Let $p q r$ be a three digit number. Then, $p q r + q r p + r p q$ is not divisible by

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p + q + r

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Solution

The correct option is A
9

$p q r = 100 p + 10 q + r$

$q r p = 100 q + 10 r + p$

$r p q = 100 r + 10 p + q$
$A d d i n g a l l t h r e e,$
$\Rightarrow$ $p q r + q r p + r p q = 100 (p + q + r) + 10 (p + q + r) + (p + q + r)$
$= 111 (p + q + r)$
$= 37 \times 3 (p + q + r)$
$(p q r + q r p + r p q) i s d i v i s i b l e b y 37, 3 a n d (p + q + r)$

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