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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## G(x) is the greatest integer less tagged by: VJesus12 ##### This topic has 2 expert replies and 0 member replies ## G(x) is the greatest integer less G(x) is the greatest integer less than or equal to x and L(x) is the least integer greater than or equal to x. When x is not an integer, which of the following is the value of L(x)-G(x)? A. -2 B. -1 C. 0 D. 1 E. 2 The OA is the option D. How can I know the value of L(x)-G(x) without knowing the value of x? Experts, may you help me here? I'd be thankful. ### GMAT/MBA Expert GMAT Instructor Joined 04 Oct 2017 Posted: 551 messages Followed by: 11 members Upvotes: 180 Top Reply Hello Vjesus12. Let's take a look at your question. Let's suppose that x=5.2. Then $$G\left(x\right)=G\left(5.2\right)=5\ ;\ \ and\ \ \ \ L\left(x\right)=L\left(5.2\right)=6.$$ Therefore, $$L\left(x\right)-G\left(x\right)=1.$$ This situation happens every time that x is not an integer. Hence, the correct solution is option D=1. I hope this may help you. Feel free to ask me again if you have a doubt. Regards. _________________ GMAT Prep From The Economist We offer 70+ point score improvement money back guarantee. Our average student improves 98 points. Free 7-Day Test Prep with Economist GMAT Tutor - Receive free access to the top-rated GMAT prep course including a 1-on-1 strategy session, 2 full-length tests, and 5 ask-a-tutor messages. Get started now. ### GMAT/MBA Expert Elite Legendary Member Joined 23 Jun 2013 Posted: 9949 messages Followed by: 493 members Upvotes: 2867 GMAT Score: 800 Hi VJesus12, We're told that G(X) is the greatest integer LESS THAN OR EQUAL to X and L(X) is the least integer GREATER THAN OR EQUAL to X. When X is NOT an integer, we're asked which of the following is the value of L(X)-G(X). This question can be solved rather easily by TESTing VALUES (as the other explanation shows). It's also a fairly straight-forward 'concept' question - meaning that you don't have to do much math to answer it if you recognize the concepts involved. We're told that X is NOT an integer, so the least integer that is GREATER THAN OR EQUAL to X would be the integer that is immediately to the "right" of X on a number line. In that same way, the greatest integer that is LESS THAN OR EQUAL to X would be the integer that is immediately to the 'left' of X on a number line. We're asked to calculate the larger number minus the smaller number - and that will always be 1. Final Answer: D GMAT assassins aren't born, they're made, Rich _________________ Contact Rich at Rich.C@empowergmat.com • Magoosh Study with Magoosh GMAT prep Available with Beat the GMAT members only code • Free Practice Test & Review How would you score if you took the GMAT Available with Beat the GMAT members only code • Award-winning private GMAT tutoring Register now and save up to$200

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