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Four children stand in a row on a giant number line painted in the playground. From left to right they are P, Q, R and S. Q is standing on −4 and R is standing on 1. Which statement must be true?

Class 6IntegersIntegers
  • AP is less than −4 and S is greater than 1
  • BP is greater than −4 and S is greater than 1
  • CP and S are both negative
  • DP is −5 and S is 2

Step-by-Step Solution

P stands to the left of Q, so P < −4, and S stands to the right of R, so S > 1. That is everything the picture forces. S must in fact be positive, and neither P nor S is pinned to one particular value, so the other options can all fail.
Answer: A) P is less than −4 and S is greater than 1

Key idea: Integers on the number line

Draw a line, mark zero in the middle, and step off equal distances. To the right: 1, 2, 3, …. To the left: −1, −2, −3, …. Every integer has its own spot. The further left, the smaller the integer. The further right, the larger. This single picture is the foundation for everything else in this topic — when in doubt, draw the line.

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