OG What is the value of x if x^3 < x^2

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What is the value of x if x^3 < x^2?

(1) -2 < x < 2
(2) x is an integer greater than -2

B

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by [email protected] » Fri Nov 17, 2017 12:57 pm

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AbeNeedsAnswers wrote:What is the value of x if x^3 < x^2?

(1) -2 < x < 2
(2) x is an integer greater than -2
We need to determine the value of x, given that x^3 < x^2.

Statement One Alone:

-2 < x < 2

We see that x could be, for example, -1 or -½.

For either of these values, we have x^3 < x^2, since x^3 will be negative and x^2 will be positive. Since we don't have a unique value for x, statement one alone is not sufficient.

Statement Two Alone:

x is an integer greater than -2.

We see that if x = -1, then x^3 < x^2, since x^3 = -1 and x^2 = 1.

If x = 0, then x^3 = x^2, since x^3 = 0 and x^2 = 0 (so x can't be 0).

Similarly, if x = 1, then x^3 = x^2, since x^3 = 1 and x^2 = 1 (so x can't be 1).

If x is an integer > 1, then x^3 will always be greater than x^2. Thus, x can't be any integer > 1.

Therefore, we see that the only value x can be is -1. Since we have a unique value for x, statement two alone is sufficient.

Answer: B

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by [email protected] » Sat Nov 18, 2017 11:14 am

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Hi AbeNeedsAnswers,

We're told that X^3 is LESS than X^2. We're asked for the value of X. This question can be solved with a mix of Number Properties and TESTing VALUES.

To start, there are only certain types of values that will fit the given information that X^3 is less than X^2:
-ANY negative value
-Positive fractions (0 < X < 1)

1) -2 < X < 2

With Fact 1, we have LOTS of different possible values for X: any negative value and any positive fraction in that range.
Fact 1 is INSUFFICIENT

2) X is an INTEGER greater than -2

The information in Fact 2 eliminates most of the possibilities that we started with. Since X has to be an INTEGER, none of the positive fractions are possible and since X has to be GREATER than -2, there's only one option possible: -1
Fact 2 is SUFFICIENT

Final Answer: B

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AbeNeedsAnswers wrote:
Sat Aug 19, 2017 2:49 pm
What is the value of x if x^3 < x^2?

(1) -2 < x < 2
(2) x is an integer greater than -2

B
Target question: What is the value of x?

Given: x³ < x²
If we do a little bit of work, we'll see that this given information tells us A LOT about x
x² must be POSITIVE here (since we can see that x ≠ 0, otherwise we can't have x³ < x²). So, we can safely divide both sides of the inequality by x² to get: x < 1
So, x < 1 AND x ≠ 0

Statement 1: –2< x < 2
There are several values of x that satisfy statement 1 (and the given information). Here are two:
Case a: x = -1
Case b: x = 0.5
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: x is an integer greater than –2
So, x is an INTEGER that's less than 1, but greater than -2 AND x ≠ 0
There's only one x-value (x = -1) that satisfies these conditions. So, x must equal -1
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: B

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