Distance Budget
GMAT glossary · Playbook
Definition
Reading |x-a| + |x-b| on a number line: inside the anchors the sum equals the gap; outside, each step away costs 2.
Distance Budget in plain English
Pull Distance Budget for absolute-value sums or diffs on a number line with two anchors. Clues include |x-a| + |x-b|, lampposts, or between two points. Inside the anchors the sum is constant (the gap). Outside, each step farther away costs 2 because both distances grow. Casework on three regions is slower once the budget story is clear and you can read the flat middle at a glance. Micro-example: |x-2| + |x-8|. For x between 2 and 8 the sum is always 6. Outside, moving one unit farther increases the sum by 2, so the budget climbs in even steps. If the stem asks for a minimum of the sum, any point between the anchors works; if it asks for a specific budget above the gap, solve the outside rays.
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