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Game coins in a board game are placed at locations A, B, C, D, and E,

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Bunuel
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Game coins in a board game are placed at locations A, B, C, D, and E, [#permalink] New post   24 Apr 2018, 06:10
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72% (01:45) correct 28% (01:56) wrong based on 86 sessions
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Game coins in a board game are placed at locations A, B, C, D, and E, in the ratio 1:2:3:4:5, respectively. To win the game, a player must acquire at least 50 percent of the coins in each of three or more of the five locations. What minimum percent of the total coins must a player acquire to win the game?

(A) 10%
(B) 20%
(C) 30%
(D) 40%
(E) 50%
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Game coins in a board game are placed at locations A, B, C, D, and E, [#permalink] New post   24 Apr 2018, 07:08
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1+2+3+4+5 = 15. Choose a convenient number to represent the total. Choose 30.

Therefore location A has 2 coins, B has 4 coins, C has 6 coins, D has 8 coins, and E has 10 coins. 2+4+6+8+10 = 30.

50% of minimum of locations A, B and C = 50% (2+4+6) = 50%(12) = 6

6 is 20% of 30.

6 (20% of total) is minimumof the total coins must a player acquire to win the game?


Hence B = 20% is the answer.
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Re: Game coins in a board game are placed at locations A, B, C, D, and E, [#permalink] New post   24 Apr 2018, 19:38
The answer will change depending on the number of coins and odd/even.

e.g Number of coins 1,2,3,4,5
To win you have to pick min: 1 in A, 1 in B, 2 in C . Total 4 of 15 = 26.6%, wich is closer to Answer C (30%) rather than Answer B (20%).

In each case the number will be in some range. I think that the question should be modified, saying "the number of coins in each slot is even)
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Game coins in a board game are placed at locations A, B, C, D, and E, [#permalink] New post   25 Apr 2018, 05:02
Hero8888 wrote:
The answer will change depending on the number of coins and odd/even.

e.g Number of coins 1,2,3,4,5
To win you have to pick min: 1 in A, 1 in B, 2 in C . Total 4 of 15 = 26.6%, wich is closer to Answer C (30%) rather than Answer B (20%).

In each case the number will be in some range. I think that the question should be modified, saying "the number of coins in each slot is even)



Hello Hero8888,

the question is "What minimum percent of the total coins must a player acquire to win the game?". The question expect us to think of when the minimum is possible. The minimum will be possible when the coins at each location are even in number.
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Re: Game coins in a board game are placed at locations A, B, C, D, and E, [#permalink] New post   25 Apr 2018, 07:25
houston1980 wrote:
Hero8888 wrote:
The answer will change depending on the number of coins and odd/even.

e.g Number of coins 1,2,3,4,5
To win you have to pick min: 1 in A, 1 in B, 2 in C . Total 4 of 15 = 26.6%, wich is closer to Answer C (30%) rather than Answer B (20%).

In each case the number will be in some range. I think that the question should be modified, saying "the number of coins in each slot is even)



Hello Hero8888,

the question is "What minimum percent of the total coins must a player acquire to win the game?". The question expect us to think of when the minimum is possible. The minimum will be possible when the coins at each location are even in number.


Hi houston1980,

Thank you for explanation. But the Q askes " ... must a player acquire to win the game'', which has nothing to do with "find possible min". Since there are no conditions for even/odd of coins, both cases should be implied e.g. any DS question :-D
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Re: Game coins in a board game are placed at locations A, B, C, D, and E, [#permalink] New post   25 Apr 2018, 07:45
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Bunuel wrote:
Game coins in a board game are placed at locations A, B, C, D, and E, in the ratio 1:2:3:4:5, respectively. To win the game, a player must acquire at least 50 percent of the coins in each of three or more of the five locations. What minimum percent of the total coins must a player acquire to win the game?

(A) 10%
(B) 20%
(C) 30%
(D) 40%
(E) 50%


To start, we know we have to have at least 50% of the coins in 3 of the 5 locations. Easiest way to do this is use the ratio given to us (no manipulation is required) and take half of 1, 2, and 3 (first 3 of the 5 ratios). This gives us 1/2, 1, and 3/2, which totals to 3. We know the sum of the ratios equals 15 (1+2+...+5); therefore, 3/15 can be reduced to 1/5, which equates to 20%. Answer choice B.
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Re: Game coins in a board game are placed at locations A, B, C, D, and E, [#permalink] New post   25 Apr 2018, 09:34
el2010 wrote:
Bunuel wrote:
Game coins in a board game are placed at locations A, B, C, D, and E, in the ratio 1:2:3:4:5, respectively. To win the game, a player must acquire at least 50 percent of the coins in each of three or more of the five locations. What minimum percent of the total coins must a player acquire to win the game?

(A) 10%
(B) 20%
(C) 30%
(D) 40%
(E) 50%


To start, we know we have to have at least 50% of the coins in 3 of the 5 locations. Easiest way to do this is use the ratio given to us (no manipulation is required) and take half of 1, 2, and 3 (first 3 of the 5 ratios). This gives us 1/2, 1, and 3/2, which totals to 3. We know the sum of the ratios equals 15 (1+2+...+5); therefore, 3/15 can be reduced to 1/5, which equates to 20%. Answer choice B.


We can not have the half of a coin, as if we couldn't have the half of a human. When you have 3 people/coins, at least 50% of them is 2, but not 1.5. When you have 4 coins/people, indeed you can pick 2 of them to get "at least 50%". I know how to calculate all this stuff, my comment was on the fact that % will be changing due to odd/even factor x of the ratio 1x, 3x, 5x.
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Re: Game coins in a board game are placed at locations A, B, C, D, and E, [#permalink] New post   25 Apr 2018, 13:15
Bunuel wrote:
Game coins in a board game are placed at locations A, B, C, D, and E, in the ratio 1:2:3:4:5, respectively. To win the game, a player must acquire at least 50 percent of the coins in each of three or more of the five locations. What minimum percent of the total coins must a player acquire to win the game?

(A) 10%
(B) 20%
(C) 30%
(D) 40%
(E) 50%



Let's assume we are having 15 (1+2+3+4+5) coins on the board,

To win we need 7.5 coins that is 50 percent of the total coins

Maximum coin on the board is in location E, Hence E needs to acquire 3 more to win the game

Therefore the minimum percent of the total coin, to win the game = 3/15 * 100 = 20%

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Re: Game coins in a board game are placed at locations A, B, C, D, and E, [#permalink] New post   26 Apr 2018, 15:32
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Bunuel wrote:
Game coins in a board game are placed at locations A, B, C, D, and E, in the ratio 1:2:3:4:5, respectively. To win the game, a player must acquire at least 50 percent of the coins in each of three or more of the five locations. What minimum percent of the total coins must a player acquire to win the game?

(A) 10%
(B) 20%
(C) 30%
(D) 40%
(E) 50%


We can let the total coins = x + 2x + 3x + 4x + 5x = 15x.

Taking 50% of the smallest number of coins we have:

0.5(x + 2x + 3x) = 0.5x + x + 1.5x = 3x

So the minimum percent of the total coins a player must acquire to win the game is 3x/15x = 1/5 = 0.2 = 20%.

Answer: B
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Re: Game coins in a board game are placed at locations A, B, C, D, and E, [#permalink]
26 Apr 2018, 15:32
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