Difference between revisions of "2017 AMC 10B Problems/Problem 23"
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<math>\textbf{(A)}\ 1\qquad\textbf{(B)}\ 4\qquad\textbf{(C)}\ 9\qquad\textbf{(D)}\ 18\qquad\textbf{(E)}\ 44</math> | <math>\textbf{(A)}\ 1\qquad\textbf{(B)}\ 4\qquad\textbf{(C)}\ 9\qquad\textbf{(D)}\ 18\qquad\textbf{(E)}\ 44</math> | ||
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+ | The same way, you can get N=4(Mod 5) and 0(Mod 9). By The Chinese remainder Theorem, the answer come out to be 9-(C) | ||
==Solution== | ==Solution== |
Revision as of 11:02, 27 March 2020
Problem 23
Let be the
-digit number that is formed by writing the integers from
to
in order, one after the other. What is the remainder when
is divided by
?
Solution2 The same way, you can get N=4(Mod 5) and 0(Mod 9). By The Chinese remainder Theorem, the answer come out to be 9-(C)
Solution
We only need to find the remainders of N when divided by 5 and 9 to determine the answer.
By inspection, .
The remainder when
is divided by
is
, but since
, we can also write this as
, which has a remainder of 0 mod 9. Therefore, the answer is
.
See Also
2017 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 22 |
Followed by Problem 24 | |
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.