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2016 AMC 10B Problems/Problem 24

Revision as of 09:35, 21 February 2016 by Mathlogin (talk | contribs) (Created page with "==Problem== How many four-digit integers <math>abcd</math>, with <math>a \not\equiv 0</math>, have the property that the three two-digit integers <math>ab<bc<cd</math> form a...")
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Problem

How many four-digit integers $abcd$, with $a \not\equiv 0$, have the property that the three two-digit integers $ab<bc<cd$ form an increasing arithmetic sequence? One such number is $4692$, where $a=4$, $b=6$, $c=9$, and $d=2$.

$\textbf{(A)}\ 9\qquad\textbf{(B)}\ 15\qquad\textbf{(C)}\ 16\qquad\textbf{(D)}\ 17\qquad\textbf{(E)}\ 20$

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