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# 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? [#permalink]

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22 Jun 2017, 13:50
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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.

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Re: What is the value of x if x^3 < x^2? [#permalink]

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28 Jun 2017, 06:47
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AbdurRakib wrote:
What is the value of x if x³ < x²?

(1) –2< x < 2
(2) x is an integer greater than –2.

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

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Re: What is the value of x if x^3 < x^2? [#permalink]

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22 Jun 2017, 13:58
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What is the value of x if $$x^3 < x^2$$ ?

(1) -2<x<2
We do not know if x is an integer.
If x=-1, -1 < 1(Condition satisfied)
If x=-1/2. -1/8 < 1/4(Condition satisfied)
Insufficient.

(2) x is an integer greater than -2
The only integer greater than -2 which satisfies the conditions
is x=-1. Every other number after that does not satisfy the condition
Sufficient(Option B)
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Re: What is the value of x if x^3 < x^2? [#permalink]

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22 Jun 2017, 14:35
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1) Not Sufficient.
2) According to the question stem x<1 and x>-2 => x = -1 so satisfy the conditional mentioned in the stem.
Hence. B. What's the OA?

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Re: What is the value of x if x^3 < x^2? [#permalink]

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22 Jun 2017, 17:23
1) first one is not sufficient since if I substitute 1.5, the positive number.
2)option b clearly says greater than -2;applying -1 in above condition we will get the answer.

Hence option B

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Re: What is the value of x if x^3 < x^2? [#permalink]

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23 Jun 2017, 00:46
AbdurRakib wrote:
What is the value of x if $$x^3 < x^2$$ ?

(1) -2<x<2

(2) x is an integer greater than -2

$$x^3 < x^2$$
The above condition is possible only when x is negative
For example,
if x=-5 $$-125<25$$
if x=-3$$-27<9$$

St1: x can have values in the range of $$-1<=x<=0$$
For x= -1,-0.9,-0.8 the equation holds true
No unique value NS

St2: x is int and x>-2
Then x can have only one value in this range x=-1
Since, x>0(Positive values) will not hold true; hence eliminated Suff

Option B
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Re: What is the value of x if x^3 < x^2? [#permalink]

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28 Jun 2017, 06:50
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RaguramanS wrote:

$$x^3 < x^2$$
The above condition is possible only when x is negative
For example,
if x=-5 $$-125<25$$
if x=-3$$-27<9$$

The above condition is possible only when x is negative
This is not quite true.
x can be any number less than 1 (but not equal to zero)
For example x = 1/2 satisfies the inequality x^3 < x^2

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Re: What is the value of x if x^3 < x^2? [#permalink]

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17 Nov 2017, 12:46
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AbdurRakib 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.

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Re: What is the value of x if x^3 < x^2? [#permalink]

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19 Nov 2017, 13:43
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Hi All,

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

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Special Offer: Save $75 + GMAT Club Tests Free Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/ ***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*********************** Manager Status: Turning my handicaps into assets Joined: 09 Apr 2017 Posts: 120 Re: What is the value of x if x^3 < x^2? [#permalink] ### Show Tags 03 May 2018, 02:10 Why when we solve x^3<x^2 algebraicly we get (0;1) as an answer, but not negative possibilities of x. I mean x^3<x^2 x^3-x^2<0 x^2(x-1)<0 x=0 x=1 So answer is 0<x<1 Whats wrong with this solution? Isn't there any fixed approach for this kind of inequalities or we have to think out of box/logically everytime? _________________ If time was on my side, I'd still have none to waste...... EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 11984 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: What is the value of x if x^3 < x^2? [#permalink] ### Show Tags 03 May 2018, 18:31 Hi Mehemmed, To start, you're treating this inequality as if it were an EQUATION - which it is NOT. The two values of X that you solved for actually do not "fit" the given inequality at all. Once you get to this point: (X^2)(X-1)<0 You still have deal with the fact that the 'left side' of the inequality has to be be LESS than 0. Since (X^2) with either be 0 or positive, we need to focus on the other piece. With (X-1), you MUST end up with a negative.... so what values of X will make that result happen...? IF X is a positive fraction (re: 0 < X < 1) OR X is ANY negative number. GMAT assassins aren't born, they're made, Rich _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com # Rich Cohen Co-Founder & GMAT Assassin Special Offer: Save$75 + GMAT Club Tests Free
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Re: What is the value of x if x^3 < x^2? [#permalink]

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04 May 2018, 19:15
I manipulated the inequality
X^3 < X^2

X^3 - X^2 < 0
X^2 * (X-1)<0

St1: Insufficient because the values -2 and -1 satisfy. Both will result in an answer less than 0
St2: sufficient. The statement says x is greater than -2 and that it is an integer. Only -1 satisfies this statement.
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Re: What is the value of x if x^3 < x^2? [#permalink]

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04 May 2018, 21:16
Wavy Curve method for inequality is a very important tool
Wavy curve method

See this question approach using this method.
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Re: What is the value of x if x^3 < x^2?   [#permalink] 04 May 2018, 21:16
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