CAT Practice : Number System - HCF, LCM

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Find LCM and subtract the common remainder!

Minimum number of students

    Q.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

 

  • Correct Answer
    Choice C. 1196

Detailed Solution

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


Correct Answer: 1196 students minimum

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Number Theory is one of the most heavily tested topics. Within this, one should get the basics on factors, multiples, HCF, LCM very clear before moving on to the tougher sets.