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Arithmetic Sequences in Four Digit Numbers

Source: Problem #24 2016 AMC 10B

February 21, 2016
arithmetic sequenceAMCAMC 102016 AMC 10BAMC 10 B

Problem Statement

How many four-digit integers abcdabcd, with a0a \neq 0, have the property that the three two-digit integers ab<bc<cdab<bc<cd form an increasing arithmetic sequence? One such number is 46924692, where a=4a=4, b=6b=6, c=9c=9, and d=2d=2.
<spanclass=latexbold>(A)</span> 9<spanclass=latexbold>(B)</span> 15<spanclass=latexbold>(C)</span> 16<spanclass=latexbold>(D)</span> 17<spanclass=latexbold>(E)</span> 20<span class='latex-bold'>(A)</span>\ 9\qquad<span class='latex-bold'>(B)</span>\ 15\qquad<span class='latex-bold'>(C)</span>\ 16\qquad<span class='latex-bold'>(D)</span>\ 17\qquad<span class='latex-bold'>(E)</span>\ 20