Math Problem of the Week - Middle School - Sept. 19, 2021 to Sept. 25, 2021

Sep 22, 2021 | West Covina

 

 

Middle School

 

Question: Owen can't remember the address number of his friend's house, but he does remember noticing that all four of the digits were even, that they were in order from least to greatest, and that the first two digits form a number with half the value as the number formed by the last two digits. How many possible street address numbers are there with the details Owen remembers?

 

 

 

 

Answer: 3 possible numbers: 2244, 2448, and 4488

 

 

Solution:  Since all the digits have to be even, only 2s, 4s, and 8s can appear in the address number—6 cannot appear in the address because halving or doubling it would cause an odd digit. So, 22, 24, and 44 can all can be doubled to make a number whose digits are in the set of usable digits. That means 2244, 2448, and 4488 are the possible numbers.

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