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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 ## A wire is cut into three equal parts. The resulting... tagged by: BTGmoderatorLU ##### This topic has 3 expert replies and 0 member replies ### Top Member ## A wire is cut into three equal parts. The resulting... A wire is cut into three equal parts. The resulting segments are then cut in 4, 6 and 8 equal parts respectively. If each of the resulting segments has an integer length, what is the minimum length of the wire? A. 24 B. 36 C. 48 D. 54 E. 72 The OA is E. I'm confused with this PS question. Experts, any suggestion? How can I determine the minimum length? Thanks in advance. ### GMAT/MBA Expert GMAT Instructor Joined 04 Oct 2017 Posted: 551 messages Followed by: 11 members Upvotes: 180 Quote: A wire is cut into three equal parts. The resulting segments are then cut in 4, 6 and 8 equal parts respectively. If each of the resulting segments has an integer length, what is the minimum length of the wire? A. 24 B. 36 C. 48 D. 54 E. 72 The OA is E. I'm confused with this PS question. Experts, any suggestion? How can I determine the minimum length? Thanks in advance. Hi LUANDATO, Let's take a look at your question. Suppose that the minimum length of wire be 3x. If it is cut into three equal pieces, length of each piece will be x. The resulting segments are then cut in 4, 6 and 8 equal parts respectively. 4 pieces will be of length x/4 each. 6 pieces will be of length x/6 each. 8 pieces will be of length x/8 each. Since, each of the resulting segments has an integer length, therefore, x/4, x/6 and x/8 will result into integer values. It means x is the least common multiple of 4, 6, 8. Multiples of 4 = 4, 8, 12, 16, 20, 24, ... Multiples of 6 = 6, 12, 18, 24, 30, ... Multiples of 8 = 8, 16, 24, 32, ... LCM of 4, 6 and 8 = 24 It means x = 24 The minimum length of wire = 3x = 3(24) = 72 Therefore, Option E is correct. Hope it helps. I am available if you'd like any follow up. _________________ 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 GMAT Instructor Joined 25 May 2010 Posted: 15383 messages Followed by: 1872 members Upvotes: 13060 GMAT Score: 790 LUANDATO wrote: A wire is cut into three equal parts. The resulting segments are then cut in 4, 6 and 8 equal parts respectively. If each of the resulting segments has an integer length, what is the minimum length of the wire? A. 24 B. 36 C. 48 D. 54 E. 72 We can PLUG IN THE ANSWERS, which represent the minimum length of the wire. When we plug in the correct answer, we will be able to divide the wire first into 3 equal parts and then into 4, 6, and 8 equal parts. Since the question stem asks for the MINIMUM length, start with the smallest answer choice. A: 24 If a 24-inch wire is divided into 3 equal parts, the length of each part = 24/3 = 8. The value in red cannot be divided into 6 equal parts. Eliminate A. B: 36 If a 36-inch wire is divided into 3 equal parts, the length of each part = 36/3 = 12. The value in red cannot be divided into 8 equal parts. Eliminate B. C: 48 If a 48-inch wire is divided into 3 equal parts, the length of each part = 48/3 = 16. The value in red cannot be divided into 6 equal parts. Eliminate C. D: 54 If a 54-inch wire is divided into 3 equal parts, the length of each part = 54/3 = 18. The value in red cannot be divided into 8 equal parts. Eliminate D. The correct answer is E. E: 72 If a 72-inch wire is divided into 3 equal parts, the length of each part = 72/3 = 24. Success! The value in green can be divided into 4, 6, and 8 equal parts. _________________ 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. ### GMAT/MBA Expert GMAT Instructor Joined 09 Apr 2015 Posted: 1465 messages Followed by: 19 members Upvotes: 39 LUANDATO wrote: A wire is cut into three equal parts. The resulting segments are then cut in 4, 6 and 8 equal parts respectively. If each of the resulting segments has an integer length, what is the minimum length of the wire? A. 24 B. 36 C. 48 D. 54 E. 72 We see that each of the 3 equal parts must be a multiple of 4, 6 and 8. Since we want the minimum length of the wire, we want the length of each of the equal parts to be the least common multiple (LCM) of 4, 6 and 8. The LCM of 4, 6 and 8 is 24. Thus the minimum length of each of the 3 equal parts is 24 and the minimum length of the original wire is 3 x 24 = 72. Answer: E _________________ Jeffrey Miller Head of GMAT Instruction jeff@targettestprep.com See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. 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