TMUA Practice Question — Worked Solution

P2·Number Theory & Divisibility·6.0Mock 0 · P2 · Q17

digit sumsdivisibility testunit fractionsDiophantine equationterminating decimalscounterexample

Consider the following statements about positive integers.

If the sum of the digits of a positive integer

N

is divisible by

27

, then

N

is divisible by

27

x

y

and

z

are positive integers with

x y z = 2 (x y + y z + z x)

, then

x = y = z

III

a

and

b

are positive integers and

\frac{a}{b}

is a terminating decimal, then

b

has no prime factor other than

2

and

5

Which of these statements is/are true?

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