Bunuel wrote:
If y < 0 and 4x > y, which of the following could be equal to x/y ?
(A) 0
(B) 1/4
(C) 1/2
(D) 1
(E) 4
We can see we can create x/y on the left side but that requires you to divide both sides by y. Since y is negative that will flip the inequality sign.
Hence we start with \(4x > y\) and divide both sides by y to get \(\frac{4x}{y} < 1\). Then move 4 over to get \(\frac{x}{y} < \frac{1}{4}\).
Only choice A is below \(\frac{1}{4}\) so that is our answer.
Another nice tactic here is to plug in numbers for x/y and verify if y < 0 and 4x > y can both be true.
For example, in choice A we let x = 0 and y = -1, and plug those in to find it is true.
Choice B we check with x = -1 and y = -4 (beware y has be negative!), to find -4 > -4 so choice B is incorrect.
Ans: A
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