What is the value of x if x^3 < x^2?
(1) 2 < x < 2
(2) x is an integer greater than 2
B
OG What is the value of x if x^3 < x^2
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We need to determine the value of x, given that x^3 < x^2.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
Statement One Alone:
2 < x < 2
We see that x could be, for example, 1 or Â½.
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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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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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
GMAT assassins aren't born, they're made,
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Target question: What is the value of x?AbeNeedsAnswers wrote: ↑Sat Aug 19, 2017 2:49 pmWhat is the value of x if x^3 < x^2?
(1) 2 < x < 2
(2) x is an integer greater than 2
B
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 xvalue (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
Cheers,
Brent