Question

If pqr is a three digit number, then pqr + qrp + rpq is not always divisible by .

• A. 37
• B. 3
• C. 9
• D. p+q+r

Answer 1

The correct option is C 9

pqr = 100p + 10q + r

qrp = 100q + 10r + p

rpq = 100r + 10p + q

Adding all three,
$\Rightarrow$ pqr + qrp + rpq = 100(p + q +r) + 10(p + q + r) + (p + q + r) = 111 (p + q +r) = 37 $\times$ 3 (p + q + r)

(pqr + qrp + rpq) is always divisible by 111, 37, 3 and (p + q + r).