This tip on improving your GMAT score was provided by Brian Galvin at Veritas Prep.
As you’ve likely read over and over in this space, the GMAT is much more a test of reasoning than a test of content, and one of the more challenging types of problems to exemplify this is the Minimum/Maximum question. These problems are typically challenging because they don’t lend themselves to “equation math” but instead need to be reasoned through trial and error. Consequently, a lot of high-scoring students still struggle mightily on these questions, even though the questions are among the most applicable to the business world. Let’s first consider an example and put some strategy around how to attack Min/Max problems:
A dental licensure exam requires a 75 percent minimum score in order to pass each section. Did Jennifer pass the 30-question third section?
(1) Jennifer recorded eight more correct answers on the second half of the third section than she did on the first half of the third section.
(2) Jennifer answered one more question correctly on the third section than she did on the 28-question second section, which she passed.
(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 asked; but NEITHER statement ALONE is sufficient
(D) EACH statement ALONE is sufficient to answer the question asked
(E) Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed
These problems earn the name “Min/Max” because there isn’t usually an equation to solve for a specific value. Instead, you have to use the situation presented in the problem to determine whether the minimum and maximum values of the situation will both give the same answer (either “yes” or “no”) to the overall question, or whether two different answers are possible.
In this case, we know that Jennifer needs to score 75 percent or better on this section, and we know that there are 30 questions. Since 75 percent of 30 is 22.5, she’ll pass with 23 or better and fail with 22 or fewer. You want to know whether she passed, so your goal is to determine whether she definitely scored 23 or higher; definitely scored 22 or lower; or could have scored either higher or lower.
Statement 1 tells you that she answered eight more questions correctly on the second half of that 30-question section than on the first, and here’s where thinking of these questions as Min/Max really comes in handy. First, calculate her minimum score. She could have answered 0 correctly on the first 15 questions, which would mean eight correct on the second 15 for a total of eight out of 30. Clearly with this score she would not pass that section, so it’s certainly possible to get the “no” answer. But then maximize the values. Here the constraint is the second half—there are only 15 questions, so the best she can do is 15. And since she got eight fewer correct on the first half, that means the best she could have done there is seven, for a total of 22 correct. This is less than the 23 she would have needed, so this also gives the answer “no, she did not pass.” Given statement 1, she could not have passed, so statement 1 is sufficient.
Statement 2 is very similar. It tells us that she passed a 28-question section, which means that she got between 21 and all 28 correct. And on this third section in question—the 30-question section—she answered one more correctly. So again, minimize and maximize that value. If she got all 28 correct on the second section, one more than that is 29, and clearly she would have passed the third section. But then minimize it: If she got the minimum, 21, correct on the second section, one more than that is 22. Since 22 correct answers is insufficient to pass the third section, we know from statement 2 that at her maximum she would have passed and at her minimum she would not have, so statement 2 is not sufficient.
What can you learn from this?
• Min/Max problems are almost always “close”—the test makers pick values that hug the border between a “yes” and “no” answer, so you’ll need to push the minimum and maximum limits allowed by the question to make sure you know whether the information is sufficient or not.
• Min/Max problems typically also use situations for which the numbers need to be integers. This also makes problems tricky, since they’re not really “equation” algebra problems but instead, trial-and-error problems.
• As you see more Min/Max problems you can develop a knack for sniffing out which end—the minimum or maximum value—will be the “close” one, saving your time. But in the meantime, or whenever you’re in doubt, your goal is to minimize the variable in question and then maximize the value in question. Doing so will allow you to find the possible range of values, and that’s the key to answering these questions.
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