Is x^2 greater than x? (1) x^2 is greater than 1 (2) x is greater than

The question asks whether \(x<0\) or \(x>1\):So, whether x is in the blue ranges above.

(1) says that \(x<-1\) or \(x>1\). Now, let me ask you a question: is x in the blue ranges???

Hi All,

This DS question is based on a couple of Number Property rules; if you know the rules, then you can answer this question with a more logic-based approach. If you don't know the rules, then you can still discover the patterns involved by TESTing VALUES.

We're asked if X^2 is greater than X. This is a YES/NO question.

By doing a little bit of work up-front, we can make dealing with the two Facts easier. We just have to think about what X COULD be and whether that would make X^2 greater than X (or not).

IF... X = ANY negative value....
Then X^2 = positive and X^2 > X. The answer to the question would be YES.

IF.... X = 0 or X = 1
Then X^2 = X. The answer to the question would be NO.

IF.... X = A positive FRACTION...
Then X^2 < X. The answer to the question would be NO.

IF.... X > 1
Then X^2 > X. The answer to the question would be YES.

Fact 1: X^2 is greater than 1

Here, X COULD be any negative LESS than -1 (eg. -2, -3, -4, -1.5, etc.)....and the answer to the question would be YES.
X COULD also be any positive GREATER than 1 (e.g. 2, 3, 4, 1.5, etc.)...and the answer to the question would also be YES.
The answer to the question is ALWAYS YES.
Fact 1 is SUFFICIENT.

Fact 2: X is greater than -1

X COULD be 0...and the answer to the question would be NO.
X COULD also be any positive GREATER than 1 (e.g. 2, 3, 4, 1.5, etc.)...and the answer to the question would be YES.
Fact 2 is INSUFFICIENT

Final Answer:

GMAT assassins aren't born, they're made,
Rich

Solution:

We need to determine whether x^2 is greater than x. Notice that x^2 is greater than x if x > 1 or x < 0.

Statement One Alone:

Since x^2 is greater than 1, x is either greater than 1 or less than -1. Either way we have x^2 > x. Statement one alone is sufficient.

Statement Two Alone:

Statement two alone is not sufficient. For example, if x = 2, then x^2 > x. However, if x = 0, then x^2 is not greater than x.

Answer: A

BrentGMATPrepNow
Please help me understand this concept...

how does sign for x(x-1)>0 become x<0 Why does sign got changed. We didn’t multiply by negative

Posted from my mobile device

I believe you're referring to statement 1 (x² > 1)
If x² > 1, then EITHER x > 1 OR x < -1

Let's examine both cases...
case i: If x > 1, then x is positive, and (x - 1) is positive, which means x(x-1) = (positive)(positive) = positive.
In other words, if x > 1, then x(x-1) > 0
case ii: If x < -1, then x is negative, and (x - 1) is negative, which means x(x-1) = (negative)(negative) = positive.
In other words, if x < -1, then x(x-1) > 0

Since both cases yield a result in which x(x-1) > 0, we can be certain that statement 1 is sufficient

Does that help?

Bunuel
I realize that Brent discusses testing values above. But, what approach did you take to get from x(x-1)>0 to then x<0 or x>1?

"
Hi Bunuel,

for x(x-1)>0 how is x<0

If x is negative, then x(x-1) = negative*negative = positive.

Check the links below for more:

9. Inequalities

• Theory
  Inequalities Made Easy!
  Inequalities: Tips and hints
  Arithmetic with Inequalities
  Wavy Line Method Application - Complex Algebraic Inequalities
  Solving Quadratic Inequalities: Graphic Approach
  Inequalities - Quadratic Inequalities
  Graphic approach to problems with inequalities
  Inequalities trick
  INEQUATIONS(Inequalities) Part 1
  INEQUATIONS(Inequalities) Part 2
  
  • Questions
    Inequality and absolute value questions from my collection
    DS Questions
    PS Questions

Bunuel

In this question, (Link - https://gmatclub.com/forum/is-1-p-r-r-2 ... 86165.html) you didn't bring LHS to the RHS, you simply divided these terms with the same variable. However, in this question you brough "x" in the RHS to LHS. Why is it different in both these questions? Kindly let me know.