kangaroo math Exam Logical Reasoning

An equilateral triangle starts in a given position and is moved to new positions in a
sequence of steps. At each step it is rotated about its centre, first by 3◦
, then by a further 9◦
,
then by a further 27◦
, and so on (at the n-th step it is rotated by a further (3n
)

). How many
different positions, including the initial position, will the triangle occupy? Two positions are
considered equal if the triangle covers the same part of the plane.

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kangaroo math Other Question

The tango is danced in pairs, each consisting of one man and one woman. At a dance
evening no more than 50 people are present. At one moment 3/4 of the men are dancing with
4/5 of the women. How many people are dancing at that moment?
(A) 20 (B) 24 (C) 30 (D) 32 (E) 46