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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.


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­Original percentage of orange juice:
  • x/x+y
Statement 1 -> 
New mixture after replacing 2 liters of carrot juice with 2 liters of orange juice:

x+2​/(x+2)+(y−2)=x+2/x+y 

on solving we get 
x= 2 
but not y , therefore not sufficient

Statement 2->

New mixture after replacing half of the carrot juice with an equal amount of orange juice:

(x+y/2) / x + y/2 + y/2 

According to the statement, this new percentage is double the original percentage:

(above eq on solving)  
(x + y/2)   /  x+ y = 2x/x+y

on solving we get  y = 2x 

we can get juice by volume

x / x + 2y

x/3x

1/3

33.333 %
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­Question stem provide us with following information,
Mix juice = x litre of orange + y litre of carrot.

We need to find percent of the mixture, by volume, is orange juice.
So,
we need to find \(\frac{100x }{ x+y}\)

 ­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.

So, new carrot juice = \(y - 2 \)
new orange juice = \(x + 2\)
total =\( x+y-2+2 = x+y\)

And percentage of orange juice by volume in the mixture would double compared to original.
\(100 *\frac{ x+2 }{ x+y}\) = \(\frac{2*100x }{ x+y}\)

\( x + 2 = 2x\)
\(x = 2\)

But we don't know value of \(y\).
So statement is insufficient.

 ­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.

new carrot juice = \(\frac{y}{2}\)
new orange juice = \(x + \frac{y}{2}\)
new total = \(x + \frac{y}{2} + \frac{y}{2}\)­ = \(x + y\)­

the percentage of orange juice by volume in the mixture would double compared to original.

\(100 *\frac{ x+ 0.5y }{ x+y}\) = \(\frac{2*100x }{ x+y}\)
\( ­x+0.5y = 2x \)
\(y = 2x\)

We can find \(\frac{100x }{ x+y}\)  from this.
= \(\frac{100x }{ x+y}\)

= \(\frac{100x }{ x+2x}\)

= \(\frac{100}{3}\) %
 ­
Statement-2 is sufficient

Final answer is B.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.­
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Total Volume of the mixture= x+y
Orange juice percent of the mixture, by volume, is = \(\frac{x}{(x+y)}*100\)
Carrot juice percent of the mixture, by volume, is =\(\frac{ y}{(x+y})*100\)

(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.
 New Volume of Carrot Juice is "yn" and  New Volume of Orange Juice is "xn"
 yn= y-2
xn=x+2
\(\frac{x+2}{(x+y)}\)=\(2*\frac{x}{(x+y)}\)
x=2
Volume % of x = \(\frac{2}{(2+y)}\)
Not sufficient.

(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.
New Volume of Carrot Juice is "yn" and  New Volume of Orange Juice is "xn"
yn= \(y-\frac{y}{2}\)
xn= \(x+\frac{y}{2}\)

\(\frac{xn}{(x+y)}\)=  \(2*\frac{x}{(x+y)}\)

\(x+\frac{y}{2} = 2x\)
\(x=\frac{y}{2}\)
y=2x

Volume of x = \(\frac{x }{(x+2x)}*100\)= 1/3 = 100/3 = 33.33%

2  is sufficient. IMO B.­
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orange juice = x ltr
carrot juice = y ltr

we have to find % of orange juice which is = (x / (x+y) ) * 100

statement 1 : 2 ltr of carrot juice replaced by 2 ltr of orange juice the orange volume % will double

OJ = x-2 ltr
CJ = y-2 ltr

overall volume remains the same = (x+y) ltr

(x-2)/(x+y) = 2(x/(x+y))
solving we get x = 2 ltr , not sufficient

statement 2 : half of carrot juice by volume replaced by half of orange juice in the mixture , volume % of orange juice will double

OJ = x+y/2
CJ = y/2

total volume remains the same
equating and solving we get y = 2x , sufficient to tell volume % of OJ in the mixture
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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.


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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?

Given:
Orange juice: x litres
Carrot juice: y litres
Mixture: x+y litres.
x=?

(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.
Given condition,
Orange juice: x+2 litres
Carrot juice: y-2 litres
Mixture: x+y litres.
Original % of orange juice= x/(x+y)*100; New %=(x+2)/(x+y)*100
Given, (x+2)/(x+y)*100=2*x/(x+y)*100
x+2=2x; Here even if we find x, we are not able to find y, hence Statement A not sufficient.

(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,
Orange juice: x+a litres .. (a= y/2 or amount of orange juice added)
Carrot juice: y/2 litres
Mixture: x+y litres.

So, (x+a)/(x+y)=2*(x/(x+y))
x+a=2x; or x=a or x=y/2 or y=2x.
From this, we can derive value of x%, which will be (x/3x)*100.
Hence B.
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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.


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This question was provided by GMAT Club
for the GMAT Club Olympics Competition

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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
­
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Asked - 100(x)/(x+y).
From 1 -
(x+2)/(x+y) = (2x)/(x+y)
--> x = 2. y not known. A not sufficient.
Remaining options BDE

From 2
x+(y/2) = 2x
---> This can give us the ratio of x/(x+y).
B is sufficient. Option B.
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Statement (1) alone is sufficient because it provides a specific condition that allows us to set up an equation and solve for the percentage of orange juice in the mixture.

Statement (2) alone is also sufficient for the same reason, as it provides another specific condition that allows us to set up a different equation and solve for the percentage.

Thus, each statement alone is sufficient to answer the question.

D. EACH statement ALONE is sufficient to answer the question asked.
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