For each positive integer n, p (n) is defined to be the product of the digits of n. for example, p (724) = 56, since 7 × 2 × 4 = 56. which of the following statements must be true? i. p(10n) = p(n) ii. p(n + 1) > p(n) iii. p(2n) = 2p(n)

  none of the above

Step-by-step explanation:

Consider the following:

  p(129) = 1·2·9 = 18

  p(10·129) = p(1290) = 1·2·9·0 = 0 . . . . . statement I is not true

  p(129+1) = p(130) = 1·3·0 = 0 . . . . . . . . . statement II is not true

  p(2·129) = p(258) = 2·5·8 = 80 . . . . . . . statement III is not true

None of the offered statements must be true.

Statement I must be true if p(n) is the product of the non-zero digits of n.

180

step-by-step explanation: