Abhyank Srinet 
Table of Contents
- Introduction
- Where Do Mixture Problems Fit in the Current GMAT?
- What Are GMAT Mixtures and Alligations?
- Which Formulas Are Used for GMAT Mixtures and Alligations?
- How Does the Alligation Method Work on GMAT Questions?
- When Should You Use Alligation Instead of Algebra?
- What Types of GMAT Mixture Problems Should You Practise?
- How Do You Solve GMAT Mixture Questions Step by Step?
- What Are the Most Common Mistakes in GMAT Alligation Questions?
- How Should Indian Applicants Prepare for GMAT Mixture Problems?
- Where Can You Practise Official GMAT Mixture Skills?
- Related Blogs
GMAT mixtures and alligations are arithmetic word problems that use ratios, percentages, weighted averages and conservation of quantity. For two source values, alligation gives the weaker-to-stronger quantity ratio as (stronger − target):(target − weaker). GMAC does not publish a fixed number of mixture questions, so Indian applicants should learn both alligation and algebra, then practise the concept in official Quantitative Reasoning sets.
Introduction
GMAT mixtures and alligations test whether you can combine quantities with different concentrations, prices or average values. The mathematics is based on ratios, percentages and weighted averages. Alligation is not a separate official GMAT question type; it is a preparation shortcut that can turn a two-component weighted-average problem into a ratio calculation.
The current GMAT Quantitative Reasoning section contains 21 Problem Solving questions completed in 45 minutes without a calculator. In this blog, we explain the correct formulas, show when the alligation method for GMAT questions works, solve common problem types and identify the mistakes that lead to reversed ratios.
Where Do Mixture Problems Fit in the Current GMAT?
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Mixture problems fit within the arithmetic and algebra tested through Quantitative Reasoning Problem Solving questions. The official GMAT exam content states that Quantitative Reasoning measures foundational arithmetic and algebra. GMAC does not promise a fixed number of GMAT mixtures and alligations questions in any test.
The table below places this topic within the current exam without using outdated section labels.
| Exam detail | Current official format | Relevance to mixture problems |
|---|---|---|
| Quantitative Reasoning | 21 Problem Solving questions in 45 minutes | Mixture questions may test arithmetic, algebra, ratios, percentages and weighted averages. |
| Calculator | Not available in Quantitative Reasoning | Use clean equations, fraction simplification and mental arithmetic. |
| Data Sufficiency | Part of Data Insights, not Quantitative Reasoning | A mixture-style situation may appear in a reasoning context, but pure calculation is not the main task. |
| Official source | GMAT exam structure | Use the official structure when planning timed practice. |
What Are GMAT Mixtures and Alligations?
GMAT mixture problems ask you to track how much of a value or active component exists before and after quantities are combined, removed or replaced. The tracked value may be salt concentration, alcohol percentage, price per kilogram, average score or another quantity that combines linearly.
Alligation works in the reverse direction of a weighted average. A weighted-average question gives the quantities and asks for the final value. An alligation question gives two source values and the target value, then asks for the ratio of the two quantities.
The distinction becomes clearer in the following comparison.
| Concept | What is given? | What is usually required? |
|---|---|---|
| Mixture or weighted average | Source values and quantities | Final concentration, cost or average |
| Alligation | Lower value, higher value and target value | Quantity ratio of the two sources |
| Replacement | Initial mixture, amount removed and replacement amount | Amount or concentration remaining |
Which Formulas Are Used for GMAT Mixtures and Alligations?
The main formula is conservation of the tracked component: the amount contributed by each source equals the amount in the final mixture. Weighted average, alligation and replacement formulas are different ways of applying that principle.
