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11 Jul 2024, 07:00
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Difficulty:
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Question Stats:
46% (02:19) correct
54%
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wrong
based on 405
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A mixture of orange and carrot juices consists of x liters of orange juice and y liters of carrot juice. What percent of the mixture, by volume, is orange juice?
(1) If 2 liters of carrot juice were replaced with 2 liters of orange juice, the percentage of orange juice by volume in the mixture would double.
(2) If half of the carrot juice by volume were replaced with an equal amount of orange juice, the percentage of orange juice by volume in the mixture would double.
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) If 2 liters of carrot juice were replaced with 2 liters of orange juice, the percentage of orange juice by volume in the mixture would double.
(2) If half of the carrot juice by volume were replaced with an equal amount of orange juice, the percentage of orange juice by volume in the mixture would double.
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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11 Jul 2024, 08:45
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A mixture of orange and carrot juices consists of x liters of orange juice and y liters of carrot juice. What percent of the mixture, by volume, is orange juice?
Essentially, the question asks to find the value of x/(x + y)*100.
(1) If 2 liters of carrot juice were replaced with 2 liters of orange juice, the percentage of orange juice by volume in the mixture would double.
This operation increases the amount of orange juice by 2 liters while keeping the total volume the same. This implies that 2 liters is enough to double the original percentage, meaning the original amount of orange juice must also be 2 liters. However, without knowing the value of y, we cannot calculate 2/(2 + y) * 100. Not sufficient.
* For those preferring algebra, here is what this statement means:
\(\frac{x + 2}{x + y} * 100= 2p\).
Since \(\frac{x}{x + y} * 100= p\), then:
\(\frac{x + 2}{x + y} * 100=2* \frac{x}{x + y} * 100\)
\(x + 2 = 2x\)
\(x =2\).
(2) If half of the carrot juice by volume were replaced with an equal amount of orange juice, the percentage of orange juice by volume in the mixture would double.
This operation implies that replacing y/2 liters of carrot juice with y/2 liters of orange juice doubles the percentage of orange juice in the mixture. By the same logic as above, we can infer that x = y/2, which gives y = 2x. Therefore, x/(x + y) * 100 = x/(x + 2x) * 100 = 33 1/3%. Sufficient.
* For those preferring algebra, here is what this statement means:
\(\frac{x + \frac{y}{2}}{x + y} * 100= 2p\).
Since \(\frac{x}{x + y} * 100= p\), then:
\(\frac{x + \frac{y}{2}}{x + y} * 100= \frac{x}{x + y} * 100\)
\(x + \frac{y}{2}= 2x\)
\(y =2x\).
Answer: B.
GMAT Club Official Explanation:
A mixture of orange and carrot juices consists of x liters of orange juice and y liters of carrot juice. What percent of the mixture, by volume, is orange juice?
Essentially, the question asks to find the value of x/(x + y)*100.
(1) If 2 liters of carrot juice were replaced with 2 liters of orange juice, the percentage of orange juice by volume in the mixture would double.
This operation increases the amount of orange juice by 2 liters while keeping the total volume the same. This implies that 2 liters is enough to double the original percentage, meaning the original amount of orange juice must also be 2 liters. However, without knowing the value of y, we cannot calculate 2/(2 + y) * 100. Not sufficient.
* For those preferring algebra, here is what this statement means:
\(\frac{x + 2}{x + y} * 100= 2p\).
\(\frac{x + 2}{x + y} * 100=2* \frac{x}{x + y} * 100\)
\(x + 2 = 2x\)
\(x =2\).
This operation implies that replacing y/2 liters of carrot juice with y/2 liters of orange juice doubles the percentage of orange juice in the mixture. By the same logic as above, we can infer that x = y/2, which gives y = 2x. Therefore, x/(x + y) * 100 = x/(x + 2x) * 100 = 33 1/3%. Sufficient.
* For those preferring algebra, here is what this statement means:
\(\frac{x + \frac{y}{2}}{x + y} * 100= 2p\).
\(\frac{x + \frac{y}{2}}{x + y} * 100= \frac{x}{x + y} * 100\)
\(x + \frac{y}{2}= 2x\)
\(y =2x\).
Answer: B.
General Discussion
Emkicheru
Joined: 12 Sep 2023
Last visit: 12 Sep 2025
Posts: 119
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Given Kudos: 11
Location: Kenya
Schools: Anderson (UCLA) Sloan (MIT) Columbia '27
GMAT 1: 780 Q50 V48
GRE 1: Q167 V164
GPA: 3.7
Schools: Anderson (UCLA) Sloan (MIT) Columbia '27
GMAT 1: 780 Q50 V48
GRE 1: Q167 V164
Posts: 119
Kudos:
22
11 Jul 2024, 07:29
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We find that the statements are sufficient and both cannot work without the other. Hence all information are sufficient to the effect of the solution.
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