Question Number 121732 by ZiYangLee last updated on 11/Nov/20
$$\mathrm{Given}\:\mathrm{that}\:{a},{b},{c},{d},{e}\:\mathrm{and}\:{f}\:\mathrm{are}\:\mathrm{positive} \\ $$ $$\mathrm{integers}\:\mathrm{where}\:{a}<{b}<{c}<{d}<{e}<{f}\:\mathrm{and} \\ $$ $${a}+{b}+{c}+{d}+{e}+{f}=\mathrm{100},\:\mathrm{find}\:\mathrm{the} \\ $$ $$\mathrm{largest}\:\mathrm{value}\:\mathrm{of}\:{e}. \\ $$ $${A}.\mathrm{46}\:\:\:{B}.\mathrm{44}\:\:\:\:{C}.\mathrm{43}\:\:\:\:{D}.\mathrm{40}\:\:\:{E}.\mathrm{45} \\ $$
Answered by bemath last updated on 11/Nov/20
$${e}_{{max}} \:{when}\:{the}\:{value}\:{of}\:{a},{b},{c}\:{and}\: \\ $$ $${d}\:{must}\:{be}\:{minimum} \\ $$ $$\Rightarrow\:\mathrm{1}+\mathrm{2}+\mathrm{3}+\mathrm{4}+{e}+{f}\:=\:\mathrm{100}\: \\ $$ $$\Rightarrow{e}\:+\:{f}\:=\:\mathrm{90}\:,\:{since}\:{e}\:<\:{f}\:,\:{it} \\ $$ $${follows}\:{that}\:{e}_{{max}} \:=\:\mathrm{44}\:\wedge\:{f}_{{min}} \:=\:\mathrm{46}. \\ $$
Commented byZiYangLee last updated on 11/Nov/20
$$\mathrm{Yes}\:\mathrm{thanks}! \\ $$