statements is true?

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Mon Oct 17, 2011 1:57 am

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

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Source: Beat The GMAT — Problem Solving | Mon Oct 17, 2011 1:57 am

shankar.ashwin: Legendary Member; Posts: 966; Joined: Sat Jan 02, 2010 8:06 amFollowed by: 21 members; Thanked: 230 times

by shankar.ashwin » Mon Oct 17, 2011 2:02 am

D IMO.

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neelgandham: Community Manager; Posts: 1060; Joined: Fri May 13, 2011 6:46 amFollowed by: 52 members; Location: Utrecht, The Netherlands; Thanked: 318 times

by neelgandham » Mon Oct 17, 2011 2:05 am

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

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GmatKiss: Legendary Member; Posts: 2789; Joined: Tue Jul 26, 2011 12:19 amFollowed by: 43 members; Location: Chennai, India; Thanked: 206 times; GMAT Score:640

by GmatKiss » Mon Oct 17, 2011 3:25 am

shankar.ashwin wrote: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

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shankar.ashwin: Legendary Member; Posts: 966; Joined: Sat Jan 02, 2010 8:06 amFollowed by: 21 members; Thanked: 230 times

by shankar.ashwin » Mon Oct 17, 2011 3:42 am

In statement II:

X>0 and Y<0.

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

GmatKiss wrote:
shankar.ashwin wrote: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

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enjoylife1788: Senior | Next Rank: 100 Posts; Posts: 38; Joined: Sat Aug 15, 2009 10:31 pm; Location: India

by enjoylife1788 » Mon Oct 17, 2011 4:39 am

sanju09 wrote: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.

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Abhishek009: Master | Next Rank: 500 Posts; Posts: 359; Joined: Wed Mar 11, 2009 4:37 amFollowed by: 2 members; Location: Kolkata, India; Thanked: 50 times

by Abhishek009 » Mon Oct 17, 2011 6:44 am

sanju09 wrote: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

Abhishek

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