Difference between revisions of "2005 AMC 10B Problems/Problem 13"
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How many numbers between <math>1</math> and <math>2005</math> are integer multiples of <math>3</math> or <math>4</math> but not <math>12</math>? | How many numbers between <math>1</math> and <math>2005</math> are integer multiples of <math>3</math> or <math>4</math> but not <math>12</math>? | ||
− | <math>\ | + | <math>\textbf{(A) } 501 \qquad \textbf{(B) } 668 \qquad \textbf{(C) } 835 \qquad \textbf{(D) } 1002 \qquad \textbf{(E) } 1169 </math> |
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== Solution 1 == | == Solution 1 == |
Revision as of 14:41, 15 December 2021
Contents
Problem
How many numbers between and
are integer multiples of
or
but not
?
Solution 1
To find the multiples of or
but not
, you need to find the number of multiples of
and
, and then subtract twice the number of multiples of
, because you overcount and do not want to include them. The multiples of
are
The multiples of
are
. The multiples of
are
So, the answer is
Solution 2
From 1-12, the multiples of 3 or 4 but not 12 are 3, 4, 6, 8, and 9, a total of five numbers. Since of positive integers are multiples of 3 or 4 but not 12 from 1-12, the answer is approximately
=
See Also
2005 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 12 |
Followed by Problem 14 | |
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.