Edition 5

1. If none of the faces of a tetrahedron is an isosceles triangle, what is the minimum number of edges no two of which have the same length?

(A) 3

(B) 4

(C) 5

(D) 6

(E) 8

2. Consider the following two statements about two triangles:

  • P: They have equal area, and two sides of one are equal to two sides of the other.
  • Q: They are congruent.

Which of the following statements is true?

(A) P is necessary and sufficient for Q.

(B) P is necessary but not sufficient for Q.

(C) P is sufficient but not necessary for Q.

(D) P is neither necessary nor sufficient for Q.

(E) None of these

3. In the sequence 1, 4, 8, 10, 16, 21, 25, 30 and 43, how many blocks of consecutive terms have sums divisible by 11?

(A) 1

(B) 2

(C) 5

(D) 6

(E) None of these

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