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 Number Theory-ish Problem

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skittles
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PostSubject: Number Theory-ish Problem   Wed Aug 13, 2008 6:17 pm

Make more forums, Dojo. Razz

Mr. Jones has eight children of different ages. On a family trip, his oldest child, who is age 9, spots a license plate with a 4-digit number in which each of two digits appears two times. "Look daddy!" she exclaims. "That number is evenly divisible by the age of each of us kids!" "That's right," replies Mr. Jones, "and the last two digits just happen to be my age." Which of the following is not the age of one of Mr. Jones's children?

A. 4
B. 5
C. 6
D. 7
E. 8

Source: AMC 10
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isabella2296
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PostSubject: Re: Number Theory-ish Problem   Sat Aug 16, 2008 8:01 am

Two Things:

1) It's "we kids" not "us kids". Razz

2) I don't think this is possible to solve...
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herefishyfishy1
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PostSubject: Re: Number Theory-ish Problem   Sat Aug 16, 2008 8:09 am

(1) It is "us kids" because the pronoun is the object of the preposition (yes, "of" is a preposition), and "us" is used in place of "we" whenever the word is an object.

(2) Why would an impossible problem be on the AMC 10?

(3) I'm way too interested with correcting grammar.
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isabella2296
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PostSubject: Re: Number Theory-ish Problem   Sat Aug 16, 2008 8:12 am

Could you please post the solution? It sounds like an awful lot of brute force to me...
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skittles
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PostSubject: Re: Number Theory-ish Problem   Sat Aug 16, 2008 3:04 pm

Here's the AoPS Wiki solution:

http://www.artofproblemsolving.com/Wiki/index.php/2006_AMC_10B_Problems/Problem_25

Brute force and logic was pretty much my solution.
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AIME15
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PostSubject: Re: Number Theory-ish Problem   Sat Aug 16, 2008 5:46 pm

Hey! I was still working on it!

I know i coudl have not read the answer, but i was tempted :DDD

nice problem. i took that in a practice test and had no clue

Oh yeah, and skittles, move this to the AMC 10/12 forum.
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