If a ≠ 0, is a + a−1 2? (1) a 0 (2) a

Question

If  a ≠ 0 , is  a + a^{−1} > 2 ?

(1)  a > 0 
(2)  a < 1

GMATinsight · Answer

Question : is a + a^{−1} > 2 ? CONCEPT: For any positive value of a, a + \frac{1}{a} ≥ 2 Statement1 : a > 0 a + a^{−1} may be Greater than or Equal to 2 (equal for a=1) hence NOT SUFFICIENT Statement 2 : a < 1 If 0 < a < 1 then a + a^{−1} > 2 If a < 0 then a + a^{−1} < -2 hence NOT SUFFICIENT Combining the two statements 0 < a < 1, therefore a + \frac{1}{a} > 2 SUFFICIENT Answer: Option C

GMATGuruNY · Answer

CRITICAL POINTS occur when the two sides of the inequality are EQUAL or when the inequality is UNDEFINED. Given a + a^{−1} > 2 : The two sides are equal when a=1, since 1 + 1^{−1} = 1 + \frac{1}{1^1} = 2 . The inequality is undefined when a=0, since 0^{-1} = \frac{1}{0^1} = undefined. To determine which ranges satisfy the inequality, test one value to the left and one value to the right of each critical point. Here, we must test a<0, 01. If we test a=-1, a=1/2 and a=2, only a=1/2 and a=2 satisfy a + a^{−1} > 2 , implying that the valid ranges are 01. Question stem, rephrased: Is a a positive value other than 1? Statement 1: If a=2, the answer to the rephrased question stem is YES. If a=1, the answer to the rephrased question stem is NO. INSUFFICIENT. Statement 2: If a=1/2, the answer to the rephrased question stem is YES. If a=-1, the answer to the rephrased question stem is NO. INSUFFICIENT. Statements combined: Since 0

TheUltimateWinner · Answer

GMATGuruNY 
Thank you so much for your response. Sir, could explain a bit the highlighted part? i mean: how do someone convinced that we  must  test those values? 
Also, why it is  other than 1 
Thanks__

GMATGuruNY · Answer

The critical points, plotted on a number line: <------ 0 ------- 1------> 0 and 1 are the only values where the a + a^{−1} is undefined or where a + a^{−1} = 2 . Implication: In each of the colored ranges, a + a^{−1} < 2 or a + a^{−1} > 2 . To determine in which ranges a + a^{−1} > 2 , we must test only one value in each of the colored ranges. a=-1 is in the red range. When a=-1, a + a^{−1} < 2 . Thus, the red range (a<0) is not valid. a=1/2 is in the green range. When a=1/2, a + a^{−1} > 2 . Thus, the green range (0 2 . Thus, the blue range (a>1) is valid. Result: a + a^{−1} > 2 when a is in the green range (01). Together, the green and blue ranges include every positive value except for 1. Thus, the answer to the question stem is YES if a is ANY POSITIVE VALUE OTHER THAN 1. Question stem. rephrased: Is a a positive value other than 1?

Karpov92 · Answer

Bunuel
I tried to solve it using algebra. Here's my process. Is it right?
a+a^-1>2
or a+1/a-2>0
or (a-1)^2. a^-1>0
So, the question becomes is 1/a>0 when a≠1?
1. a>0, It works in all the cases except when a=1. so, Not sufficient
2. a<1, a can be + or -. So, Not sufficient.
(1) + (2) = 0<a<1 , So, Clearly a is + & a≠1. So, Sufficent . Answer. (C)

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.

If a ≠ 0, is a + a−1 > 2? (1) a > 0 (2) a < 1

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