S99-06

Question

Is  (x - 2)^2 \gt x^2 ?

(1)  x^2 \gt x

(2)  \frac{1}{x} \gt 0

Bunuel · Answer

Official Solution:

Rephrase the question by expanding the left side of the inequality:
 
Is  x^2 - 4x + 4 \gt x^2 ?
 
Is  -4x + 4 \gt 0 ?
 
Is  4 \gt 4x ?
 
Is  1 \gt x ?
 
Statement 1: INSUFFICIENT. The values of  x  for which  x^2 \gt x  are either negative or greater than 1. (Test numbers to prove this.) However, we do not know whether  x  is less than or greater than 1.
 
Statement 2: INSUFFICIENT. The expression  \frac{1}{x}  is positive when  x  itself is positive. However, again we do not know whether  x  is less than or greater than 1.
 
Statements 1 & 2 together: SUFFICIENT. Combining the two conditions, we see that  x  must be greater than 1. This provides a definitive "No" answer to the given question, and thus we have sufficiency.

Answer: C

amrit3982 · Answer

Looking at the second condition of 1/x >1. it is imperative that x<1 for all x>0, So, I thought condition 2 will be sufficient....Dunno whether I am right? :roll:

Bunuel · Answer

The question asks whether x < 1, while 1/x > 0 means that x > 0. So, the second statement is not sufficient: if x = 1/2, then the answer will be YES but if x = 2, then the answer will be NO.

aaigla · Answer

Bunuel  Can you walk me through a? This is what I'm doing.

x^2>X
X^2-X>0
x(X-1)>0
X>0 or X>1

How is it that these values are then "less than or greater than one?" I get it when I plug in numbers but I don't know where my algebra is going amiss. Why would we switch the direction of the > sign to be <0?

Bunuel · Answer

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.

siddharthkapoor · Answer

aaigla

You are right till the step x(x-1)>0. The correct implication of x(x-1)>0 is that x>1 or x<0. You're wrong to deduce that x>0. We can check this by taking a value between 0 and 1, for example, 0.5. At x=0.5, the expression x(x-1)>0 becomes 0.5(-0.5)>1, which is not true.

I hope you're clear now.

rajeev kabad · Answer

if x^2>x
then x>1 right so we know that then why should we doo all these steps i think stat 1 is sufficent

Showmeyaa · Answer

Wow, I just discovered this side of the GmatClub world and I'm amazed with the question pool. Curiosity aside, let's try to solve this: Is (x - 2)^2 \gt x^2 ? (x-2)^2 - x^2 \gt 0 -2(2x - 2) \gt 0 -4x + 4 \gt 0 Is x < 1 ? 1) x^2 - x > 0 x(x-1) > 0 Using wavy-curve: x > 1 or x < 0 - Insufficient, as we have 2 different values for x 2)1/x > 0 This means that x is positive (x > 0) Case1: x = 0.1 x < 1 - Case2: x = 2 x > 1, Insufficient! Combining (1) & (2): x > 1 - Sufficient! IMO, (C)!

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