Question

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)

Answer 1

none of the above

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.

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