Quote:
If a, b, c and d are positive integers and a/b < c/d, which of the following must be true?
a/b < c/d
as a, b, c and d are positive integers, rearranging the terms of the inequality
a/c < b/d
Adding 1 to each side of the inequality
a/c + 1 < b/d + 1
(a+c)/c < (b+d)/d
(a+c)/(b+d) < c/d
I. (a+c)/(b+d) < c/d This is always true
II. (a+c)/(b+d) < a/b
(a+c)/(b+d) is less than c/d but whether it is less than a/b is not known. Not always true
III. (a+c)/(b+d) = a/b + c/d
As (a+c)/(b+d) < c/d, left hand side cannot be equal to the right hand side. False
IMO B
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