The set S contains fractions a/b, where a and b are positive integers, which don’t share any prime factor. How many of these fractions have the following property: when both numerator and denominator are increased by 1, the value of fraction is increased by 10%?  Choose the correct choice.
A) 0  B) 1  C) 2  D) 3  E) 4
he fraction with 1 added to the numerator &amp; denominator is 10% larger than the original. A 10% increase is equivalent to multiplying by the multiplier 1.1 or 11/10. Thus   a+1/b+1=11/10×a/b   Now, cross multiply   10ab + 10 b = 11ab + 11a   10 b = 1ab + 11a   Divide by b.   10=a+11 a/b   10−a/11=a/b   From here, it's obvious that b has to have a factor of 11 in it, so I just said: let b = 11. Then (10 - a) = a, so a = 5, and we get the fraction   a/b=5/11   When we add 1 to the numerator and denominator, we get 6/12 = 1/2, which is 10% greater than 5/11.   The question demands that x and y should have no common factors except 1, so they are co-prime. From that list only on pair is co-prime   .   ANSWER:1
<result>B</result>
The set S contains fractions a/b, where a and b are positive integers, which don’t share any prime factor. How many of these fractions have the following property: when both numerator and denominator are increased by 1, the value of fraction is increased by 10%?