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• ### $450 Tuition Credit & Official CAT Packs FREE December 15, 2018 December 15, 2018 10:00 PM PST 11:00 PM PST Get the complete Official GMAT Exam Pack collection worth$100 with the 3 Month Pack ($299) • ### FREE Quant Workshop by e-GMAT! December 16, 2018 December 16, 2018 07:00 AM PST 09:00 AM PST Get personalized insights on how to achieve your Target Quant Score. # Is |x − 6| > 5 ?  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics Author Message TAGS: ### Hide Tags Manager Joined: 03 Oct 2009 Posts: 51 Is |x − 6| > 5 ? [#permalink] ### Show Tags 16 Jan 2012, 21:50 5 00:00 Difficulty: 25% (medium) Question Stats: 73% (01:27) correct 27% (01:37) wrong based on 439 sessions ### HideShow timer Statistics Is |x − 6| > 5 ? (1) x is an integer (2) x^2 < 1 M25-01 [Reveal] Spoiler: When (x-6) is positive x-6 > 5 => x > 11 When (x-6) is negative 6 - x > 5 => x < 1 So the question is (is this re-phrasing of question correct?) - Is x > 11 or Is x < 1 1)x is an integer - doesn't help much. 2)x^2 < 1 => x lies between -1 and 1 exclusive; means x is less than 1. answers the question. Does this solution look okay? though it's not the most elegant. Considering |x-6| as distance is quite lucid. SVP Status: Top MBA Admissions Consultant Joined: 24 Jul 2011 Posts: 1520 GMAT 1: 780 Q51 V48 GRE 1: Q800 V740 Re: Is |x − 6| > 5 ? [#permalink] ### Show Tags 16 Jan 2012, 23:45 |x-6| > 5 if x>11 OR x<1 Using statement (1), we know that x is an integer. However, it may lie between 1 and 11 or not. Insufficient. Using statement (2), x^2<1 => x lies between -1 and 1 (both not inclusive). This satisfies the condition that x<1. Sufficient. The answer is therefore (B). _________________ GyanOne | Top MBA Rankings and MBA Admissions Blog Top MBA Admissions Consulting | Top MiM Admissions Consulting Premium MBA Essay Review|Best MBA Interview Preparation|Exclusive GMAT coaching Get a FREE Detailed MBA Profile Evaluation | Call us now +91 98998 31738 GMAT Tutor Joined: 24 Jun 2008 Posts: 1325 Re: Is |x − 6| > 5 ? [#permalink] ### Show Tags 16 Jan 2012, 23:57 1 Apex231 wrote: Is |x-6| > 5? 1)x is an integer 2)x^2 < 1 When (x-6) is positive x-6 > 5 => x > 11 When (x-6) is negative 6 - x > 5 => x < 1 So the question is (is this re-phrasing of question correct?) - Is x > 11 or Is x < 1 1)x is an integer - doesn't help much. 2)x^2 < 1 => x lies between -1 and 1 exclusive; means x is less than 1. answers the question. Does this solution look okay? though it's not the most elegant. Considering |x-6| as distance is quite lucid. Yes, all of your work looks perfect. I personally prefer the 'distance approach' (|x - 6| is just the distance between x and 6 on the number line, so the question is just asking if that distance is greater than 5, from which we see right away that the question is asking if we can be sure that either x > 11 or x < 1), but the algebraic cases approach also works, of course. _________________ GMAT Tutor in Toronto If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com Manager Joined: 13 Oct 2013 Posts: 136 Concentration: Strategy, Entrepreneurship Re: Is |x − 6| > 5 ? [#permalink] ### Show Tags Updated on: 27 Nov 2013, 00:46 2 Is |x − 6| > 5 ? (1) x is an integer (2) x^2 < 1 M25-01 _________________ --------------------------------------------------------------------------------------------- Kindly press +1 Kudos if my post helped you in any way Originally posted by sunita123 on 26 Nov 2013, 17:32. Last edited by Bunuel on 27 Nov 2013, 00:46, edited 1 time in total. Renamed the topic, edited the question and added the OA. Intern Joined: 22 Apr 2013 Posts: 5 Re: Is |x − 6| > 5 ? [#permalink] ### Show Tags 26 Nov 2013, 20:43 my understanding of the ques -- Is |x−6|>5 ? i.e. is 1<x<11 ? is x between 1 and 11 (1) x is an integer -- insuff as there can be infinite values (2) x^2<1 i..e. (x-1)(x+1) <0 so both the terms have opposite sign and are