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GMAT overview

Worked example

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Dilution Mixtures

A public mixture question that shows how to track the unchanged amount of solute with a proportion when a solution is diluted.

Question

A lab technician has 3030 liters of a 20%20\% saline solution. How many liters of pure water must be added to dilute it to a 12%12\% saline solution?

  1. a.88 liters
  2. b.1818 liters
  3. c.2020 liters
  4. d.5050 liters

Correct answer

C. 2020 liters

Full reasoning

  1. 1Adding pure water leaves the salt unchanged: the solution contains 0.20×30=60.20 \times 30 = 6 liters of salt throughout.
  2. 2Let ww be the liters of water added and set up the proportion for the target concentration: 630+w=12100\dfrac{6}{30 + w} = \dfrac{12}{100}.
  3. 3Solve: 30+w=6÷0.12=5030 + w = 6 \div 0.12 = 50, so w=50−30=20w = 50 - 30 = 20 liters.
  4. 4Check: 66 liters of salt in 5050 liters of solution is 650=12%\tfrac{6}{50} = 12\%, as required.

Why each choice is right or wrong

Choice A

This subtracts the percentage points, 20−1220 - 12, and reads the difference as a volume, but percentage points are not liters.

Choice B

This scales the starting volume by 1220\tfrac{12}{20}, shrinking the batch instead of finding the extra water that grows the total to 5050 liters.

Choice C

Correct. The salt stays at 0.20×30=60.20 \times 30 = 6 liters, so 630+w=0.12\tfrac{6}{30 + w} = 0.12 gives 30+w=5030 + w = 50 and w=20w = 20 liters of added water.

Choice D

This solves 6÷0.12=506 \div 0.12 = 50 correctly but reports the new total volume instead of subtracting the original 3030 liters.

Related formula

Dilution proportion with fixed solute

c0V0V0+w=ctarget\frac{c_0 V_0}{V_0 + w} = c_{\text{target}}

Assumptions: Only pure solvent is added, so the amount of solute never changes. Volumes are additive when the solvent is mixed in.

Related topic and practice

Rates, Work, and MixturesCombined Work RatesSuccessive percentage changesCreate a free account to practice

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Sources

Authored for this public explainer registry. It has no database question ID and is not copied from a protected or official exam bank.

  1. Prealgebra 2e, Section 6.5: Solve Proportions and Their Applications — OpenStax. Accessed 2026-07-11. OpenStax textbook content is CC BY 4.0; attribute and avoid verbatim reuse beyond short cited references.
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Sources and corrections

Sources last checked 2026-08-07

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