Number Line and Ordering

GRE Quantitative · Axiom Academy

LESSON Number Line and Ordering The number line isn't just a picture — position tells you order, and distance tells you size. Master both and every "which is greater" question becomes automatic. 1. Position on the Line Is the Order Every real number has an exact spot on the number line, and numbers increase left to right . So comparing two numbers is really just asking: which one sits further right? Watch -5 and -2 take their positions below — even though both are negative, -2 sits to the right, so . This is the single most common GRE trap: with negatives, the number closer to zero is the greater one. 2. Distance from Zero Is Absolute Value Position tells you order ; distance tells you size . The absolute value |x| is just how far x sits from 0 on the line — direction doesn't matter, only the length of the trip. Watch the two arrows below grow from 0 out to -7 and -3 : the arrow to -7 is longer, so |-7| = 7 is greater than |-3| = 3 , even though -7 itself is the smaller (further left) number. Order and magnitude are different questions. — on the line, -7 sits to the left, so it's the smaller number. — the trip from 0 to -7 is longer. "Which is greater, |-7| or |-3| ?" is really "which arrow is longer" — read the length off the line, not the sign of the number itself. 3. A Range of Numbers Is a Piece of the Line

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