1995 AMC 12 Problem 30
Attempt Problem 30 of the 1995 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1995 AMC 12 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
30.
A large cube is formed by stacking unit cubes. A plane is perpendicular to one of the internal diagonals of the large cube and bisects that diagonal. The number of unit cubes that the plane intersects is
Answer: D
Small hint:
Model the large cube as and write the plane through its center perpendicular to the diagonal
Big hint:
Index each unit cube by its minimum value of and determine which index sums allow an intersection
Solution:
Take the large cube as The plane is A unit cube with lower corner where contains values of from to It intersects the plane exactly when or The coefficients of in are Thus the plane intersects unit cubes, and the correct answer is D.
Problem 30 in other years
- 1950 AMC 12
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