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

CAT Questions | Number Theory | Minimum number of students

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

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 2022
Limited Seats Available - Register Now!

Explanatory Answer

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.


CAT Online Coaching | CAT Number Systems questions Videos On YouTube

Other useful sources for Number System Questions | Number Theory HCF and LCM Sample Questions

CAT Questions | CAT Quantitative Aptitude

CAT Questions | CAT DILR

CAT Questions | Verbal Ability for CAT

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
Mobile: (91) 99626 48484
WhatsApp: WhatsApp Now