SOLUTION: Let E(n) denote the sum of the even digits of n, For example, E (5681)= 6+8=14 Find E(1)+E(2)+E(3)+...+E(100). (A) 200 (B) 360 (C) 400 (D) 900 (E) 2250

Algebra ->  Equations -> SOLUTION: Let E(n) denote the sum of the even digits of n, For example, E (5681)= 6+8=14 Find E(1)+E(2)+E(3)+...+E(100). (A) 200 (B) 360 (C) 400 (D) 900 (E) 2250      Log On


   

Question 1064995: Let E(n) denote the sum of the even digits of n, For example, E (5681)= 6+8=14
Find E(1)+E(2)+E(3)+...+E(100).
(A) 200 (B) 360 (C) 400 (D) 900 (E) 2250
Answer by ikleyn(52776) About Me  (Show Source):
You can put this solution on YOUR website!
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1.  E(1) + E(2) + E(3) + . . . + E(9) = 2 + 4 + 6 + 8 = 20.


2.  E(10) + E(11) + E(12) + . . . + E(99) = 

    = 2*9 + 4*9 + 6*9 + 8*9 (counted as the units digits) 

    + 2*10 + 4*10 + 6*10 + 8*10 (counted as the tens digits) 

    = 9*(2 + 4 + 6 + 8) + 10*(2 + 4 + 6 + 8) = 9*20 + 10*20 = 19*20 = 380.


3.  20 + 380 = 400.

Answer. 400.