Is alligation a real GMAT topic?

The GMAT doesn't officially label a topic 'alligation' — mba.com's exam-content page describes Quantitative Reasoning as testing general arithmetic and algebra without itemizing named subtopics. What test-prep resources call alligation is simply a mixture/weighted-average problem where the weights are volumes and the averages are concentration percentages, and the see-saw method solves it the same way.

Does the GMAT Quant section include Data Sufficiency questions on weighted averages?

No. The GMAT Focus Edition's Quantitative Reasoning section is 21 Problem Solving questions only, per mba.com. Data Sufficiency questions still exist on the exam, but they're part of the separate Data Insights section, not Quant.

Can I use a calculator for GMAT weighted average problems?

No. mba.com states plainly that no calculator is permitted during the Quantitative Reasoning section, which is why the see-saw method's ratio shortcut is worth practicing — it's usually faster by hand than setting up and solving the full weighted-sum equation.

What formula do I use for three or more groups?

Use the direct weighted-sum equation, sum of (group size × group average) divided by total size — the see-saw ratio shortcut only works cleanly for two groups. You can chain two see-saw steps for three groups, but the direct sum is faster and less error-prone.

How many weighted-average or mixture questions appear on a real GMAT?

GMAC hasn't published an official per-topic question count or percentage breakdown for the Quantitative Reasoning section. mba.com groups these under general arithmetic and algebra content without a stated frequency, so treat weighted-average and mixture problems as a recurring category within the 21-question Quant section rather than expecting an exact number.

GMAT Weighted Average Problems: The See-Saw Method

A weighted average combines two or more groups of different sizes, each with its own average, into one overall average — and you cannot just average the group averages together. For exactly two groups, the fastest tool is the see-saw method: picture the two group averages as weights sitting on a balance beam, with the overall average as the fulcrum. The beam balances when each weight's distance from the fulcrum, multiplied by its size, equals the other side's — so the overall average always sits closer to whichever group has more members. Past two groups, the see-saw shortcut breaks and you need the direct weighted-sum formula instead. Both are covered below with fully worked examples.

Situation	Method	Formula
Exactly 2 groups, one static blend	See-saw (balance) method	$n_{1} (\overset{a}{ˉ} - a_{1}) = n_{2} (a_{2} - \overset{a}{ˉ})$
3 or more groups	Weighted-sum formula	$\overset{a}{ˉ} = \frac{\sum _{i} n _{i} a _{i}}{\sum _{i} n _{i}}$
Multi-round removal-and-replacement	Repeated-dilution formula	$(1 - \frac{r}{V})^{n}$

Why Doesn't a Simple Average Work?

Because a simple average treats every group as equally important, regardless of size. The correct formula weights each group's average by its size:

$\overset{a}{ˉ} = \frac{n _{1} a _{1} + n _{2} a _{2}}{n _{1} + n _{2}}$

Example: A class has two sections. Section 1 has 12 students who averaged 78 on the midterm; Section 2 has 18 students who averaged 92. The simple average of 78 and 92 is 85 — but that's wrong, because Section 2 has 50% more students and should pull the overall average closer to its own number.

The correct weighted average:

$\overset{a}{ˉ} = \frac{( 12 ) ( 78 ) + ( 18 ) ( 92 )}{12 + 18} = \frac{936 + 1656}{30} = \frac{2592}{30} = 86.4$

86.4, not 85 — the extra six students in the higher-scoring section pull the true average up past the midpoint.

How Does the See-Saw Method Work for Two Groups?

The see-saw method skips the full sum and finds the answer from ratios alone. The balance condition is:

$n_{1} (\overset{a}{ˉ} - a_{1}) = n_{2} (a_{2} - \overset{a}{ˉ})$

In words: (size of group 1) × (its distance below the overall average) equals (size of group 2) × (its distance above the overall average) — exactly like a physical see-saw balancing around its fulcrum. Rearranged, the ratio of the two group sizes equals the inverse ratio of their distances from the overall average:

$\frac{n _{1}}{n _{2}} = \frac{a _{2} - a ˉ}{a ˉ - a _{1}}$

Checking it against the class example above: the overall average (86.4) sits 8.4 points above Section 1's average (78) and 5.6 points below Section 2's average (92). The ratio of those distances is $5.6 : 8.4 = 2 : 3$ — which matches the ratio of the group sizes, $12 : 18 = 2 : 3$ , exactly. The larger group (18 students) sits closer to the overall average (5.6 away) than the smaller group (8.4 away). That's the core intuition GMAT weighted-average questions test: the overall average is always pulled toward the group with more weight, not toward the middle.

This is fastest when the GMAT gives you the two group averages and their ratio (or asks you to find the ratio), rather than raw counts — you can solve directly from the distances without ever computing a sum.

How Do You Apply the See-Saw Method to Mixture Problems?

Mixture (alligation-style) problems are weighted averages in disguise: the "weight" is volume, and the "average" is a concentration percentage.

Example: Mixture A is 20% alcohol. Mixture B is 50% alcohol. They're combined into 15 gallons of a mixture that's 30% alcohol. How many gallons of Mixture A are in it?

