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When positive integer \(m\) is divided by positive integer \(x\), the reminder is 7 and when positive integer \(n\) is divided by positive integer \(y\), the reminder is 11. Which of the following is a possible value for \(x + y\)?
I. 18
II. 19
III. 20
A. I only B. II only C. III only D. II and III only E. None
When positive integer \(m\) is divided by positive integer \(x\), the reminder is 7 and when positive integer \(n\) is divided by positive integer \(y\), the reminder is 11. Which of the following is a possible value for \(x + y\)?
I. 18
II. 19
III. 20
A. I only B. II only C. III only D. II and III only E. None
The remainder is ALWAYS less than the divisor, thus \(x > 7\) and \(y > 11\). Therefore the least values of \(x\) and \(y\) are 8 and 12, respectively, making the least value of \(x + y\) equal to 20.
Hi! If x>7 and y>11, isn't it possible to say that x+y>18? Then, the answer could also be 19. I understand that if we consider each equation separately, the answer has to be 20, but I wanted to check if we're allowed to combine the equations to get "19".
Hi! If x>7 and y>11, isn't it possible to say that x+y>18? Then, the answer could also be 19. I understand that if we consider each equation separately, the answer has to be 20, but I wanted to check if we're allowed to combine the equations to get "19".
The point is, we are told that x and y are positive integers. For positive integers x and y, where x > 7 and y > 11, it's not possible that x + y = 19.
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72% (01:05) correct 
