INTRODUCING 5 - days-a-week problem solving session for Math Olympiad and ISI Entrance. Learn More

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*In mathematics and statistics, average refers to the sum of a group of values divided by n, where n is the number of values in the group. An average is also known as a mean. *

* Driving along a highway, Megan noticed that her odometer showed 15951 (miles). This number is a palindrome-it reads the same forward and backward. Then 2 hours later , the odometer displayed the next higher palindrome. What was her average speed, in miles per hour, during this 2 - hour period ?*

*A) 50 B) 55 C)60 D) 65 E) 70 *

Source

Competency

Difficulty

Suggested Book

**American Mathematics Competition 10 (AMC 10B), {2020}, {Problem Number 6}**

Average

**4 out of 10**

**Mathematics can be fun**

First hint

*Do you really need any hint ???*

*Try this out:*

*In order to get the smallest palindrome greater than 15951 , 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.*

Second Hint

*So what can we do here ?*

*We can raise 9 to the next largest value, 10 , but obviously, that's not how place value works, so we're in the 16000 s now . To keep this a palindrome, our number is now 16061.*

Final Step

*If you really need the final hint this can be the life saver for this sum :*

* So Megan drove 16061 - 15951 = 110 miles . Since this happened over 2 hours , she drove at \(\frac {110}{2}\) = 55 mph . *

- https://www.cheenta.com/probability-problem-from-amc-10a-2020-problem-no-15/
- https://youtu.be/L4awwIFiBq4

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