Fred's birthday was on a Monday and was exactly 37 days after Pat's birthday. Julie's birthday was 67 days before Pat's birthday. On what day of the week was Julie's birthday?
(A) Saturday
(B) Sunday
(C) Monday
(D) Tuesday
(E) Wednesday
Solution 1

Julie's birthday was $37+67=104$ days before Fred's birthday.

When we divide 104 by 7 (the number of days in one week), we obtain a quotient of 14 and a remainder of 6 .

In 14 weeks, there are $14 \times 7=98$ days, so 98 days before Fred's birthday was also a Monday. Since Julie's birthday was 104 days before Fred's, this was 6 days still before the Monday 98 days before Fred's birthday. The 6th day before a Monday is a Tuesday.

Therefore, Julie's birthday was a Tuesday.

## Solution 2

37 days is 5 weeks plus 2 days. Since Fred's birthday was on a Monday and Pat's birthday was 37 days before Fred's, then Pat's birthday was on a Saturday.

67 days is 9 weeks plus 4 days. Since Pat's birthday was on a Saturday and Julie's birthday was 67 days before Pat's, then Julie's birthday was on a Tuesday.

ANSWER: (D)