Question

in a large school auditorium the students are made to sit to watch the programmes.Of the teachers make each row of 16 students ,there will be 5 students left. If they make each row of 25 students,there will be 5 students left,if they make each row of 30 students,there will be 5 students left.what is the minimum number of students present in the school?

Answer 1

Answer:

1196

Step-by-step explanation:

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"