Is it true that x > 0?
(1) x^2 = 2x
(2) x^3 = 3x
What's the best way to determine which statement is sufficient? Any experts help please?
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Is it true that x > 0?
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Statement 1:ardz24 wrote:Is it true that x > 0?
(1) x^2 = 2x
(2) x^3 = 3x
x² - 2x = 0
x(x-2) = 0.
The resulting equation is satisfied by x=0 (in which case the answer to the question stem is NO) or by x=2 (in which case the answer to the question stem is YES).
INSUFFICIENT.
Statement 2:
x³ - 3x = 0
x(x² - 3) = 0.
The resulting equation is satisfied by x=0 (in which case the answer to the question stem is NO) or by ±√3 (in which case the answer to the question could be YES or NO).
INSUFFICIENT.
Statements combined:
Only x=0 satisfies both statements.
Thus, the answer to the question stem is NO.
The correct answer is C.
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x^2 = 2xardz24 wrote:Is it true that x > 0?
(1) x^2 = 2x
(2) x^3 = 3x
We can solve the equation as follows:
x^2 - 2x = 0
x(x - 2) = 0
x = 0 or x = 2
We see that if x = 0, then x is not greater than 0. However, if x = 2, then x is greater than 0. Statement one alone is not sufficient.
Statement Two Alone:
x^3 = 3x
We can solve the equation as follows:
x^3 - 3x = 0
x(x^2 - 3) = 0
x = 0 or x^2 = 3
x = 0 or x = √3 or x = -√3
We see that if x = 0 or -√3, then x is not greater than 0. However, if x = √3, then x is greater than 0. Statement two alone is not sufficient.
Statements One and Two Together:
Using both statements, we see that x can only be 0. Thus, x is not greater than 0. Both statements together are sufficient.
Answer: C
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