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

###### CAT Questions | Number Theory | No of sweet boxes

The question is about No of sweet boxes. 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. 2IIM has provided fabulous questions with detailed solution for the topic of HCF and LCM in the Free CAT Question bank.

Question 9: 6 different sweet varieties of count 32, 216, 136, 88, 184, 120 were ordered for a particular occasion. They need to be packed in such a way that each box has the same variety of sweet and the number of sweets in each box is also the same. What is the minimum number of boxes required to pack?

1. 129
2. 64
3. 48
4. 97

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##### Method of solving this CAT Question from Number Theory - HCF and LCM: Find HCF and divide total sweets by that!

All sweets need to packed and each box has the same variety.
This implies the number of sweets in each box should be HCF of different count of sweets
HCF of 32, 216, 136, 88, 184, 120 = 23 = 8
Minimum number of boxes = (32 + 216 + 136 + 88 + 184 + 120) / 8 = 97

The question is "What is the minimum number of boxes required to pack?"

##### Hence the answer is "97 boxes"

Choice D is the correct answer.

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