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Bunuel
A sports league encourages collaboration by awarding 3 points for each goal scored without assistance and 5 points for each goal scored with assistance. A total of 48 points were scored by a team in a single game. Which of the following CANNOT be the number of goals scored without assistance by this team in this game?

A. 1
B. 6
C. 11
D. 12
E. 16

Let’s let a = the number of goals scored with assistance and b = the number of goals scored without assistance. We can create the equation:

5a + 3b = 48

5a = 48 - 3b

5a = 3(16 - b)

a = 3(16 - b)/5

Since 3 is not evenly divisible by 5, we see that (16 - b) must be evenly divisible by 5. Thus, b can be 1, 6, 11, or16.

So b cannot be 12.

Answer: D
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