AMC8 2011

AMC8 2011 · Q21

AMC8 2011 · Q21. It mainly tests Logic puzzles, Primes & prime factorization.

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?

学生们猜测Norb的年龄是24、28、30、32、36、38、41、44、47和49。Norb说：“至少有一半人猜得太低，你们中有两人差了一岁，我的年龄是一个质数。”Norb多大年龄？

(A) 29 29

(B) 31 31

(D) 43 43

(E) 48 48

Answer

Correct choice: (C)

正确答案：（C）

Solution

At least half the guesses are too low, so Norb's age must be greater than $36$. If two of the guesses are off by one, then his age is in between two guesses whose difference is $2$. It could be $31,37,$ or $48,$ but because his age is greater than $36$ it can only be $37$ or $48$. Lastly, Norb's age is a prime number so the answer must be $\boxed{\textbf{(C)}\ 37}$.

至少一半的猜测太低，所以Norb的年龄必须大于$36$。如果两个猜测差一岁，那么他的年龄在两个相差$2$的猜测之间。可能是$31,37$或$48$，但因为年龄大于$36$，只能是$37$或$48$。最后，Norb的年龄是质数，所以答案是$\boxed{\textbf{(C)}\ 37}$。

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