Difference between revisions of "2002 AMC 10B Problems/Problem 14"
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== Problem == | == Problem == | ||
− | The number <math>5^{64}\cdot | + | The number <math>5^{64}\cdot 64^{25}</math> is the square of a positive integer <math>N</math>. In decimal representation, the sum of the digits of <math>N</math> is |
<math> \mathrm{(A) \ } 7\qquad \mathrm{(B) \ } 14\qquad \mathrm{(C) \ } 21\qquad \mathrm{(D) \ } 28\qquad \mathrm{(E) \ } 35 </math> | <math> \mathrm{(A) \ } 7\qquad \mathrm{(B) \ } 14\qquad \mathrm{(C) \ } 21\qquad \mathrm{(D) \ } 28\qquad \mathrm{(E) \ } 35 </math> |
Revision as of 12:09, 26 December 2016
Problem
The number is the square of a positive integer . In decimal representation, the sum of the digits of is
Solution
Taking the root, we get .
Now, we have .
Combing the 's and 's gives us .
This is the number with a string of sixty-four 's at the end. Thus, the sum of the digits of is
See also
2002 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 13 |
Followed by Problem 15 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AMC 10 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.