Question Number 45166 by peter frank last updated on 09/Oct/18
Answered by MrW3 last updated on 10/Oct/18
$${N}={number}\:{of}\:{students} \\ $$$${when}\:{the}\:{students}\:{are}\:{divided}\:{into} \\ $$$$\mathrm{12}\:{groups},\:{the}\:{last}\:{group}\:{has}\:\mathrm{5}\:{students}, \\ $$$${i}.{e}.\:{the}\:{other}\:\mathrm{11}\:{groups}\:{have}\:{x}\:{students} \\ $$$${with}\:{x}\neq\mathrm{5}. \\ $$$${N}=\mathrm{11}{x}+\mathrm{5}\:{with}\:{x}\neq\mathrm{5} \\ $$$${similarly} \\ $$$${N}=\mathrm{8}{y}+\mathrm{5}\:{with}\:{y}\neq\mathrm{5} \\ $$$${since}\:{the}\:{LCM}\:{of}\:\mathrm{11}\:{and}\:\mathrm{8}\:{is}\:\mathrm{88}, \\ $$$$\Rightarrow{N}=\mathrm{88}{k}+\mathrm{5}\:{with}\:{k}\in\mathbb{N} \\ $$$${i}.{e}.\:{the}\:{class}\:{has}\:\mathrm{93}\:{students}.\:{and} \\ $$$${the}\:{classroom}\:{is}\:{very}\:{large}. \\ $$$$ \\ $$$${The}\:{question}\:{may}\:{mean}\:{something} \\ $$$${different},\:{but}\:{the}\:{language}\:{gives} \\ $$$${this}\:{result}. \\ $$
Commented by peter frank last updated on 10/Oct/18
$$\mathrm{thank}\:\mathrm{you}\:\mathrm{sir} \\ $$