GMAT ratios strategies

GMAT ratios test whether you can scale parts to a total. These strategies cover the core proportion formula, the total-parts method for distributing a known total, the trap of adding ratios directly, and a worked example you can follow step by step.

The core formula

A proportion states that two ratios are equal: $\frac{a}{b} = \frac{c}{d}$ . Cross-multiply to solve: $ad = bc$ . If 3 workers assemble 12 widgets in an hour, how many widgets do 5 workers assemble in the same time? The proportion is $\frac{3}{12} = \frac{5}{x}$ . Cross-multiply: $3x = 60$ , so $x = 20$ . Cross multiplication turns a proportion into a one-step equation.

The total-parts method

When a ratio describes how a total is split, find the total number of parts, then multiply each share by the ratio fraction. A ratio of 2 to 3 means 2 parts to 3 parts, 5 parts total. If the total is 100, each part is 20, so the shares are 40 and 60. The ratio fraction for the first share is $\frac{2}{5}$ and for the second is $\frac{3}{5}$ . Multiplying the total by the fraction gives the share directly. This method avoids the error of adding the ratio numbers to the total instead of treating them as proportions of it.

The most common trap

Adding ratios directly instead of finding the total parts

A mixture has water and juice in a 1 to 4 ratio. The total volume is 30 liters. You add 1 plus 4 to get 5 and then write 30 plus 5 equals 35, or you multiply 30 by 1 and 30 by 4. Both are wrong. The ratio means 1 part water to 4 parts juice, 5 parts total. Each part is 30 divided by 5, which is 6 liters. So water is 6 liters and juice is 24 liters. The answer choices include values derived from adding the ratio to the total because the test writers know this mistake.

Step-by-step strategy

When to use: any question that gives a ratio and asks for a quantity, or that gives quantities and asks for a ratio.

1Write the ratio as a fraction and find the total number of parts by adding the ratio numbers.
2If the total is known, divide it by the total parts to get the value per part, then multiply by each ratio number.
3If the total is unknown, use cross multiplication on the proportion to solve for the missing value.
4Verify the shares sum to the total before selecting an answer.

When not to use: when the question is about rates (work per time) rather than part-to-part or part-to-whole ratios.

Worked example

In a classroom, the ratio of boys to girls is 3 to 5. If there are 6 more girls than boys, how many students are in the class? Step 1: Write the ratio. Boys to girls is 3 to 5. The total parts are $3 + 5 = 8$ . Step 2: Use the difference. The ratio difference between girls and boys is $5 - 3 = 2$ parts. The actual difference is 6 students. So 2 parts equal 6, meaning 1 part equals 3 students. Step 3: Find each count. Boys are 3 parts times 3 students per part, which is 9. Girls are 5 parts times 3 students per part, which is 15. Step 4: Verify. The difference is $15 - 9 = 6$ , which matches. The total is $9 + 15 = 24$ . The answer is 24.

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