<s>[INST] $17!=3556xy428096000,$then $(x+y)$ equals?(without using a calculator) $17!=3556xy428096000,$then $(x+y)$ equals?
a)$15$ b)$6$ c)$12$ d)$13$
With help of calculator $(x+y)$ can be easily calculated as $15$.But without a calculator,I can only conclude that the sum of digits $(3+5+5+6+x+y+4+2+8+9+6)$ is a multiple of $3$, & excluding $(x+y)$ the sum of the digits $(3+5+5+6+4+2+8+9+6) =48$.Thus excluding option d) the ans can be any of a),b) or c).
Please help me to find the exact answer.
Thank you 
 [/INST] First use the fact that the factorial is divisible by $9$, and therefore the digit sum is divisible by $9$. 
Then use the fact that the number with decimal representation $abcdefg\dots$ is divisible by $11$ if and only if $a-b+c-d+e-f+\cdots$ is divisible by $11$.
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