How many pairs of positive integers x, y exist such that HCF of x, y = 35 and sum of x and y = 1085?
A)12 B)8 C)8 D)30

• let x=35a
  y=35b,
  x+y=35(a+b);
  1085=35(a+b);
  a+b=31;
  We need to find pairs of co-prime integers that add up to 31,
  Since 31 is prime. All pairs of integers that add up to 31 will be co-prime to each other. Or, there are totally 15 pairs that satisfy this condition
  so the ans is 15;
• 4 years agoHelpfull: Yes(2) No(1)