x and y are positive integers. When x is divided by 12, the remainder is 5, and when x is divided by 13, the remainder is 3. When y is divided by 14, the remainder is 5, and when y is divided by 7, the remainder is 5. What is the least possible value of x + y?
Answers:
A) 24
B) 12
C) 64
D) 48
E) 25
When x is divided by 12, the remainder is 5: So, the possible values of x are: 5, 17, 29, 41, etc.   When x is divided by 13, the remainder is 3: So, the possible values of x are: 3,16,29... STOP. Since both lists include 29, the smallest possible value of x is 29.   When y is divided by 14, the remainder is 5: So, the possible values of y are: 5, 19, 33,47 etc.   When y is divided by 7, the remainder is 5: So, the possible values of y are: 5, 19 ...STOP. Since both lists include 19, the smallest possible value of y is 19   Since the smallest possible values of x and y are 29 and 19 respectively, the smallest possible value of x + y is 48. So,48 is the correct answer to the original question.
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x and y are positive integers. When x is divided by 12, the remainder is 5, and when x is divided by 13, the remainder is 3. When y is divided by 14, the remainder is 5, and when y is divided by 7, the remainder is 5. What is the least possible value of x + y?