5.5 Formulas, Units & Measurement Conversion

The Official Sub-Topic Most Testers Skip

Official Guide Quantitative Review 2026–2027 Math Review lists 3.2.7 Formulas and Measurement Conversion as the closing sub-topic of Algebra, Equalities, and Inequalities. It looks like the least glamorous entry on the outline, and it is the one that most often turns a two-minute item into a four-minute item.

A formula is an algebraic equation whose variables carry specific meanings. To use one, assign quantities to variables so the meanings line up. The official text is blunt about the knowledge bar: you do not need to learn outside formulas such as physics relationships. A GMAT question that needs one will give it to you.

The single most useful rule in this sub-topic is a scoping rule:

Except for units of time, a GMAT question that requires converting one unit of measure to another will give the relationship between those units.

Two consequences follow immediately. First, stop memorizing conversion tables; there is nothing to memorize except time. Second, if a stem hands you "1 mile = 5,280 feet," that line is not decoration — it is a required step you are being told to take.

Time is the exception, so know it cold

Mixed times cause more errors than any conversion factor. 2 hours 20 minutes is 140 minutes, not 150 and not 2.2 hours. Convert the whole quantity to one unit before you multiply by a rate.

The Unit-Factor Method

A supplied relationship is a disguised 1. Since $1{,}000\text{ m} = 1\text{ km}$, the fraction $\dfrac{1{,}000\text{ m}}{1\text{ km}}$ equals 1, and so does its reciprocal. Multiplying by 1 never changes a value — that is the multiplicative identity from Chapter 2 — so you may multiply by whichever orientation cancels the unit you want gone.

Protocol:

1. Write the starting quantity as a fraction with its unit attached.
2. Multiply by supplied relationships, orienting each so the unwanted unit sits opposite where it currently is.
3. Cancel units the way you cancel numbers.
4. Multiply the surviving numbers last.

Worked example (the official pattern). A train travels at a constant 25 meters per second. How many kilometers does it travel in 5 minutes, given that 1 kilometer = 1,000 meters?

$25\ \frac{\text{m}}{\text{s}} \times 60\ \frac{\text{s}}{\text{min}} \times 5\ \text{min} = 7{,}500\ \text{m} = 7.5\ \text{km}$

The seconds cancel against the seconds, the minutes cancel against the minutes, and only then does the 1,000 arrive. Note which relationship came from where: the 60 is time, so you supplied it; the 1,000 was printed in the stem.

Worked example (rate conversion). A car travels 90 kilometers per hour. Express that in meters per second, given 1 kilometer = 1,000 meters.

$90\ \frac{\text{km}}{\text{h}} \times \frac{1{,}000\ \text{m}}{1\ \text{km}} \times \frac{1\ \text{h}}{3{,}600\ \text{s}} = \frac{90{,}000}{3{,}600} = 25\ \frac{\text{m}}{\text{s}}$

The useful shortcut to keep: dividing kilometers per hour by 3.6 gives meters per second, because 1,000/3,600 = 1/3.6.

Compound units square and cube the factor

A length factor does not carry over unchanged to area or volume. If $1\ \text{yd} = 3\ \text{ft}$, then

$1\ \text{yd}^2 = (3\ \text{ft})^2 = 9\ \text{ft}^2 \qquad\text{and}\qquad 1\ \text{yd}^3 = (3\ \text{ft})^3 = 27\ \text{ft}^3$

GMAC builds a distractor from the un-squared factor every time this appears. Converting 45 square feet to square yards divides by 9, not by 3.

Working With a Formula You Have Never Seen

When a stem prints an unfamiliar formula, it is testing substitution and rearrangement, not recall. Three moves cover the item type.

1. Substitute directly. Match each given quantity to its named variable, then evaluate. If a stem defines $F = ma$ and says a 2-kilogram mass accelerates at 5 meters per second squared, then $F = 2 \times 5 = 10$. No physics is required, and none is being tested.

2. Solve the formula for the variable the question asks about. If a question gives $C = \frac{5}{9}(F - 32)$ and asks for $F$, isolate it once rather than guessing and checking:

$\frac{9}{5}C = F - 32 \quad\Longrightarrow\quad F = \frac{9}{5}C + 32$

3. Set two expressions of the same quantity equal. Formula items often ask when one reading equals, doubles, or falls below another. Translate the sentence into an equation in one variable and solve.

Worked example. Using $F = \frac{9}{5}C + 32$, at what Celsius reading is the Fahrenheit value exactly 40 more than the Celsius value? Set $F = C + 40$:

$C + 40 = \frac{9}{5}C + 32 \quad\Longrightarrow\quad 8 = \frac{4}{5}C \quad\Longrightarrow\quad C = 10$

Check: $F = \frac{9}{5}(10) + 32 = 50$, and $50 - 10 = 40$.

Formulas already on your Quant map

The official Reference Sheet groups a small set of relationships you should recognize on sight, all of which are just formulas with named variables:

Each of these gets a full treatment elsewhere in this guide. The point here is structural: they behave exactly like the unfamiliar formula in the stem. Assign the variables, watch the units, and solve for what was asked rather than for what was easiest to find.

The Three Errors That Cost the Most Time

1. Answering in the wrong unit. The arithmetic is right and the answer is wrong because the stem asked for kilometers and you stopped at meters. Circle the requested unit before you compute.
2. Converting a mixed time incorrectly. 1 hour 45 minutes is 105 minutes or 1.75 hours — never 1.45.
3. Applying a length factor to an area or a volume. Square the factor for area and cube it for volume.

A fourth habit is worth adding: convert once, at the start. Testers who carry three units through a five-step chain lose the thread. Pick the unit the answer choices use, convert everything into it immediately, and keep the rest of the work unit-free.