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19 Jul 2024, 07:00
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Question Stats:
60% (02:10) correct
40%
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An alloy is made by mixing certain quantities of iron, copper, and lead. If the average (arithmetic mean) cost of the alloy is $20 per kilogram, what is the ratio of the weight of iron to the weight of copper to the weight of lead in the alloy?
(1) The cost per kilogram of iron, copper, and lead is $10, $20, and $30, respectively.
(2) The cost of the copper used in the alloy equals the cost of the lead used in the alloy.
A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
C. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
D. EACH statement ALONE is sufficient to answer the question asked.
E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
(1) The cost per kilogram of iron, copper, and lead is $10, $20, and $30, respectively.
(2) The cost of the copper used in the alloy equals the cost of the lead used in the alloy.
A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
C. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
D. EACH statement ALONE is sufficient to answer the question asked.
E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
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19 Jul 2024, 08:15
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An alloy is made by mixing certain quantities of iron, copper, and lead. If the average (arithmetic mean) cost of the alloy is $20 per kilogram, what is the ratio of the weight of iron to the weight of copper to the weight of lead in the alloy?
Assuming x kilograms of iron, y kilograms of copper, and z kilograms of lead were used to make the alloy, the question asks us to find the ratio x : y : z.
(1) The cost per kilogram of iron, copper, and lead is $10, $20, and $30, respectively.
Since the average cost of the alloy is $20 per kilogram, from the above statement we can deduce that (10x + 20y + 30z)/(x + y + z) = 20. Simplifying this equation gives x = z. Thus, we have the relationship x : z = 1 : 1. However, we still don't know the relationship between y and x, or y and z to get the final ratio of x : y : z. Not sufficient.
(2) The cost of the copper used in the alloy equals the cost of the lead used in the alloy.
This statement alone is clearly not sufficient to determine the desired ratio.
(1) + (2) Since from (1) the cost per kilogram of copper and lead is $20 and $30, respectively, then from (2) we can deduce 20y = 30z, which gives y : z = 3 : 2. Therefore, combining with x = z from statement (1), we get x : y : z = 2 : 3 : 2. Sufficient.
Answer: C.
GMAT Club Official Explanation:
An alloy is made by mixing certain quantities of iron, copper, and lead. If the average (arithmetic mean) cost of the alloy is $20 per kilogram, what is the ratio of the weight of iron to the weight of copper to the weight of lead in the alloy?
Assuming x kilograms of iron, y kilograms of copper, and z kilograms of lead were used to make the alloy, the question asks us to find the ratio x : y : z.
(1) The cost per kilogram of iron, copper, and lead is $10, $20, and $30, respectively.
Since the average cost of the alloy is $20 per kilogram, from the above statement we can deduce that (10x + 20y + 30z)/(x + y + z) = 20. Simplifying this equation gives x = z. Thus, we have the relationship x : z = 1 : 1. However, we still don't know the relationship between y and x, or y and z to get the final ratio of x : y : z. Not sufficient.
(2) The cost of the copper used in the alloy equals the cost of the lead used in the alloy.
This statement alone is clearly not sufficient to determine the desired ratio.
(1) + (2) Since from (1) the cost per kilogram of copper and lead is $20 and $30, respectively, then from (2) we can deduce 20y = 30z, which gives y : z = 3 : 2. Therefore, combining with x = z from statement (1), we get x : y : z = 2 : 3 : 2. Sufficient.
Answer: C.
General Discussion
19 Jul 2024, 07:34
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Given : An alloy is made by mixing certain quantities of iron, copper, and lead.
Asked: If the average (arithmetic mean) cost of the alloy is $20 per kilogram, what is the ratio of the weight of iron to the weight of copper to the weight of lead in the alloy?
Let the ratio of the weight of iron to the weight of copper to the weight of lead in the alloy = i : c : l
(1) The cost per kilogram of iron, copper, and lead is $10, $20, and $30, respectively.
The average (arithmetic mean) cost of the alloy = (10i + 20c + 30l)/(i + c + l) = $20
10i + 20c + 30l = 20i + 20c + 20l
10i = 10l
i = l
The ratio of the weight of iron to the weight of copper to the weight of lead in the alloy = l : c : l
Since ratio of c & l can not be determined.
NOT SUFFICIENT
(2) The cost of the copper used in the alloy equals the cost of the lead used in the alloy.
Since the cost of the copper & cost of the lead $/kg are not provided.
NOT SUFFICIENT
(1) + (2)
(1) The cost per kilogram of iron, copper, and lead is $10, $20, and $30, respectively.
The average (arithmetic mean) cost of the alloy = (10i + 20c + 30l)/(i + c + l) = $20
10i + 20c + 30l = 20i + 20c + 20l
10i = 10l
i = l
(2) The cost of the copper used in the alloy equals the cost of the lead used in the alloy.
20c = 30l
c = 1.5l
The ratio of the weight of iron to the weight of copper to the weight of lead in the alloy = l : 1.5l : l = 1: 1.5: 1 = 2:3:2
SUFFICIENT
IMO C
Asked: If the average (arithmetic mean) cost of the alloy is $20 per kilogram, what is the ratio of the weight of iron to the weight of copper to the weight of lead in the alloy?
Let the ratio of the weight of iron to the weight of copper to the weight of lead in the alloy = i : c : l
(1) The cost per kilogram of iron, copper, and lead is $10, $20, and $30, respectively.
The average (arithmetic mean) cost of the alloy = (10i + 20c + 30l)/(i + c + l) = $20
10i + 20c + 30l = 20i + 20c + 20l
10i = 10l
i = l
The ratio of the weight of iron to the weight of copper to the weight of lead in the alloy = l : c : l
Since ratio of c & l can not be determined.
NOT SUFFICIENT
(2) The cost of the copper used in the alloy equals the cost of the lead used in the alloy.
Since the cost of the copper & cost of the lead $/kg are not provided.
NOT SUFFICIENT
(1) + (2)
(1) The cost per kilogram of iron, copper, and lead is $10, $20, and $30, respectively.
The average (arithmetic mean) cost of the alloy = (10i + 20c + 30l)/(i + c + l) = $20
10i + 20c + 30l = 20i + 20c + 20l
10i = 10l
i = l
(2) The cost of the copper used in the alloy equals the cost of the lead used in the alloy.
20c = 30l
c = 1.5l
The ratio of the weight of iron to the weight of copper to the weight of lead in the alloy = l : 1.5l : l = 1: 1.5: 1 = 2:3:2
SUFFICIENT
IMO C
