# CAT Quantitative Aptitude Questions | CAT Number Systems - HCF and LCM questions

###### CAT Questions | Number Theory | Number of carpenters

The question is about Number of carpenters. It is a simple question. It is an application based question. It tests the understanding of LCM and HCF. A range of CAT questions can be asked based on this simple concept. HCF and LCM from CAT Number Systems is oft tested not just in the context of CAT Number Systems but also inside CAT Quantitative Aptitude questions from other topics.

Question 12: 4 logs of woods of lengths 5 $$frac{1}{4}\\$ m , 1 $\frac{13}{15}\\$ m , 3 $\frac{1}{2}\\$ m and 4 $\frac{9}{10}\\$ m are cut into small pieces, all of which have equal length. Each piece of wood is as lengthy as possible. Each cut piece is given to a set of 2 carpenters to work on something. How many carpenters are there in all to work? 1. 148 2. 210 3. 332 4. 266 ## 🎉🎉Special Independence day offer - get up to ₹ 10,000 off on our courses! #### Register Now ## Best CAT Online Coaching Try upto 40 hours for free Learn from the best! #### 2IIM : Best Online CAT Coaching. ## Best CAT Coaching in Chennai #### CAT Coaching in Chennai - CAT 2022Limited Seats Available - Register Now! ### Explanatory Answer ##### Method of solving this CAT Question from Number Theory - HCF and LCM: HCF of fractions HCF$5 $$frac{1}{4}\\$ , 1 $\frac{13}{15}\\$ , 3 $\frac{1}{2}\\$ , 4 $\frac{9}{10}\\$ ) = HCF$$$frac{21}{4}\\$ , $\frac{28}{15}\\$ , $\frac{7}{2}\\$ ,$\frac{49}{10}\\$) = $\frac{HCF$21, 28, 7, 49$}{LCM(4, 15, 2, 10)}$ = $\frac{7}{60}\\$ Hence, total number of pieces = $\frac{21}{4}\\$ * $\frac{60}{7}\\$ + $\frac{28}{15}\\$ * $\frac{60}{7}\\$ + $\frac{7}{2}\\$ * $\frac{60}{7}\\$ + $\frac{49}{10}\\$ * $\frac{60}{7}\\$ = 45 + 16 + 30 + 42 = 133 The question is "How many carpenters are there in all to work?" ##### Hence the answer is "266" Choice D is the correct answer. ###### 🎉Special Independence day offer - get up to ₹ 10,000 off on our courses! ★ Register now ###### Best CAT Online Coaching Try upto 40 hours for free Learn from the best! ###### Already have an Account? ###### CAT Coaching in ChennaiCAT 2024 Classroom Batches Starting Now! @Gopalapuram and @Anna nagar ###### Best CAT Coaching in Chennai Attend a Demo Class ###### Best Indore IPM & Rohtak IPM CoachingSignup and sample 9 full classes for free. Register now! ## CAT Online Coaching | CAT Number Systems questions Videos On YouTube #### Other useful sources for Number System Questions | Number Theory HCF and LCM Sample Questions ##### Where is 2IIM located? 2IIM Online CAT Coaching A Fermat Education Initiative, 58/16, Indira Gandhi Street, Kaveri Rangan Nagar, Saligramam, Chennai 600 093 ##### How to reach 2IIM? Phone:$91) 44 4505 8484
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