Difference between revisions of "2020 AMC 10B Problems/Problem 6"
(Created page with "==Problem== Driving along a highway, Megan noticed that her odometer showed <math>15951</math> (miles). This number is a palindrome-it reads the same forward and backward. Th...") |
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==Solution== | ==Solution== | ||
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| + | In order to get the smallest palindrome greater than <math>15951</math>, 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. | ||
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| + | So we raise <math>9</math> to the next largest value, <math>10</math>, but obviously, that's not how place value works, so we're in the <math>16000</math>s now. To keep this a palindrome, our number is now <math>16061</math>. | ||
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| + | So Megan drove <math>16061-15951=110</math> miles. Since this happened over <math>2</math> hours, she drove at <math>\frac{110}{2}=\boxed{\textbf{(B) }55}</math> mph. ~quacker88 | ||
==See Also== | ==See Also== | ||
Revision as of 17:19, 7 February 2020
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
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. 