See-saw setup: the overall concentration (30%) sits 10 points above A's 20% and 20 points below B's 50%. By the inverse-distance rule, the volume ratio is:

$\frac{V _{A}}{V _{B}} = \frac{50 - 30}{30 - 20} = \frac{20}{10} = \frac{2}{1}$

So the mixture is $\frac{2}{3}$ Mixture A and $\frac{1}{3}$ Mixture B. With 15 gallons total: $V_{A} = \frac{2}{3} (15) = 10$ gallons, $V_{B} = \frac{1}{3} (15) = 5$ gallons.

Check: $(0.20) (10) + (0.50) (5) = 2 + 2.5 = 4.5$ , and $0.30 \times 15 = 4.5$ . It balances.

The trap here: it's easy to flip the ratio and assign the larger share to the mixture that's farther from the target concentration. Anchor on the balance-beam picture — the group closer to the target average is always the heavier one.

What About Removal-and-Replacement Mixture Problems?

This is where students misapply the see-saw method. Removal-and-replacement problems — remove some volume, replace it with a different substance, repeat — are not a single static blend of two groups, so the linear distance-ratio shortcut does not apply. You need the repeated-dilution formula instead:

$remaining fraction of original substance = (1 - \frac{r}{V})^{n}$

where $V$ is the total volume, $r$ is the amount removed and replaced each time, and $n$ is the number of times the process repeats.

Example: A 10-liter container is full of pure antifreeze. You remove 2 liters and replace it with water, then repeat the same step once more. What fraction of the final 10-liter mixture is antifreeze?

$(1 - \frac{2}{10})^{2} = (0.8)^{2} = 0.64$

64% antifreeze remains — 6.4 liters of the final 10-liter mixture. Each removal takes away 20% of whatever mixture is currently in the container (not 20% of the original pure antifreeze), which is why the fractions multiply rather than subtract in a straight line. Trying to force this into the two-group balance-beam setup (treating it as one blend of "20% removed, 80% kept") gives the right answer for a single removal but silently breaks the moment there's a second round, because the second 2 liters removed is no longer pure antifreeze.

When Does the See-Saw Method Break Down?

Past two distinct groups, there's no single clean ratio to balance, so drop the shortcut and use the full weighted-sum formula:

$\overset{a}{ˉ} = \frac{\sum _{i} n _{i} a _{i}}{\sum _{i} n _{i}}$

Example: A GMAT prep class has three sections: 10 students averaged 80, 15 students averaged 90, and 5 students averaged 70. The overall average:

$\overset{a}{ˉ} = \frac{( 10 ) ( 80 ) + ( 15 ) ( 90 ) + ( 5 ) ( 70 )}{10 + 15 + 5} = \frac{800 + 1350 + 350}{30} = \frac{2500}{30} = 83. \overline{3}$

You can chain two see-saw operations — combine groups 1 and 2 into one intermediate group, then balance that against group 3 — but it takes two setup steps and two chances to make an arithmetic error, versus one direct sum. Default to the sum formula whenever a question names three or more groups.

What Common Mistakes Trip Students Up on These Questions?

Computing a simple average instead of a weighted one. Before averaging anything, check whether the GMAT has told you the size of each group. If group sizes differ and the question wants one combined figure, a simple average is wrong by construction.
Reversing the see-saw ratio. The larger group sits closer to the overall average, not farther. If your answer puts the bigger group farther from the combined average than the smaller group, you've inverted the ratio — flip it.
Applying the two-group balance to a multi-round removal/replacement problem. The linear see-saw ratio only holds for one static blend. Once a process repeats (remove, replace, remove again), switch to the $(1 - r / V)^{n}$ formula.
Skipping the sanity-check range. A weighted average must always fall between the smallest and largest individual group average — never below the minimum or above the maximum. In the three-section example above, 83.3 falls between 70 and 90, confirming no arithmetic slip. If your answer falls outside that range, you've made an error before you even check your work.
Treating a part-to-part ratio as a part-to-total value. A volume ratio of $2 : 1$ means $\frac{2}{3}$ and $\frac{1}{3}$ of the total, not "2 gallons and 1 gallon" unless the total happens to be 3. Re-normalize the ratio against the actual total the question gives you.

Where Do Weighted Averages Fit on the Real GMAT?

The GMAT Focus Edition's Quantitative Reasoning section is 21 Problem Solving questions in 45 minutes, with no calculator allowed — Data Sufficiency questions are no longer part of Quant; they now sit in the separate Data Insights section. mba.com's own content description covers "algebraic and arithmetic foundational knowledge" without publishing a topic-by-topic breakdown or question count, so there's no official figure for exactly how many weighted-average or mixture questions to expect on a given exam. Treat them as a recurring category within that 21-question set worth being fast at, rather than counting on a specific number showing up. TestPrepOS's adaptive GMAT Quant practice drills weighted-average and mixture problems specifically, with step-by-step explanations that flag which of the mistakes above caused a wrong answer.

Take a free diagnostic to see whether weighted averages are currently a strength or a gap in your Quant score before you build a study plan around a guess.