saxon McClintock is a professional GMAT tutor for Varsity Tutors. She earned a BS in Business Administration from Pepperdine University and is currently an MBA candidate at UCLA Anderson. She scored a 770 on the GMAT.
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