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1969 AMC 12 Question 24

AMC12 · 1969 AMC 12

Question 24

When the natural numbers $P$ and $P',$ with $P\gt P',$ are divided by the natural number $D,$ the remainders are $R$ and $R',$ respectively. When $PP'$ and $RR'$ are divided by $D,$ the remainders are $r$ and $r',$ respectively. Then:
  1. $r\gt r'$ always
  2. $r\lt r'$ always
  3. $r\gt r'$ sometimes, and $r\lt r'$ sometimes
  4. $r\gt r'$ sometimes, and $r=r'$ sometimes
  5. $r=r'$ always