Multiple choice

Let x and y be the 3-digit numbers such that their difference is 729 and HCF is 81. Find the value of (x+y)?

  1. $1053$
  2. $891$
  3. $1539$
  4. $1377$
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A Correct answer
Explanation

If two numbers have HCF 81 and difference 729, let them be 81a and 81b where a and b are coprime. Then 81(a-b)=729, so a-b=9. For 3-digit numbers, valid pairs are (11,2) giving x+y=81(11+2)=1053, or (12,3) giving x+y=1215 (not an option). Thus x+y=1053.

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