Math Mania 2016

1. How many liters of a 10% salt solution must be added to 6 liters of a 20% salt solution to obtain a 13% salt solution?
2. What is the first time after 1 pm when the angle between the hands of a clock is 80 degrees?
3. An equilateral triangle and a regular octagon are joined along an edge as shown in the figure. A third regular polygon can be placed at vertex A so that it shares a side with each of the other two polygons. How many sides does the third polygon have?
   
4. If a standard six-sided die is rolled four times, what is the probability that at least one of the rolls is a 3?
5. When a polynomial is divided by x − 1, the remainder is 5; when it's divided by x + 2 , the remainder is −4. What is the remainder when the polynomial is divided by (x − 1)(x + 2)?
6. Some of the diagonals of a regular octagon are drawn to form a square (shaded in the figure). What is the ratio of the area of the octagon to the area of the square?
   

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