Difference between revisions of "2020 AMC 10B Problems/Problem 6"
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Revision as of 16:20, 6 April 2021
Contents
Problem
Driving along a highway, Megan noticed that her odometer showed 
(miles). This number is a palindrome-it reads the same forward and backward. Then 
hours later, the odometer displayed the next higher palindrome. What was her average speed, in miles per hour, during this -hour period?
Solution
In order to get the smallest palindrome greater than , we need to raise the middle digit. If we were to raise any of the digits after the middle, we would be forced to also raise a digit before the middle to keep it a palindrome, making it unnecessarily larger.
So we raise 
to the next largest value, 
, but obviously, that's not how place value works, so we're in the 
s now. To keep this a palindrome, our number is now 
.
So Megan drove 
miles. Since this happened over hours, she drove at 
mph. ~quacker88
Video Solution
~IceMatrix
~savannahsolver
See Also
| 2020 AMC 10B (Problems • Answer Key • Resources) | ||
| Preceded by Problem 5 |
Followed by Problem 7 | |
| 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 | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
