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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 ## How many integers are there between, but not including, ##### This topic has 2 expert replies and 1 member reply ### Top Member ## How many integers are there between, but not including, ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult How many integers are there between, but not including, integers r and s ? (1) s-r=10 (2) There are 9 integers between, but not including, r + 1 and s + 1. OA D Source: Official Guide ### GMAT/MBA Expert GMAT Instructor Joined 09 Oct 2010 Posted: 1449 messages Followed by: 32 members Upvotes: 59 Top Reply BTGmoderatorDC wrote: How many integers are there between, but not including, integers r and s ? (1) s-r=10 (2) There are 9 integers between, but not including, r + 1 and s + 1. Source: Official Guide $$?\,\, = \,\,s - r - 1\,\,\,\,\left( {{\rm{the\,\, fingers}}\,\,{\rm{counting}}\,\,{\rm{technique}}} \right)$$ $$\left( 1 \right)\,\,s - r = 10\,\,\,\,\,\, \Rightarrow \,\,\,\,\,? = 9\,\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{SUFF}}.\,\,\,\,\,$$ $$\left( 2 \right)\,\,\left( {s + 1} \right) - \left( {r + 1} \right) - 1 = 9\,\,\,\left( {{\rm{same}}\,\,{\rm{technique}}} \right)\,\,\,\,\,\, \Rightarrow \,\,\,\,\,? = 9\,\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{SUFF}}.\,\,\,\,$$ This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio. _________________ Fabio Skilnik :: GMATH method creator ( Math for the GMAT) English-speakers :: https://www.gmath.net Portuguese-speakers :: https://www.gmath.com.br ### Top Member Legendary Member Joined 02 Mar 2018 Posted: 1104 messages Followed by: 2 members Top Reply Number of integers between two numbers r and s without including r and s can be stated as $$\left(s-r\right)+\left(1-2\right)=s-r-1$$ Find the value of $$s-r-1$$ $$statement\ 1=\ s-r=10$$ $$from\ s-r-1$$ we have 10-1=9 integers between r and s not including r and s, hence statement 1 is INSUFFICIENT Statement 2 There are integers between but nut including $$\ r+1\ and\ s+1$$ $$\left(s+1\right)-\left(r+1\right)-1=9$$ $$s+1-r-1-1=9$$ $$s-r-1=9$$ $$hence\ statement\ 2\ is\ INSUFFICIENT$$ ### GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 15348 messages Followed by: 1864 members Upvotes: 13060 GMAT Score: 790 BTGmoderatorDC wrote: How many integers are there between, but not including, integers r and s ? (1) s-r=10 (2) There are 9 integers between, but not including, r + 1 and s + 1. Statement 1: Case 1: r=0 and s=10 Integers between r and s: 1, 2, 3, 4, 5, 6, 7, 8, 9 --> 9 integers Case 2: r=1 and s=11 Integers between r and s: 2, 3, 4, 5, 6, 7, 8, 9, 10 --> 9 integers Case 3: r=2 and s=12 Integers between r and s: 3, 4, 5, 6, 7, 8, 9, 10, 11 --> 9 integers In every case, the number of integers between r and s = 9. SUFFICIENT. Statement 2: On the number line: ...r...r+1...8 integers...s...s+1 Here, the 9 integers in color lie between r+1 and s+1. As the number line illustrates, between r and s there are a total of 9 integers: r+1 and the 8 integers in blue. SUFFICIENT. The correct answer is D. _________________ Mitch Hunt Private Tutor for the GMAT and GRE GMATGuruNY@gmail.com If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon. Available for tutoring in NYC and long-distance. For more information, please email me at GMATGuruNY@gmail.com. Student Review #1 Student Review #2 Student Review #3 Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now. • 1 Hour Free BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • Magoosh Study with Magoosh GMAT prep Available with Beat the GMAT members only code • FREE GMAT Exam Know how you'd score today for$0

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