Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

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

Show Tags

28 Jun 2017, 05:47

5

Top Contributor

4

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

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

Show Tags

22 Jun 2017, 12:58

2

1

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)
_________________

You've got what it takes, but it will take everything you've got

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

Show Tags

22 Jun 2017, 16:23

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.

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

Show Tags

22 Jun 2017, 23:46

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
_________________

Never stop fighting until you arrive at your destined place - that is, the unique you. Have an aim in life, continuously acquire knowledge, work hard, and have the perseverance to realise the great life.A. P. J. Abdul Kalam

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

Show Tags

28 Jun 2017, 05:50

Top Contributor

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

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

Show Tags

17 Nov 2017, 11:46

1

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.

Answer: B
_________________

Scott Woodbury-Stewart Founder and CEO

GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions

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

Show Tags

19 Nov 2017, 12:43

1

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

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

Show Tags

03 May 2018, 17:31

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.

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

Show Tags

04 May 2018, 18:15

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.

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

Show Tags

23 Aug 2018, 09:13

GMATPrepNow wrote:

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

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

Show Tags

19 Oct 2018, 09:31

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.

Since \(x^3 < x^2\) is true only if x is NONZERO, we can divide by \(x^2\), which must be POSITIVE: \(\frac{x^3}{x^2} < \frac{x^2}{x^2}\) \(x < 1\) Question stem, rephrased: If x is a nonzero value less than 1, what is the value of x?

Statement 1: Here, x can be any nonzero value between -2 and 1. INSUFFICIENT.

Statement 2: Here, x must be a nonzero integer such that -2 < x < 1. Thus, x=-1. SUFFICIENT.

GMAT and GRE Tutor Over 1800 followers Click here to learn more GMATGuruNY@gmail.com New York, NY If you find one of my posts helpful, please take a moment to click on the "Kudos" icon. Available for tutoring in NYC and long-distance. For more information, please email me at GMATGuruNY@gmail.com.

gmatclubot

Re: What is the value of x if x^3 < x^2? &nbs
[#permalink]
19 Oct 2018, 09:31