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Whichever book Mr. A reads, Mr. B also reads that book. Whichever book Mr. B reads, Mrs. C also reads that book. Which of the following must be true ?

  • A.Mr. B has not read the Shiva trilogy. So Mrs. C could not have read it.
  • B.Mr. B has read the Harry Potter series. So Mr. A must have read it.
  • C.Mrs. C has not read the autobiography of Mahatma Gandhi. Mr. A could not have read it either.
  • D.Mrs. C has read all the books written by Paulo Coelho. Mr. A must have read all of those as well.

Answer: C

The statement that must be true is Mrs. C has not read the autobiography of Mahatma Gandhi. Mr. A could not have read it either.

Every book A reads, B reads, and every book B reads, C reads. So every book A has read, C has also read. If C has not read a book, A cannot have read it, which is the contrapositive of that chain; the third statement is therefore certain.

The others reverse the direction of the rule. B not reading a book says nothing about C, who may read books B has not. B reading Harry Potter does not mean A did, and C reading all of Coelho does not mean A did, because the rule carries books only from A to B to C, not back.

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