If in a six-digit integer $N,$ $F(k)$ is the value of the $k-th$ digit, is $N$ divisible by $7$ (For example,

If in a six-digit integer $N,$ $F(k)$ is the value of the $k-th$ digit, is $N$ divisible by $7$ (For example, $F(4)$ is the value of the hundreds digit of $N)?$

(1) $F(1)=F(4),\, F(2)=F(5), \, F(3)=F(6)$

(2) $F(1)=F(2)=\cdots=F(6)$

Answer: D

Source: GMAT Club Tests

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