If y y, which of the following could be equal to x/y ?

Question

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

chetan2u · Answer

Since y<0, let us divide both sides by y. INEQUALITY sign gets changed since y<0.

4x>y………\frac{x}{y}<\frac{1}{4}

Only 0 is possible

A

MathRevolution · Answer

4x > y \frac{x}{y} < \frac{1}{4} (Sign changed since y < 0) => Possible value 0 Answer A

BrushMyQuant · Answer

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

TestPrepUnlimited · Answer

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

rushimehta · Answer

I understood the answer explanation... But I do have a query...

Since, there were 2 inequalities, I tried adding the inequalities... and I got x/y < 1/2...

Any reason why we aren't getting the same answer by adding inequalities... ?? And if this can't be solved by adding inequalities... what's the reason? Is there anything I am missing...

chetan2u   Bunuel

Bunuel · Answer

You cannot add inequalities with the signs in the opposite directions.

Check here  Manipulating Inequalities

GMATinsight · Answer

Hi rushimehta Bunuel has already answer to your doubts so I will dictate rules here 1) Two inequalities may be added only if their inequality signs are the same e.g. x > 4 and y > 5 then we can say x+y > (4+5) But if e.g. x > 4 and y < 5 then we can NOT say x+y > (4+5) so what can we do then? 2) We can substrate two inequalities when their inequality signs are opposite e.g. x > 4 and y < 5 then we can say x-y > (4-5) WHY? because y < 5 can be re-written as -y > -5 (multiply -1 both sides and flip inequality sign) I hope this clears your doubts There is the video of whole inequality class that you watch for better clarity VIDEO: https://www.youtube.com/watch?v=dnWC37yPs7s

rushimehta · Answer

Hello Bunuel , GMATinsight , chetan2u

Thanks for your responses...

Yes, I understand that we can't add the inequalities with opposite signs...

But, What I did is change the inequalities as below...
y < 0 --> Kept this as it is
4x > y --> Changed (Just reversed the order) this as "y < 4x"... (Let me know if my thought process here is wrong)

And then I added them... to get "2y < 4x", which leads me to below steps -
1. Dividing by y, and reversing inequality, as y is negative, giving me -- "2 > 4(x/y)"
2. Dividing by 4, and keeping the inequality as same, as 4 is positive, giving me -- "2/4 > x/y" i.e. "x/y < 1/2"

And since it is a CBT question, I thought that 1/4 can be the answer as well -- as it is less than 1.2...

Please let me know where I am going wrong...

much appreciated, thanks in advance!

chetan2u · Answer

y<4x gives you x/y < 1/4...
Now when you multiply y with a larger number it will become lesser 100y<2y<y<4x..
So picking up 2y<4x will still give you a true statement but not exact range..

100y<4x will give x/y<25

All are true as x/y < 1/4 < 1/2 < 25. But the least value you know is < 1/4, so it cannot be 1/4.

GMATinsight · Answer

Hi rushimehta Let me explain in this way You got x/y < 1/2 Which is fine But you also got (which you can't conveniently ignore) y < 4x which is also same as 1/4 > x/y (Divide by 4y both sides and change inequality sign because y is negative) Now, take the range that satisfies both results obtained i.e. x/y < 1/2 and 1/4 > x/y You conclusively get a range which is x/y < 1/4 hence you have to choose 0 as possible value of x/y as per options Point is is you have x < 2 and also x < -3 then the actual range of x is taken as x < -3 which satisfies all obtained results coherently I hope this help!

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

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

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