PrepTest 129, Section 4, Question 25

What we’re looking for

Working the answers

• A
  Correct

  The number of protrusions at a given stage depends on how many times we have repeated the construction, not the starting line's length. Start with a short line or a long line: the first operation still produces one bump. Repeating the same number of stages creates the same pattern at different sizes.

  The infinite theoretical process doesn't mean every intermediate stage already contains infinitely many protrusions. A is wrong because changing the initial length changes the scale, not the number produced at that stage.

• B

  This follows. Each new segment is one-third the length of the segment it replaces, so successive stages use shorter segments.

• C

  This also follows theoretically. Continuing to divide the segment length by three makes the segments arbitrarily small. A screen's inability to display that detail doesn't stop the theoretical construction.

• D

  All segments at a given stage have equal length because equal segments undergo the same operation. Their lengths decrease between stages, but remain equal within each stage.

• E

  Length does depend on the initial line. At the first stage, each segment is one-third of that starting length; at the next, it is one-ninth. A longer initial line therefore produces longer segments at the same stage.