Menu Close

Given-that-a-b-c-d-e-and-f-are-positive-integers-where-a-lt-b-lt-c-lt-d-lt-e-lt-f-and-a-b-c-d-e-f-100-find-the-largest-value-of-e-A-46-B-44-C-43-D-40-E-45-

Tinku Tara 0 Comments
Pin




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

Pin

Leave a Reply

Your email address will not be published. Required fields are marked *