statements is true?

[sanju09]

If x - y is positive, which of the following statements is true?
I. 0 > x > y
II. x > 0 > y
III. y > x > 0
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) II and III only

[shankar.ashwin]

D IMO.

[neelgandham]

I. 0 > x > y
adding -y to all the terms, -y > x-y > 0 True !

II. x > 0 > y
adding -y to all the terms, x-y > -y > 0 True !

III. y > x > 0
adding -y to all the terms, 0 > x-y > -y Beep Beep !

Option D

[GmatKiss]

D IMO.

If x - y is positive, which of the following statements is true?
I. 0 > x > y
II. x > 0 > y
III. y > x > 0

If X is 10 and Y is 2 , II fails

IMO:A

[shankar.ashwin]

In statement II:

X>0 and Y<0.

So Y cannot take 2, it would be -2 and 10-(-2) = 12 which is +ve

D IMO.

If x - y is positive, which of the following statements is true?
I. 0 > x > y
II. x > 0 > y
III. y > x > 0

If X is 10 and Y is 2 , II fails

IMO:A

[enjoylife1788]

If x - y is positive, which of the following statements is true?
I. 0 > x > y
II. x > 0 > y
III. y > x > 0
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) II and III only

Statement 1 says, both x and y are negative. So, the only way to make x - y positive is make y smaller than y ( higher -ve number smaller), this in turn when multiplied by -, will make it a bigger positive number, making the answer positive. So I is true

statement 2 says, x is +ve and y is -ve. Again, when y being -ve multiplied by -, will make it positive. So, two result is two positive integers being added. So, II is also true

Statement 3 says, both x and y are positive and y is greater than x. So for eg, y is 4 and x is 3. so x-y is -1 and hence false. So statement III is false.

Hence Answer should be D which says both statements I and II are true.

[Abhishek009]

If x - y is positive, which of the following statements is true?
I. 0 > x > y
II. x > 0 > y
III. y > x > 0
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) II and III only

For such problems I use a diff approach -

I. 0 > x > y

Or,0 > x > x-1 ( Substituting y = x - 1 , to show y < x )

Now lets find out if the condition satisfies -

x - y = > x - ( x - 1 ) = 1

Answer is +ve , so this is possible...

II. x > 0 > y

x > 0 > x - 1 ( Substituting y = x - 1 , to show y < x , Here if it seems complex U can also substitute with the help of some numbers )

Now lets find out if the condition satisfies -

x - y = > x - ( x - 1 ) = 1

Answer is +ve , so this is possible...

III. y > x > 0

y > x > 0

Let y = x + 1 ( To show Y > X )

Now , lets find out if the condition satisfies -

x - y => x - ( x + 1 ) = -1

Answer is -ve , so this is not possible...


hence option I and II satisfies while option III doesn't , so the correct answer is option D