How many three digit numbers are there which are equal to 3434 times the sum of their digits?	Choose the most appropriate option:  A) 4  B) 5  C) 6  D) 7  E) 8
If the product is written abcabc in decimal, then we have   100a+10b+c=34(a+b+c)   100a+10b+c=34(a+b+c)   (a,b,c&lt;10,a≠0a,b,c&lt;10,a≠0). Thus   66a−33c=24b   66a−33c=24b   and, since 1111 divides the left-hand side, 11|b11|b. Since b&lt;10b&lt;10, b=0b=0. We're left with two requirements: 2a=c2a=c and 34|a0c1034|a0c10. Testing the possibilities afforded by 2a=c2a=c, we see 102102 is divisible by 3434, so all its multiples are answers also, and the answer is 4.   4nswer is 4
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How many three digit numbers are there which are equal to 3434 times the sum of their digits?