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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. # For How many integer values of x, is |2x-5|+|x+1|+|x|<10?  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics Author Message TAGS: ### Hide Tags Senior SC Moderator Joined: 14 Nov 2016 Posts: 1324 Location: Malaysia For How many integer values of x, is |2x-5|+|x+1|+|x|<10? [#permalink] ### Show Tags 13 Feb 2017, 05:29 7 00:00 Difficulty: 65% (hard) Question Stats: 57% (02:08) correct 43% (02:17) wrong based on 155 sessions ### HideShow timer Statistics For how many integer values of x, is $$|2x-5|+|x+1|+|x|<10$$? A. 1 B. 2 C. 4 D. 5 E. Infinite _________________ "Be challenged at EVERY MOMENT." “Strength doesn’t come from what you can do. It comes from overcoming the things you once thought you couldn’t.” "Each stage of the journey is crucial to attaining new heights of knowledge." Rules for posting in verbal forum | Please DO NOT post short answer in your post! Advanced Search : https://gmatclub.com/forum/advanced-search/ ##### Most Helpful Expert Reply Math Expert Joined: 02 Sep 2009 Posts: 51218 Re: For How many integer values of x, is |2x-5|+|x+1|+|x|<10? [#permalink] ### Show Tags 13 Feb 2017, 05:59 1 5 ##### General Discussion 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: For How many integer values of x, is |2x-5|+|x+1|+|x|<10? [#permalink] ### Show Tags 13 Feb 2017, 21:21 Hi ziyuenlau, We're told that X must be an INTEGER, so since we're adding the sums of 3 absolute values - AND we're looking for sums that are LESS than 10 - there cannot be an infinite number of possibilities. Thus, based on the answer choices, there can't be more than 5 possible integer values for N. As such, we can use a bit of 'brute force' to find all of the possible values without too much trouble. We're given the inequality: |2X - 5| + |X + 1| + |X| < 10. Let's start with... X = 0.... |-5| + |1| + |0| = 6 so X could be 0 Now let's work our way "up"... X = 1.... |-3| + |2| + |1| = 6 so X could be 1 X = 2.... |-1| + |3| + |2| = 6 so X could be 2 X = 3.... |1| + |4| + |3| = 8 so X could be 3 X = 4.... |3| + |5| + |3| = 11 so X CANNOT be 4 Now let's work our way "down".... X = -1.... |-7| + |0| + |-1| = 8 so X could be -1 At this point, we have 5 possible values of X; since that it the largest of the possible values, we can stop working. 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: For How many integer values of x, is |2x-5|+|x+1|+|x|<10?  [#permalink]

### Show Tags

02 Jan 2018, 00:45
Bunuel mikemcgarry MathRevolution: Is the below method correct to solve the given type of inequality questions ? Is this another correct way instead of considering the individual ranges ?

1. Taking all positive terms :
2x-5+x+1+x<10
4x-4<10
x<7/2

2. Taking all negative terms :
5-2x-x-x-x<10
x>-3/2

So the range is -3/2<x<7/2

Therefore , the possible values are -1,0,1,2,3...so 5 values
Re: For How many integer values of x, is |2x-5|+|x+1|+|x|<10? &nbs [#permalink] 02 Jan 2018, 00:45
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