Is x positive? (1) ( x – 3) 2 > 0 (2) x 3 – 1 >

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Is x positive?

(1) ( x - 3) 2 > 0

(2) x 3 - 1 > 0

For a question like above, where there is no limitation on x (i.e. x!=0 or x is an integer), would we test for the fringe cases? i.e. test when x is a fraction or when x = 0 etc..

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by GMATGuruNY » Mon Aug 25, 2014 8:56 pm
[email protected] wrote:Is x positive?

(1) ( x - 3) 2 > 0

(2) x 3 - 1 > 0

For a question like above, where there is no limitation on x (i.e. x!=0 or x is an integer), would we test for the fringe cases? i.e. test when x is a fraction or when x = 0 etc..
Statement 1: (x-3)² > 0.
It's possible that x=0, since (0-3)² = 9.
It's possible that x=1, since (1-3)² = 4.
Since x is not positive in the first case but x is positive in the second case, INSUFFICIENT.

Statement 2: x³ - 1 > 0
Thus, x³ > 1.
If x<0, then x³<0.
If x=0, then x³=0.
Thus, for it to be true that x³>1, x must be positive.
SUFFICIENT.

The correct answer is B.
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by Brent@GMATPrepNow » Tue Aug 26, 2014 9:31 am
Som_A wrote:Is x positive?

(1) (x - 3)² > 0
(2) x³ - 1 > 0
IMPORTANT CONCEPTS
Rule #1: EVEN powers are always greater than or equal to zero. So, (POSITIVE value)^(EVEN integer) > 0, and (NEGATIVE value)^(EVEN integer) > 0

Rule #2: ODD powers PRESERVE the sign. In other words, (POSITIVE value)^(ODD integer) = POSITIVE value, and (NEGATIVE value)^(ODD integer) = NEGATIVE value



Target question: Is x positive?

Statement 1: (x - 3)² > 0
The ONLY thing this tells us is that x ≠ 0 (see Rule #1)
So, there are many values of x that satisfy this condition. Here are two:
Case a: x = 1, in which case x is positive
Case b: x = -1, in which case x is NOT positive
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: x³ - 1 > 0
Add 1 to both sides to get: x³ > 1
In other words, x³ is POSITIVE
Since x is raised to an ODD power, we can apply rule #2 to conclude that x must be positive
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = B

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by [email protected] » Tue Aug 26, 2014 8:42 pm
HI Som_A,

When you choose to TEST Values on a DS question, it's important to think about exactly what the question asks about. Here, we're asked "is x positive?", so the issue is really about "positive" vs. "non-positive (0 or negative)"; since this question is relatively simple, we likely would NOT need to test anything that you would consider to be "fringe." Notice in both Brent's and Mitch's explanations that simple integers and some basic Number Properties were enough to get to the correct answer.

When a question provides some significant "limitation" (such as X > 0, which means that X CANNOT be 0 and CANNOT be negative), that's when "fringe" test cases might be something to think about.

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by Jim@StratusPrep » Wed Aug 27, 2014 7:14 am
Statement 1: (x-3)² > 0.
The only restriction here is that x cannot equal 0, INSUFFICIENT.

Statement 2: x³ - 1 > 0
Thus, x³ > 1.
Odd exponents will not change the sign of the base, meaning X must be positive if it is greater than 1
SUFFICIENT.

B
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by GMATinsight » Sat Aug 30, 2014 3:47 am
Is x positive?

(1) (x - 3)² > 0
(2) x³ - 1 > 0
Question : Is x > 0?

Statement 1) (x - 3)² > 0

Point to Think : Square of anything is always Greater than or Equal to zero so what's so special about this statement?
Answer: The only special thing about this statement is (x - 3)² is not equal to 0 i.e. x is not 3

INSUFFICIENT

Statement 2) x³ - 1 > 0

Point to think: What happens when a number is cubed???
Answer: The sign remains same

i.e. x³ > 1
i.e. x > 1
SUFFICIENT

Answer: Option B
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