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avatar+117 

For how many different digits \(n\) is the two-digit number \(\underline{6n}\) divisible by \(n\)? (The expression \(\underline{6n}\) should be interpreted as a two-digit integer with tens digit 6 and units digit \(n\), not as 6 times \(n\).)

 Dec 28, 2020
 #1
avatar+117576 
+2

If

 

n  =1        then    6n    =  61      OK

n  =2                           =  62      OK

n = 3                          =   63      OK

n = 4                          =   64      OK

n = 5                         =    65      OK

n = 6                         =    66      OK

 

These are the only ones that work    [ 67/7 , 68/8  , 69/9   and 60/0      are not integers  (the last is undefined)]

 

So.....6 values of  n

 

 

cool cool cool

 Dec 28, 2020
 #2
avatar+117 
+2

Thank you!

cryptoaops  Dec 28, 2020

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