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# In a rare coin collection, one in six coins is gold, and all coins are

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Math Expert
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In a rare coin collection, one in six coins is gold, and all coins are  [#permalink]

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03 Dec 2014, 08:17
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Difficulty:

45% (medium)

Question Stats:

75% (02:20) correct 25% (03:00) wrong based on 117 sessions

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Tough and Tricky questions: Word Problems.

In a rare coin collection, one in six coins is gold, and all coins are either gold or silver. If 10 silver coins were to be subsequently traded for an additional 10 gold coins, the ratio of gold coins to silver coins would be 1 to 4. Based on this information, how many gold coins would there be in this collection after the proposed trade?

A) 50
B) 60
C) 180
D) 200
E) 300

Kudos for a correct solution.

Source: Chili Hot GMAT

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Re: In a rare coin collection, one in six coins is gold, and all coins are  [#permalink]

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03 Dec 2014, 09:30
3
one in six coins is gold, and all coins are either gold or silver

So if x is the number of gold coins, the number of silver coins is 5x

Now after the trade number of gold coins become x+10 and the number of silver coins become 5x-10

Therefore (x+10)/ (5x - 10) = 1/4; solving for x we get x = 50

Therefore there will be 60 gold coins after the trade.

Hence B
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Re: In a rare coin collection, one in six coins is gold, and all coins are  [#permalink]

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03 Dec 2014, 20:36
2

Gold .................... Silver .................... Total

x ............................ 5x .......................... 6x (Say "x" are the gold coins)

x+10 ..................... 5x-10 ...................... (After trade)

$$\frac{x+10}{5x-10} = \frac{1}{4}$$

x = 50

Gold coins after trade = 50+10 = 60
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In a rare coin collection, one in six coins is gold, and all coins are  [#permalink]

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03 Jul 2017, 15:51
Bunuel wrote:

Tough and Tricky questions: Word Problems.

In a rare coin collection, one in six coins is gold, and all coins are either gold or silver. If 10 silver coins were to be subsequently traded for an additional 10 gold coins, the ratio of gold coins to silver coins would be 1 to 4. Based on this information, how many gold coins would there be in this collection after the proposed trade?

A) 50
B) 60
C) 180
D) 200
E) 300

Kudos for a correct solution.

Source: Chili Hot GMAT

1. Original ratio, where all coins are gold or silver, and one in six coins is gold (other 5 are silver)

$$\frac{G}{S}$$ = $$\frac{1x}{5x}$$

2. Ten silver coins are traded for ten gold coins, and the new ratio of gold coins to silver coins is 1 to 4:

$$\frac{x + 10}{5x - 10}$$ = $$\frac{1}{4}$$

4(x + 10) = 5x - 10
4x + 40 = 5x - 10
x = 50 -- that's the multiplier

Originally there were 1x = 50 gold coins; after the trade, there are 10 more. Total is 60.

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Re: In a rare coin collection, one in six coins is gold, and all coins are  [#permalink]

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30 Mar 2018, 10:58
Bunuel wrote:

Tough and Tricky questions: Word Problems.

In a rare coin collection, one in six coins is gold, and all coins are either gold or silver. If 10 silver coins were to be subsequently traded for an additional 10 gold coins, the ratio of gold coins to silver coins would be 1 to 4. Based on this information, how many gold coins would there be in this collection after the proposed trade?

A) 50
B) 60
C) 180
D) 200
E) 300

If one in six coins is gold and all coins are either gold or silver, then we have one gold coin for every 5 silver coins. In other words, the ratio of gold coins to silver coins is 1 : 5. We can let the number of gold coins before the trade = g, and thus the number of silver coins before the trade = 5g. We can create the equation:

(g + 10)/(5g - 10) = 1/4

4(g + 10) = 5g - 10

4g + 40 = 5g - 10

50 = g

Thus, after the proposed trades, the number of gold coins would be 50 + 10 = 60.

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Re: In a rare coin collection, one in six coins is gold, and all coins are   [#permalink] 30 Mar 2018, 10:58
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