Events & Promotions
|
|
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Nov 2211:00 AM IST
-01:00 PM IST
Do RC/MSR passages scare you? e-GMAT is conducting a masterclass to help you learn – Learn effective reading strategies Tackle difficult RC & MSR with confidence Excel in timed test environment- Nov 23
11:00 AM IST
-01:00 PM IST
Attend this free GMAT Algebra Webinar and learn how to master the most challenging Inequalities and Absolute Value problems with ease. 
Nov 2510:00 AM EST
-11:00 AM EST
Prefer video-based learning? The Target Test Prep OnDemand course is a one-of-a-kind video masterclass featuring 400 hours of lecture-style teaching by Scott Woodbury-Stewart, founder of Target Test Prep and one of the most accomplished GMAT instructors.
11 Jul 2024, 08:50
Kudos
Bookmarks
Juice mixture contains x liters of orange juice and y liters of carrot juice.
Percent of the mixture, by volume, is orange juice means (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.
After replacing 2 liters of carrot juice with 2 liters of orange juice, new volumes = x+2 liters of orange juice and
y−2 liters of carrot juice.
So, new percentage of orange juice = {x+2/(x+2)+y-2}*100 = (x+2/x+y)*100
As per this statement, new percentage = 2*original percentage,
So, (x+2/x+y)*100 = 2*(x/x+y)×100
upon simplification, x+2 = 2x, x=2.
No info about y. Hence, 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.
If half of the carrot juice y/2 replaced with same volume of orange juice, then new volumes become x+y/2 liters of orange juice and y/2 liters of carrot juice.
New percentage of orange juice = {(x+y/2)/x+y/2+y/2}*100= {(x+y/2)/x+y}*100
As per this statement, new percentage =2* original percentage
{(x+y/2)/x+y}*100 = 2*(x/x+y)*100
x+y/2= 2x
y=2x
Not sufficient as no values of x and y available.
1) +2) we know that x=2 & y=2x, so y=4. So we can substitute both x and y into x/x+y*100 and get unique value.
Hence sufficient.
IMO answer is C.
Percent of the mixture, by volume, is orange juice means (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.
After replacing 2 liters of carrot juice with 2 liters of orange juice, new volumes = x+2 liters of orange juice and
y−2 liters of carrot juice.
So, new percentage of orange juice = {x+2/(x+2)+y-2}*100 = (x+2/x+y)*100
As per this statement, new percentage = 2*original percentage,
So, (x+2/x+y)*100 = 2*(x/x+y)×100
upon simplification, x+2 = 2x, x=2.
No info about y. Hence, 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.
If half of the carrot juice y/2 replaced with same volume of orange juice, then new volumes become x+y/2 liters of orange juice and y/2 liters of carrot juice.
New percentage of orange juice = {(x+y/2)/x+y/2+y/2}*100= {(x+y/2)/x+y}*100
As per this statement, new percentage =2* original percentage
{(x+y/2)/x+y}*100 = 2*(x/x+y)*100
x+y/2= 2x
y=2x
Not sufficient as no values of x and y available.
1) +2) we know that x=2 & y=2x, so y=4. So we can substitute both x and y into x/x+y*100 and get unique value.
Hence sufficient.
IMO answer is C.
11 Jul 2024, 09:03
Kudos
Bookmarks
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.
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.
Answer: E - Statements (1) and (2) TOGETHER are NOT sufficient to answer the question, and additional data is needed.
- Original orange juice volume: x
- Original carrot juice volume: y
- New orange juice volume: x+2
- New carrot juice volume: y−2
- New percentage: \frac{{x + 2}{x + y}[}{fraction]
- Given:[fraction]{x + 2}{x + y}} =2 × \frac{{x}{x+y}[}{fraction]
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.
- Original orange juice volume: x
- Original carrot juice volume: y
- New orange juice volume: x+[fraction]{y}{2}}
- New carrot juice volume:\frac{{y}{2}[}{fraction]
- New percentage: x+[fraction]{y}{2}}\frac{x+y[}{fraction]
- Given: x+[fraction]{y}{2}}\frac{x+y[}{fraction]=2 × x [fraction]x+y}
- From Statement (1): x=y−2
- From Statement (2): x=[fraction]{y}{2}[/fraction]
Answer: E - Statements (1) and (2) TOGETHER are NOT sufficient to answer the question, and additional data is needed.
11 Jul 2024, 09:05
Kudos
Bookmarks
percentage of orange juice by volume in the mixture = \(\frac{X}{X+Y}\)
Statement 1
Equations are not needed here.
Since total volume of the mixture is not changing, and adding 2 L of orange juice doubles the percentage, it is clear that orange juice in the original mixture also will be 2L.
However, we don't know the value of Y. Y can be anything. Hence we will not be able to calculate the percentage of range juice by volume in the mixture. Hence not sufficient.
Statement 2
Let us calculate the percentage of range juice by volume in the mixture after the changes in statement 2 are done.
= \(\frac{x+\frac{y}{2}}{x+y}\)
Notice that the total volume (x+y) is not changing and it is also given that this percentage is equal to double that of original mix.
Hence,
\(\frac{x+\frac{y}{2}}{x+y}\) = \(2 * \frac{x}{x+y}\)
\(x+\frac{y}{2} = 2x\)
y = 2x
Substituting value of y as 2x we can calculate percentage of range juice by volume in the original mixture. Hence sufficicent.
Correct asnwer B
Statement 1
Equations are not needed here.
Since total volume of the mixture is not changing, and adding 2 L of orange juice doubles the percentage, it is clear that orange juice in the original mixture also will be 2L.
However, we don't know the value of Y. Y can be anything. Hence we will not be able to calculate the percentage of range juice by volume in the mixture. Hence not sufficient.
Statement 2
Let us calculate the percentage of range juice by volume in the mixture after the changes in statement 2 are done.
= \(\frac{x+\frac{y}{2}}{x+y}\)
Notice that the total volume (x+y) is not changing and it is also given that this percentage is equal to double that of original mix.
Hence,
\(\frac{x+\frac{y}{2}}{x+y}\) = \(2 * \frac{x}{x+y}\)
\(x+\frac{y}{2} = 2x\)
y = 2x
Substituting value of y as 2x we can calculate percentage of range juice by volume in the original mixture. Hence sufficicent.
Correct asnwer B
