Questions on Mixtures and Alligation are found fairly frequently in the Quant section of the GMAT. Mixtures questions are applications of the concept of weighted average.
Weighted average itself is based on the concept of ratios. As such, it's very natural to see a lot of test takers using the concept of ratios by forming equations to solve Mixtures questions. Well, the method works undoubtedly. But, if you have more than one unknown in a particular question, this method becomes very cumbersome and time consuming.
So, what is tested on mixtures questions? At a very fundamental level, your knowledge of ratios is tested. As such, you will have to be strong with your ratio concepts and interpretation of the type of language that is used in Ratio questions. Your knowledge of the concept of averages is also tested.
When two items are mixed with each other, they are mixed based on their qualities. Examples for qualities could be the concentration of a particular liquid OR the price OR the percentage of a particular alloy and so on. The final quality of the resultant mixture will be the weighted average of the qualities of the two items being mixed.
This is where one VERY IMPORTANT property of 'Average' needs to be remembered. The value of any average will always lie in between the highest and the lowest values. Therefore, the average quality of a mixture will always lie in between the best and the worst qualities i.e. it will be better than the worst but will be worse than the best. This is the principle which forms the basis for the alligation diagram.
Using the Alligation diagram is THE MOST efficient method to solve questions on mixtures. The Alligation diagram is essentially a re-organization of the weighted average equation. But, it's much faster and easier than using the equation itself. What's more, it can be used to solve questions from a variety of topics ranging from weighted averages to interest.
Here's an image showing the standard form of an Alligation diagram.
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Alligation Diagram.jpg [ 39.58 KiB | Viewed 4455 times ]
You will have to follow the diagram to the T, if you don't want to get confused. Follow the arrows and frame an equation with the 5 terms involved in the diagram. To make life easier for you, we have shown the equation in the box beside the diagram, to give you an idea of the flow of information through the arrows.
Of the 5 terms in the alligation diagram, one will be the unknown term. Having an independent equation with an unknown will help you solve for the unknown. In some cases, there may be a question with two unknowns and more often that not, the question will ask you to find out the ratio of these two unknowns. The ratio can be obtained from the diagram as well.
The best way to achieve proficiency in using the alligation diagram is to solve 8 to 10 direct questions on Mixtures by this method. Once you know how to comprehend the different pieces of information given, you will become adept at applying the alligation diagram in questions where the qualities may be given as fractions or ratios. The moment you are able to do this, you may rest assured that you have added a potent tool to your arsenal of problem solving techniques for GMAT Quant.
Here's a free resource for all of y'all - a video recording of one of our most recent webinars on Mixtures and Alligation.
https://youtu.be/UyXokETXnXUGo ahead and watch the video to gain useful insights about how to deal with Mixtures questions. Here's a question for you apply what you learned in the video.
https://gmatclub.com/forum/ben-combines ... 20815.htmlHappy Learning!