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A football league consists of 800 total players, 65 percent of whom pl

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A football league consists of 800 total players, 65 percent of whom pl  [#permalink]

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New post 30 Jan 2019, 00:37
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A football league consists of 800 total players, 65 percent of whom play on offense. If there are only offensive and defensive players in the league, how many defensive players would have to join for the defensive players to comprise at least 40 percent of the league?
A) 63
B) 64
C) 65
D) 66
E) 67

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Re: A football league consists of 800 total players, 65 percent of whom pl  [#permalink]

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New post 30 Jan 2019, 01:30
Abhi077 wrote:
A football league consists of 800 total players, 65 percent of whom play on offense. If there are only offensive and defensive players in the league, how many defensive players would have to join for the defensive players to comprise at least 40 percent of the league?
A) 63
B) 64
C) 65
D) 66
E) 67


Currently there are 35% defensive players. Defensive players need to be added to get 40% defensive players.

w1/w2 = (100 - 40)/(40 - 35) = 12/1

So for 12 current players, we need to add 1 new defensive player.
For 800 correct players, we need to add 800/12 = 66.67 players i.e. 67 players
The defensive players need to be at least 40%. If we add 67 players, they will be just above 40%.

Answer (E)
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Re: A football league consists of 800 total players, 65 percent of whom pl  [#permalink]

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New post 30 Jan 2019, 01:40
Abhi077 wrote:
A football league consists of 800 total players, 65 percent of whom play on offense. If there are only offensive and defensive players in the league, how many defensive players would have to join for the defensive players to comprise at least 40 percent of the league?
A) 63
B) 64
C) 65
D) 66
E) 67



Another method..

65% means Offensive are \(800\frac{65}{100}=520\)..

The ONLY change is in the number of Defensive player, so offensive players will remain the same as 520..
Say the new total is x.
But if D are atleast 40%, O will be at the most 60%, that is O\(\leq{\frac{60}{100}*x\)=> \(520\leq{\frac{60}{100}*x\)=> \(x\geq{520*100/60}......x\geq{866.66}\)

The number cannot be a decimal, so take the decimal as complete or 867..
The new player added = 867-800=67

E
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Re: A football league consists of 800 total players, 65 percent of whom pl  [#permalink]

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New post 30 Jan 2019, 01:50
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Abhi077 wrote:
A football league consists of 800 total players, 65 percent of whom play on offense. If there are only offensive and defensive players in the league, how many defensive players would have to join for the defensive players to comprise at least 40 percent of the league?
A) 63
B) 64
C) 65
D) 66
E) 67


total players = 800
offense players= 800*.65= 520

so now to make a team which has 40% defensive players ,keeping the count of offense players same i.e 520 it would be 60% of total league players

520= x* 60/100
x= 867

addition of players required = 867-800
= 67
IMO E
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Re: A football league consists of 800 total players, 65 percent of whom pl   [#permalink] 30 Jan 2019, 01:50
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