2007 AMC 10B Problems/Problem 8
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Problem 8
On the trip home from the meeting where this AMC10 was constructed, the Contest Chair noted that his airport parking receipt had digits of the form where
and
was the average of
and
How many different five-digit numbers satisfy all these properties?
Solution
For the average, to be an integer,
and
have to either both be odd or both be even. There are
ways to choose a set of two even numbers and
ways to choose a set of two odd numbers. Therefore, the number of five-digit numbers that satisfy these properties is
See Also
2007 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 7 |
Followed by Problem 9 | |
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 |
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