22. Four of the following six-digit integers are always divisible by 7, regardless of the values of the digits $P$ and $Q$.
Which of the following is not necessarily a multiple of 7 ?
A ' $P Q Q P Q Q$ '
$\mathrm{B}$ ' $P Q P Q P Q$ '
C ' $Q P Q P Q P$ '
D ' $P P P P P P$ '
$\mathrm{E}$ ' $P P P Q Q Q$ '
22. E Note that $1001=7 \times 143$, so that any six-digit number of the form ' $X Y Z X Y Z$ ' $=1001 \times$ ' $X Y Z$ ' is necessarily a multiple of 7 . So options $\mathrm{A}$ and $\mathrm{D}$ are both multiples of 7 .
Also, $10101=7 \times 1443$, so that any six-digit number of the form ' $X Y X Y X Y$ ' $=10101 \times$ ' $X Y$ ' is necessarily a multiple of 7 . So options $\mathrm{B}$ and $\mathrm{C}$ are both multiples of 7 .
However, ' $P P P Q Q Q$ ' $=111 \times(1000 P+Q)=3 \times 37 \times(1000 P+Q)$ is not necessarily a multiple of 7 . For example, when $P=1$ and $Q=2,1000 P+Q=1002=143 \times 7+1$.