Schools Mathematics Grand Challenge
PROBLEM 13:
One year, 50,000 students do junior cert maths. Most are honest,
but 1% try cheating. When the exams are marked, a special system
is used to make a list of students who might have cheated. The
system is good, but not perfect. It puts 99% of the cheaters on the
list, but, by mistake, a third of a percent of honest students are
also on the list.
What percentage of the students on the list actually tried cheating?
Give your answer to the nearest percent.
PROBLEM 14:
A tortoise, a hare and a cheetah start to run on a circular track from
the same point at the same time and run around the path in a clockwise
direction. The tortoise runs at a constant speed of 1 lap per hour;
the hare at a constant speed of 7 laps per hour; and the cheetah runs
at a constant speed of 13 laps per hour. After how many minutes will
all three animals again be at the same point on the track at the same
time?
PROBLEM 15:
The picture below illustrates a magical trick - we can rearrange the same
set of 4 pieces into two identical big triangles. However somehow during
the rearrangement a gap appears!
Using maths we can figure out what is going on here. First, check out the
Tip of the Week to find out what the Tan of an angle is. Then figure out
120*Tan(A)-120*Tan(B)? The result is the answer to this puzzle.
You should now understand why the trick works!!
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