SAT官方数学习题
Read the following SAT test question, then click on a button to select your answer.
If = x2, the value of x can be which of the following?
–
0
A. I only
B. II only
C. III only
D. II and III only
E. I, II, and III
Correct Answer: D
Here‘s Why:
Roman Numeral Answer Format
Roman Numeral I: Can the value of x be –?
You could test this answer by substituting – for x in the equation and seeing whether the result is true. But you can also reason this question out without substituting numbers:
If x = – , then is a positive number, because any nonzero number squared is positive.
If x = –, then is negative.
So is negative and x2 is positive.
Therefore, x cannot be –.Mark Roman numeral I with an “F” for false.
Roman Numeral II: Can the value of x be 0?
This is a very easy substitution to make:
= x2
= 02 = 0
Roman numeral II is true, so mark it with a “T” for true.
Roman Numeral III: Can the value of x be ?
Substitute for x:
If x = , then = .
Also, x2 = = .
Roman numeral III 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:
I is false.
II is true.
III is true.
Find the choice that says only II and III are true.
Difficulty: Hard
