ps:inequality

arjunshn wrote:if ab>cd and a,b,c and d are all greater than zero, which of the following cannot be true?
a) c>b
b) d>a
c) b/c>d/a
d) a/c>d/b
e)(cd)^2<(ab)^2

A can be true (if a=8, b=1, c=3, d=2), so we'll eliminate A
B can be true (if a=1, b=8, c=3, d=2), so we'll eliminate B
For C, if we multiply both sides by c and by a, we get ba > cd, which are told is true
For D, , if we multiply both sides by c and by b, we get ba > cd, which are told is true
By POE, this leaves E, which we should take without proving. However, we can see that E is also true. (for example, it's true when a=8, b=1, c=3, d=2

So, it looks like there is no correct answer here.

Aside: We can use a helpful rule to show why E it always true. The rule that says, If 0 < x < y, then 0 < x^2 < y^2

Since ab > 0 and cd > 0, and since 0 < cd < ab, then it must be true that 0 < (cd)^2 < (ab)^2