The following formula table covers the methods needed for the main GMAT mixture problems.
| Method | Formula | Best use |
|---|---|---|
| Conservation equation | q1v1 + q2v2 = (q1 + q2)vt | Any two-component concentration, price or average problem |
| Weighted average | vt = (q1v1 + q2v2) ÷ (q1 + q2) | Finding the final value when quantities are known |
| Alligation | quantity at lower value : quantity at higher value = (higher − target):(target − lower) | Finding the ratio of two quantities when the target is known |
| Repeated replacement | An = A0(1 − r/V)n | Tracking a substance after equal removal-and-replacement cycles |
In these formulas, q represents quantity, v represents concentration, price or average value, A0 is the initial amount of the tracked substance, r is the amount replaced, V is total volume and n is the number of identical replacement cycles. The same conservation equation also covers GMAT weighted average problems involving scores, prices or rates.
How Does the Alligation Method Work on GMAT Questions?
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The alligation method works by assigning each source the opposite difference between its value and the target. The cross-differences produce the quantity ratio, not the concentration ratio.
Use the following sequence when a GMAT mixtures and alligations question gives two source values and asks for a mixing ratio.
- Write the lower source value and the higher source value.
- Place the required target value between them.
- Subtract the target from the higher value.
- Subtract the lower value from the target.
- Assign the differences across the target and simplify the ratio.
- Verify the ratio with the weighted-average formula.
Two-Solution Alligation Example
A 20% solution and a 50% solution must be mixed in a 2:1 ratio to produce a 30% solution. Apply the cross-difference rule:
quantity of 20% solution : quantity of 50% solution = (50 − 30):(30 − 20) = 20:10 = 2:1
Verify the answer: [(2 × 20) + (1 × 50)] ÷ 3 = 30. This check exposes the most common error in GMAT alligation questions: reversing the ratio.
MiM-Essay Expert Rule: “If the target does not lie between the two source values, standard two-component alligation cannot produce a valid positive mixing ratio.”
When Should You Use Alligation Instead of Algebra?
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Use alligation when there are exactly two source values, one target weighted average and a ratio to find; use algebra when the quantities, additions or constraints are more complex. Alligation is a shortcut, while the conservation equation is the general method.
The comparison below helps you choose a method before calculating.
| Question setup | Recommended method | Reason |
|---|---|---|
| Two values, target value, ratio required | Alligation | Cross-differences give the ratio directly. |
| Two values and both quantities are known | Weighted average | The final value follows directly from total contribution divided by total quantity. |
| One ingredient is added to or removed from an existing mixture | Conservation equation | The unchanged component provides the simplest equation. |
| Repeated equal replacement | Replacement formula | The same remaining fraction is applied after every cycle. |
| Three or more unknown quantities | Algebra with all stated constraints | A unique ratio may not exist without additional information. |
What Types of GMAT Mixture Problems Should You Practise?
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You should practise concentration, price-blend, replacement and multi-component problems because each tests the same conservation idea through a different setup. Learning the setup is more useful than memorising separate tricks for every story.
Common GMAT Mixture Problem Categories
GMAT mixture problems commonly involve combining two concentrations, calculating weighted averages, blending products with different prices, adding or removing an ingredient, and repeated replacement. Applicants should practise each category because the same conservation principle may be presented through different real-world situations, units and question formats.
Two-Component Concentration Problems
These GMAT mixture problems combine liquids or materials with different percentages. The question may ask for the final concentration, a missing quantity or the ratio needed to reach a target concentration.
Cost and Price Blend Problems
Price-blend questions combine products with different costs per unit. Treat price per kilogram or litre like concentration and use a weighted average. If two source prices and a target price are given, the alligation method for GMAT questions can produce the required quantity ratio.
Replacement and Dilution Problems
Replacement questions remove part of a uniform mixture and add another substance. The removed portion contains each component in the same proportion as the mixture immediately before removal. Track the component that is not being added back.
Three-or-More Component Problems
When three or more unknown quantities are mixed, one target-average equation may not determine a unique ratio. Use every additional condition in the question. Do not force the two-source alligation formula onto an underdetermined setup.
How Do You Solve GMAT Mixture Questions Step by Step?
Solve each question by identifying the tracked value, writing total contribution before and after the change, choosing the shortest valid method and checking whether the result is reasonable. The following worked examples cover the highest-value variations.
Weighted-Average Concentration Example
Mixing 12 litres of a 20% solution with 18 litres of a 50% solution produces a 38% solution.
