1951 AMC 12 Problem 33

Attempt Problem 33 of the 1951 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 1951 AMC 12 solutions, or check the answer key.

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33.

The roots of the equation x2−2x=0x^2-2x=0 can be obtained graphically by finding the abscissas of the points of intersection of each of the following pairs of equations except the pair:
y=x2,y=x^2, y=2xy=2x
y=x2−2x,y=x^2-2x, y=0y=0
y=x,y=x, y=x−2y=x-2
y=x2−2x+1,y=x^2-2x+1, y=1y=1
y=x2−1,y=x^2-1, y=2x−1y=2x-1
Answer: C
Concepts:functionquadraticalgebraic manipulation
Small hint:
Set the two right-hand sides in each pair equal
Big hint:
Four pairs reduce to x2−2x=0x^2-2x=0; one pair reduces to an impossible constant equation
Solution:
Choices A, B, D, and E all reduce their intersection condition to x2−2x=0.x^2-2x=0. Choice C instead requires x=x−2, x=x-2, which has no solution and therefore cannot produce the desired roots.
Thus, the correct answer is C.
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