The SAT exam allows for about two minutes to solve each math problem. The key to conquering the math section of the test is knowing how to break down a deliberately confusing question and sift through unnecessary details to quickly find the answer.

In a Quora thread of the most difficult SAT math problems, one question emerged as "the meanest test problem ever."

It reads:

*In a class of* p* students, the average (arithmetic mean) of the test scores is 70.*

*In another class of *n* students, the average of the scores for the same test is 92.*

*When the scores of the two classes are combined, the average of the test scores is 86.*

*What is the value of *p/n*?*

Can you figure out how to solve it?

If not, don't fear — Presh Talwalkar, a math whiz who wrote the book "The Joy of Game Theory: An Introduction to Strategic Thinking" and tackles math questions and riddles on his YouTube channel and blog, both called MindYourDecisions, shared a step-by-step solution to this notoriously tough problem.

There are a few ways to solve it, but Talwalkar presents a simple shortcut.

The first class had an average of 70. That's 16 points below the average score of 86. In other words, 86 - 70 = 16. Since there are *p* students in the class, the difference from the average is 16*p*.

The second class had an average of 92. That's 6 points more than the average of 86. In other words, 92 - 86 = 6. There are n students in this class, so the difference from the average is 6*n*.

Because these classes average out together — as the problem says "when the scores of the two classes are combined" — the deficit of points has to be equal to the surplus of points. Therefore, 16*p* is equal to 6*n*.

Turning that into an equation, we can easily figure out what *p/n* is:

16*p* = 6*n*

*p/n* = 6/16, or 3/8

Still stumped? You can watch Talwalkar's full explanation of the solution below or read more on his blog.

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