Don't fall for the trap here! This problem is

NOT about the raw math. Many explanations in this forum focus rather blindly on the math, but they fail to realize that the GMAT is a critical-thinking test, not a "

let's-see-if-we-can-do-the-math-the-long-way-around" test. Oftentimes, the shape and structure of a problem can point to leverage that allows you to avoid a lot of messy mathematical gymnastics. This problem is no exception.

First of all, the problem asks you about the probability that a sum of a set of numbers is "

even." This is MASSIVE leverage. It means you don't have to care about the numbers; you only need to worry about whether the numbers are odd or even. Since a 12-sided die has 6 evens (\(2\),\(4\),\(6\),\(8\),\(10\)) and 6 odds (\(1\),\(3\),\(5\),\(7\),\(9\),\(11\)), it basically can be treated as a coin toss where one side is even and the other side is odd. You have the same chance of getting either.

Since

odd+odd = even, the sum of \(7\) integers will be odd if there are an

odd number of odds! (Pairs of odd values will effectively cancel each other out.) There is no reason to do any complicated math here, and certainly no reason to pull out combinatorics equations. Just visualize what is happening. For every combination of odds/evens, there is its "mirror" that reverses the odds and evens. (In other words, for every

\(O+O+O+O+O+E+E\) with \(5\) odds and \(2\) evens, there is an

\(E+E+E+E+E+O+O\) with 5 evens and 2 odds.)

You don't need to spend time messily calculating the number of combinations. Since every "odd" combination can be paired with an "even" combination, then the chance of getting an odd sum will be 50%.

The answer is B.

Now, let’s look back at this problem through the lens of strategy. Your job as you study for the GMAT isn't to memorize the solutions to specific questions; it is to internalize strategic patterns that allow you to solve large numbers of questions. This problem can teach us patterns seen throughout the GMAT. This solution is an application of a strategy I call in my classes "

Number Crunchers." The idea is simple: Watch for

patterns of numbers, especially when it asks for "

positive/negative" issues or "

odd/even" issues. You just need to look at how the problem is structured and determine what would limit or define the value you are looking for. Determine what those limits are, and you have your answer. Patterns turn "inefficient" math into great critical-thinking opportunities. And

that is how you think like the GMAT.

_________________

Aaron J. PondVeritas Prep Elite-Level InstructorHit "+1 Kudos" if my post helped you understand the GMAT better.

Look me up at https://www.veritasprep.com/gmat/aaron-pond/ if you want to learn more GMAT Jujitsu.