Bunuel wrote:

If x and y are both positive numbers, is x/y > y/x?

(1) 4y/x = 5

(2) x +4 = y

since x and y are both positive... we can cross-multiply without fear of sign.

The question is...x/y > y/x ?

or,

\(x^2 > y^2\) ?

or,

\(x^2/y^2 > 1\) ?

(1) 4y/x = 5 implies y/x = 5/4 (divide by 4)

Squaring both sides...

\(y^2/x^2 = 25/16 >1\)

Sufficient as the original question is reciprocal of this, so answer is "No".

(2)

This is the tricky part. x + 4 = y

Since we know x>0 and y>0 ... hence min value of y is now 4.

since y is always 4 more than x, y^2 will always be larger than x^2.

SufficientHence

Option (D) is correct.