Difference between revisions of "2003 AMC 12B Problems"

Let $n$ be a 5-digit number, and let q and r be the quotient and remainder, respectively, when $n$ is divided by 100. For how many values of $n$ is $q + r$ divisible by 11?

$\text {(A) } 8180 \qquad \text {(B) } 8181 \qquad \text {(C) } 8182 \qquad \text {(D) } 9000 \qquad \text {(E) } 9090$

Solution

Problem 19

Let $S$ be the set of permutations of the sequence $1,2,3,4,5$ for which the first term is not $1$ . A permutation is chosen randomly from $S$ . The probability that the second term is $2$ , in lowest terms, is $a/b$ . What is $a+b$ ?

$\mathrm{(A)}\ 5 \qquad\mathrm{(B)}\ 6 \qquad\mathrm{(C)}\ 11 \qquad\mathrm{(D)}\ 16 \qquad\mathrm{(E)}\ 19$

Solution

Problem 20

Solution

Problem 21

Solution

Problem 22

Solution

Problem 23

Solution

Problem 24

Solution

Problem 25

Solution

@@ Line 84: / Line 84: @@
 == Problem 19 ==
+Let <math>S</math> be the [[set]] of [[permutation]]s of the [[sequence]] <math>1,2,3,4,5</math> for which the first term is not <math>1</math>. A permutation is chosen randomly from <math>S</math>. The [[probability]] that the second term is <math>2</math>, in lowest terms, is <math>a/b</math>. What is <math>a+b</math>?
+<math>\mathrm{(A)}\ 5
+\qquad\mathrm{(B)}\ 6
+\qquad\mathrm{(C)}\ 11
+\qquad\mathrm{(D)}\ 16
+\qquad\mathrm{(E)}\ 19</math>
 [[2003 AMC 12B Problems/Problem 19|Solution]]

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Difference between revisions of "2003 AMC 12B Problems"

Revision as of 01:22, 19 July 2008

Contents

Problem 1

Problem 2

Problem 3

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

Problem 17

Problem 18

Problem 19

Problem 20

Problem 21

Problem 22

Problem 23

Problem 24

Problem 25

See also