Discussion
The number 897159*2 is divisible by 4. What is the sum of all possible values of *?
Answer: C
Correct answer: 25
A number is divisible by 4 when the number formed by its last two digits is divisible by 4. Here those digits are *2, so we need the two-digit endings 02, 12, 22, ... , 92 that 4 divides.
\[12 = 4\times 3,\quad 32 = 4\times 8,\quad 52 = 4\times 13,\quad 72 = 4\times 18,\quad 92 = 4\times 23\]
The remaining endings - 02, 22, 42, 62 and 82 - are each 2 more than a multiple of 4, so they fail. The admissible values of * are therefore 1, 3, 5, 7 and 9, and their sum is \(1+3+5+7+9 = 25\).
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