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Problem 240

AMC 10/12, early questions

Number theory Difficulty 3.9 Find the answer South African Mathematics Olympiad · South Africa

If today is Thursday, what day of the week will it be in 150 days from now?
(A) Sunday
(B) Monday
(C) Tuesday
(D) Wednesday
(E) Thursday

Your answer

Official solution

Every multiple of $7$ represents a full week. Since today is Thursday, in one day's time it will be Friday. Thus each full week after today starts on a Friday and ends on a Thursday. $150$ days divided by $7$ equals $21$ full weeks with a remainder of $3$ days. The $147$ th day from now will thus be a Thursday (end of $21$ st full week), and consequently the $150$ th day from now will be a Sunday.

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