QUANTITATIVE REASONING · GMAT-Q-AL-01

Linear Equations and Translating Word Problems

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

Concepts and problem-solving strategy

a x + b = c \Rightarrow x = \frac{c - b}{a} (a \neq = 0)

{x + y = s x - y = d \Rightarrow x = \frac{s + d}{2}, y = \frac{s - d}{2}

Total = price per unit \times number of units

Name the unknown, express all quantities in terms of it, then check that the equation answers the actual question.

Use elimination when coefficients already align.

Check the result in the original situation, including units and signs.

The sum of two numbers is 52 and their difference is 18. Find the larger number.

x + y = 52, x - y = 18 \Rightarrow 2 x = 70 \Rightarrow x = 35

Adding the two equations eliminates the smaller number.

A taxi costs $5 plus $3 per kilometer. How far can a traveler ride for $29?

5 + 3 d = 29 \Rightarrow d = 8

Subtract the fixed fee before dividing by the variable rate.