2011 AMC 8 Problem 21

Below is the professionally curated solution for Problem 21 of the 2011 AMC 8, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2011 AMC 8 solutions, or check the answer key.

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Concepts:logical deduction prime

Difficulty rating: 1470

21.

Students guess that Norb's age is $24, 28, 30, 32, 36, 38, 41, 44, 47,$ and $49.$ Norb says, "At least half of you guessed too low, two of you are off by one, and my age is a prime number." How old is Norb?

$29$

$31$

$37$

$43$

$48$

Solution:

The first part of the statement means that Norb's age is greater than $36.$

The second part means that Norb's age is either between $36$ and $38$ or between $47$ and $49.$

Since $37$ is prime and $48$ is not, Norb's age is $37.$

Thus, C is the correct answer.

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