Question

Let pqr be a three digit number. Then, pqr + qrp + rpq will not be always divisible by

• A. 9
• B. 37
• C. 3
• D. p + q + r

Answer 1

The correct option is A

9

pqr = 100p + 10q + r

qrp = 100q + 10r + p

rpq = 100r + 10p + q

Adding them we get:
100(p + q +r) + 10(p + q + r) + (p + q + r)
= 111 (p + q +r)
= 3 $\times$ 37 $\times$ (p + q + r)

Hence, (pqr + qrp + rpq) is divisible by 3, 37 and (p + q + r).
But it is not be divisible by 9 unless (p + q + r) is divisible by 9.