Mathematics > Standard Multiple Choice

Read the following SAT test question and then click on a button to select your answer. 

If , the value of  can be which of the following?

. 

. 

. 

(A) only

(B) only

(C) only

(D)and only

(E),and

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The correct answer is D

Explanation

Roman Numeral Answer Format

Roman Numeral : Can the value of  be ?

You could test this answer by substituting  for  in the equation and seeing whether the result is true. But you can also reason this question out without substituting numbers:

If= , then  is a positive number, because any nonzero number squared is positive.

If = , then  is negative.

So  is negative and  is positive.

Therefore,  cannot be .

Mark Roman numeral  with an “F” for false.

Roman Numeral : Can the value of  be ?

This is a very easy substitution to make:

Roman numeral  is true, so mark it with a “T” for true.

Roman Numeral : Can the value of  be ?

Substitute  for :

If =, then .

Also, .

Roman numeral  is true, so mark it with a “T” for true.

Check the Answers:

You now know whether each of the Roman numeral statements is true or false:

 is false.

 is true.

 is true.

Find the choice that says only  and