We are told that a,b,c,d are positive integers, we need to find if a/b < c/dcatty2004 wrote:If a, b, c, and d, are positive numbers, is a/b < c/d?
1) 0 < (c-a) / (d-b)
2) (ad/bc)^2 < (ad)/(bc)
Now:
a/b < c/d
=> a/b - c/d < 0
=> (ad-bc)/(bd)<0
=> ad-bc<0 (b and d are positive, Hence multiplying both sides by bd doesn't change the sign)
=> ad<bc
So we need to find it ad < bc
With that in mind let's look at the options:
1) 0 < (c-a) / (d-b)
This means that both c-a and d-b have the same sign:
If both are positive c-a>0, and d-b>0 => c>a and d>b. So we can't say anything about ad>bc.
We need not check the both less than 0 case now, because the both are positive case already led us to Insufficient data condition. Hence Insufficient.
2) (ad/bc)^2 <(ad/bc)
Since ad/bc is positive, dividing both sides by ad/bc
ad/bc <1 => ad < bc. So we get that ad < bc. Hence ad is definitely not greater than bc. Sufficient.
Hence B is the correct answer.
