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11 Jul 2024, 07:00
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
48% (02:19) correct
52%
(02:16)
wrong
based on 423
sessions
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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.
(A) Statement 1 alone is sufficient, but statement 2 alone is not.
(B) Statement 2 alone is sufficient, but statement 1 alone is not.
(C) Both statements together are sufficient, but neither alone is sufficient.
(D) Each statement alone is sufficient.
(E) Neither statement is sufficient, even when combined.
(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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(A) Statement 1 alone is sufficient, but statement 2 alone is not.
(B) Statement 2 alone is sufficient, but statement 1 alone is not.
(C) Both statements together are sufficient, but neither alone is sufficient.
(D) Each statement alone is sufficient.
(E) Neither statement is sufficient, even when combined.
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:
Since \(\frac{x}{x + y} * 100= p\), then:
(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:
Since \(\frac{x}{x + y} * 100= p\), then:
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:
\(\frac{x + 2}{x + y} * 100= 2p\).
Since \(\frac{x}{x + y} * 100= p\), then:
\(\frac{x + 2}{x + y} * 100=2* \frac{x}{x + y} * 100\)
\(x + 2 = 2x\)
\(x =2\).
\(x + 2 = 2x\)
\(x =2\).
(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:
\(\frac{x + \frac{y}{2}}{x + y} * 100= \frac{x}{x + y} * 100\)
\(x + \frac{y}{2}= 2x\)
\(y =2x\).
\(x + \frac{y}{2}= 2x\)
\(y =2x\).
Answer: B.
General Discussion
Emkicheru
Joined: 12 Sep 2023
Last visit: 12 Sep 2025
Posts: 119
Own Kudos:
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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11 Jul 2024, 07:32
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The answer according to me is B, only 2nd statement is sufficient.
It is given in the question that we have to find, [x/(x+y)]*100. Let's assume it to be P.
According to the first statement, 100*[(x+2)/(x+y)]=2P. Subtracting the above equation from this equation, P=2/(x+y)=x/(x+y). Here, although we are able to find the value of x, due to y being unknown we can't find the volume ratio.
Now, according to the 2nd statement, [(x+0.5y)/(x+y)]*100=2P. From this equation, we'll get that y=2x. Using this in the original equation, we get (x/3x)*100, i.e. 33.33%
It is given in the question that we have to find, [x/(x+y)]*100. Let's assume it to be P.
According to the first statement, 100*[(x+2)/(x+y)]=2P. Subtracting the above equation from this equation, P=2/(x+y)=x/(x+y). Here, although we are able to find the value of x, due to y being unknown we can't find the volume ratio.
Now, according to the 2nd statement, [(x+0.5y)/(x+y)]*100=2P. From this equation, we'll get that y=2x. Using this in the original equation, we get (x/3x)*100, i.e. 33.33%
