In a rare coin collection, one in six coins is gold, and all coins are GMAT Problem Solving

Question: 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 be there in this collection after the proposed trade?

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

Answer: B

Approach Solution (1):
Since all of the values in the problem are multiples of 10, the current number of coins is almost certainly a multiple of 10.
Since 1 of every six coins is gold, G : S = 1:5, implying that the number of silver coins is 5 times the number of gold coins.
Options for G and S:
G = 10, S = 50
G = 20, S = 100
G = 30, S = 150
G = 40, S = 200
G = 50, S = 250
In the list above, exchanging 10 silver coins for 10 gold coins must yield G : S = 1:4, implying that the resulting number of silver coins must be 4 times the resulting number of gold coins.
If in each option we increase the value of G by 10 and decrease the value of S by 10, we get:
New G = 20, new S = 40
New G = 30, new S = 90
New G = 40, new S = 140
New G = 50, new S = 190
New G = 60, new S = 240.
Only in the green option is the resulting number of silver coins if 4 times the resulting number of gold coins.
Thus, New G = 60
Correct option: B

Approach Solution (2):
Algebra:
One in six coins is gold and all coins are either gold or silver.
Since G : S = 1 : 5, let G = the original number of gold coins and 5G = the original number of silver coins.
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.
Thus, increasing the value of G by 10 and decreasing the value of 5G by 10 must yield a 1 : 4 ratio:
(G+10)/(5G-10) = 1/4
4G + 40 = 5G - 10
50 = G
How many gold coins would there be in this collection after the proposed trade?
The proposed trade increases the value of G by 10:
G + 10 = 50 + 10 = 60
Correct option: B

Approach Solution (3):
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
Correct option: B

“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 be there in this collection after the proposed trade?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

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