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

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

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

1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.        
2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.        
3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.        
4. EACH statement ALONE is sufficient.        
5. Statements (1) and (2) TOGETHER are not sufficient.

‘What is the value of x if x^3 < x^2?’ – is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken f0rom the book "GMAT Quantitative Review". GMAT Quant section consists of a total of 31 questions. GMAT Data Sufficiency questions consist of a problem statement followed by two factual statements. GMAT data sufficiency comprises 15 questions which are two-fifths of the total 31 GMAT quant questions.

Solution and Explanation

Approach Solution 1:

There is only one solution to this problem.

Given: x³ < x²
Find out: x

If we see the question and work around it properly, 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:

Statement 1 says: –2< x < 2
There are several values of x that satisfy statement 1 (and the given information).We have taken two following cases:
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.

Hence, B is the correct answer.
Correct Answer: B

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