Word problems turn a real-life scenario into a small amount of algebra. On the GMAT Focus the most frequent families are percentages (discounts, taxes, interest), work rates (pumps, pipes, machines) and distance, speed and time. The mathematics is simple; the setup is where points are won or lost.
For percentages, turn every change into a multiplier. A 15% discount is × 0.85 and an 8% tax is × 1.08, and successive changes multiply rather than add. For work problems, think in rates: a pump that fills a tank in 6 hours does 1/6 of the job per hour, and the rates of machines working together add up. For travel problems, use distance = rate × time, and remember that the average speed for a round trip is total distance divided by total time. It is not the simple average of the two speeds, because more time is spent at the slower one.
Before you solve, write down what the question asks for. Many wrong answers are correct intermediate values: the hours one pump works alone instead of the total time, or the discounted price before tax. Picking friendly numbers, such as a 90-mile route or a 100-dollar price, often makes the setup obvious and removes fractions.
The last question is a Data Sufficiency rate problem, where the only question is whether the time can be found at all.
4 practice questions
Problem SolvingPercents and Interest ProblemsEasy
Question 1
A jacket is marked at $\$240$. It is sold at a $15\%$ discount, and then an $8\%$ sales tax is charged on the discounted price. What is the final price the customer pays?
A$\$204.00$
B$\$216.00$
C$\$220.32$
D$\$223.20$
E$\$259.20$
Show answer & explanation
Correct answer: C
Key Concept or Approach
Successive percent changes multiply: apply $\times 0.85$ for the discount, then $\times 1.08$ for the tax.
Common trap: \$223.20 - netting the changes to a single 7% discount (240 x 0.93) instead of multiplying them.
Problem SolvingWork/Rate ProblemsEasy
Question 2
Pump A alone can fill a tank in $6$ hours, and pump B alone can fill it in $9$ hours. Both pumps start filling the empty tank together, and after $2$ hours pump A is shut off while pump B continues alone. How many hours after the start does the tank become full?
A$4$
B$4.5$
C$5$
D$5.5$
E$6$
Show answer & explanation
Correct answer: E
Key Concept or Approach
Add rates while pumps work together, then find the time for B to finish the remaining fraction.
Step-by-Step Solution
Step 1: Combined rate: $\frac{1}{6}+\frac{1}{9}=\frac{5}{18}$ tank per hour; in 2 hours they fill $\frac{10}{18}=\frac{5}{9}$.
Step 2: Remaining: $\frac{4}{9}$ of the tank. B needs $\frac{4}{9}\div\frac{1}{9}=4$ hours.
Step 3: Total time from start: $2 + 4 = 6$ hours.
Final Answer
Answer: E
Common trap: 4 - the time B works alone, forgetting to add the first 2 hours.
Problem SolvingDistance/Rate ProblemsMedium
Question 3
A courier drives from a depot to a client at an average speed of $30$ miles per hour and returns along the same route at an average speed of $45$ miles per hour. What is the courier's average speed, in miles per hour, for the entire round trip?
A$35$
B$36$
C$37.5$
D$38$
E$40$
Show answer & explanation
Correct answer: B
Key Concept or Approach
Average speed = total distance / total time. Equal distances, so do not average the speeds.
Step-by-Step Solution
Step 1: Let each leg be $90$ miles. Time out: $3$ h; time back: $2$ h.
Step 2: Total: $180$ miles in $5$ hours.
Step 3: Average speed $= 180/5 = 36$ mph.
Final Answer
Answer: B
Common trap: 37.5 - the simple average of 30 and 45, which ignores that more time is spent at the slower speed.
Data SufficiencyWork/Rate ProblemsMedium-hard
Question 4
Pipes P and Q each fill a tank at their own constant rate. Working together, how many hours do they take to fill the empty tank?
(1) Working alone, pipe P takes 3 hours longer than pipe Q to fill the empty tank.
(2) Working alone, pipe P takes twice as long as pipe Q to fill the empty tank.
AStatement (1) ALONE is sufficient, but statement (2) ALONE is NOT sufficient.
BStatement (2) ALONE is sufficient, but statement (1) ALONE is NOT sufficient.
CBOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
DEACH statement ALONE is sufficient.
EStatements (1) and (2) TOGETHER are NOT sufficient.
Show answer & explanation
Correct answer: C
Key Concept or Approach
Let $p$ and $q$ be the solo times in hours. The time together is $\frac{1}{1/p + 1/q}$, so both $p$ and $q$ are needed.
