QUANTITATIVE REASONING · GMAT-Q-WORD

Word Problems: Ages, Prices, Totals

GMAT lesson development preview · DRAFT · Original learning and assessment material

Concepts and problem-solving strategy

Core mathematical relationship

x + 2 x = 3 x

Translate the condition

Name the unknown and express each quantity in terms of it. Use one equation that matches the full relationship described in words.

Test the result

Substitute the result into the original relationship and check the units. A rate, time, and total must fit the same equation.

Think Like a GMAT Test-Taker

Write a rate or multiplier equation with units before solving.

Faster Methods

Translate the target into an equation before calculating.

Check the result against the original conditions and units.

Worked example 1

An adult is twice as old as a child. Their combined age is 36 years. How old is the adult?

c + 2 c = 36 ⟹ c = 12, 2 c = 24

Let the child age be 12. The adult is twice that age, so the adult is 24; their total of 36 confirms the model.

Worked example 2

A shop buys 24 mugs at $8 each and sells all of them at one price. What selling price gives total profit of $96?

Cost = 24 (8) = 192, Revenue = 192 + 96 = 288, p = \frac{288}{24} = 12

Separate cost, revenue and profit before writing the equation. Revenue must cover cost and the desired profit. Dividing the profit alone by the number of mugs would give profit per mug, not the selling price.

Worked example 3

One pipe fills a tank in 5 hours and a drain empties it in 20 hours. Both run at constant rates. How long does it take to fill an empty tank?

r = \frac{1}{5} - \frac{1}{20} = \frac{3}{20}, t = \frac{20}{3} hours

Use one tank as the work unit. The drain removes part of what the inlet adds, so subtract their rates. The time must exceed five hours because filling is slower with the drain open.

Common Traps

Keep domain restrictions after simplifying.
Do not confuse the requested output with an intermediate quantity.