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Difference between revisions of "2003 AMC 12B Problems"

(→‎Problem 18)
(→‎Problem 18)
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Let <math>n</math> be a 5-digit number, and let q and r be the quotient and remainder, respectively, when <math>n</math> is divided by 100.  For how many values of <math>n</math> is <math>q + r</math> divisible by 11?
 
Let <math>n</math> be a 5-digit number, and let q and r be the quotient and remainder, respectively, when <math>n</math> is divided by 100.  For how many values of <math>n</math> is <math>q + r</math> divisible by 11?
  
−
\[
+
<math>
 
\text {(A) } 8180 \qquad \text {(B) } 8181 \qquad \text {(C) } 8182 \qquad \text {(D) } 9000 \qquad \text {(E) } 9090
 
\text {(A) } 8180 \qquad \text {(B) } 8181 \qquad \text {(C) } 8182 \qquad \text {(D) } 9000 \qquad \text {(E) } 9090
−
\]
+
</math>
  
 
[[2003 AMC 12B Problems/Problem 18|Solution]]
 
[[2003 AMC 12B Problems/Problem 18|Solution]]

Revision as of 09:04, 5 February 2008

Problem 1

Which of the following is the same as

\[\frac{2-4+6-8+10-12+14}{3-6+9-12+15-18+21}\]?

$\text {(A) } -1 \qquad \text {(B) } -\frac{2}{3} \qquad \text {(C) } \frac{2}{3} \qquad \text {(D) } 1 \qquad \text {(E) } \frac{14}{3}$

Solution

Problem 2

Solution

Problem 3

Solution

Problem 4

Solution

Problem 5

Solution

Problem 6

Solution

Problem 7

Solution

Problem 8

Solution

Problem 9

Solution

Problem 10

Solution

Problem 11

Solution

Problem 12

Solution

Problem 13

Solution

Problem 14

Solution

Problem 15

Solution

Problem 16

Solution

Problem 17

Solution

Problem 18

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

Solution

Problem 20

Solution

Problem 21

Solution

Problem 22

Solution

Problem 23

Solution

Problem 24

Solution

Problem 25

Solution

See also

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