Difference between revisions of "2017 AMC 12B Problems"
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==Problem 19== | ==Problem 19== | ||
+ | Let <math>N=123456789101112\dots4344</math> be the <math>79</math>-digit number that is formed by writing the integers from <math>1</math> to <math>44</math> in order, one after the other. What is the remainder when <math>N</math> is divided by <math>45</math>? | ||
+ | |||
+ | <math>\textbf{(A)}\ 1\qquad\textbf{(B)}\ 4\qquad\textbf{(C)}\ 9\qquad\textbf{(D)}\ 18\qquad\textbf{(E)}\ 44</math> | ||
+ | |||
+ | [[2017 AMC 12B Problems/Problem 19|Solution]] | ||
==Problem 20== | ==Problem 20== |
Revision as of 16:10, 16 February 2017
WORK IN PROGRESS
2017 AMC 12B (Answer Key) Printable versions: • AoPS Resources • PDF | ||
Instructions
| ||
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 |
Contents
[hide]- 1 Problem 1
- 2 Problem 2
- 3 Problem 3
- 4 Problem 4
- 5 Problem 5
- 6 Problem 6
- 7 Problem 7
- 8 Problem 8
- 9 Problem 9
- 10 Problem 10
- 11 Problem 11
- 12 Problem 12
- 13 Problem 13
- 14 Problem 14
- 15 Problem 15
- 16 Problem 16
- 17 Problem 17
- 18 Problem 18
- 19 Problem 19
- 20 Problem 20
- 21 Problem 21
- 22 Problem 22
- 23 Problem 23
- 24 Problem 24
- 25 Problem 25
- 26 See also
Problem 1
Kymbrea's comic book collection currently has comic books in it, and she is adding to her collection at the rate of
comic books per month. LaShawn's collection currently has
comic books in it, and he is adding to his collection at the rate of
comic books per month. After how many months will LaShawn's collection have twice as many comic books as Kymbrea's?
Problem 2
Real numbers ,
, and
satify the inequalities
,
, and
.
Which of the following numbers is necessarily positive?
Problem 3
Supposed that and
are nonzero real numbers such that
. What is the value of
?
Problem 4
Problem 5
Problem 6
Problem 7
Problem 8
Problem 9
Problem 10
Problem 11
Problem 12
Problem 13
Problem 14
Problem 15
Problem 16
The number has over
positive integer divisors. One of them is chosen at random. What is the probability that it is odd?
Problem 17
Problem 18
The diameter of a circle of radius
is extended to a point
outside the circle so that
. Point
is chosen so that
and line
is perpendicular to line
. Segment
intersects the circle at a point
between
and
. What is the area of
?
Problem 19
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
?
Problem 20
Problem 21
Problem 22
Problem 23
Problem 24
Problem 25
See also
2017 AMC 12B (Problems • Answer Key • Resources) | |
Preceded by 2017 AMC 12A Problems |
Followed by 2018 AMC 12A Problems |
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 12 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.