QUANTITATIVE REASONING · GMAT-Q-RR-01

Ratios, Proportions & Unit Rates

Learn the reasoning, choose a fast method, then demonstrate mastery with a separate set of assessment questions.

Original GMAT-style pilot content · Unofficial and not calibrated to GMAC scoring

Understand → Recognise → Solve efficiently

Start by deciding whether the problem describes a part-to-part ratio, a rate per unit, or two agents working together. Avoid unnecessary algebra by using a common multiplier.

Core idea · Ratios represent parts

A:B=3:5\quad\Longrightarrow\quad A=3k,\ B=5k

Worked example · Split a known total

Question: The ratio of junior to senior staff is 3:5. If the company has 96 staff members, how many are junior and how many are senior?

3k+5k=96\Longrightarrow k=12\Longrightarrow A=36,\ B=60

Worked example · Translate units before solving

Question: A vehicle covers 180 kilometers in three hours at constant speed. Find its speed in kilometers per hour.

\frac{180\ \mathrm{km}}{3\ \mathrm{h}}=60\ \mathrm{km/h}

Work-rate questions · Add rates, not times

\frac1{T}=\frac1{a}+\frac1{b}

GMAT shortcut · Choose an efficient multiplier

\frac{A}{B}=\frac{4}{7}\Longrightarrow A=4k,\ B=7k

Part-to-part versus part-to-whole

\frac{A}{A+B}=\frac{3}{8}\quad\text{when}\quad A:B=3:5

Unknown multiplier in a three-part ratio

A:B:C=2:3:5\Rightarrow(A,B,C)=(2k,3k,5k)

Align the common term before combining ratios

A:B=3:2,\quad A:C=5:4\Rightarrow A:B:C=15:10:12

A ratio fixes relative values, not actual quantities

A:B=4:7\Rightarrow A=4k,\ B=7k\quad(k>0)

GMAT First Move

Translate the relationship: are you comparing parts, totals, speeds, or rates of work?

Faster Method

For a ratio a:b, write ak and bk. For combined work, add fractions of a task completed per hour.

Common Traps

Treating 3:5 as 3 out of 5 rather than 3 out of 8 total parts.
Adding work completion times rather than rates.
Mixing hours and minutes in a unit-rate question.
Changing both sides of a ratio when only one amount changes.