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?
Answer & explanation
Correct answer: option 4
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]