MathDB

13

Part of 2001 AMC 10

Problems(1)

Telephone number!

Source: 2001 AMC-12 #6

12/3/2005
A telephone number has the form ABC \minus{} DEF \minus{} GHIJ, where each letter represents a different digit. The digits in each part of the numbers are in decreasing order; that is, A>B>C A > B > C, D>E>F D > E > F, and G>H>I>J G > H > I > J. Furthermore, D D, E E, and F F are consecutive even digits; G G, H H, I I, and J J are consecutive odd digits; and A \plus{} B \plus{} C \equal{} 9. Find A A. <spanclass=′latex−bold′>(A)</span> 4<spanclass=′latex−bold′>(B)</span> 5<spanclass=′latex−bold′>(C)</span> 6<spanclass=′latex−bold′>(D)</span> 7<spanclass=′latex−bold′>(E)</span> 8 <span class='latex-bold'>(A)</span> \ 4 \qquad <span class='latex-bold'>(B)</span> \ 5 \qquad <span class='latex-bold'>(C)</span> \ 6 \qquad <span class='latex-bold'>(D)</span> \ 7 \qquad <span class='latex-bold'>(E)</span> \ 8
AMC