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    • Problem Solving #3






    Question #1: In the x,y plane, which of the following statements are true?
     I. Line y + x = 5 is perpendicular to line y - x = 5.
    II. Lines y + x = 5 and y - x = 5 intersect each other on the y axis.
    III. Lines y + x = 5 and y - x = 5 intersect each other on the x axis.









    Question #2: If a is an integer chosen randomly from the set {3, 5, 6, 9} and b is an integer chosen randomly from the set {2, 3, 4}, what is the probability that a/b is an integer?









    Question #3: What is the value of integer a, if x = 2 is a solution of the equation √(a + x) = 2·x?









    Question #4: What is the value of (3x + 1 - 3x) / (3x - 3x - 1)?









    Question #5:Two diameters of a circle create an angle AOB of 45o between them. What is the length of arc AB if the radius of the circle is 10/¶?









    Question #6: A bus travels from town A to town B for 2 hours at a speed of 60 miles/hour. The bus stops in town B for 2 hours and then travels from town B to town C for 1 hour, at a speed of 50 miles/hour. What is the average speed of the bus?









    Question #7: If a·b + b·c + c·a = 0, what is (a + b)2 + (b + c)2 + (c + a)2?









    Question #8:
    Column A Column B
    x2 + 1 x + 1








    Question #9:
    2·m - n = 4
    m + 2·n = 12
    Column A Column B
    (m + n)2 61







    Question #10: If a and b are positive integers and a·b = 200, which of the following can be the sum a + b?









     

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