Demystifying Difficult GRE Math Problems

In the art world, the term trompe l’oeil refers to perspectival illusionism—literally, “to fool the eye.” On the GRE math section, you may notice test questions that use a similar technique in which a readily solvable problem will try to distract you from the very information that makes its solution accessible.
Here’s an example of this tricky sort of test question that appears to involve some rather difficult GRE math:
If x + 2y = 30, then

=

• A. 8
• B. 16
• C. 18
• D. 20
• E. 30

Many test-takers will take one look at this problem and see it more like this:
If x + 2y = 30, then [SCREAMINGLY HORRIBLE, MUST FIND COMMON DENOMINATOR, ARGH!!!] =
Because the latter portion of the problem is so intimidating, many test takers will neglect to notice the answer choices given.

The clever test taker, on the other hand, will force herself to focus on exactly the parts of the test question that are most easy to ignore, first seeing the problem this way:
If x + 2y = 30, then [let’s not worry about finding the common denominator for now] =

• A. 8
• B. 16
• C. 18
• D. 20
• E. 30

Suddenly, by ignoring the intimidating parts of the GRE math, two important ideas come into sharp focus:

1. First, the testmaker is telling you that in order to solve the problem, it matters that x + 2y = 30.
2. Second, despite there being two variables and only one equation, that scary-looking expression can somehow be reduced to a fairly innocent and more manageable integer.

These two observations hold the key to unlocking the solution and avoiding the Test Day panic of rushing to calculate a common denominator head on.
Now, breathe and examine that horrible fractional expression again, looking for x + 2y within it.

In fact, there are two fractions with x as the numerator and two fractions with 2y as the numerator. One of each is over a 3 in the denominator, and the others are over a 5 in the denominator.
It turns out, this is just an addition problem. There’s no reason to have to look at it in the order the test maker gave it to you. Instead, regroup the expression into a more sensible arrangement to simplify the math:

By focusing on the simple information the test maker provides, you can now dispose of this problem easily by replacing each x + 2y with 30:

Making sure that you don’t ignore the subtle signals given by the test makers—rather than being distracted or intimidated by seemingly-impossible GRE math questions—will serve you well on Test Day.

How to Approach the Hardest GRE Math Problems

Difficult GRE math questions can become more manageable when you change your approach. Along with looking for ways to regroup an expression, try these strategies when a solution isn’t immediately clear:

• Start with a simpler version. Use an easier example to understand the underlying concept, then check what changes in the original problem. In probability questions, for instance, selecting items without replacing them changes what’s available for the next selection.
• Examine the answer choices before calculating. A question involving a large factorial may only require you to identify its factors. Consider whether you can evaluate the choices without calculating the full value.
• Draw the relationships. For coordinate geometry questions, sketch lines or plot sample points to make abstract information easier to interpret. Use the sketch to guide your reasoning, then confirm it mathematically.
• Evaluate every option in select-all-that-apply questions. Check each statement independently. Finding one correct answer doesn’t mean you’re finished; all of the listed options could be correct.