每日一题

Mathematics>Standard Multiple Choice

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

If x/3 = x^2, the value of x can be which of the following?

I.-1/3
II. 0
III. 1/3

(A) I only
(B) II only
(C) III only
(D) II and III only
(E) I, II, and III

答案和解析

答案：D

解析：

Roman Numeral I: Can the value of x be -1/3?

You could test this answer by substituting -1/3 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 = -1/3, then (-(1/3))^2 is a positive number, because any nonzero number squared is positive.

If x = -1/3, then x/3 is negative.

So x/3 is -and x^2 is positive.

Therefore, x cannot be -1/3.

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:

x/3 = x^2

0/3 = 0^2 = 0

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

Roman Numeral III: Can the value of x be 1/3?

Substitute 1/3 for x:

If x = 1/3, then x/3 = 1/9.

Also, x^2 = (1/3)^2 = 1/9.

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.