Question Number 178064 by aurpeyz last updated on 12/Oct/22
$${A}\:{group}\:{of}\:{n}\:{people}\:{is}\:{categorized}\:{as}\:{follows}. \\ $$$$\mathrm{14}\:{people}\:{are}\:{shorter}\:{than}\:\mathrm{5}\frac{\mathrm{1}}{\mathrm{2}}\:{feet} \\ $$$$\mathrm{9}\:{people}\:{are}\:{taller}\:{than}\:\mathrm{6}\:{feet} \\ $$$$\mathrm{12}\:{people}\:{are}\:{under}\:\mathrm{21}\:{years}\:{old}. \\ $$$${if}\:{each}\:{person}\:{in}\:{the}\:{group}\:{is}\:{in}\:{at}\:{least} \\ $$$${one}\:{of}\:{the}\:{three}\:{categories}.\:{then}\:{n}\:{can}\:{be} \\ $$$${any}\:{integer}\:{between}\: \\ $$$${a}.\:\mathrm{9}\:{and}\:\mathrm{14}\:{inclusive} \\ $$$${b}.\:\mathrm{12}\:{and}\:\mathrm{21}\:{inclusive} \\ $$$${c}.\:\mathrm{14}\:{and}\:\mathrm{23}\:{inclusive} \\ $$$${d}.\:\mathrm{21}\:{and}\:\mathrm{26}\:{inclusive} \\ $$$${e}.\:\mathrm{23}\:{and}\:\mathrm{35}\:{inclusive} \\ $$$$ \\ $$
Answered by mr W last updated on 12/Oct/22
Commented by Tawa11 last updated on 12/Oct/22
$$\mathrm{Great}\:\mathrm{sir} \\ $$
Commented by mr W last updated on 12/Oct/22
$${at}\:{most}\:{people}\:{when}\:{C}\:{is}\:{outside} \\ $$$${A}\:{and}\:{B},\:{then}\:{n}_{{max}} =\mathrm{14}+\mathrm{9}+\mathrm{12}=\mathrm{35} \\ $$$${at}\:{least}\:{people}\:{when}\:{C}\:{is}\:{inside}\:{A}, \\ $$$${then}\:{n}_{{min}} =\mathrm{14}+\mathrm{9}=\mathrm{23}. \\ $$$$\Rightarrow{answer}\:{e} \\ $$
Commented by aurpeyz last updated on 12/Oct/22
$${thank}\:{you}\:{Sir}. \\ $$$${can}\:{n}_{{min}} \:\:=\mathrm{12}+\mathrm{9}=\mathrm{21}\:{if}\:{they}\:{had}\:{included}\: \\ $$$${an}\:{option}\:{like}\:\mathrm{21}\:{to}\:\mathrm{35}\:{inclusive}.\:{or}\:{was}\:{there}\: \\ $$$${any}\:{special}\:{reason}\:{why}\:{it}\:{was}\:\mathrm{12}\:{that}\:{you} \\ $$$${considered}\:{to}\:{be}\:{either}\:{out}\:{or}\:{in}?\: \\ $$$$ \\ $$
Commented by aurpeyz last updated on 12/Oct/22
$${also}.\:{is}\:{it}\:{possible}\:{for}\:{two}\:{groups}\:{to}\:{be}\: \\ $$$${considered}\:{to}\:{get}\:{the}\:{n}_{{min}.\:} {e}.{g}\:{if}\:{i}\: \\ $$$${consider}\:{C}\:{and}\:{A}\:{to}\:{be}\:{inside}\:{and}\:{n}_{{min}} =\mathrm{9}. \\ $$$${although}\:\mathrm{9}\:{and}\:\mathrm{35}\:{is}\:{not}\:{in}\:{the}\:{option}. \\ $$
Commented by mr W last updated on 13/Oct/22
$${people}\:{shorter}\:{than}\:\mathrm{5}.\mathrm{5}\:{feet}\:{and}\:{people} \\ $$$${taller}\:{than}\:\mathrm{6}\:{feet}\:{are}\:{always}\:{there}, \\ $$$${because}\:{they}\:{can}\:{not}\:{be}\:{the}\:{same}\: \\ $$$${people}! \\ $$$${people}\:{under}\:\mathrm{20}\:{years}\:{can}\:{be}\:{those} \\ $$$${between}\:\mathrm{5}.\mathrm{5}\:{feet}\:{and}\:\mathrm{6}\:{feet},\:\Rightarrow{n}_{{max}} . \\ $$$${people}\:{under}\:\mathrm{20}\:{years}\:{can}\:{also}\:{be}\:{those} \\ $$$${smaller}\:{than}\:\mathrm{5}.\mathrm{5}\:{feet},\:\Rightarrow{n}_{{min}} . \\ $$
Commented by aurpeyz last updated on 12/Oct/22
$${thank}\:{you}\:{Sir} \\ $$