consecutive so only possible values 1 and -1...so x is zero and is suff so B seems to be the ans..that is stmt 2 is suff..Please confirm is B is the right ans. Manager Joined: 13 Oct 2013 Posts: 136 Concentration: Strategy, Entrepreneurship Re: Is |x − 6| > 5 ? [#permalink] ### Show Tags 26 Nov 2013, 21:24 himapm1l wrote: my understanding of the ques -- Is |x−6|>5 ? i.e. is 1<x<11 ? is x between 1 and 11 (1) x is an integer -- insuff as there can be infinite values (2) x^2<1 i..e. (x-1)(x+1) <0 so both the terms have opposite sign and are consecutive so only possible values 1 and -1...so x is zero and is suff so B seems to be the ans..that is stmt 2 is suff..Please confirm is B is the right ans. yes, ans is B. Still I have a question when I solved |x−6|>5 , i got x<1 and x>11 but from your explanation, it says 1<x<11. Can you pls clarify _________________ --------------------------------------------------------------------------------------------- Kindly press +1 Kudos if my post helped you in any way Math Expert Joined: 02 Sep 2009 Posts: 51218 Re: Is |x − 6| > 5 ? [#permalink] ### Show Tags 27 Nov 2013, 00:47 1 1 sunita123 wrote: Is |x − 6| > 5 ? (1) x is an integer (2) x^2 < 1 M25-01 Is $$|x - 6| > 5$$? Let's work on the stem first. For which values of $$x$$ inequality $$|x - 6| > 5$$ is true? If $$x<6$$ --> $$-x+6>5$$ --> $$x<1$$. If $$x\geq{6}$$ --> $$x-6>5$$ --> $$x>11$$. So we have that inequality $$|x - 6| > 5$$ holds true for $$x<1$$ and $$x>11$$. (1) $$x$$ is an integer. Clearly not sufficient. $$x$$ can be 12 and the inequality holds true as we concluded OR $$x$$ can be 5 and inequality doesn't hold true. (2) $$x^2<1$$ --> $$-1<x<1$$, as all $$x$$-es from this range are in the range $$x<1$$, hence inequality $$|x - 6| > 5$$ holds true. Sufficient. Answer: B. P.S. Please rad carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html Pay attention to the rules 3 and 7. Thank you. _________________ Manager Status: Kitchener Joined: 03 Oct 2013 Posts: 89 Location: Canada Concentration: Finance, Finance GPA: 2.9 WE: Education (Education) Re: Is |x − 6| > 5 ? [#permalink] ### Show Tags 06 Feb 2015, 15:32 Bunuel wrote: sunita123 wrote: Is |x − 6| > 5 ? (1) x is an integer (2) x^2 < 1 M25-01 Is $$|x - 6| > 5$$? Let's work on the stem first. For which values of $$x$$ inequality $$|x - 6| > 5$$ is true? If $$x<6$$ --> $$-x+6>5$$ --> $$x<1$$. If $$x\geq{6}$$ --> $$x-6>5$$ --> $$x>11$$. So we have that inequality $$|x - 6| > 5$$ holds true for $$x<1$$ and $$x>11$$. (1) $$x$$ is an integer. Clearly not sufficient. $$x$$ can be 12 and the inequality holds true as we concluded OR $$x$$ can be 5 and inequality doesn't hold true. (2) $$x^2<1$$ --> $$-1<x<1$$, as all $$x$$-es from this range are in the range $$x<1$$, hence inequality $$|x - 6| > 5$$ holds true. Sufficient. Answer: B. P.S. Please rad carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html Pay attention to the rules 3 and 7. Thank you. Dear Bunuel, I have question when I tried under the case that X >0 I got that X >11 so I chose the common range x>11 and when I tried under the case x <0 I got that x<1 so here I chose the common range x<0 is that correct? _________________ Click +1 Kudos if my post helped Intern Joined: 11 Aug 2016 Posts: 9 Location: United States (PA) Concentration: Finance, General Management GMAT 1: 710 Q48 V40 GPA: 2.42 WE: Other (Mutual Funds and Brokerage) Question M25-01: is |x-6| > 5 [#permalink] ### Show Tags 21 Sep 2016, 17:10 Just a question about the solution to this problem: Is |x−6|>5 ? (1) x is an integer (2) x^2 < 1 The explanation provided is as follows: Let's work on the stem first. For which values of x inequality |x−6|>5 is true? If x<6, then −x+6>5 or x<1. If x≥6, then x−6>5 or x>11. My question is this: How did we come to the text in red? If x<6, why would the sign change on the 6? For x values from x=5 to x=2, we have x<6 and |x-6|<5, not >5 Appreciate any insight, even if its a link to