Misleading questions

Misleading questions are some of the most frustrating questions you’ll see on the GRE because they’re intentionally written to push you toward an incorrect conclusion.

These questions usually ask you to compare quantities when the needed information is missing, or when the question is effectively meaningless until you analyze it carefully. This question type appears most often in quantitative comparison problems, and the correct answer is often D.

What ETS is really testing here is your logical understanding of core math principles: can you recognize when a value (or even a range of values) can’t be determined from the information given? To make this harder, misleading questions often include extra facts or variables that don’t actually help.

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 Quantity B are each unsolvable on their own doesn’t automatically mean the answer is D. As we discuss in the min-max extremes chapter, sometimes knowing a range of possible values is enough to determine a relationship.

But if you don’t even have enough information to determine a range of values for the quantities, then the quantities may truly be 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: why can’t the relationship between the quantities be determined?

The $y$-intercept of a line is the $y$-value when $x=0$. If you had an equation for each line, you could plug in $x=0$ and solve for $y$.

But here, you aren’t given equations - only one point on each line. Another way to find a $y$-intercept is to start at the given point and “move” along the line using its slope until you reach $x=0$. However, you aren’t given the slopes either.

Because there’s no way to determine either $y$-intercept, each intercept could take many possible values. That means either quantity could be greater, or they could be equal, so the relationship can’t be determined.

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. Why?

The median of a list is the middle value when the list is sorted. With 9 numbers, the median is the 5th number in the sorted list.

This question tells you only:

• the minimum value
• the maximum value
• the number of values in the list

But it tells you nothing about the other 7 numbers in each list. Those numbers could be anywhere between the minimum and maximum, and values can repeat. Since the two ranges overlap, the median of either list could fall in the overlap region, and either median could end up larger.

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).

Because there are many valid lists that fit each set of conditions - and those valid lists can produce different medians - the relationship between the quantities cannot be determined.