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A sports league encourages collaboration by awarding 3 points for each

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Bunuel
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A sports league encourages collaboration by awarding 3 points for each [#permalink] New post   10 Oct 2019, 00:41
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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
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D
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Re: A sports league encourages collaboration by awarding 3 points for each [#permalink] New post   10 Oct 2019, 08:04
Bunuel wrote:
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


given
3x+5y=48
5y=48-3x
factor of 5 integer value
only not possible at x=12
IMO D
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Re: A sports league encourages collaboration by awarding 3 points for each [#permalink] New post   10 Oct 2019, 11:08
Bunuel wrote:
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


Work with options -

(A) 1*3 + 5*9 = 48 ( Possible )
(B) 6*3 + 5*6 = 48 (Possible )
(C) 11*3 + 5*3 = 48 (Possible )
(D) 12*3 + 5*2 + 2 = 48 (Not Possible )
(E) 16*3 + 5*0 = 48 (POssible )

Hence, ANswer must be (D)
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Re: A sports league encourages collaboration by awarding 3 points for each [#permalink] New post   13 Oct 2019, 18:23
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Bunuel wrote:
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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Re: A sports league encourages collaboration by awarding 3 points for each [#permalink]
13 Oct 2019, 18:23
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