Understand what "MUST BE TRUE?" questions are asking.

Brent Hanneson - September 19, 2021

To set things up, try answering the question above. 

Answer and solution

I like giving this question to my students because it often reveals a common misunderstanding regarding “MUST be true” questions that involve inequalities.

The most common pushback goes something like this: The answer can’t be E because it says x2 could equal -3, and everyone knows that the square of a number is always greater than or equal to zero.

The problem with this rationale is that answer choice E isn’t saying x2 can equal -3; it’s saying x2 is greater than or equal to -4.

Consider this analogous (and very unofficial) question:

Hint: The shortest living adult is 54.6 cm, and the tallest living adult is 252 cm. 

The correct answer here is C. Does this mean person Q could be -5 centimeters tall? No. All we're concluding is that the value of x is greater than -10, which is definitely true. 

Now consider this much different wording:

In this case, the correct answer is E, since we’re looking for only those values of x that could be person Q’s height.   

Here are a few questions to practice with: 

“MUST be true” Questions

“Specify all possible values” Questions


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