2015 AMC 12A Problem 5
Attempt Problem 5 of the 2015 AMC 12A 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 2015 AMC 12A solutions, or check the answer key.
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5.
Amelia needs to estimate the quantity where and are large positive integers. She rounds each of the integers so that the calculation will be easier to do mentally. In which of these situations will her answer necessarily be greater than the exact value of
She rounds all three numbers up.
She rounds and up, and she rounds down.
She rounds and up, and she rounds down.
She rounds up, and she rounds and down.
She rounds up, and she rounds and down.
Answer: D
Solution:
To make larger, round the numerator up and the denominator down. To make larger, round down.
Only choice does all three: it rounds up while rounding and down, so every change pushes the estimate above the exact value. In the other choices at least one change works the wrong way, so the estimate is not guaranteed to be larger.
Thus, the correct answer is D.
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