SOLUTION: Let n,7874185de be a base-ten numeral with d and e its last two digits. Give all of the choices of the two-digit numbers de for which n is divisible by 12.

Question 1169153: Let n,7874185de be a base-ten numeral with d and e its last two digits. Give all of the choices of the two-digit numbers de for which n is divisible by 12.
Answer by Edwin McCravy(20064) (Show Source): You can put this solution on YOUR website!

Since "de" = 10d + e,









So  must be a non-negative integer, which we can represent by the letter A



Multiply through by 12 to clear of fractions:







Since de = 10d+e must be a 2-digit number, so must 12A-4

The smallest 2-digit number is 10 and the largest 2-digit number is 99, so



Add 4 to all three sides



Divide through by 12





Since A must be a non-negative integer,



So there are 7 choices for A, 2 through 8, inclusive



A  12A-4  de       n = 7874185de (to check) 
----------------------------------------
2   20    20           787418520 = (12)(65618210) 
3   32    32           787418532 = (12)(65618211)
4   44    44           787418544 = (12)(65618212)
5   56    56           787418556 = (12)(65618213)
6   68    68           787418568 = (12)(65618214)
7   80    80           787418580 = (12)(65618215)
8   92    92           787418592 = (12)(65618216)

The 7 choices for de are in red.  

Edwin

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SOLUTION: Let n​,​7874185de be a​ base-ten numeral with d and e its last two digits. Give all of the choices of the​ two-digit numbers de for which n is divisible by 12.

SOLUTION: Let n,7874185de be a base-ten numeral with d and e its last two digits. Give all of the choices of the two-digit numbers de for which n is divisible by 12.