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2014 AMC 10B Problem 14

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2014 AMC 10B Problem 14AMC 10 Step by Step

Name: Date: September 13, 2026

Bases & Digits · difficulty 3 of 5 · about 4 min · position P11-15

Danica drove her new car on a trip for a whole number of hours, averaging $55$ miles per hour. At the beginning of the trip, $abc$ miles was displayed on the odometer, where $abc$ is a 3-digit number with $a \ge 1$ and $a + b + c \le 7$ . At the end of the trip, the odometer showed $cba$ miles. What is $a^2 + b^2 + c^2$ ?

A)
$26$
B)
$27$
C)
$36$
D)
$37$
E)
$41$

2014 AMC 10B Problem 14

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