catty2004
If a, b, c, and d, are positive numbers, is \(\frac{a}{b} < \frac{c}{d}\)?
(1) \(0 < \frac{(c-a)}{(d-b)}\)
(2) \((\frac{ad}{bc})^2 < \frac{(ad)}{(bc)}\)
Solution:
Question Stem Analysis:We need to determine whether a/b < c/d given that a, b, c and d are positive. Since all quantities are positive, we can cross-multiply, obtaining ad < bc. In other words, we can rewrite the question as: Is ad < bc ?
Statement One Alone:
This is not sufficient. For example, if a = b = 1, c = 3 and d = 2, then ad = 2 and bc = 3, and the answer to the question is yes.. However, if a = 3, b = 2, and c = d = 1, we see that ad = 3 and bc = 2, and the answer to the question is no..
Statement Two Alone:The square of a quantity is less than itself if the quantity has a value between 0 and 1. Therefore, ad/bc < 1. Since bc is positive, multiplying both sides by bc, we have ad < bc. Statement two alone is sufficient.
Answer: B