How to Translate Word Problems in GMAT Quant
The GMAT uses words to hide math. Every unknown, every relationship, every comparison has a precise mathematical equivalent. Getting the translation right is where most marks are won or lost.
The Step Most Students Rush Past
The algebra in GMAT Quant problems is almost never the hard part. Two or three steps of manipulation, a substitution, and you have the answer. What kills scores is arriving at that algebra with the wrong equation, built from a misread sentence.
Translation is the conversion of English into mathematics. Every word problem follows the same structure: a set of unknowns, a set of relationships between them, and a question about those unknowns. Your job, before touching any calculation, is to write those relationships as clean mathematical expressions.
This is a learnable, systematic skill. The GMAT uses a limited set of English patterns, each with a consistent mathematical equivalent. Once you know the dictionary, most word problems become mechanical.
The Complete Keyword Dictionary
Every operation and relationship has a set of English phrases that reliably signal it. Learn these and you can parse most sentences on autopilot.
 GMAT Panda | ||
|---|---|---|
| Symbol | Keywords to look for | Quick example |
| = | is, was, are, were, would be, equals, equates to, represents | "The total was 100" → Total = 100 |
| + | total, together, combined, sum of, more than, older than, higher than, increased by, added to, in addition to | "Tom is 10 years older than Jerry" → T = J + 10 |
| − | less than, lower than, younger than, difference, gap, leftover, discount, shortfall, decreased by, reduced by, excess | "X is 5 less than Y" → X = Y − 5 |
| × | of, per, each, product of, times, twice, double, triple, multiplied by, at a rate of | "5 dollars per ticket, t tickets" → 5 × t |
| X/Y | ratio of X to Y “to” becomes the fraction bar; denominator always follows “to” | "ratio of oranges to apples is 3 to 2" → O/A = 3/2 |
| < > | less than, greater than, strictly less/greater than, below, above, under, over (boundary excluded) | "x is less than 5" → x < 5 |
| ≤ ≥ | at most, at least, maximum, minimum, no more than, no less than, cannot exceed, up to (boundary included) | "at most 5" → x ≤ 5 (5 is allowed) |
| P/100 × X | percent of, % of “of” → multiply percent → divide by 100 first “of what?” → identifies X | "30% of X" → 0.30 × X |
| nY vs (n+1)Y | n times as many as Y → nY n times more than Y → (n+1)Y n times less than Y → Y/n | "3 times more than Y" → 4Y (not 3Y); "3 times as many as Y" → 3Y |
Two words to watch above all others: “of” (almost always multiplication) and “to” in a ratio statement (always the fraction bar).
Percentages, Fractions, and the Word “Of”
In almost every percentage and fraction statement, “of” signals multiplication. The question “of what?” tells you what to multiply by.
Divide by 100, then multiply by X.
The fraction multiplies the quantity after 'of'.
'More than' keeps the original and adds the percentage.
'Less than' keeps the original and subtracts.
Each percentage applies to the new amount, not the original X.
Share ÷ Base. Multiply by 100 for the percent value.
Sequential changes use the updated base. “X was increased by 20%, then by 15%” is X × 1.20 × 1.15, not X × 1.35. The 15% applies to the already-increased amount.
Ratios and the Word “To”
In a ratio statement, “to” works exactly like “of” in percentages: it signals a specific operation. The word “to” becomes the fraction bar. Whatever comes before “to” is the numerator; whatever comes after is the denominator.
'To' is the fraction bar. Oranges before 'to' → numerator.
Adjust each side before setting 'to' as the fraction bar.
Each 'to' creates its own fraction bar independently.
The two ratios are inverses of each other — handle the 'to' in each separately.
Key Formulas to Know Cold
Several word problem types rely on a standard formula. If you derive these under time pressure you lose time and introduce errors. Know them before you sit down.
Profit
Profit margin = Profit ÷ Revenue (not ÷ Cost — a common reversal).
Revenue / Cost per Item
Cost = Unit Cost × Quantity. Unit price is per item, not the total.
Distance
Rearranges to Rate = Distance ÷ Time, or Time = Distance ÷ Rate.
Taxes and Gratuities
A 15% tip on $40 → 40 × 1.15 = $46. A 20% tax on $200 → 200 × 1.20 = $240.
Average
Rearranges to Sum = Average × Count, which is often the more useful form.
Fixed + Variable Cost
Common in pricing: a flat fee plus a per-unit charge.
Translation In Action
Here is what it looks like to apply the keyword dictionary on a real question. Five different translation rules appear in the same problem.
On a certain day, a bakery produced a batch of rolls at a total production cost of $300. On that day, 4/5 of the rolls in the batch were sold, each at a price that was 50 percent greater than the average production cost per roll. The remaining rolls in the batch were sold the next day, each at a price that was 20 percent less than the price of the day before. What was the bakery’s profit on this batch of rolls?
“total production cost of $300” — name the unknowns before writing anything else
c = cost per roll → c = 300 ÷ N
“4/5 of the rolls” — the fraction multiplies the total; the rest is the complement
Day 2 rolls sold: (1/5) × N
“50 percent greater than c” and “20 percent less than the day before” — each applies to the updated amount
Day 2 price: (c × 1.50) × 0.80 = c × 1.20
Substitute c = 300/N — the N cancels, so the total number of rolls never needs to be known
Day 2: (1/5)N × 1.20 × (300/N) = 72
Typical Mistakes GMAT Takers Make
These five errors account for a large share of translation losses. Each one looks innocent under time pressure, which is why it costs marks.
Naming Variables Inefficiently
Using X, Y, or a single letter for two different quantities creates confusion at every step. Name variables to match what they represent, preferably using the letter or word the question itself provides.
Confusing 'Times More Than' with 'Times As Many As'
“3 times as many as Y” is 3Y. “3 times more than Y” keeps the original Y and adds 3Y on top, giving 4Y. “Times less” means divide, not subtract.
Using the Wrong Inequality Symbol
One word separates < from ≤. “Less than 5” excludes 5; “at most 5” includes it. The boundary keywords (at most, at least, cannot exceed, no more than) all allow the boundary value.
Writing a Ratio in the Wrong Order
“Ratio of X to Y” = X/Y. The denominator always follows the word “to”. Reversing the words reverses the fraction, giving the reciprocal of the intended relationship.
Confusing Share, Percentage, and Base
When a question gives a part and a whole and asks for the percentage, the formula is: Percentage = Share ÷ Base. Share is the part; Base is the total. Flipping the fraction gives the reciprocal, which is almost always far above 100%.
The phrase “what percent of [Base] is [Share]” and “[Share] is what percent of [Base]” both translate to Share ÷ Base × 100.
Putting It Into Practice
Translation errors compound: a misread phrase leads to the wrong equation, which leads to the wrong answer, even when every arithmetic step after that is correct. The fix is to slow down at the translation step and treat it as its own distinct phase.
Before writing anything mathematical, read the problem once to identify the unknowns. Name them. Then read each sentence a second time and write the corresponding equation directly under the relevant phrase. Only once every relationship is translated should you start solving.
For arithmetic shortcuts that buy back the time translation costs, see the GMAT Quant speed guide.
Related reading
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Practice translation with step-by-step feedback
GMAT Panda walks you through every translation step on real questions, showing exactly which keyword maps to which operation, so the pattern becomes automatic.