2020 AMC 10B Problems/Problem 6
Contents
[hide]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 (HOW TO CRITICALLY THINK!!!)
~Education, the Study of Everything
Video Solution
https://youtu.be/OHR_6U686Qg https://youtu.be/0bfIDBkfcZs
~savannahsolver
Video Solution
https://youtu.be/ZhAZ1oPe5Ds?t=1361
See Also
2020 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 5 |
Followed by Problem 7 | |
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All AMC 10 Problems and Solutions |
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