Bunuel
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.
Lets consider volume of Orange juice as x & volume of Carrot Juice as y in mixture A.
% of orange juice in mixture A =x/x+y%
In order to get the %, we need the values of x & y.
(1) gives us: Mixture B: Carrot Juice=y-2 ; Orange juice=x+2
% of Orange juice in mixture B= x+2/x+y
%orange juice in Mixture B=2 times the % orange juice in mixture A
=> x+2/x+y=2x/x+y
=> x=2. This alone can't give the answer. Therefore A & D are rejected.
(2) gives us: Mixture C: Carrot Juice: y/2; Orange Juice=x+y/2
%orange juice in mixture C= x+y/2/x+y
%orange juice in C=2 times % orange juice in A
=> x+y/2/x+y = 2x/x+y
=> x=y/2; y=4.....substituting value of x from statement 1. B&E are rejected..
we have values of x & y. Therefore % of orange juice is 2/(2+4) % = 33%.
Answer is C