MathDB

20

Part of 2009 National Olympiad First Round

Problems(1)

5-digit numbers with even number of digits are even.

Source: 0

4/28/2009
Let A A be the numbers of 5-digit positive numbers satisfying following condition: The first digit is odd. Remaining 0 0, or 2 2 or 4 4 digit/digits are even.
Let B B be the numbers of 5-digit positive numbers satisfying following condition: The first digit is even. Remaining 0 0, or 2 2 or 4 4 digit/digits are even.
A \minus{} B \equal{} ?
<spanclass=′latex−bold′>(A)</span> 5000<spanclass=′latex−bold′>(B)</span> 4640<spanclass=′latex−bold′>(C)</span> 3200<spanclass=′latex−bold′>(D)</span> 0<spanclass=′latex−bold′>(E)</span> None<span class='latex-bold'>(A)</span>\ 5000 \qquad<span class='latex-bold'>(B)</span>\ 4640 \qquad<span class='latex-bold'>(C)</span>\ 3200 \qquad<span class='latex-bold'>(D)</span>\ 0 \qquad<span class='latex-bold'>(E)</span>\ \text{None}