Catonsville Mathematics Competition
- If you have only lots of 5c and 32c stamps, what is the largest postage amount you
A) $0.99 B) $1.23 C) $1.37 D) $1.53
- A said, "B always speaks the truth."
B said, "A is lying."
C said, "A and B are both lying."
Who is speaking the truth?
A) A B) B C) C D) None of them
- If a2 + b2 = c2, where a, b, c are positive
integers and if a = 103 then b is
A) 207 B) 672 C) 5304 D) 6702
- Tom, Dick, and Harry were in a room where a murder was committed. One of them is
the murderer and the other two were witnesses. Each made a statement to the police as follows:
Tom said, "I am innocent."
Dick said, "Tom and I are innocent."
Harry said, "Tom and Dick are innocent."
If one and only one is speaking the truth, who is the murderer?
A) Tom B) Dick C) Harry D) There is no unique solution.
- Which one of the following numbers cannot be the area of a triangle with
A) 96 B) 144 C) 169 D) 175
- A polygon has 629 distinct diagonals. What is the number of its sides?
A) 29 B) 33 C) 37 D) 43
- a, b are positive integers (a > b). When a2 + b2 is
divided by the a + b, the quotient is q and the remainder is r. If
q2 + r = 1996, what is a?
A) 44 B) 48 C) 54 D) 62
- A murder was committed by someone. Three suspects, A, B, and C were interrogated.
A and B claimed innocence while C confessed to the crime. Assuming only one of them is
lying, who is the murderer?
A) A B) B C) C D) None of the three
- ABCD is a quadrilateral on a plane and a point P moves on the plane in such a
way that the sum of the squares of its distance from the four points A, B, C, D remains
constant. What is the curve traced out by the point P?
A) a circle B) a hyperbola C) a parabola D) a line
- What is the smallest positive integer which can be written as the sum of
cubes of two positive integers in two ways?
A) 341 B) 1155 C) 1729 D) 2331
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