Is x y?

Question

Is x > y?

(1) x^2 > y

(2) x – |y| > 0

KarishmaB · Answer

Statement 1 is clearly not sufficient alone. Only if we know that x > x^2, will we get a definite answer. But x > x^2 only when x lies between 0 and 1 which is not given. So statement 1 is not sufficient.

Statement 2 tells you that x > |y|. This means x is greater than the absolute value of y. Then x has to be greater than y too. 
Think about it: |y| is either equal to y (when y is +ve or 0) or it is greater than y (when y is negative). So if x is greater than |y|, it has to be greater than y too.

You can also take an example to understand this.
Say y = -4
Given x > |y| i.e. x > 4
Then x has to be greater than -4 too.
Say y = 4
Given x > |y| i.e. x > 4
In either case, x has to be greater than y.
So statement 2 alone is sufficient.

PTK · Answer

The best way is to test cases.

1) take x=-2, y=1 and x=2 , y=1. NS

2) rewrite it , so x>|y|
in this case x is positive , so x>0 , thus in any case of y whether positive or negative x>y.

philipssonicare · Answer

(1)  x^2 > y

x could be negative or positive
 2^2>1 
 (-2)^2>1 
(2)  x – |y| > 0 
 x>|y| 
Following the rule  |x|≥x 
 x>|y|≥y 
 x>y

B

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Is x > y?

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