2011 AMC 10B Problem 3

Attempt Problem 3 of the 2011 AMC 10B 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 2011 AMC 10B solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

At a store, when a length is reported as $x$ inches that means it is at least $x - 0.5$ inches and at most $x + 0.5$ inches. Suppose the dimensions of a rectangular tile are reported as $2$ inches by $3$ inches. In square inches, what is the minimum area for the rectangle?

$3.75$

$4.5$

$5$

$6$

$8.75$

Answer: A

Concepts:area optimization

Difficulty rating: 770

Solution:

The smallest possible dimensions are $1.5\times 2.5,$ so the area is $1.5\cdot 2.5=3.75.$

Thus, the correct answer is A .

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