Misleading questions

Misleading questions are some of the most frustrating questions you’ll come across on the GRE… because they’re intentionally designed to be misleading.

These questions usually ask for information that is either unsolvable, or the question is just meaningless to start, but it’s impossible to know until you examine the question closely. This question type almost exclusively appears in quantitative comparison problems, and the correct answer is almost always D. These question types essentially test your logical understanding of some core mathematical principle, as ETS wants to see if you can quickly understand that something cannot be determined. Be aware these questions may include a variety of inconsequential facts or variables to distract you from the key information.

Some common examples of misleading questions include:

• You need to solve for an average, but you aren’t given the sum or the number of elements in the set

• You need to solve for a final amount after some percent change, but no original amount was given

• You need to solve for an angle, but can’t seem to identify its measurements or relation to the given geometry

Be careful though! Just because Quantity A and B are individually unsolvable, that doesn’t necessarily mean the answer is D. As we discuss in the min-max extremes chapter, just knowing a range of values can be enough to determine an answer. But if you don’t even have enough information to determine a range of values for the quantities, they may be truly unknowable, and you’re dealing with a misleading question.

Here’s a concrete example of a misleading question:

Line $k$ crosses through point $(4,3)$
Line $m$ crosses through point $(-4,-3)$

Quantity A: The $y$-intercept of line $k$
Quantity B: The $y$-intercept of line $m$

The answer is D, but the point is to do the exercise. Do you know why the relationship between the quantities can’t be determined?

The $y$-intercept of any line can be found by solving for the $y$ value when the $x$ value is $0$. Because there are no equations for the two lines, this method cannot be used. An alternative method is to use the slope of the line to trace from the given point to the $y$-intercept, but we don’t know the slope of these lines either. Given that there is no way to solve for the $y$-intercept of either line, their values could be anything, and it’s impossible to know which quantity is greater.

Here’s another example:

Quantity A: The median of a list of 9 numbers that has a minimum of 1 and a maximum of 11
Quantity B: The median of a list of 9 numbers that has a minimum of 5 and a maximum of 15

Again, the answer is D. But do you know why?

The median of a list is the middle-most value when the list is sorted. This question gives us the minimum and maximum values in the lists and the size of the lists, but that’s it. Essentially, we have two known extremes in both lists, but the other numbers could be anything in between. The two lists overlap, and the numbers could repeat, so the median of either list could be anything between the minimum and the maximum.

For example, the first list could be (1, 11, 11, 11, 11, 11, 11, 11, 11), and the second list could be (5, 5, 5, 5, 5, 5, 5, 5, 15). Or it could be reversed, with (1, 1, 1, 1, 1, 1, 1, 1, 11) and (5, 15, 15, 15, 15, 15, 15, 15, 15). There is a significant overlap between these two ranges and many possibilities for either median to be greater than the other. Therefore, the relationship between the quantities cannot be determined.