make the cut vs pull through

make the cut

verb
  • To succeed at something or meet a requirement; to be chosen out of a field of candidates or possibilities. 

pull through

verb
  • To come through pain and trouble through perseverance. 

  • To clean the barrel of a firearm using a pull through. 

  • To assist someone through difficulties, injury, pain, etc. 

noun
  • The trick of apparently cutting the cards while leaving the deck in the same sequence as before. 

  • A length of cord about a metre long with a narrow cylindrical weight at one end and loops at the other. Used for cleaning rifle barrels, by pulling through a piece of cloth. 

How often have the words make the cut and pull through occurred in a corpus of books? (source: Google Ngram Viewer )