If |2x| |3y|, is x y?

Question

If |2x| > |3y|, is x > y?

(1) x > 0
(2) y > 0

chetan2u · Answer

Hi...
|2x|>|3y|......|x|>3/2*|y|

So the numeric value( without considering the sign) of x is GREATER than that of y..
If x is NEGATIVE, y>x
If x is POSITIVE, x>y

Let's see the statements..
1) x>0
As can be seen above, x>y
Sufficient
2) y>0
Nothing about x..
Say x is 5 and y is 3, |2*5| > |3*3| and x>y
But if x=-5 and y=3,|2*-5|>|3*3| but y>x
Insufficient

A

niks18 · Answer

Square both sides of the question stem to get 4x^2-9y^2>0 or, (2x-3y)(2x+3y)>0 => x>\frac{3}{2}y or x<\frac{-3}{2}y So x>1.5y or x<-1.5y Statement 1 : this implies x is positive, so x<-1.5y is not possible hence only possible solution is x>1.5y . Clearly x is more than y by at least 1.5 times, hence x>y . Sufficient Statement 2 : in this case both the situations are possible x>1.5y so x>y and x<-1.5y so x\frac{3}{2}|y| => |x|>1.5|y| Statement 1 : x>0 so x is positive now if y>0 , then x>1.5y so x>y and if y<0 , then x will always be greater than y because x is positive. Hence Sufficient Statement 2 : implies |x|>1.5y (because y is positive). but nothing mentioned about x . if x=-2 and y=1 , then x1.5y will be true and if x=2 & y =1 , then x>y and |x|>1.5y is also true. Hence No unique solution. Insufficient

ccooley · Answer

Inequalities + absolute values + Data Sufficiency makes this a good problem to use a number line.

Start by understanding the question itself. On a number line, |2x| > |3y| means that 2x is further from the origin than 3y.

'is x > y' means that we want to know whether x is to the right of y, or to the left of y. If we're testing cases, we'll be trying to find a case where x is to the left, and another case where x is to the right. That's the only way we can prove insufficiency.

Statement 1 :

x > 0 means that x must be to the right of 0.

So, 2x must be to the right of 0.

https://i.imgur.com/5MaEcSr.png

From the question stem, we know that 3y must be closer to the origin than 2x is.

However, 3y could be on either side of the origin, as long as it's closer.

It could be on the left, in which case the situation looks like this:

https://i.imgur.com/dDzXjJq.png

Or it could be on the right, in which case the situation looks like this:

https://i.imgur.com/TCffLqh.png

Either way, y is definitely to the left of x. So the answer to the question is 'yes', and this statement is sufficient.

Statement 2 :

This time, we know that y is to the right of the origin. 3y will also be to the right of the origin, like this:

https://i.imgur.com/KenNMe2.png

2x could be to the left of the origin, like this:

https://i.imgur.com/WlIKorK.png

It could also be to the right of the origin, like this. It does have to be closer to the origin than 3y, but let's take it to an extreme. Let's make 2x just a tiny bit closer than 3y.

https://i.imgur.com/Yp27zCr.png

We've drawn one picture with x to the left of y, and another picture with x to the right. Since the result can go either way, statement 2 is insufficient.

The answer is A .

NandishSS · Answer

ccooley  Great Explanation indeed!!!

rohan911 · Answer

What if y=0 and x is negative say we we take the value of x as -1 then x<y and if we take the value of x as 1 then x>y so should 'nt the answer be C

dadaquest · Answer

ccooley 
in the last diagram the 2x should be to the right of 3y. Very well explained.

If |2x| > |3y|, is x > y?

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