a different forum thread. I tried searching for my question but had trouble funding something this specific. (forgot to add above, official answer was B, (2) is sufficient but (1) is not.) Manager Joined: 24 Aug 2016 Posts: 68 Location: India WE: Information Technology (Computer Software) Re: Question M25-01: is |x-6| > 5 [#permalink] ### Show Tags 21 Sep 2016, 17:55 Quote: My question is this: How did we come to the text in red? If x<6, why would the sign change on the 6? For x values from x=5 to x=2, we have x<6 and |x-6|<5, not >5 |x-6| means distance of X from 6 on the number line. And distance will always be positive. If x < 6, |x-6| becomes a negative integer, so we multiply it with -1. |x-6| > 5 --> -(x-6) > 5 --> -x+6 > 5 --> X < 1 If x < >, |x-6| becomes a positive integer. |x-6| > 5 --> (x-6) > 5 --> x-6 > 5 --> X > 11 So, X < 1 or X > 11 In above example, |X| = k --> means x = -k or x = k but distance will be always positive K. _________________ "If we hit that bullseye, the rest of the dominos will fall like a house of cards. Checkmate." Math Expert Joined: 02 Sep 2009 Posts: 51218 Re: Is |x − 6| > 5 ? [#permalink] ### Show Tags 21 Sep 2016, 21:10 blitheclyde wrote: Just a question about the solution to this problem: Is |x−6|>5 ? (1) x is an integer (2) x^2 < 1 The explanation provided is as follows: Let's work on the stem first. For which values of x inequality |x−6|>5 is true? If x<6, then −x+6>5 or x<1. If x≥6, then x−6>5 or x>11. My question is this: How did we come to the text in red? If x<6, why would the sign change on the 6? For x values from x=5 to x=2, we have x<6 and |x-6|<5, not >5 Appreciate any insight, even if its a link to a different forum thread. I tried searching for my question but had trouble funding something this specific. (forgot to add above, official answer was B, (2) is sufficient but (1) is not.) Merging topics. Please refer to the discussion above. _________________ Intern Joined: 26 Jun 2015 Posts: 37 Location: India Concentration: Entrepreneurship, General Management WE: Engineering (Energy and Utilities) DS - Absolute value and Inequalities [#permalink] ### Show Tags 13 Jun 2017, 17:24 Is |x-6|>5 ? (1) x is an integer (2) x^2<1 Manager Joined: 19 Feb 2017 Posts: 137 Location: India GMAT 1: 690 Q50 V31 Re: DS - Absolute value and Inequalities [#permalink] ### Show Tags 13 Jun 2017, 20:01 Answer is B. Basically the question boils down to, is 1<x<11. Statement 1 is not sufficient as x can be any integer. Statement 2 basically says, -1<x<1. So this is sufficient. Ans B. Sent from my ONE A2003 using GMAT Club Forum mobile app Math Expert Joined: 02 Sep 2009 Posts: 51218 Re: Is |x − 6| > 5 ? [#permalink] ### Show Tags 13 Jun 2017, 21:38 hotcool030 wrote: Is |x-6|>5 ? (1) x is an integer (2) x^2<1 Merging topics. Please refer to the discussion above. _________________ EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 13087 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: Is |x − 6| > 5 ? [#permalink] ### Show Tags 08 Mar 2018, 11:31 Hi All, We're asked if |X-6| > 5. This is a YES/NO question. This question is perfect for TESTing Values. Fact 1: X is an integer. If X = 6, then the answer to the question is NO If X = 100, then the answer to the question is YES Fact 1 is INSUFFICIENT Fact 2: X^2 < 1 Here, we have a really limited range…. -1 < X < 1 No matter what we pick for X, the answer remains consistent... If X = .99, then the answer to the question is YES If X = 0, then the answer to the question is YES If X = -.99, then the answer to the question is YES Fact 2 is SUFFICIENT. Final Answer: GMAT assassins aren't born, they're made, Rich _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com # Rich Cohen Co-Founder & GMAT Assassin Special Offer: Save$75 + GMAT Club Tests Free
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Re: Is |x − 6| > 5 ? &nbs [#permalink] 08 Mar 2018, 11:31
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