1960 AMC 12 Problem 14
Attempt Problem 14 of the 1960 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 1960 AMC 12 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
14.
If and are real numbers, the equation has a unique solution [the symbol means that is different from zero]:
for all and
if
if
if
if
Answer: E
Small hint:
Collect the -terms on one side
Big hint:
A linear equation has a unique solution when the coefficient of is nonzero
Solution:
Rearranging gives This has a unique solution exactly when or
Thus, the correct answer is E.
Problem 14 in other years
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