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The five-digit number $\overline{a679b}$ is divisible by 72. Find the digits a and b.

 Jul 22, 2021
 #1
avatar+74 
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a=3 b=2

 Jul 22, 2021
 #2
avatar+18 
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Thanks Wsai, here is another way to do it

 

Divisibility rule for 72 : Divisible by 8 and 9

\(\overline{a679b} \) = 10000a+6000+700+90+b

 

so we have two equations:

 

(790+b)/8 is an integer

a + 6+7+9+b is divisible by 9

 

so a=3 and b=2

 

Check

 

(790+2)/8 = 99 :)

(3 + 6  + 7 + 9 + 2)/9 = 3:)

 

angelangelangel

 Jul 22, 2021

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