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.
Apr 2212:30 AM EDT
-01:30 AM EDT
At one point, she believed GMAT wasn’t for her. After scoring 595, self-doubt crept in and she questioned her potential. But instead of quitting, she made the right strategic changes. The result? A remarkable comeback to 695. Check out how Saakshi did it.
Apr 1612:00 PM EDT
-11:59 PM EDT
You’re first to know: Save $200 on GMAT prep starting tomorrow, 4/13. Get 6 official practice tests and study with real questions. Be ready to save!
Apr 2301:30 AM EDT
-02:30 AM EDT
Struggling with GMAT Verbal as a non-native speaker? Harsh improved his score from 595 to 695 in just 45 days—and scored a 99 %ile in Verbal (V88)! Learn how smart strategy, clarity, and guided prep helped him gain 100 points.
Apr 2308:00 PM PDT
-09:00 PM PDT
Video explanations + diagnosis of 10 weakest areas + 150+ short videos + study plan!
Apr 2610:00 AM EDT
-11:00 AM EDT
The Target Test Prep course represents a quantum leap forward in GMAT preparation, a radical reinterpretation of the way that students should study. Try before you buy with a 5-day, full-access trial of the course for FREE!
Apr 2711:00 AM EDT
-12:00 PM EDT
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
Apr 2808:00 AM PDT
-11:00 AM PDT
Whether you are just beginning your MBA journey or fine-tuning your path to a 700+ score, GMAT Day is designed to give you a competitive edge.
21 Mar 2022, 06:15
Kudos
Bookmarks
A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
66% (03:22) correct
34%
(03:19)
wrong
based on 334
sessions
History
Date
Time
Result
Not Attempted Yet
The ratio of cranberry to apple to orange juice in a certain cocktail containing no other liquids is x: 5: 3. After 6 gallons of water are added to the cocktail, the ratio of orange juice to total liquid becomes 1: 4. After another 24 gallons of water are added to the cocktail, the ratio of apple juice to total liquid becomes 1: 4. What fraction of the original cocktail is cranberry juice?
A. 1/5
B. 1/4
C. 1/3
D. 1/2
E. 2/3
Are You Up For the Challenge: 700 Level Questions
A. 1/5
B. 1/4
C. 1/3
D. 1/2
E. 2/3
Are You Up For the Challenge: 700 Level Questions
General Discussion
21 Mar 2022, 07:55
Kudos
Bookmarks
You could notice here, seeing that the "cocktail" becomes 1/4 orange juice after we dilute it, that the original mixture must be more than 1/4 orange juice. So using the x to 5 to 3 ratio, x must be less than 4. But then the ratio of cranberry to the other things is less than 4 to 8, so the original mix is less than 4/12 = 1/3 cranberry, and the answer can only be A or B. If the answer were B, then x turns out not to be an integer -- not impossible, but not likely -- so you could assume the answer is 1/5, and thus that x = 2, and test it to confirm. It turns out to be right, and we have 30 gallons of mixture, with 6 gallons, 15 gallons and 9 gallons of cranberry, apple, and orange respectively.
There are of course lots of algebraic solutions, but quite a bit faster I think is just to notice it's a weighted average. After we add the first 6 gallons of water, we have a solution that is 25% orange. Then when we add 24 gallons, we get a solution that is 25% apple. But we never change the amount of apple and orange, and we know from the "x to 5 to 3" ratio that the amount of orange is 3/5 the amount of apple. So if this new solution is 25% apple, it must be (3/5)(25%) = 15% orange. So we just have a standard weighted average situation: we start with a 25% orange solution, mix it with a 0% orange solution (pure water), and get a 15% orange solution. Using a number line:
----0----------15------25----
taking the ratio of the distances to the middle, we must be mixing the two parts (25% solution and water) in a 15 to 10 ratio, or a 3 to 2 ratio. Since we used 24 gallons of water, we must have (3/2)(24) = 36 gallons of 25% mixture. So we had 30 gallons to start with (here we need to remember to subtract the 6 gallons we added to the solution at first), and now using the two "1/4" ratios in the problem, we can see we have 9 gallons of orange, and 15 of apple, so the rest, or 6 gallons, is cranberry.
Here I used "alligation" to solve the weighted average part of the problem -- if that method is unfamiliar, the solution might seem a bit mysterious, but there are many places (including my Word Problems book and my problem sets) that explain that approach to weighted average and mixture problems.
There are of course lots of algebraic solutions, but quite a bit faster I think is just to notice it's a weighted average. After we add the first 6 gallons of water, we have a solution that is 25% orange. Then when we add 24 gallons, we get a solution that is 25% apple. But we never change the amount of apple and orange, and we know from the "x to 5 to 3" ratio that the amount of orange is 3/5 the amount of apple. So if this new solution is 25% apple, it must be (3/5)(25%) = 15% orange. So we just have a standard weighted average situation: we start with a 25% orange solution, mix it with a 0% orange solution (pure water), and get a 15% orange solution. Using a number line:
----0----------15------25----
taking the ratio of the distances to the middle, we must be mixing the two parts (25% solution and water) in a 15 to 10 ratio, or a 3 to 2 ratio. Since we used 24 gallons of water, we must have (3/2)(24) = 36 gallons of 25% mixture. So we had 30 gallons to start with (here we need to remember to subtract the 6 gallons we added to the solution at first), and now using the two "1/4" ratios in the problem, we can see we have 9 gallons of orange, and 15 of apple, so the rest, or 6 gallons, is cranberry.
Here I used "alligation" to solve the weighted average part of the problem -- if that method is unfamiliar, the solution might seem a bit mysterious, but there are many places (including my Word Problems book and my problem sets) that explain that approach to weighted average and mixture problems.
