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

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22 Jun 2017, 12:58

2

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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, 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]

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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
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(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

\(x^3 < x^2\) 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

(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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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