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

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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.


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