If y < 0 and 4x > y, which of the following could be equal to x/y ?

y < 0 and 4x > y and we need to find the possible value of x/y

4x > y => divide both the sides by y we get
\(\frac{4x}{y}\) < 1 [Since y is negative so we will have to reverse the inequality sign]

Divide both sides by 4 we get
\(\frac{4x}{4y}\) < \(\frac{1}{4}\)
=> \(\frac{x}{y}\) < \(\frac{1}{4}\)

Only option choice which is less than \(\frac{1}{4}\) is 0

So, answer will be A
Hope it helps!

Watch the following video to learn Basics of Inequalities

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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