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

###### CAT Questions | Number Theory | Minimum number of students CAT Questions

The question is about Minimum number of students. 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 10: In a large school auditorium, the students are made to sit to watch the programmes. If the teachers make a row of students of 16 each, there will be 12 students left. If they make rows of 24 each, then there will be 20 students left, if they make rows of 25 each, there will be 21 students left and if they make rows of 30 each, there will be 26 students left. What is the minimum number of students present in the school?

1. 1216
2. 1784
3. 1196
4. 2396

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##### Method of solving this CAT Question from Number Theory - HCF and LCM: Find LCM and subtract the common remainder!

16 in a row --> 12 left
24 in a row --> 20 left
25 in a row --> 21 left
30 in a row --> 26 left

In all the 4 cases above, the remainder is 4.
(16 – 12) = (24 – 20) = (25 – 21) = (30 – 26)

Hence the required students = LCM (16, 24, 25, 30 ) – 4
= 1200 – 4
= 1196

The question is "What is the minimum number of students present in the school?"

##### Hence the answer is "1196 students minimum"

Choice C is the correct answer.

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