When asked for total students in a class, the teacher replied, "if you divide the total numbers of students by 3, 5, 6, 8 and 9 each time, you will find a remainder of 1.  But if you divide it by 11, the remainder is 0."  How many students in the class is?

1441

LCM of 3, 5, 6, 8, 9 = 360

Required number = 360K + 1 [which is exactly divisible by 11 for certain value of K]

Lets find out that number:

⇒ \(\frac{360K\;+\;1}{11}\) = \(\frac{352K\;+\;(8K\;+\;1}{11}\) = \(\frac{8K\;+\;1}{11}\)

Put K = 4

= \(\frac{32\;+\;1}{11}\) = \(\frac{33}{11}\) = 0 Remainder

Therefore,

Number of students = (360 × 4) + 1 = 1441 [which is exactly divisible by 11]