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12 Jul 2024, 04:41
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Find \(\frac{x }{ (x+y)}\) = ?
Statement (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
\(x + 2 = 2x\)
\(X = 2\)
This alone does not give us the value of y, so statement (1) alone is not sufficient
Statement (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. From this, we derived,
\(y = 2x\)
Thus, \(\frac{x }{ (x +y)}\) = \(\frac{x }{ 3x}\) = 33.34%
Since we can determine the percentage of orange juice using statement (2) alone and without knowing the exact values of ( x ) and ( y ), statement (2) alone is indeed sufficient. Correct answer is B
12 Jul 2024, 05:05
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(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.
Based on the information, Let's assume, x= 2 and y=4 where x= 33.33%. Now, If 2 liters of carrot juice were replaced with 2 liters of orange juice, the percentage of orange juice would be 66.66. Now, take another example, x=2 and y=8 where x=25%. Now, If 2 liters of carrot juice were replaced with 2 liters of orange juice, the orange juice would be 4 corresponds 50%. From this, we can say that certainty, A is non sufficient to answer the question.
(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.
Now, consider (2), it can be easily identified that half of the carrot juice is actually equal to the entire amount of orange juice. Meaning, the carrot juice should be 66.66% and orange should be 33.33%. No alternative is possible. So, B is sufficient to answer the question.
Answer, B.
Based on the information, Let's assume, x= 2 and y=4 where x= 33.33%. Now, If 2 liters of carrot juice were replaced with 2 liters of orange juice, the percentage of orange juice would be 66.66. Now, take another example, x=2 and y=8 where x=25%. Now, If 2 liters of carrot juice were replaced with 2 liters of orange juice, the orange juice would be 4 corresponds 50%. From this, we can say that certainty, A is non sufficient to answer the question.
(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.
Now, consider (2), it can be easily identified that half of the carrot juice is actually equal to the entire amount of orange juice. Meaning, the carrot juice should be 66.66% and orange should be 33.33%. No alternative is possible. So, B is sufficient to answer the question.
Answer, B.