The first solution contributes 12 × 0.20 = 2.4 litres of the active component. The second contributes 18 × 0.50 = 9 litres. The combined amount is 11.4 litres in a total volume of 30 litres.
Final concentration = 11.4 ÷ 30 = 0.38 = 38%
Target-Ratio Alligation Example
A 25% solution and a 70% solution must be mixed in a 2:1 ratio to create a 40% solution.
quantity of 25% solution : quantity of 70% solution = (70 − 40):(40 − 25) = 30:15 = 2:1
Verification gives [(2 × 25) + (1 × 70)] ÷ 3 = 40.
Price-Blend Example
Tea priced at ₹400 per kilogram and ₹700 per kilogram must be mixed in a 2:1 ratio to create a blend worth ₹500 per kilogram.
quantity at ₹400 : quantity at ₹700 = (700 − 500):(500 − 400) = 200:100 = 2:1
The weighted price is [(2 × ₹400) + (1 × ₹700)] ÷ 3 = ₹500 per kilogram.
Single-Replacement Example
A 60-litre mixture that is 40% acid becomes 30% acid after 15 litres are removed and replaced with water.
The initial acid amount is 60 × 0.40 = 24 litres. Removing 15 litres, or one-fourth of the uniform mixture, removes one-fourth of the acid: 24 × 1/4 = 6 litres. The mixture retains 18 litres of acid. After water restores the total volume to 60 litres, the concentration is 18 ÷ 60 = 30%.
What Are the Most Common Mistakes in GMAT Alligation Questions?
The most common errors are reversing the cross-difference ratio, using a target outside the source range and applying alligation when more information is required. These mistakes can produce an answer that looks tidy but fails a weighted-average check.
Use this checklist while reviewing GMAT mixtures and alligations practice sets.
- Reversed ratio: The difference from the higher value belongs to the lower-value quantity, and the difference from the lower value belongs to the higher-value quantity.
- Impossible target: A positive mixture of two sources must have a target between their values.
- Wrong denominator: Concentration equals active amount divided by total mixture amount.
- Unequal units: Convert litres, millilitres, kilograms or prices to consistent units before calculating.
- Unmixed replacement assumption: Removal formulas assume the mixture is uniform before each removal.
- Unverified shortcut: Substitute the final ratio into the weighted-average formula before accepting it.
How Should Indian Applicants Prepare for GMAT Mixture Problems?
Indian applicants should treat mixtures as a short arithmetic subtopic, connect it with ratios and percentages, and practise without a calculator. Candidates familiar with CAT-style alligation should still adapt to the current GMAT format, which rewards clear reasoning through Problem Solving rather than a separate “mixtures and alligations” question category.
A focused preparation sequence is more useful than a large collection of shortcuts.
- Revise fractions, percentages, ratios and weighted averages first.
- Learn the conservation equation before using the alligation shortcut.
- Solve untimed examples until you stop reversing the ratio.
- Move to short mixed Quant sets instead of practising only one topic for long periods.
- Record setup errors, unit errors and calculation errors separately in an error log.
- Confirm your method through official practice rather than relying only on coaching shortcuts.
For a wider topic sequence, use the MiM-Essay guide to the GMAT Quantitative Reasoning section.
Where Can You Practise Official GMAT Mixture Skills?
Use official GMAT questions to practise the arithmetic, algebra and reasoning behind mixture problems, even when the platform does not label every question by the word “mixture.” The GMAT Official Starter Kit includes official questions and Practice Exams 1 and 2.
Begin with topic practice to learn the setup, then use timed mixed sets to test whether you can recognise the method without being told which formula to apply. Review every incorrect answer and any correct answer that took too long.
Related Blogs
Use these MiM-Essay guides to connect GMAT mixtures and alligations with the wider Quant syllabus and a structured study plan.
Conclusion
GMAT mixtures and alligations become easier when you focus on conservation, choose the method that fits the setup and verify every shortcut with a weighted average. Build accuracy first, then apply the same reasoning in timed mixed practice.
