2020 AMC 10 B
Complete problem set with solutions and individual problem pages
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?(2020 AMC 10B, Question #6)
- A.
- B.
- C.
- D.
- E.
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 now. To keep this a palindrome, our number is now . So Megan drove miles. Since this happened over 2 hours, she drove at (B) 55 mph.
