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2016 AMC 10B Question 24

AMC10 · 2016 AMC 10B

Question 24

How many four-digit positive integers $abcd,$ with $a \neq 0,$ 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 $d=2.$
  1. $ \ 9 $
  2. $ \ 15 $
  3. $ \ 16 $
  4. $ \ 17 $
  5. $ \ 20 $