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# A sports league encourages collaboration by awarding 3 points for each

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Math Expert
Joined: 02 Sep 2009
Posts: 52230
A sports league encourages collaboration by awarding 3 points for each  [#permalink]

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31 Oct 2018, 00:42
00:00

Difficulty:

25% (medium)

Question Stats:

87% (01:39) correct 13% (01:33) wrong based on 15 sessions

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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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Joined: 09 Jun 2018
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Re: A sports league encourages collaboration by awarding 3 points for each  [#permalink]

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31 Oct 2018, 06:17
Let x be goals without assistance, w be goals with assistance. x and w are integers.

Hence, 3x + 5w = 48

Now, plug in all options as x to check which option does not give an integer value for w.
A: 3*1 + 5w = 48 gives 5w = 45 can be solved
B gives 5w = 30 can be solved
C gives 5w = 15 can be solved
D gives 5w = 12 CANNOT be solved
E gives 5w = 0 can be solved

Hence Option D
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Re: A sports league encourages collaboration by awarding 3 points for each &nbs [#permalink] 31 Oct 2018, 06:17
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