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

Question

Is  x^2  greater than x ?

(1)  x^2  is greater than 1.
(2) x is greater than -1.

Bunuel · Accepted Answer

SOLUTION Is x^2 greater than x ? Is x^2 > x ? --> is x(x-1)>0 ? --> is x in the following ranges: x<0 or x>1 ? (1) x^2 is greater than 1 --> x^2>1 --> x<-1 or x>1 . Sufficient. (2) x is greater than -1 --> x>-1 . Not sufficient. Answer: A. 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 For more check Ultimate GMAT Quantitative Megathread Hope it helps.

abid1986 · Answer

Hi Bunuel, If the answer choice satisfy any one of the "Or" inequality does it mean its sufficient? for eg in 1) x > 1 satisifies ( x >1 or x < 0 ) but x < -1 dosent,

Bunuel · Answer

The question asks whether x<0 or x>1 : MSP101751cei440531bcgfbc0000210f0c958eb6ie40.gif 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???

EMPOWERgmatRichC · Answer

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:  A

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

ScottTargetTestPrep · Answer

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

iamvishnu · Answer

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

BrentGMATPrepNow · Answer

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?

woohoo921 · Answer

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?

Johnny1989 · Answer

"
Hi Bunuel,

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

Bunuel · Answer

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

wwcd · Answer

Hi guys. I'm new to Inequalities and I had a very similar doubt as many of you : How to derive the range from the equation? Thanks to GMAT club, I now know that you use the wavy line method. Step 1 : Rewrite the equation in the form of (x - a)(x - b) > 0. So, x (x - 1) > 0 can be rewritten as (x - 0)(x - 1) > 0. Step 2 : Find the points on the number line where LHS = 0. Basically, for what values of x will the LHS = 0? So, when x = 0 : (0 - 0)(0 - 1) = 0. Therefore, LHS = 0 Or, when x = 1 : (1 - 0)(1 - 1) = 0. Therefore, LHS = 0 These two points on the number line are called critical points. (0 , 1) Step 3 : Draw the curve on the number line. So you can see that for all x < 0 and x > 1 : x (x - 1) > 0 and for all x such that 0 < x < 1 : x (x - 1) < 0. This ties back to the question : is x in the following ranges: x<0 or x>1? I hope this helps (And I also hope I'm right). PS : I don't come from a quant background, so I need to learn from the absolute basics. I put this up for the very miniscule set of people who are in the same boat as me. PPS : This seems like a long drawn out process, but as you can see, everyone else who has posted has pretty much calculated this in their heads in less than 2 seconds.

ShreyashGupta188 · Answer

I did the same mistake !

Let me simplify :

When we solve inequality like equality like this :
x(x−1)>0 would get us x>0 and x>1 which is not WRONG , this would be correct in Equalities but not in Inequalities

Step 1: Find the Critical Points

Set the expression equal to zero(Equality method):
x(x−1)=0

The critical points are x = 0 and x = 1.

Step 2: Test Intervals

The critical points divide the number line into three intervals:

x<0 (e.g., x=−1)
0<x<1 (e.g., x=0.5)
x>1 (x=2)

Now, check the sign of x(x−1)>0 in each region:

For x<0
Pick x=−1 then (−1)(−2)=2>0 ✅
For 0<x<1:
Pick x=0.5x, then (0.5)(−0.5)=−0.25<0 ❌
For x>1:
Pick x=2 then (2)(1)=2>0 ✅

Step 3: Write the Solution

x<0 or x>1

iamvishnu

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

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

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