Points

Regional Level Test
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1. The sequence 1, x, 6, y is an arithmetic progression.
Find x+y. 
..

2. The squares in the diagram have side length
1. What is the area of the slanted rectangle?




3. In how many ways may the numbers {1, 2, 3, 4, 5, 6} be
ordered such that no two consecutive terms have a sum which
is divisible by 2 or 3?


4. The positive integers 30, 72, and N have the property that
the product of any two of them is divisible by the third. What is the
smallest possible value of N?


5. Two sisters go up 40step escalators. The older sister
rides the up escalator, but can only take 10 steps up during
the ride since it is quite crowded. The younger sister runs
up the empty down escalator, arriving at the top at the same
time as her sister. How many steps does the younger sister
take?


6. Michael Jordan's probability of hitting any basketball
shot is three times greater than mine, which never exceeds a
third. To beat him in a game, I need to hit a shot myself
and have Jordan miss the same shot. If I pick my shot
optimally, what is the maximum probability of winning which
I can attain?


7. A quadrilateral inscribed in a circle has side lengths
whose squares are 17, 99, 19, and 97. Find the area of the
circle.


Reg Level Soln
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