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CEMC Gauss (Grade 8), 2015

Algebra Difficulty 2.7 Junior Find the answer Canada

There are 3 times as many boys as girls in a room. If 4 boys and 4 girls leave the room, then there will be 5 times as many boys as girls in the room. In total, how many boys and girls were in the room originally?

Pick one

Solution

Since the number of digits that repeat is 6, then the digits $142857$ begin to repeat again after 120 digits (since $120=6\times20$ ).
That is, the $121^{st}$ digit is a 1, the $122^{nd}$ digit is a 4, and the $123^{rd}$ digit is a 2.

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