If 4xy and y

Question

If 4x>y and y<0 then which of the following could be the value of x/y ?

A)0
B)1/4
C)1/2
D)1
E)2

Kurtosis · Accepted Answer

4x > y

Divide by y on both sides, since y is negative the sign changes

4x/y < 1 
x/y < 1/4

Answer: A

enantiodromia · Answer

I substituted the value of x=-1 and got the value of 1/4

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Kurtosis · Answer

If x = -1 then y = -4. So, it violates the condition 4x > y.

joondez · Answer

Very smart...usually you cannot divide inequalities by a variable but since we know here that y<0 then we can divide by y, we just have to switch the inequality. That makes 4(x/y) < 1, or (x/y) < (1/4). The only answer that is less than (1/4) is A, or zero.

ar500 · Answer

With the info given we do not know if x is positive or negative. It could be any non-negative number, or a negative number larger than y/4 (or think of it as smaller in absolute value).

If x were a positive non-zero number then x/y would be negative because y is negative. If x is a negative number it would have to be greater than y/4 so the fraction would have to be smaller than 1/4. "0" is the only option smaller than 1/4.

ishan92 · Answer

Subtracting y<0 from 4x>y, we get 4x-y>y 4x>2y 2x>y x/y<1/2 (switched sign as y is negative) So dont option (a) 0 and option (b) 1/4, satisfy this? Where am i going wrong?

Hero8888 · Answer

You got 4x>y, where y<0 , so 4x> or = 0 - clearly that x>=0. In answer choices you have 0 and rest +ve answers, but if "x" is +ve, then if you devide it by -ve "y" the ratio must be -ve, and you don't have -ve in answer choices. The only option you have is 0. Answer A is correct.

ScottTargetTestPrep · Answer

We are given that 4x > y and y < 0; dividing the first inequality by 4y (and remembering to switch the inequality sign), we have:

x/y < 1/4

The only choice that is less than 1/4 is 0; so x/y could be 0.

Answer: A

hero_with_1000_faces · Answer

If 4x>y and y<0 then which of the following could be the value of x/y ?

This mean either X => 0; and "Y" Negative Integer or Fraction.
Thus, if Y is negative the answer has to be negative or Zero incase X is Zero
Hence, x/y has to be either negative or Zero, thus "A" as there are no negative answers.

Can someone confirm this approach  chetan2u   VeritasPrepKarishma   niks18

KarishmaB · Answer

Consider a case in which y = -10 and x = -(1/4)

In this case 4x is -1 which is greater than -10.

x/y = 1/40 (which is positive)

So it is not necessary that x/y has to be 0 or negative.

hero_with_1000_faces · Answer

Thanks a lot Karishma

I am really having a hard time with inequalities, every question seems like a different category to me. Any tips ?

LeoN88 · Answer

Question asking which one could be x/y, I see a zero in the answer so let's start with the easy one.

x=0, y<0
Satisfies 4x > y, Bingo  A

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If 4x>y and y<0 then which of the following could be the value of x/4

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