2016 AMC 10B Problems/Problem 24

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 $d=2$ .

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

Solution

Answer is (D) for those of you wondering (verified by coding). Still need solution. abcd that satisfy problem conditions: 1234 1357 1482 2345 2468 2470 2593 3456 3579 3581 4567 4692 5678 5680 6789 6791 8890

2016 AMC 10B (Problems • Answer Key • Resources)
Preceded by Problem 23	Followed by Problem 25
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25
All AMC 10 Problems and Solutions

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2016 AMC 10B Problems/Problem 24

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