Is x 2? (1) 2/x x

Question

Is x > 2, where  x
eq{0} ?

(1) 2/x < 1
(2) 4/x > x

yashikaaggarwal · Answer

To find: Is x > 2?

(1) 2/x < 1
2 < x ( when x is positive) such as 2/3 < 1 ( x > 2)
-2 > x ( when x is negative) 2/-3 < 1 ( x < 2)
Insufficient

(2) 4/x > x
4 > X^2
2 > +/-x
2 > x > -2
therefore value of X will always be less than 2
SUFFICIENT

Answer is B

Kinshook · Answer

Asked: Is x > 2? (1) 2/x < 1 2/x - 1 < 0 (2-x)/x < 0 (x-2)/x > 0 x>2 or x<0 NOT SUFFICIENT (2) 4/x > x 4/x - x > 0 (4-x^2)/x > 0 (x^2-4)/x < 0 (x-2)(x+2)/x < 0 02 SUFFICIENT IMO B

rajatchopra1994 · Answer

Explanation: Statement 1: 2/x < 1 2/x - 1 < 0 2-x/x < 0 x-2/x > 0 x>2 or x<0 Not Sufficient Statement 2: 4/x > x 4/x - x > 0 (4-x^2)/x > 0 (x^2-4)/x < 0 (x-2)(x+2)/x < 0 0

Kritisood · Answer

this question tests the basic concept on inequalities: you cannot multiply both sides by an unknown unless you know the sign of it (x in this case) st 1: \frac{2}{x}-1<0 \frac{(2-x)}{x}<0 taking neg sign out of the expression as to plot on wavy line the expression needs to be of the form (x-a) \frac{(x-2)}{x}>0 plot this on the wavy line you get x>2 OR x<0 two answers hence NS st 2: \frac{4}{x}>x \frac{4}{x}-x>0 \frac{(4-x)^2}{x}>0 \frac{(2+x)(2-x)}{x}>0 taking -ve out of (2-x) expression as to plot on wavy line the expression needs to be of the form (x-a) \frac{(x+2)(x-2)}{x}<0 (sign changes as we are multiplying by neg on both sides) plot on the wavy line x<-2 OR 0

chetan2u · Answer

It is better to mention in the question that x eq{0} (1) \frac{2}{x} < 1 If x<0, \frac{2}{x}<0 < 1 ... so answer to 'Is x>2?' will be NO. If x>0, \frac{2}{x} < 1 => 22?' will be YES. Insufficient (2) 4/x > x \frac{4}{x} - x>0 \frac{4-x^2}{x}>0 If x>0, 4-x^2>0....x^2<4 , that is x<2... answer is NO If x<0... answer will again be NO. Sufficient B

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

Is x > 2? (1) 2/x < 1 (2) 4/x > x

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions